Excel
Excel
Get the Results You Want!
Year 8 Mathematics
Revision & Exam Workbook
This is a revised and extended edition with over fifty extra pages of work for students to complete.
In this book you will find:
Topics covering the complete Year 8 Australian Curriculum Mathematics course
Over 170 pages of practice exercises
Fourteen topic tests
Four practice exams
E S S E N TI AL S KIL L S
This book is suitable for students of all abilities studying
Year 8 Mathematics. It has been specifically written to help
students revise their work and succeed in all their class tests,
half-yearly and yearly exams.
Answers to all questions
AS Kalra is the author of many successful Mathematics books, including the Excel Essential Skills
Mathematics Revision & Exam Workbook series for Years 7–10 (eight titles), and Excel Essential
Skills The Complete Fractions Workbook Year 7.
Your own checklist for Excel books for Year 8 students:
Bookseller reference
Books
Level
✓
English books:
978-1-74125-411-2
Excel Essential Skills Grammar and Punctuation Workbook
Years 7–8
978-1-74125-408-2
Excel Essential Skills Reading and Vocabulary Workbook
Years 7–8
978-1-74125-414-3
Excel Essential Skills Writing and Spelling Workbook
Years 7–8
978-1-74020-037-0
Excel Essential Skills English Workbook
Year 8
Mathematics books:
978-1-74020-040-3
Excel Essential Skills Step-by-Step Algebra 1 Workbook
Years 7– 8
978-1-74020-316-6
Excel Essential Skills Mathematics Extension Revision & Exam Workbook
Year 8
978-1-74125-435-8
Excel Essential Skills Problem Solving Workbook
Year 8
978-1-74125-474-7
Excel SmartStudy Mathematics
Year 8
978-1-74125-007-7
Excel Mathematics Study Guide
Year 8
978-1-74020-041-7
Excel Essential Skills Step-by-Step Algebra 2 Workbook
Years 8 –10
Science books:
978-1-74125-421-1
Excel SmartStudy Science
Year 8
978-1-74125-392-4
Excel Science Study Guide
Year 8
Year 8 Mathematics Revision & Exam Workbook AS Kalra
About the author
YEAR
8
Mathematics
Revision & Exam
Workbook
Updated Edition for the
Australian Curriculum
Over 100 Units of Work
Fourteen Topic Tests and
four Exams
Get the Results You Want!
ISBN 978-1-74020-033-2
Visit our website for more information at www.pascalpress.com.au
Our address is Pascal Press PO Box 250 Glebe NSW 2037 (02) 8585 4044
9781740200332_ESS Maths RandE WB Yr8 2015 spine 11mm.indd All Pages
9 781740 200332
AS Kalra
8/07/15 12:15 PM
YEAR
8
Mathematics
Revision & Exam
Workbook
Get the Results You Want!
AS Kalra
© 2000 AS Kalra and Pascal Press
Reprinted 2001, 2002, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012 (twice)
Updated in 2014 for the Australian Curriculum
Reprinted 2015 (twice)
ISBN 978 1 74020 033 2
Pascal Press
PO Box 250
Glebe NSW 2037
(02) 8585 4044
www.pascalpress.com.au
Publisher: Vivienne Joannou
Project editor: Vivienne Joannou
Edited by Science Desk International and May McCool
Proofread by Diannah Johnston
Answers checked by Chelsea Smithies and Peter Little
Typeset by Science Desk International and lj Design (Julianne Billington)
Cover by DiZign Pty Ltd
Printed by Green Giant Press
Reproduction and communication for educational purposes
The Australian Copyright Act 1968 (the Act) allows a maximum of one chapter or 10% of this book,
whichever is the greater, to be copied by any educational institution for its educational purposes
provided that the educational institution (or the body that administers it) has given a remuneration
notice to Copyright Agency Limited (CAL) under the Act.
For details of the CAL licence for educational institutions contact:
Copyright Agency Limited
Level 15, 233 Castlereagh Street
Sydney NSW 2000
Telephone: (02) 9394 7600
Facsimile: (02) 9394 7601
Email: enquiry@copyright.com.au
Reproduction and communication for other purposes
Except as permitted under the Act (for example, any fair dealing for the purposes of study, research,
criticism or review) no part of this book may be reproduced, stored in a retrieval system, or transmitted
in any form or by any means without prior written permission. All inquiries should be made to the
publisher at the address above.
Dedication
This book is dedicated to the new generation of young Australians in whose hands lies the
future of our nation and who by their hard work, acquired knowledge and intelligence will
take Australia successfully through the 21st century.
This book is also in the loving, living and lasting memory of my dear mum, dad and uncle,
who will remain a great source of inspiration and encouragement to me for times to come.
Acknowledgements
I would especially like to express my thanks and appreciation to my dear wife and son, who have
would not have been possible.
© Pascal Press ISBN 978 1 74020 033 2
Ch00_Prelim_2015 twice.indd 2
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
24/09/2015 2:06 pm
Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
CHAPTER 1—Basic arithmetic and the
calculator
Unit 1
Approximations and rounding off . . . . . . 1
Unit 2
Mixed operations . . . . . . . . . . . . . . . . . . . . . . 2
Unit 3
Squares, cubes and powers . . . . . . . . . . . 3
Unit 4
Square roots and cube roots . . . . . . . . . . 4
Unit 5
Problem solving and the calculator . . . . 5
CHAPTER 4—Indices
Unit 1
Index notation . . . . . . . . . . . . . . . . . . . . . . . .33
Unit 2
Index laws: multiplication
with indices . . . . . . . . . . . . . . . . . . . . . . . . . . .34
Unit 3
Index laws: division with indices . . . . .35
Unit 4
Index laws: powers of powers. . . . . . . . .36
Unit 5
Index laws: the zero index . . . . . . . . . . . .37
Unit 6
Index laws: miscellaneous
questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38
Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
Topic Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
CHAPTER 2—Percentages
CHAPTER 5—Rational numbers
Unit 1
The meaning of percentage . . . . . . . . . . . . 8
Unit 1
Rounding off whole numbers . . . . . . . . . .41
Unit 2
Changing percentages to fractions . . . . . 9
Unit 2
Rounding off decimals . . . . . . . . . . . . . . . .42
Unit 3
Changing fractions to percentages . . . .10
Unit 3
Unit 4
Changing percentages to decimals . . .11
Changing fractions to terminating
decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43
Unit 5
Changing decimals to percentages . . .12
Unit 4
Unit 6
Finding a percentage of a
quantity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
Recurring and terminating
decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44
Unit 5
Irrational numbers . . . . . . . . . . . . . . . . . . . .45
Unit 7
Increasing or decreasing by a given
percentage . . . . . . . . . . . . . . . . . . . . . . . . . . .14
Unit 6
Equivalent ratios . . . . . . . . . . . . . . . . . . . . . .46
Unit 7
Using ratios . . . . . . . . . . . . . . . . . . . . . . . . . . .47
Unit 8
Expressing quantities as
percentages . . . . . . . . . . . . . . . . . . . . . . . . . .15
Unit 8
Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48
Unit 9
Unitary method and percentages . . . . .16
Unit 9
Conversion of rates . . . . . . . . . . . . . . . . . . .49
Unit 10 Commission. . . . . . . . . . . . . . . . . . . . . . . . . . .17
Unit 11 Discounts . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
. . . . . . . . . . . . . . . . . . . . . . . .19
Unit 13 Problem solving and percentages . . . . .20
Topic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
CHAPTER 3—Four operations with integers
Unit 1
Addition of integers . . . . . . . . . . . . . . . . . . .23
Unit 2
Subtraction of integers. . . . . . . . . . . . . . . .24
Unit 3
Multiplication of integers . . . . . . . . . . . . . .25
Unit 4
Division of integers . . . . . . . . . . . . . . . . . . .26
Unit 5
Mixed questions. . . . . . . . . . . . . . . . . . . . . . .27
Unit 6
Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28
Unit 7
Order of operations . . . . . . . . . . . . . . . . . . .29
Unit 8
Problem solving with integers . . . . . . . . .30
Topic Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Unit 10 Scale drawing. . . . . . . . . . . . . . . . . . . . . . . . .50
Unit 11 Problem solving. . . . . . . . . . . . . . . . . . . . . . .51
Topic Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
CHAPTER 6—Basic algebra
Unit 1
Algebraic expressions . . . . . . . . . . . . . . . . .54
Unit 2
Simplifying algebraic expressions . . . . .55
Unit 3
Collecting like terms . . . . . . . . . . . . . . . . . .56
Unit 4
Algebraic abbreviations . . . . . . . . . . . . . . .57
Unit 5
Substitution (1) . . . . . . . . . . . . . . . . . . . . . . .58
Unit 6
Substitution (2) . . . . . . . . . . . . . . . . . . . . . . .59
Unit 7
Addition and subtraction of
like terms (1) . . . . . . . . . . . . . . . . . . . . . . . . .60
Unit 8
Addition and subtraction of
like terms (2) . . . . . . . . . . . . . . . . . . . . . . . . .61
Unit 9
Multiplication of pronumerals. . . . . . . . . .62
Unit 10 Division of pronumerals . . . . . . . . . . . . . . .63
Contents
© Pascal Press ISBN 978 1 74020 033 2
iii
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Unit 11 Algebraic expressions and the
order of operations . . . . . . . . . . . . . . . . . . .64
CHAPTER 9—Circles
Unit 12 Applying the distributive law to
expand algebraic expressions . . . . . . . . .65
Unit 1
Parts of circles . . . . . . . . . . . . . . . . . . . . . . 103
Unit 2
Circumference of circles. . . . . . . . . . . . . 104
Unit 13 Common factors . . . . . . . . . . . . . . . . . . . . . .66
Unit 3
Applications of circumference . . . . . . . 105
Unit 14 Problem solving and algebra . . . . . . . . . .67
Unit 4
Area of circles . . . . . . . . . . . . . . . . . . . . . . 106
Topic Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Unit 5
Applications of area . . . . . . . . . . . . . . . . . 107
Unit 6
Miscellaneous questions . . . . . . . . . . . . 108
Unit 7
Problem solving with circles . . . . . . . . . 109
CHAPTER 7—Length, mass and time
. . . . . . . . . . . . . . . .70
Topic Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Unit 2
Units of measurement . . . . . . . . . . . . . . . .71
Unit 3
Conversion of units of length . . . . . . . . .72
CHAPTER 10—Linear relationships
Unit 4
Pythagoras’ theorem (1) . . . . . . . . . . . . . .73
Unit 1
The number plane . . . . . . . . . . . . . . . . . . 112
Unit 5
Pythagoras’ theorem (2) . . . . . . . . . . . . . .74
Unit 2
Tables of values . . . . . . . . . . . . . . . . . . . . . 113
Unit 6
Perimeter of plane shapes . . . . . . . . . . . .75
Unit 3
Graphing straight lines . . . . . . . . . . . . . . 114
Unit 7
Perimeter of irregular shapes . . . . . . . . .76
Unit 4
Unit 8
Conversion of units of mass . . . . . . . . . .77
Using the intercept method to
graph lines. . . . . . . . . . . . . . . . . . . . . . . . . . 115
Unit 9
Applications of mass . . . . . . . . . . . . . . . . .78
Unit 5
Intersection of two lines . . . . . . . . . . . . 116
Unit 10 Conversion of units of time . . . . . . . . . . .79
Unit 6
Determining whether or not a
point lies on a line . . . . . . . . . . . . . . . . . . 117
Unit 7
Using graphs to solve linear
equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Unit 11 Addition and subtraction of time . . . . . .80
Unit 12 Clocks and times . . . . . . . . . . . . . . . . . . . . .81
Unit 13 Problem solving using 12- and
24-hour time . . . . . . . . . . . . . . . . . . . . . . . . .82
Topic Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Unit 14 Problem solving with length,
mass and time . . . . . . . . . . . . . . . . . . . . . . .83
CHAPTER 11—Equations
Topic Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Unit 1
Solving equations by inspection . . . . . 121
Unit 2
One-step equations (addition
and subtraction) . . . . . . . . . . . . . . . . . . . 122
Unit 3
One-step equations (multiplication
and division) . . . . . . . . . . . . . . . . . . . . . . . 123
Unit 4
Two-step equations . . . . . . . . . . . . . . . . 124
Unit 5
Three-step equations . . . . . . . . . . . . . . . 125
Unit 6
Equations with grouping
symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
Unit 7
Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Unit 8
Problem solving with equations . . . . . 128
Unit 9
Simple equations with
one fraction. . . . . . . . . . . . . . . . . . . . . . . . . 129
CHAPTER 8—Area, volume and capacity
Unit 1
Units of measurement . . . . . . . . . . . . . . . .86
Unit 2
Formulae for plane shapes and
solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87
Unit 3
Area of parallelograms . . . . . . . . . . . . . . . .88
Unit 4
Area of trapeziums. . . . . . . . . . . . . . . . . . . .89
Unit 5
Area of rhombuses. . . . . . . . . . . . . . . . . . . .90
Unit 6
Area of kites . . . . . . . . . . . . . . . . . . . . . . . . . .91
Unit 7
Area of plane shapes. . . . . . . . . . . . . . . . . .92
Unit 8
Problem solving with area. . . . . . . . . . . . .93
Unit 9
Volume of cubes . . . . . . . . . . . . . . . . . . . . . .94
Unit 10 Volume of rectangular prisms . . . . . . . . .95
Topic Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Unit 11 Volume of triangular prisms . . . . . . . . . . .96
Unit 12 Volume of prisms—miscellaneous . . . . .97
Unit 13 Problem solving with volume . . . . . . . . . .98
Unit 14 Capacity and volume. . . . . . . . . . . . . . . . . .99
Unit 15 Problem solving with area, volume
and capacity . . . . . . . . . . . . . . . . . . . . . . . . 100
Topic Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
iv
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
CHAPTER 12—Reasoning in geometry
EXAM PAPERS
Unit 1
Angles and the value of the
pronumerals . . . . . . . . . . . . . . . . . . . . . . . 132
Exam Paper 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Unit 2
Parallel lines and angles . . . . . . . . . . . . 133
Unit 3
The angle sum of a triangle . . . . . . . . . 134
Exam Paper 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
Unit 4
Triangles and the value of the
pronumerals . . . . . . . . . . . . . . . . . . . . . . . 135
Unit 5
The angle sum of a quadrilateral . . . . 136
Unit 6
Transformations. . . . . . . . . . . . . . . . . . . . . 137
Basic arithmetic and the calculator . . . . . . . . . . 181
Unit 7
Congruence of plane shapes using
transformation . . . . . . . . . . . . . . . . . . . . . . 138
Percentages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Four operations with integers . . . . . . . . . . . . . . . 182
. . . . . . 139
Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
Recognising congruent triangles . . . . 140
Rational numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Unit 10 Naming congruent triangles . . . . . . . . . 141
Basic algebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Unit 11 Tests for congruent triangles . . . . . . . 142
Length, mass and time . . . . . . . . . . . . . . . . . . . . . . 185
Unit 12 Applying properties to solve
numerical problems . . . . . . . . . . . . . . . . . 143
Area, volume and capacity . . . . . . . . . . . . . . . . . . 185
Unit 13 More numerical problems . . . . . . . . . . . 144
Linear relationships . . . . . . . . . . . . . . . . . . . . . . . . . 187
Unit 9
Topic Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Exam Paper 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Exam Paper 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
ANSWERS
Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Reasoning in geometry . . . . . . . . . . . . . . . . . . . . . . 190
CHAPTER 13—Probability
Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Unit 1
The language of probability . . . . . . . . . 147
Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Unit 2
Sample space . . . . . . . . . . . . . . . . . . . . . . . 148
Exam Papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
Unit 3
Outcomes. . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Unit 4
Theoretical probability . . . . . . . . . . . . . . 150
Unit 5
Complementary events . . . . . . . . . . . . . 151
Unit 6
Venn diagrams . . . . . . . . . . . . . . . . . . . . . . 152
Unit 7
Language of ‘at least’, exclusive ‘or’,
inclusive ‘or’ and ‘and’ . . . . . . . . . . . . . . 153
Unit 8
Two-way tables . . . . . . . . . . . . . . . . . . . . . 154
Topic Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
CHAPTER 14—Statistics
Unit 1
Review of basic statistics. . . . . . . . . . . . 157
Unit 2
Collecting data . . . . . . . . . . . . . . . . . . . . . . 158
Unit 3
Types of sampling. . . . . . . . . . . . . . . . . . . 159
. . . . . . . . . . . . . . . . 160
sample types . . . . . . . . . . . . . . . . . . . . . . . 161
Unit 6
Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
Unit 7
Median and mode . . . . . . . . . . . . . . . . . . . 163
Unit 8
Using the mean, mode
and median . . . . . . . . . . . . . . . . . . . . . . . . . 164
Unit 9
Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Topic Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
Contents
© Pascal Press ISBN 978 1 74020 033 2
v
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Introduction
There are two workbooks in this series for the Year 8 Australian Curriculum Mathematics course:
• Excel Essential Skills Year 8 Mathematics Revision & Exam Workbook (this book) and
• Excel Essential Skills Year 8 Mathematics Extension Revision & Exam Workbook.
for the Year 8 Australian Curriculum Mathematics course and the third in a series of eight Revision
help students revise their work so that they can prepare for success in their tests during the
school year and in their half-yearly and yearly exams.
The emphasis in this book is for students to master and consolidate the core skills and concepts
of the course through extensive practice. This will ensure that students have a solid foundation on
which to build towards both the Mathematics and Advanced Mathematics courses in senior years.
The following features will help students achieve this goal:
This book is a workbook. Students write in the book, ensuring that they have all their
questions and working in the same place. This is invaluable when revising for exams—no
lost notes or missing pages!
Each page is a self-contained, carefully graded unit of work; this means students
can plan their revision effectively by completing set pages of work for each section.
Every topic from the Year 8 Mathematics syllabus is covered in this book, so if students
have a particular area of weakness they can concentrate on that topic.
A Topic Test is provided at the end of each chapter. These tests are designed to help
students test their knowledge of each syllabus topic. Practising tests similar to those they will
Four Exam Papers have been included to test students on the complete Year 8
Mathematics course, helping students prepare for their half-yearly and yearly exams.
A marking scheme is included in both the Topic Tests and Exam Papers to give students
an idea of their progress.
A Topic Test and Exam Paper Feedback Chart, found on the inside back cover,
enables students to record their scores in all tests and exams.
Answers to all questions are provided at the back of the book.
There is a page reference to the Excel Mathematics Study Guide Year 8 in the top
study guide.
A note from the author
Mathematics is best learned if you have pen and paper with you and do every question in
writing. Do not just read through the book—work through it and answer the questions,
writing down all working. If this approach is coupled with a menu of motivation, realistic
goal-setting and a positive attitude, it will lead to better marks in the examinations.
My best wishes are with you; I believe this book will help you achieve the best possible results.
Good luck in your studies!
AS Kalra, MA, MEd, BSc, BEd
vi
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Chapter 1
Basic arithmetic and the calculator
Excel Mathematics Study Guide Year 8
Pages 2–5
UNIT 1: Approximations and rounding off
QUESTION 1
Round off the following numbers to the nearest ten.
a 43
b 65
c 89
d 33
e 158
f
231
g 625
h 829
i
387
j
k 9651
l
6382
5672
QUESTION 2
Round off the following numbers to the nearest hundred.
a 763
b 530
c 248
d 2361
e 5389
f
6341
g 8935
h 6371
i
8537
j
k 935
l
621
483
QUESTION 3
Write the following decimals correct to one decimal place.
a 3.56
b 0.81
c 9.67
d 31.62
e 0.19
f
16.05
g 18.36
h 91.47
i
62.86
j
k 83.29
l
55.11
43.17
QUESTION 4
Express the following decimals correct to two decimal places.
a 5.674
b 8.937
c 9.616
d 33.258
e 41.673
f
83.189
g 52.367
h 81.289
i
63.136
j
k 129.638
l
538.632
59.325
QUESTION 5
Express the following correct to one significant figure.
a 52
b 3.456
c 89
d 9.362
e 0.006 83
f
QUESTION 6
0.0532
Express the following correct to two significant figures.
a 83.94
b 238
c 8.937
d 91.675
e 325.63
f
81.63
g 253.07
h 0.000 651
i
0.007 635
Chapter 1: Basic arithmetic and the calculator
© Pascal Press ISBN 978 1 74020 033 2
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
1
Basic arithmetic and the calculator
Excel Mathematics Study Guide Year 8
Pages 2–5
UNIT 2: Mixed operations
QUESTION 1
Use your calculator to simplify the following.
a 10 + 15 8 =
b 49 16 + 13 =
c 18 + 21 + 19 10 =
d 83 16 5 3 =
e 56 (8 + 3) =
f
(9 + 11)
g 15 4 3 2 =
h 84 3 2 2 =
i
1200
j
k 9 + 16 8 =
l
50
n 9810 9 5 2 =
o 7 15 3 + 9 =
3+4
5=
m 8 5 64 8 =
QUESTION 2
5=
6
7
5
2=
3=
Use your calculator to work out the following.
a 235.62 + 8.9 =
b 565.67 1.2 =
c 35.8 + 89.5 3.6 =
d 3 6.9 + 2 8.7 =
e 5.6 8.9 2.3 =
f
56.7 + 83.2
g 5.9 6.8 12.5 =
h 6.7 2.5 + 1.6 3.5 =
i
0.2
j
k 5.8 2.3 1.9 =
l
100.5 + 6.1
c
35 + 43 –25 =
f
8 7 ÷ 2 12 × 2 =
67.5
3.6
2.1 =
QUESTION 3
a
1
84
d
2
5
+
5
6
Calculate the following.
2
3
+
10
=
22
× 11 × 34 =
QUESTION 4
4
2
1
b 95 – 35 +63 =
e
1
8
1
2 2 × 15 ÷ 3 4 =
2=
1.8 + 8.2
2.3 =
2
2
4
2
1
1
Use your calculator to answer the following.
a 92.7 8.9 + 16.35 =
b 6.9 + (3.4 1.2) =
c 80 10 9 =
d 5673 (5.6 3.2) =
e 8.16 1.2 1.67 =
f
g 613.5 8.1 214.7 =
h 9.3 8.5 6.3 =
i
QUESTION 5
a
5
6
+
1
8
9
–
2
1.3 =
1
3
3.7 + 8.9 =
86 + 134
Use the fraction key on your calculator to work out the following.
=
1
d 34 × 4 5 ÷64 =
2
© Pascal Press ISBN 978 1 74020 033 2
b
3
7
e
12 ×22 ×32 =
+1
1
1
7
3
5
1
=
1
3
62 =
c
1
5
1
f
12 ÷ 5 × 9 =
× 7 ÷ 2 =
1
2
7
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Basic arithmetic and the calculator
Excel Mathematics Study Guide Year 8
Pages 2–5
UNIT 3: Squares, cubes and powers
QUESTION 1
a
Use the x2 key to evaluate the following.
52 =
b 62 =
d 392 =
e
c
152 =
652 =
f
892 =
g
3.52 =
h 2.12 =
i
6.72 =
j
15.252 =
k 16.32 =
l
121.32 =
b 43 =
c
53 =
25 =
f
74 =
QUESTION 2
a
Use the x y key to find the answer.
83 =
d 63 =
e
g
55 =
h 29 =
i
35 =
j
1.23 =
k 2.43 =
l
64 =
m 1.54 =
n 0.73 =
o
1.94 =
b 1.73 =
c
8.33 =
6.84 =
f
15.13 =
QUESTION 3
a
Calculate the following correct to two decimal places.
3.24 =
d 9.13 =
e
g
198.22 =
h 61.352 =
i
7.35 =
j
80.72 =
k 17.82 =
l
52.62 =
QUESTION 4
a
Evaluate the following. (Leave your answers in fraction form.)
1
2
1
2
1
3
h 32 =
1
4
k 15 =
12 =
d 53 =
g
22 =
j
13 =
b
3
5
e
65 =
3
=
2
2
1
3
2
3
1
2
1
2
1
4
1
2
c
14 =
f
82 =
i
42 =
l
23 =
Chapter 1: Basic arithmetic and the calculator
© Pascal Press ISBN 978 1 74020 033 2
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
3
Basic arithmetic and the calculator
Excel Mathematics Study Guide Year 8
Pages 2–5
UNIT 4: Square roots and cube roots
QUESTION 1
Use the square root key on your calculator to simplify the following.
b
25 =
c
36 =
121 =
e
169 =
f
225 =
g
4 + 49 =
h
36 + 64 =
i
4 × 16 =
j
625 ÷ 25 =
k
256 ÷ 64 =
l
676 – 576 =
m
441 – 196 =
n
289 + 361 =
o
484 ÷
a
9=
d
QUESTION 2
a
d
g
j
Use the cube root key on your calculator to evaluate the following.
c
3
343 =
f
3
8 × 64 =
i
b
3
729 =
e
3
125 + 512 =
h
3
1331 × 27 =
k 8 × 125 =
3
g
3
3
a
3
3
36 × 1.25 =
b
1.728 × 3 8 =
0.49 × 3 571.787 =
1
64
3
l
3
1000 ÷ 125 =
3
1.728 =
3
4×
e
10.24 × 3 2.197 =
f
0.04 × 0.64 =
h
49 ÷ 2.56 =
i
7
9
b
1
15 3 =
e
1
1
3
=
c
83 =
f
2
1
h
36 + 3 2 4 =
j
5
7
+ 3 10 =
k
93 +
5
6
n
7
3
216 =
3
3
0.343 =
125 ÷
5.76 =
Use your calculator to simplify the following correct to two decimal places.
=
6 ×
3
c
12 × 3 24 =
3
27 =
2.744 × 1.21 =
3
g
m
3
Use your calculator to simplify the following correct to one decimal place.
QUESTION 4
d
64 =
8=
QUESTION 3
d
3
3
a
121 =
=
4
© Pascal Press ISBN 978 1 74020 033 2
2
3
8
10
81
4
× 3 16 =
=
1
82 =
3
2
29 5 =
i
55 – 383 =
3
1
l
61
64
+ 25 =
o
3
31
1
72 ÷ 3=
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Basic arithmetic and the calculator
UNIT 5: Problem solving and the calculator
1
Find the perimeter of a square with side length 4.2 cm.
2
Calculate the volume of a cube with side length 5.3 cm.
3
A rectangular prism has sides 9 cm, 11.2 cm and 12.1 cm. Find its volume.
4
A cube has a volume of 4913 cm3. Find the length of each side of the cube.
5
Write 85 493 correct to the nearest thousand.
Excel Mathematics Study Guide Year 8
Pages 2–5
6
7
8
Find the cost of 25 pens at $5.95 each.
9
Find the cost of 12.5 kg of lamb at $8.95 a kilogram.
3
4
10 In a class of 32 students,
11 Find the sum of 15.09, 23.7, 18.5 and then subtract 8.75.
12 Divide $5673 equally among three people.
13 Find the average of 3.85, 8.67, 6.93 and 4.79.
1
14 Find the square root of 6 4 .
1
15 Find the cube root of 13 2 correct to two decimal places.
16
17
18 Find the value of
1
× 8.149 × 92 correct to two decimal places.
5
19 Use your calculator to evaluate 152 – 82 + (4.5)2 correct to three decimal places.
20 Cork tiles cost $55 per square metre and are sold only by the square metre. How much would I pay for
Chapter 1: Basic arithmetic and the calculator
© Pascal Press ISBN 978 1 74020 033 2
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
5
Basic arithmetic and the calculator
TOPIC TEST
PART A
Instructions • This part consists of 12 multiple-choice questions.
• Fill in only ONE CIRCLE for each question.
• Each question is worth 1 mark.
Time allowed: 15 minutes
Total marks: 12
Marks
1
2
Evaluate 6
714
9+8
390
1 12
1
2 12
1
1
27.12
27.21
17.12
1
2 20 equals:
1600
2000
1800
2400
1
103 equals:
25 000
20 000
24 000
50 000
1
0.24
0.21
0.215
1
6
7
4
1
$300
1
What is the value of
23
4
5
6
7
434
1 + 3 + 5 + 7
2 4 6 8
23
1 24
8.21 + 6.1 3.1 equals:
17.21
9
5
25
1
110
2 24
3
7.
(0.5)2
(0.2)2 equals:
0.25
132 – 122 equals:
5
8
Adrian’s pocket money is $25.75 each month. How much would he receive in 12
$309
$350
$450
1 × 1 =
9
equals:
9 9
1
2
1
9
9
81
10 9.9
0.09 equals:
9.81
11
9.19
9.081
9.009
1
6500
1
none of these
1
What is the number 6546 rounded to the nearest hundred?
7000
12
1
none of these
6600
6550
Paper clips cost 40 cents per 100. How many paper clips would $20 buy?
50
500
5000
Total marks achieved for PART A
6
© Pascal Press ISBN 978 1 74020 033 2
12
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Basic arithmetic and the calculator
TOPIC TEST
PART B
Instructions • This part consists of 15 questions.
• Each question is worth 1 mark.
• Answer each question in the space provided.
Time allowed: 20 minutes
Total marks: 15
Marks
Simplify the following correct to two decimal places.
1
536.2 + 3.864 + 0.063 + 18
1
2
84.6 ÷ 0.018
1
3
18 ÷15 × 7
4
28 +12 –14
1
5
4
3
1
6
2.83
1
7
19
31
1
7
3
5
1
3
1
3
× 3.14 × 73
Simplify the following correct to one decimal place.
8
1
17.83 + (12.15 ÷ 3.9)
24 + 38
9
1
10 64 – 8
1
11
1
3
12
3
1
17.5 + 2.52
1
13
40.2 × 9.36
18.34
1
14
(8.15)2
9.6
1
15 5.92 – 3.22
1
Total marks achieved for PART B
Chapter 1: Basic arithmetic and the calculator
© Pascal Press ISBN 978 1 74020 033 2
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
15
7
Chapter 2
Percentages
Excel Mathematics Study Guide Year 8
Pages 26–41
UNIT 1: The meaning of percentage
QUESTION 1
Complete the following sentences.
a
30% means 30 out of
c
7% means 7 out of
.
b 80% means 80 out of
.
d A percentage is actually a fraction with a denominator of
e
The symbol for per cent is
QUESTION 2
.
.
and it means out of
.
Look at the diagram on the right.
a
b
QUESTION 3
a
b
c
QUESTION 4
a
In grids of 100 squares, what percentage is unshaded when the following percentages
are shaded?
25%
b 20%
c
10%
d 67%
e
89%
f
51%
g
h 78%
i
9%
b 100% – 47% =
c
100% – 91% =
e
f
100% – 77% =
64%
QUESTION 5
a
Work out the following subtractions.
100% – 32% =
d 100% – 69% =
QUESTION 6
100% – 37% =
Add the following percentages.
a
30% + 47% =
b 80% + 5% =
c
60% + 10% + 7% =
d 12% + 27% + 42% =
QUESTIONS 7
a
b In a class spelling test if James got 86% of the words correct, what percentage of
8
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Percentages
Excel Mathematics Study Guide Year 8
Pages 26–41
UNIT 2: Changing percentages to fractions
QUESTION 1
Express the following percentages as fractions in simplest form.
a 50% =
b 40% =
c 30% =
d 10% =
e 20% =
f
60% =
g 70% =
h 80% =
i
25% =
j
75% =
k 85% =
l
100% =
m 17% =
n 90% =
o 95% =
p 49% =
q 19% =
r 23% =
QUESTION 2
Express the following percentages as fractions in simplest form.
a 2.5% =
b 8.2% =
c 4.5% =
d 36.5% =
e 3.5% =
f
27.5% =
g 84.5% =
h 40.2% =
i
62.5% =
j
k 22.5% =
l
0.8% =
m 10.5% =
n 8.5% =
o 18.3% =
p 9.25% =
q 40.5% =
r 65.5% =
0.5% =
QUESTION 3
Change the following percentages to fractions in simplest form.
c
1 =
4%
e 22 2 % =
f
52 2 % =
h 33 13 % =
i
66 3 % =
1
k 5 12 % =
l
12 2 % =
m 10 12 % =
n 25 12 % =
o 35 12 % =
q 15 12 % =
r 20 14 % =
a
d
1 =
2%
1 =
8%
b
1
g 5 12 % =
j
82%=
p 85 12 % =
QUESTION 4
1 =
3%
1
2
1
Convert the following to fractions in simplest form.
a 38% =
b 56% =
c 62% =
d 25 13 % =
e 12 14 % =
f
34%=
g 9.5% =
h 8.6% =
i
4.8% =
j
3.7% =
k 6.9% =
l
5.2% =
m 42% =
n 55% =
o 72% =
1
Chapter 2: Percentages
© Pascal Press ISBN 978 1 74020 033 2
9
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Percentages
Excel Mathematics Study Guide Year 8
Pages 26–41
UNIT 3: Changing fractions to percentages
QUESTION 1
Express the following fractions as percentages.
a
30 =
100
b
50 =
100
c
80 =
100
d
40 =
100
e
43 =
100
f
84 =
100
g
62 =
100
h
39 =
100
i
56 =
100
j
25 =
100
k
16 =
100
l
72 =
100
QUESTION 2
Express the following fractions as percentages.
a
5 =
10
b 16 =
c
7 =
10
d
4 =
5
e
6 =
20
f
9 =
50
g
9 =
25
h
7 =
25
i
7 =
50
QUESTION 3
10
Change the following fractions to percentages.
a
3 =
4
b
5 =
80
c
13 =
20
d
7 =
60
e
2 =
8
f
7 =
40
g
9 =
60
h
3 =
5
i
14 =
80
QUESTION 4
Express the following as percentages.
a
3 =
8
b
5 =
9
c
5 =
8
d
7 =
11
e
5 =
12
f
1 =
3
10
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Percentages
Excel Mathematics Study Guide Year 8
Pages 26–41
UNIT 4: Changing percentages to decimals
QUESTION 1
Express the following percentages as decimals.
a 10% =
b 80% =
c 30% =
d 50% =
e 40% =
f
60% =
g 20% =
h 70% =
i
90% =
j
k 15% =
l
65% =
100% =
QUESTION 2
Change the following percentages to decimals.
a 16% =
b 19% =
c 39% =
d 12% =
e 61% =
f
56% =
g 14% =
h 73% =
i
67% =
j
98% =
k 81% =
l
78% =
m 62% =
n 43% =
o 49% =
QUESTION 3
Convert the following percentages to decimals.
a 5% =
b 2% =
c 8% =
d 9% =
e 6% =
f
7% =
g 3% =
h 1% =
i
4% =
j
1.5% =
k 2.5% =
l
3.3% =
m 2.1% =
n 1.7% =
o 4.9% =
QUESTION 4
Change the following percentages to decimals.
a 45.5% =
b 89.2% =
c 57.4% =
d 63.9% =
e 63.2% =
f
36.5% =
g 53.8% =
h 92.7% =
i
69.7% =
j
k 15.8% =
l
21.3% =
c
3 =
8%
23.7% =
QUESTION 5
Express the following percentages as decimals.
5
=
6%
a 33 13 % =
b
d 1 12 % =
e 66 23 % =
f
1
12 2 % =
g 9 14 % =
h 20 34 % =
i
7 =
9%
Chapter 2: Percentages
© Pascal Press ISBN 978 1 74020 033 2
11
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Percentages
Excel Mathematics Study Guide Year 8
Pages 26–41
UNIT 5: Changing decimals to percentages
QUESTION 1
Express the following decimals as percentages.
a 0.15 =
b 0.25 =
c 0.35 =
d 0.95 =
e 0.14 =
f
0.85 =
g 0.18 =
h 0.55 =
i
0.17 =
j
0.45 =
k 0.67 =
l
0.65 =
m 0.91 =
n 0.75 =
o 0.72 =
QUESTION 2
Express the following decimals as percentages.
a 0.80 =
b 0.60 =
c 0.1 =
d 0.50 =
e 0.90 =
f
0.2 =
g 0.70 =
h 0.4 =
i
0.3 =
j
0.01 =
k 0.02 =
l
0.05 =
m 0.04 =
n 0.06 =
o 0.03 =
QUESTION 3
Express the following decimals as percentages.
a 0.123 =
b 0.625 =
c 0.537 =
d 0.189 =
e 0.427 =
f
0.139 =
g 0.835 =
h 0.567 =
i
0.683 =
j
0.129 =
k 0.816 =
l
0.927 =
m 0.687 =
n 0.257 =
o 0.369 =
QUESTION 4
Express the following decimals as percentages.
a 0.001 =
b 0.910 =
c 0.006 =
d 0.007 =
e 0.002 =
f
0.009 =
g 0.810 =
h 0.037 =
i
0.021 =
j
0.004 =
k 0.005 =
l
0.003 =
m 0.057 =
n 0.089 =
o 0.065 =
QUESTION 5
Express the following decimals as percentages.
a 1.20 =
b 2.50 =
c 3.60 =
d 2.56 =
e 1.31 =
f
3.57 =
g 8.25 =
h 3.41 =
i
5.63 =
j
2.84 =
k 5.34 =
l
8.13 =
m 5.27 =
n 8.03 =
o 2.06 =
12
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Percentages
Excel Mathematics Study Guide Year 8
UNIT 6: Finding a percentage of a quantity
QUESTION 1
Evaluate the following.
a 10% of 300 =
b 20% of 5000 =
c 30% of 900 =
d 40% of 630 =
e 50% of 580 =
f
g 25% of 370 =
h 35% of 144 =
i
j
60% of 225 =
k 70% of 890 =
l
100% of 79 =
m 45% of 125 =
n 80% of 830 =
o 85% of 369 =
p 65% of 1000 =
5% of 210 =
QUESTION 2
75% of 840 =
Work out the following.
a 1% of 48 =
b 8.5% of 104 =
c 2.5% of 36 =
d 3.4% of 230 =
e 6.9% of 83 =
f
g 4.3% of 55 =
h 72.5% of 935 =
i
j
36.5% of 830 =
k 12.5% of 88 =
l
87.5% of 120 =
m 37.5% of 120 =
n 92.25% of 560 =
62.5% of 890 =
1
o 33 3 % of 180 =
QUESTION 3
Pages 26–41
45.6% of 456 =
p 6.5% of 720 =
Calculate the following.
a 17% of 500 =
b 64% of $350 =
c 9% of 67 =
d 18.5% of 366 days =
1
e 5 2 % of 840 =
f
g 15% of $120 =
h 30% of 4 kg =
i
40% of $2 =
j
400% of 30 =
k 25% of 800 g =
l
25% of $812 =
m 5% of $1200 =
n 142% of $120 =
o
p 17% of 400 =
90% of 50 =
2.5% of $80 =
Chapter 2: Percentages
© Pascal Press ISBN 978 1 74020 033 2
13
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Percentages
Excel Mathematics Study Guide Year 8
Pages 26–41
UNIT 7: Increasing or decreasing by a given
percentage
QUESTION 1
Increase the following by the given percentage.
a $45 by 30% =
b $8000 by 15% =
c $80 by 45% =
d $3000 by 60% =
e $350 by 20% =
f
g 900 g by 40% =
h 50 min by 20% =
i
j
240 L by 50% =
k 36 h by 100% =
l
80 t by 75% =
m $648 by 25% =
n $320.80 by 16% =
o $199.95 by 5% =
p $149.90 by 12 2 % =
q 80 ha by 20% =
r 600 cm by 70% =
400 kg by 60% =
QUESTION 2
$750 by 35% =
1
Decrease the following by the given percentage.
a $63 by 19% =
b $84 by 32% =
c 4 m by 35% =
d 260 L by 24% =
e $930 by 10% =
f
g $134 by 25% =
h $575 by 30% =
i
j
$243.80 by 50% =
k 48 h by 25% =
l
$840 by 70% =
m $365 by 15% =
n $960 by 45% =
o $96 by 40% =
p $60.50 by 80% =
q $940 by 28% =
r $620 by 35% =
$928.50 by 15% =
$6354 by 20% =
QUESTION 3
a
Bill bought a block of land for $230 000.
b Nathan earns $1500 a week. Calculate his new
new value.
c
The price of a new car is $30 000 and after
1 year it decreases in value by 20%. Find the
new value of the car.
14
© Pascal Press ISBN 978 1 74020 033 2
d A shirt priced at $130 was sold at a discount of 25%.
Find the sale price.
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Percentages
Excel Mathematics Study Guide Year 8
UNIT 8: Expressing quantities as percentages
Pages 26–41
QUESTION 1
a Express 20 as a percentage of 200.
b Express 12 as a percentage of 30.
c Express 36 as a percentage of 63.
d
e
QUESTION 2
What percentage is:
a
b
c
d
e
f
g
h
i
j
k
l
m
n
QUESTION 3
In the following, what percentage is the first quantity of the second?
a 2 m, 16 m
b 8 s, 48 s
c 12 kg, 90 kg
d 6 L, 300 L
e 30 mL, 150 mL
f
g 70 m, 210 m
h 80 min, 320 min
i
j
30 cm, 3 m
k 18 h, 3 days
l
$2, 500c
m 240 g, 6 kg
n 32 kg, 2 t
o 300 cm, 3.6 m
p 8 min, 2 h
QUESTION 4
a
b
36 s, 2 min
125 g, 500 g
What percentage is:
c
d
e
f
g
h
i
j
k
l
m 600 g of 8 kg
n 65 min of 4 3
1
Chapter 2: Percentages
© Pascal Press ISBN 978 1 74020 033 2
15
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Percentages
Excel Mathematics Study Guide Year 8
UNIT 9: Unitary method and percentages
Pages 26–41
QUESTION 1
a
b Find the total cost if 60% of it is $90.
c
d
QUESTION 2
Use the unitary method to solve the following.
a
b
c
d
QUESTION 3 Find 100% of a number if a part of it is given.
a 40% is 80; 100% =
b 20% is 92; 100% =
c 25% is 120; 100% =
d 15% is 60; 100% =
e 50% is 70; 100% =
f
g 5% is 83; 100% =
h 45% is 119; 100% =
i
j
8% is 34; 100% =
l
12 2 % is 230; 100% =
b John’s income increased by 3%. If his income
c
Alku receives a 15% increase in her weekly wage.
d The price of a block of land increased by 20%.
e
Hari spends 40% of his weekly income on rent.
f
g
The population of a small town decreases by 8%
2% is 94; 100% =
k 16% is 46; 100% =
75% is 450; 100% =
1
QUESTION 4
a
1
If 33 3
When an amount is increased by 20% it
16
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Percentages
Excel Mathematics Study Guide Year 8
Pages 26–41
UNIT 10: Commission
QUESTION 1
Robert works for a company and gets a
commission of 9% on all sales. How much
commission will he receive in a week in which
his sales total $27 000?
QUESTION 2
Joshua is a car sales representative and is paid a retainer (basic wage) of $600 per week
and a commission of 5% on all sales made. Find his weekly income in a week in which
he sells a car to the value of:
a
$42 000
QUESTION 3
b $76 000
1
Imogen is a salesperson and earns $350 a week plus 5 2 % commission on sales.
Her weekly sales total is $75 000. What is her:
a
b
QUESTION 4
Find his commission for selling a property worth $920 000.
QUESTION 5
a
Katie sells cosmetics and is paid 12.5% on all sales.
What is her income if she sells $5870 worth
b How much would she need to sell
Chapter 2: Percentages
© Pascal Press ISBN 978 1 74020 033 2
17
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Percentages
Excel Mathematics Study Guide Year 8
Pages 26–41
UNIT 11: Discounts
QUESTION 1
Complete the following table.
Name of the item
bought
Marked price
Percentage
discount
$560
10%
calculator
$45
20%
textbook
$64
8%
e-reader
$130
5%
computer
$950
15%
study lamp
$140
25%
chair
QUESTION 2
Discount in dollars
Sale price
A study desk with a marked price of $680 is discounted by 12%. What is the:
a
b
QUESTION 3 Christina spent $235 after getting a discount of $65 on a new watch.
b
a What was the price of the watch before
1
QUESTION 4
a
A tracksuit that usually costs $248 is reduced by 12 2 %. What is the:
b
QUESTION 5
a
Steph paid $178 after receiving a discount of 15% on a pair of shoes.
b
QUESTION 6
a
A dinner set was discounted by 45% and sold for $836.
b
18
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Percentages
Excel Mathematics Study Guide Year 8
Pages 26–41
UNIT
QUESTION 1
James bought some shares for $2540 and sold them for $3200. Find:
a
b
QUESTION 2
c
Nancy bought a car for $20 600 and sold it to David at a loss of 40% after it was
involved in an accident. David repaired it and then sold it, making a profit of
50% on his purchase price.
a
QUESTION 3
b
A book is sold for $56.80 including 10% GST.
a
QUESTION 4
b
A bicycle is on sale for $450. This is
75% of the regular price. What is
the regular price?
Chapter 2: Percentages
© Pascal Press ISBN 978 1 74020 033 2
19
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Percentages
Excel Mathematics Study Guide Year 8
Pages 26–41
UNIT 13: Problem solving and percentages
1
38% of some marbles are red and 18% are blue.
2
Of 80 cars, 45% are white. How many of
3
Out of 1060 students, 30% were absent. How
4
102 out of 120 cows have calves. What percentage
6
$500 is increased by 10% and this result is then
8
A salesman sold goods worth $35 000. Find the
5
7
A car bought for $2500 is sold for $2000. What
$10 000 sales earned 7% and the amount sold
above $10 000 earned 9%.
9
10 Find the simple interest on $3560 for
Find the simple interest on $2000 for 1 year
at 9.5% per annum.
3 years at 8 1 % p.a.
4
11 Find 55% of $1640 and add it to 45% of $150.
12 In an examination, 90% of a class of 30 students
13
14 Of the 960 students at a school, 15% are in Year 8.
a
20
© Pascal Press ISBN 978 1 74020 033 2
b There are 81 boys in Year 8. What percentage
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Percentages
TOPIC TEST
PART A
Instructions • This part consists of 12 multiple-choice questions.
• Fill in only ONE CIRCLE for each question.
• Each question is worth 1 mark.
Time allowed: 15 minutes
Total marks: 12
Marks
1
0.7 expressed as a percentage is:
0.007%
0.7%
7%
70%
1
2
40%
30%
60%
50%
1
150
200
250
300
1
0.45
0.042
0.045
1
$72
$75
$80
1
3
10
3
100
3
1000
1
3
4
1
Which decimal does 4 2
0.42
5
$63
6
7
0.3% equals:
1
3
At a roll call, there were 4 students absent and 21 present. What percentage of the roll
16%
19%
25%
84%
1
$1800
$4200
$6200
$7800
1
8%
10%
11%
90%
1
10%
12%
15%
18%
1
24
96
480
600
1
$100pq
$! 100 "
8
9
10
11
12 p% of $q is:
$pq
p+q
$! 100 "
pq
Total marks achieved for PART A
Chapter 2: Percentages
© Pascal Press ISBN 978 1 74020 033 2
1
12
21
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Percentages
TOPIC TEST
PART B
Instructions • This part consists of 15 questions.
• Each question is worth 1 mark.
• Answer each question in the space provided.
Time allowed: 20 minutes
Total marks: 15
Marks
1
Find 37% of $300.
1
2
Increase 260 kg by 10% and then decrease the result by 10%.
1
3
Write 12 as a percentage correct to two decimal places.
7
4
5
1
1
After 25% of a bill has been paid, $80 still remains to be paid.
1
6
A concrete mixture contains one part cement, two parts sand
1
7
Express 700% as a fraction.
1
8
Find the simple interest on $800 at 9% p.a. for 1 year.
1
9
Express 52 as a percentage of 416.
1
10 Find 100%, given that 40% is 98.
1
11 David pays 28% of his income in tax. If he pays $14 200
1
12 A game is bought for $69.50 and sold for $89.50. What is the
1
13 Ed earns 8% commission on all his sales. Find his commission
1
when his sales total $25 000.
14 $4800 is invested in a fund giving 12% interest per year. How
1
15 The price of a television is reduced by 18% to $1722.
1
Total marks achieved for PART B
22
© Pascal Press ISBN 978 1 74020 033 2
15
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Chapter 3
Four operations with integers
Excel Mathematics Study Guide Year 8
Pages 16–17
UNIT 1: Addition of integers
QUESTION 1
a
Find the sum of the following (use a number line if necessary).
8+3=
b
d
g
e
12 + 2 =
QUESTION 2
a
7+6=
a
3+9=
2+3=
9 + 18 =
b
c
23 + 8 =
f
h
i
52 + 2 =
b
c
13 + 6 =
9 + 21 =
f
i
Find the answers to these additions.
10 + 14 =
4+8=
QUESTION 5
3 + 21 =
h
d
g
12 + 14 =
e
QUESTION 4
a
i
Add the following.
d
g
f
h
e
QUESTION 3
5+8=
b
c
e
f
h
i
Find the values of the following.
a
b
c
d
e
f
g
h
i
QUESTION 6
a
12 +
Find the missing number.
= 21
d 6+
g
15 +
6+5=
Find each sum.
d
g
c
= 29
b
c
e
f
8+
h
i
9 + 11 =
Chapter 3: Four operations with integers
© Pascal Press ISBN 978 1 74020 033 2
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
23
Four operations with integers
Excel Mathematics Study Guide Year 8
Pages 16–17
UNIT 2: Subtraction of integers
QUESTION 1
Find the answers for the following questions.
a
b
c
d
e
f
g
h
i
QUESTION 2
Complete these subtractions (use a number line if necessary).
a
b
c
d
e
f
g
h
i
QUESTION 3
Find each difference.
a
b
d
e
f
g
h
i
QUESTION 4
Find the answers for the following subtractions.
a
b
c
d
e
f
g
h
i
QUESTION 5
Find the values of the following.
a
b
c
d
e
f
g
h
i
QUESTION 6
Simplify the following.
a
b
c
d
e
f
g
h
i
24
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Four operations with integers
Excel Mathematics Study Guide Year 8
Pages 16–17
UNIT 3: Multiplication of integers
QUESTION 1
a
Multiply the following.
5×2=
b
d
g
e
6×9=
3×2=
f
b
e
9×3=
11 × 4 =
i
13 × 4 =
c
21 × 9 =
f
h
QUESTION 3
15 × 10 =
Work out the following.
d
g
2×6=
h
QUESTION 2
a
c
i
40 × 9 =
Find the answers to the following.
a
b
c
d
e
f
g
h
i
a
b
c
d
e
f
g
h
i
b –6 × –3 × 1 =
c
–7 × 5 × 10 =
d 9 × –2 × –2 =
e
–4 × 5 × –3 =
f
2 × –3 × 4 =
g
h –3 × –10 × –7 =
i
–1 × –2 × –5 × –3 =
QUESTION 4
QUESTION 5
a
Find each product.
4×8×2=
6 × 8 × –1 =
QUESTION 6
a
Simplify.
×
7
Complete the following tables.
11
b
–4
×
–5
–9
8
c
×
3
7
–4
–7
–10
12
12
Chapter 3: Four operations with integers
© Pascal Press ISBN 978 1 74020 033 2
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
–25
–100
25
Four operations with integers
Excel Mathematics Study Guide Year 8
Pages 16–17
UNIT 4: Division of integers
QUESTION 1
a
Divide the following.
24 ÷ 4 =
b
d
g
e
16 ÷ 8 =
c
28 ÷ 7 =
54 ÷ 9 =
f
i
48 ÷ 8 =
b 24 ÷ –8 =
c
15 ÷ 5 =
d –20 ÷ 4 =
e
f
28 ÷ –7 =
g
h –120 ÷ 10 =
i
21 ÷ 3 =
c
36 ÷ 12 =
QUESTION 2
a
Work out the following divisions.
12 ÷ 2 =
18 ÷ 9 =
QUESTION 3
a
h
Simplify the following.
–27 ÷ 3 =
b
d
g
e
33 ÷ –11 =
QUESTION 4
a
a
a2 ÷ b
i
27 ÷ 3 =
b b÷a
c
d÷c
e
bc ÷ a
f
d ÷ ab
h b2 ÷ c
i
ad ÷ b2
c
36 ÷
Fill in each missing number.
–48 ÷
= –8
÷ –5 = –7
d
f
If a = 2, b = –4, c = 8 and d = –24, find the value of:
d÷b
QUESTION 5
–63 ÷ 7 =
h
d ab ÷ c
g
–45 ÷ –5 =
b –50 ÷
e
–49 ÷ 7 =
f
÷ 10 = –8
–96 ÷
b –60 ÷ 3 ÷ –5
c
–20 ÷ –2 ÷ –2
d 36 ÷ –4 ÷ –3
e
f
–60 ÷ –20 ÷ –3
g
h 40 ÷ –4 ÷ –2
i
–12 ÷ –6 ÷ –2
–300 ÷ –50 =
QUESTION 6
a
÷ –6 = 4
= –4
i
g
h
= 10
= 96
Simplify the following.
–45 ÷ –9 ÷ –1
48 ÷ 4 ÷ –6
26
© Pascal Press ISBN 978 1 74020 033 2
120 ÷ –12 ÷ 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Four operations with integers
Excel Mathematics Study Guide Year 8
Pages 16–17
UNIT 5: Mixed questions
QUESTION 1
a
Find answers to the following.
–2 – 4 =
b –6 + 5 =
c
–2 + 9 =
d 3–7=
e
2 – –8 =
f
3 + –5 =
g
h –2 + –10 =
i
–5 – –12 =
c
54
–6 =
f
–56
7=
i
–3 × –4 × –6 =
b –3 × –5 =
c
10
d 10 – –2 =
e
f
–12
g
h –8 + 8 =
i
–8 × 8 =
c
(–6 + 4)
f
–3 – 7 – 8 =
i
(–4 + 12)
c
–2 –
–4 – –3 =
QUESTION 2
a
Find the value of the following.
–4 × –8 =
b –16
–8 =
d –3 × 7 =
e
g
h –100
–2 × 5 × –9 =
QUESTION 3
a
–3 + –5 =
–6 + 17 =
(3 + 4)
d –20
g
–2 =
–5
(5 + –5)
e
–38 =
9+
(4 – 5) =
12
3
h (–2 – 5)
=7
b
–2 = –100
–9 =
–7 =
7 = –6
e
=9
–81
+
–4 =
8=
–2 =
Fill in each missing number.
QUESTION 6
a
b 5
–2 =
d
g
–15 – 13 =
–2 =
Simplify the following.
QUESTION 5
a
–4 =
Work out the following.
QUESTION 4
a
11 × –7 =
+8=3
h –4 –
=5
= –3
f
– 9 = –1
i
+ 6 = –2
Complete the following tables.
3
–7
–9
12
–15
b
×
–1
–5
6
11
–8
–6
–4
5
–10
Chapter 3: Four operations with integers
© Pascal Press ISBN 978 1 74020 033 2
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
8
–9
27
Four operations with integers
Excel Mathematics Study Guide Year 8
Pages 16–17
UNIT 6: Indices
QUESTION 1
a
Evaluate the following.
3
2 =
d 32 =
b 52 =
c
–33 =
42 =
f
(–1)2 =
e
g
53 =
h 82 =
i
(–1)3 =
j
43 =
k (–2)3 =
l
(–1)4 =
m 25 =
n (–3)4 =
o
(–2)4 =
p (–3)4 =
q –52 =
r
(–5)3 =
b (–5)4 =
c
(–5)3 =
(–2)5 =
f
2 × (–4)2 =
QUESTION 2
a
Evaluate the following.
10
(–1) =
d (–1)15 =
e
g
(–1)99 =
h (–10)3 =
i
(–8)2 =
j
(–6)3 =
k (–2)6 =
l
–4 × (–3)3 =
m (9)2 =
n (7)3 =
o
(–2)2 × (–5)2 =
p (–4)3 =
q (3)4 =
r
–6 × (–3)3 =
c
(–4)3 + (–1)2 =
f
(–8)2 ÷ (2)5 =
QUESTION 3
a
Calculate the following.
(–2)3 × (–3)2 =
d 42 + (–5)2 =
b (–9)2 – (–4) =
e
(–5)2 + (–10)2 =
g
(–1)5 + (–3)3 =
h (–7)2 × (–1)3 =
i
(–5)3 + –52 =
j
82 ÷ (–2)4 =
k (–3)4 – (–5)2 =
l
(–6)2 × (–2)3 =
m 72 × (–3)2 =
n 63 + (–2)3 =
o
(–10)4 ÷ 102 =
p (–2)2 + (–2)3 =
q (–2)4 + (–3)3 =
r
83 ÷ (–2)5 =
b (–4)3 ÷ –43 =
c
(–3)2 ÷ –32 =
(–10)2 × 52 =
f
25 ÷ 22 =
QUESTION 4
a
2
Evaluate the following.
2
9 ÷3–4 ×2=
d 4 × (–2)2 + 5 × (–1)4 =
e
g
2 × 103 + (–10)2 =
h (–5)2 + 4 × –10 =
i
(–10)2 × (–10)3 =
j
–6 × (–10)3 × (–1)5 =
k (–8)2 + 2 × –20 =
l
(–5)3 + (–3)2 =
m (–9)2 + 3 × –6 =
n 3 × (–4)2 + 8 × (–2)4 =
o
(–6)3 – (–5)2 =
p (–3)2 + 32 + (–1)2 =
q (–10)3 + (–10)2 – (–2)6 =
r
–5 × (–10)2 × –10 =
28
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Four operations with integers
Excel Mathematics Study Guide Year 8
Pages 16–17
UNIT 7: Order of operations
QUESTION 1
a
2+3
d 3
g
16
j
–24
Follow the correct order of operations when finding answers to these.
5
b 12 – 5
4–6
2
8–3
6+7
g
k 28
2
(–7 + 2)
(–3 + 9)
(–2
QUESTION 3
a
5+7
d 6+3
g
–4
3
7 – 18
2
3
f
–9 – 2
i
–5
20
l
3
–5 – 2
–6
4
–7
b (3 – 7)
(2 – 5)
c
–8 + (7 – 3)
e
(5 – 9)
f
(–6 + 14)
(1 – 4 – 6)
i
–11 – (2 + 3
4)
c
[4 + (2 – 7)
3]
f
72
i
3
[6
c
5
4–6
f
54
i
10 – 7 + 4
56 – 2
h 36
3
–3
b 9
–2
e
(–2 + 8)] – 5
QUESTION 4
a
3)
[(12 – 5) – (3 – 4)]
[3 + 12
8
–3 + 21
–2
(–5 + 1)
Find answers to the following.
d 12 – (–9 + 4)
g
7+4
c
Remove the grouping symbols and simplify.
(–5 + 8)
d 12
–3
h 5 – 12
QUESTION 2
a
e
3
[6 – (5 – 8)]
[(5 + 8)
h [–1 – (2 + 3) – 7]
–2
–1
(–3 + 9) – 56
(4 – 7)
(–2 – 6)
(–2 + 11)]
Insert grouping symbols to make these statements correct.
6=2
b –3 + 5
5
e
7–5
(3 – 4) + 6]
(–2 + 7)
–7 = –3
–2 = 66
–1 = –2
–4 + 7 – 9
h 7 – 10
2 = –12
3 – 8 = 15
–9 – 2 + 7 = –15
Chapter 3: Four operations with integers
© Pascal Press ISBN 978 1 74020 033 2
3 = –30
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
–3
12 = 4
29
Four operations with integers
UNIT 8: Problem solving with integers
Excel Mathematics Study Guide Year 8
Pages 16–17
1
The temperature was –3 . It rose 7 in an hour.
What was the temperature at the end of
2
Daisy travelled 8 km east and then 5 km west.
Where did Daisy end up relative to her
3
Adelaide is 35 south of the equator and Tokyo
is 35
4
What negative number is both greater than –6
5
After it was born, a baby gained 2.5 kg. Then
6
3
7
Charlie owes $3250 on his credit card.
a He pays $1500 off the bill. How much does
b Then Charlie buys a laptop for $795 using his
8
9
10 A spider is climbing a wall. It climbs up 5 cm,
falls back 3 cm, climbs up another 4 cm, falls
3 = 9. Which other number multiplied by itself
Find the two numbers whose sum is –8 and
11 Jake had $864 in the bank. He put another $56 in the
bank and then withdrew $345. How much money
12 The temperature fell 5 degrees during the day
13 Two numbers add to 4 but multiply to –12.
14 Which of the integers, –5, 7, –9, 6, is closest
15 Start with –2, subtract 5 and multiply the result by 6.
30
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Four operations with integers
TOPIC TEST
PART A
Instructions • This part consists of 12 multiple-choice questions.
• Fill in only ONE CIRCLE for each question.
• Each question is worth 1 mark.
Time allowed: 15 minutes
Total marks: 12
Marks
1
2
3 – –5 equals:
2
–2
8
–8
1
–4 + –7 equals:
3
–3
11
–11
1
–16
–20
3
4
–5
32
–8
–24
–3
1
4
–1
9
–9
1
–7
5
–5
1
60
–12
12
1
–50
28
–32
1
–5
5
–6
6
1
(–4)2 equals:
8
–8
16
–16
1
–2
2
12
1
–20
–60
60
1
32
40
80
1
1
5
6
7
–3 + 2 5 equals:
7
–5
–4 –3 equals:
–60
–2 – 3 –10 equals:
50
8
9
10 –3 – 4 – 5 equals:
–12
11 –5
–8 – 10
20
12 (–7 + 3)
–2 equals:
(2 – 6) equals:
16
Total marks achieved for PART A
Chapter 3: Four operations with integers
© Pascal Press ISBN 978 1 74020 033 2
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
12
31
Four operations with integers
TOPIC TEST
PART B
Instructions • This part consists of 15 questions.
• Each question is worth 1 mark.
• Answer each question in the space provided.
Time allowed: 10 minutes
Total marks: 15
Marks
1
–6 – 5 =
1
2
9 – (–4) =
1
3
–7 + (–11) =
1
4
3
1
5
–24
6
5–3
7
8 + 12
8
(–10)3 =
9
–5
10 7
–5 =
1
–3 =
1
–2 =
1
–4 =
–8
1
–2 – 3
–8) + (–4
12 –2
–1
14 –3
[–36
1
5=
11 (11
13 (6 – 10)
1
–4 =
5
1
–3) =
1
–6 =
1
(–4 – 3) =
1
(–3 – 6)] =
15 At 6 am the temperature was –3 C. By 9 am it had risen 15 C.
1
Total marks achieved for PART B
32
© Pascal Press ISBN 978 1 74020 033 2
15
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Chapter 4
Indices
Excel Mathematics Study Guide Year 8
Page 15
UNIT 1: Index notation
QUESTION 1
Write the following in expanded form.
a
4
2 =
b 52 =
c
73 =
d 65 =
e
106 =
f
g
27 =
h 78 =
QUESTION 2
Write in index form.
a
2
2
2
2
2
2=
c
5
5
5
5
5
5
e
10
10
10
g
12
12
12 =
b 7
7
7
7
7=
d 3
3
3
3
3
f
6
6
6
6
6=
h 2
2
2
2
2
3
3
3=
2
2
2
c
112 =
f
105 =
i
34 =
b 8=
c
10 000 =
d 36 =
e
f
49 =
g
h 9=
i
216 =
QUESTION 3
a
5=
39 =
10 =
Evaluate the following.
4
b 33 =
2 =
d 53 =
g
e
63 =
a
132 =
h 26 =
QUESTION 4
Write the following in index form.
25 =
10 000 000 =
QUESTION 5
32 =
Write in expanded form.
a
2
3
2
3 =
b 62
74 =
c
53
24 =
d 35
5=
e
73
22 =
f
QUESTION 6
a
2=
34
23
52 =
Write each number as the product of its prime factors, giving the answer in index form.
40 =
b 48 =
c
72 =
d 225 =
e
324 =
f
486 =
g
1568 =
h 300 =
Chapter 4: Indices
© Pascal Press ISBN 978 1 74020 033 2
33
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Indices
Excel Mathematics Study Guide Year 8
Page 15
UNIT 2: Index laws: multiplication with indices
QUESTION 1
Simplify the following, writing your answers in index form.
3
2 =
b 37
32 =
c
56
d 78
73 =
e
29
22 =
f
104
g
66
63 =
h 112
112 =
i
57
55 =
j
310
36 =
k 212
210 =
l
78
79 =
a
2
5
QUESTION 2
a
6
4
d 7
g
223
j
3
105 =
Simplify the following, writing your answers in index form.
6=
b 58
5=
c
37
3=
75 =
e
27 =
f
5
510 =
214 =
39 =
QUESTION 3
a
54 =
3
2
h 109
109 =
i
15
152 =
k 1212
1212 =
l
5
b 55 × 57 =
c
52 × 59 =
43 × 46 =
f
89 × 83 =
5
53 =
Simplify the following.
2
4 ×4 =
d 28 × 26 =
e
g
37 × 35 =
h 74 × 78 =
i
33 × 34 × 37 =
j
25 × 22 × 23 =
k 39 × 312 =
l
215 × 217 =
b 95 × 94 =
c
48 × 43 =
27 × 24 =
f
53 × 57 =
QUESTION 4
a
3
Simplify the following.
2
5 ×5 =
d 89 × 82 =
e
g
33 × 45 × 32 × 42 =
h 35 × 35 =
i
63 × 62 =
j
62 × 63 =
k 75 × 73 =
l
84 × 86 =
b 3 × 37 =
c
62 × 63 =
53 × 52 =
f
74 × 78 =
QUESTION 5
a
Simplify the following.
4
5×5 =
d 7 × 75 =
e
g
45 × 49 =
h 87 × 88 =
i
45 × 43 × 42 =
j
6 × 63 =
k 24 × 23 × 22 =
l
39 × 36 =
× 56 = 59
c
74 ×
= 711
= 48
f
84 ×
= 85
QUESTION 6
Find the missing term in each of the following.
57 ×
= 510
b
d 83 ×
= 85
e
g
32 ×
= 39
h
× 32 = 33
i
× 92 = 96
j
62 ×
= 68
k
× 74 = 77
l
× 72 = 74
a
34
© Pascal Press ISBN 978 1 74020 033 2
45 ×
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Indices
Excel Mathematics Study Guide Year 8
Page 15
UNIT 3: Index laws: division with indices
QUESTION 1
a
Simplify the following, writing your answers in index form.
75 ÷ 72 =
d 510 ÷ 57 =
b 28 ÷ 26 =
c
39 ÷ 33 =
29 ÷ 24 =
f
68 ÷ 64 =
e
g
1010 ÷ 102 =
h 74 ÷ 72 =
i
315 ÷ 35 =
j
212 ÷ 23 =
k 117 ÷ 11 =
l
52 ÷ 5 =
QUESTION 2
a
Simplify the following, writing your answers as basic numerals.
58 ÷ 57 =
b 39 ÷ 37 =
d 710 ÷ 78 =
e
514 ÷ 511 =
c
23 ÷ 22 =
f
37 ÷ 36 =
g
613 ÷ 611 =
h 25 ÷ 2 =
i
56 ÷ 55 =
j
1010 ÷ 104 =
k 34 ÷ 3 =
l
212 ÷ 29 =
QUESTION 3
a
215
23 =
Simplify the following, writing your answers in index form.
b
5 20
55 =
e
28
24 =
i
216
2 =
QUESTION 4
a
c
7 49
77 =
d
318
36 =
f
59
53 =
g
67
66 =
h
321
37 =
j
1010
10 2 =
k
7 35
75 =
l
12 36
12 24 =
Simplify the following.
310 ÷ 32 =
d 58 ÷ 52 =
b 911 ÷ 95 =
c
521 ÷ 516 =
212 ÷ 23 =
f
79 ÷ 73 =
e
g
715 ÷ 77 =
h 423 ÷ 48 =
i
918 ÷ 96 =
j
821 ÷ 814 =
k 632 ÷ 618 =
l
1054 ÷ 1028 =
c
87 ÷ 86 =
f
98 ÷ 97 =
QUESTION 5
a
Simplify the following.
37 ÷ 34 =
b 59 ÷ 52 =
d 98 ÷ 93 =
e
125 ÷ 122 =
g
27 ÷ 24 =
h 79 ÷ 74 =
i
510 × 48 ÷ (57 × 42) =
j
810 × 37 ÷ (88 × 34) =
k 25 × 39 ÷ (23 × 34) =
l
29 × 36 ÷ (24 × 35) =
c
812 ÷
79 ÷ 76 =
f
= 67
i
38 ÷ 35 =
48
= 46
QUESTION 6
a
59 ÷
d
g
Find the missing term in each of the following.
= 54
b 514 ÷
÷ 3 = 36
e
= 82
h
86 ÷
6
2
= 58
= 87
28 × 312
j
24 × 34 ÷
= 23 × 32
k
÷ 52 = 56
l
Chapter 4: Indices
© Pascal Press ISBN 978 1 74020 033 2
= 25 × 36
35
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Indices
Excel Mathematics Study Guide Year 8
Page 15
UNIT 4: Index laws: powers of powers
QUESTION 1
a
Simplify, leaving your answers in index form.
5 2
(2 ) =
d (73)5 =
b (36)3 =
c
(54)4 =
(27)4 =
f
(69)2 =
e
g
(510)5 =
h (38)2 =
i
(112)2 =
j
(103)6 =
k (512)5 =
l
(36)6 =
b (25)2 =
c
(73)3 =
(52)6 =
f
(64)2 =
QUESTION 2
a
Use a calculator to find the value of the following.
2 4
(3 ) =
d (24)5 =
e
g
(37)2 =
h (26)3 =
i
(72)2 =
j
(23)4 =
k (112)3 =
l
(35)3 =
b (25)4 =
c
(67)2 =
(72)3 =
f
(113)7 =
QUESTION 3
a
Simplify, leaving your answers in index form.
7 3
(3 ) =
d (59)4 =
e
g
(210)10 =
h (102)5 =
i
(64)3 =
j
(122)4 =
k (77)7 =
l
(26)5 =
b (37)5 =
c
(810)4 =
(215)6 =
f
(512)7 =
QUESTION 4
a
Simplify the following.
5 3
(4 ) =
d (518)8 =
e
g
(79)2 =
h (410)8 =
i
(211)6 =
j
(916)3 =
k (79)7 =
l
(314)9 =
QUESTION 5
a
2
Complete the following to express each in simplest index form.
2 2
b 83 =
36 = (6 )
362 =
83 =
d 1252 =
e
1252 =
QUESTION 6
c
812 =
812 =
494 =
f
494 =
323 =
323 =
Simplify the following, leaving your answers in simplest index form.
2 3
a
(4 ) =
b (83)4 =
c
(94)5 =
d (816)4 =
e
(1214)2 =
f
g
(253)2 =
h (10005)3 =
i
(162)5 =
j
36
© Pascal Press ISBN 978 1 74020 033 2
(272)5 =
(274)6 =
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Indices
Excel Mathematics Study Guide Year 8
Page 15
UNIT 5: Index laws: the zero index
QUESTION 1
a
2
3 ÷3 =9÷9
b 23 ÷ 23 =
32 ÷ 32 =
b 23 ÷ 23 =
d 53
53 =
d 53
53 =
QUESTION 2
a
Complete the following.
2
÷
72 ÷ 72 =
e
72 ÷ 72 =
d 53 ÷ 53 =
a
a
f
25 ÷ 25 =
÷
72 ÷ 72 =
f
25 ÷ 25 =
c
60 =
f
(–2)0 =
h ( 2 )0 =
i
2580 =
b 50 – 80 =
c
110 + 40 – 30 =
9 – 70 =
f
100 – 2 =
h 15 + 150 – 20 =
i
70 + 50 + 4 =
k (5 + 9)0 =
l
4
b y0 =
c
a0 =
f
5m0 =
e
370 =
1
190 =
.
Find the value.
0
2 +3 =
d 6 + 60 =
e
g
120 – 90 – 60 =
j
2
a
25 ÷ 25 =
104 ÷ 104 =
b 90 =
30 =
QUESTION 6
f
Find the value.
7 =
0
104 ÷ 104 =
Fill in the blank.
0
QUESTION 5
c
÷
c
e
d 230 =
g
104 ÷ 104 =
b 23 ÷ 23 =
Any (non-zero) number raised to the zero power is equal to
QUESTION 4
÷
c
Use the index laws to simplify, leaving the answer in index form.
32 ÷ 32 =
QUESTION 3
e
÷
60 + 6
80 =
Simplify.
0
x =
d 2x0 =
e
3b0 =
g
(4k)0 =
h (3t)0 =
i
(7n)0 =
j
(2a2)0 =
k (pq)0 =
l
pq0 =
n 9a0 – 80 =
o
5a0 + (5a)0 =
m 7x0 + 3y0 =
Chapter 4: Indices
© Pascal Press ISBN 978 1 74020 033 2
37
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Indices
Excel Mathematics Study Guide Year 8
Page 15
UNIT 6: Index laws: miscellaneous questions
QUESTION 1
a
Simplify the following, leaving the answers in index form.
74 × 75 =
d 46 × 46 =
g
a
49 ÷ 46 =
a
4
a
(54)3 × (55)2 =
a
i
6 × 62 =
b 28 ÷ 25 =
c
67 ÷ 65 =
47 ÷ 44 =
f
38 ÷ 36 =
h 56 ÷ 54 =
i
46 ÷ 43 =
c
(73)2 =
f
(87)2 ÷ 86 =
i
(53)4 =
c
8n0 =
f
(x2)0 =
i
96 ÷ 94 =
(63)2 × 64 =
6
h (35) =
Simplify the following.
4m0 =
b (6m)0 =
(5y3)0 =
QUESTION 5
h 53 × 52 =
e
d 5m0 × (8m)0 =
g
82 × 8 × 83 =
b (23)2 =
(3 ) =
QUESTION 4
f
Give the answers in simplest index form.
2 3
d (43) =
g
32 × 37 =
e
36 ÷ 32 =
QUESTION 3
76 × 72 =
Simplify, giving answers in index form.
d 55 ÷ 53 =
g
c
e
82 × 83 =
QUESTION 2
b 22 × 25 =
e
26 b0 =
h 57 ÷ 57 =
Simplify the following, giving the answers in index form.
87 ÷ 82 =
2
d (53) =
b 69 × 62 =
e
53 ÷ 5 =
c
(25)4 =
f
52 × 52 =
g
22 × 63 × (24 × 63) =
h 43 × 36 ÷ (42 × 34) =
i
32 × 3 =
j
92 ÷ 9 =
k 77 × 49 ÷ (75 × 47) =
l
(42)2 =
38
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Indices
TOPIC TEST
PART A
Instructions • This part consists of 12 multiple-choice questions.
• Fill in only ONE CIRCLE for each question.
• Each question is worth 1 mark.
Time allowed: 15 minutes
Total marks: 12
Marks
1
2
3
4
5
6
7
8
9
4
3 equals:
3+3+3+3
4+4+4
3×3×3×3
4×4×4
1
38 ÷ 34 equals:
34
32
14
12
1
72 × 74 equals:
496
498
76
78
1
5 8 × 31
5 4 × 34 2equals:
5
33
54
33
52 × 33
54 × 33
44 × (410 ÷ 42) equals:
420
412
410
46
1
(102)4 equals:
100 000
1 000 000
10 000 000
100 000 000
1
(43)2 equals:
164
432
46
45
1
3 + 40 equals:
1
2
4
7
1
310
314
38
1
78
764
716
1
59
2518
259
1
26 × 38
624
69
1
1
34 × 38
32 equals:
36
10 (710 ÷ 72)2 equals:
725
11 53 × 56 equals:
518
12 (23 × 34)2 equals:
25 × 36
Total marks achieved for PART A
Chapter 4: Indices
© Pascal Press ISBN 978 1 74020 033 2
12
39
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Indices
TOPIC TEST
PART B
Instructions • This part consists of 15 questions.
• Each question is worth 1 mark.
• Answer each question in the space provided.
Time allowed: 15 minutes
Total marks: 15
Marks
Simplify the following, giving your answer in index form.
1
3
60 × (62) =
2
57 ÷ 55 =
1
1
3
4 4t0 + (7t)0 + (9t3)0 =
(83)2 =
1
1
5
2
320 ÷ (34) =
1
Simplify the following, giving your answer in index form.
6
39 × 35 =
8
7 ×5
74 ×52 =
6
4
7
98 ÷ 94 =
9
5 ×3
33 =
0
1
1
9
1
1
10 (92) ÷ 93 =
2
1
Simplify the following, writing your answers in the simplest index form.
11 37 × 34 × 33 =
12 90 ÷ 9–2 =
1
1
13 (1000a12b15)0 =
14 50 + 20 + (34)0 =
1
1
15 252 × 252 × 643 × 643 =
1
Total marks achieved for PART B
40
© Pascal Press ISBN 978 1 74020 033 2
15
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Chapter 5
Rational numbers
Excel Mathematics Study Guide Year 8
Pages 2–5
UNIT 1: Rounding off whole numbers
QUESTION 1
a
Round off the following numbers to the nearest whole number.
b 11.6
c
14.5
d 9.16
e
7.45
f
7.913
g
6.499
h 34.501
i
23.148
QUESTION 2
Round off the following numbers to the nearest ten.
b 52
c
93
d 397
e
f
82
g
h 377
i
568
a
8.3
68
145
QUESTION 3
a
74
Round off the following numbers to the nearest hundred.
169
b 578
c
435
d 671
e
814
f
950
g
h 332
i
2541
281
QUESTION 4
Round off the following numbers to the nearest thousand.
a
5632
b 8199
c
7650
d 4781
e
2369
f
g
4961
h 5831
i
6289
j
QUESTION 5
3334
9325
Round off the following numbers to the nearest ten thousand.
a
24 683
b 91 561
c
32 655
d 47 960
e
52 390
f
g
74 634
h 83 597
i
48 139
j
QUESTION 6
61 833
20 613
Round off the following numbers to the nearest million.
a
2 600 000
b 5 718 000
c
8 123 000
d 5 672 000
e
28 671 500
f
g
48 361 410
h 92 234 612
i
8 714 321
j
31 814 632
31 234 612
Chapter 5: Rational numbers
© Pascal Press ISBN 978 1 74020 033 2
41
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Rational numbers
Excel Mathematics Study Guide Year 8
Pages 2–5
UNIT 2: Rounding off decimals
QUESTION 1
a
Write the following decimals correct to one decimal place.
2.34 =
b 8.915 =
c
30.612 =
d 81.14 =
e
f
41.36 =
g
89.47 =
h 32.143 =
i
54.156 =
j
53.345 =
k 91.831 =
l
39.418 =
QUESTION 2
a
92.83 =
Write the following decimals correct to the nearest tenth.
81.348 =
b 32.149 =
c
36.481 =
d 41.943 =
e
62.458 =
f
92.357 =
g
51.318 =
h 39.615 =
i
42.835 =
j
28.471 =
k 58.653 =
l
73.852 =
QUESTION 3
a
Write the following decimals correct to two decimal places.
7.813 =
b 19.625 =
c
21.538 =
d 63.829 =
e
51.367 =
f
72.123 =
g
84.351 =
h 63.839 =
i
41.638 =
j
64.836 =
k 75.612 =
l
81.139 =
QUESTION 4
a
Write the following decimals correct to the nearest hundredth.
7.417 =
b 15.632 =
c
28.139 =
d 0.941 =
e
33.458 =
f
47.438 =
g
53.235 =
h 64.831 =
i
78.356 =
j
81.892 =
k 92.635 =
l
125.836 =
QUESTION 5
a
Write the following decimals correct to three decimal places.
5.6781 =
b 25.8314 =
c
19.7156 =
d 37.8395 =
e
42.8386 =
f
59.2347 =
g
63.6152 =
h 72.8192 =
i
81.3419 =
j
93.1453 =
k 120.6158 =
l
92.1835 =
QUESTION 6
a
Write the following decimals correct to the nearest thousandth.
88.6152 =
b 63.3412 =
c
230.3614 =
d 95.6487 =
e
f
512.1581 =
g
120.1581 =
h 134.6429 =
i
832.3248 =
j
435.2345 =
k 437.1298 =
l
531.6413 =
42
© Pascal Press ISBN 978 1 74020 033 2
94.8325 =
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Rational numbers
Excel Mathematics Study Guide Year 8
Pages 2–5
UNIT 3: Changing fractions to terminating decimals
QUESTION 1
a
d
g
3
10
43
10
Write the following as decimals.
=
b
=
e
93
100
=
=
7
100
239
100
c
=
f
=
i
=
12
100
=
783
1000
=
764
10 000
b 8 + 10 =
c
15 + 100 =
d 28 + 100 =
e
16 + 100 =
f
94 + 10 =
g
123 + 100 =
h 128 + 10 =
i
532 + 100 =
j
81 + 10 =
k 58 + 10 =
l
94 + 100 =
c
3
100
=
k
QUESTION 2
a
3
10
5+
a
d
g
j
5
3
5
1
4
d
g
j
d
g
j
Change each fraction to a decimal.
b
=
e
=
h
=
k
8
80
249
100
63
50
b
=
h
=
3
1000
6
15
k
=
63
1000
7
50
=
=
8
125
f
i
=
=
9
50
=
68
1000
304
100
11
250
=
=
=
b
e
h
k
37
19
3
8
7
8
c
3
15
=
56
20
i
=
l
12
50
c
5
8
f
=
322
1000
=
i
l
=
=
=
=
=
415
10 000
f
=
27
200
7
=
114
10 000
6
20
7
l
Write the following as decimals.
=
103
500
11
40
e
=
9
500
6
10
Express the following as decimals.
=
QUESTION 5
a
7
=
17
100
1
8
3
QUESTION 4
a
9
3
1
10
=
Change the following to decimals.
=
QUESTION 3
6342
10 000
7
10
l
j
549
1000
h
9
10
=
=
935
1000
=
=
=
37
50
32
25
=
=
28
500
=
Chapter 5: Rational numbers
© Pascal Press ISBN 978 1 74020 033 2
43
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Rational numbers
Excel Mathematics Study Guide Year 8
Pages 2–5
UNIT 4: Recurring and terminating decimals
QUESTION 1
a
Which of the following are recurring decimals and which are terminating?
0.125
b 0.333 ...
c
1.32
!!
d 0.43
e
2.43
f
0.4545 ...
g
0.1111 ...
h 1.8345
i
0.8231
j
0.7
k 0.8835
l
9.8
QUESTION 2
a
Write the following recurring decimals in the shorter way.
0.3333 ... =
b 0.777 ... =
c
0.533 33 ... =
d 0.8888 ... =
e
0.272 727 ... =
f
0.266 666 ... =
g
0.434 343 ... =
h 0.121 212 12 ... =
i
0.818 181 ... =
j
0.6666 ... =
k 0.428 571 428 571 ... =
l
0.080 808 ... =
QUESTION 3
a
4.3! =
Write the following recurring decimals in the expanded way.
!! =
d 0.31
b 8.6! =
c
0.1! =
0.7! =
f
2.2! =
e
g
!! =
1.72
!! =
h 0.227
i
!! =
1.24
j
0.7083! =
k 0.5! =
l
!! =
0.15
b 0.2222 ... =
c
1.4444 ... =
d 1.689 292 92 ... =
e
1.6363 ... =
f
5.123 123 ... =
g
6.230 693 069 ... =
h 5.0666 ... =
i
3.255 55 ... =
j
0.456 456 ... =
k 2.1111 ... =
l
0.936 936 ... =
b 0.3333 ... =
c
0.666 ... =
d 0.3888 ... =
e
f
0.153 33 ... =
g
1.7272 ... =
h 0.444 ... =
i
1.7777 ... =
j
0.002 22 ... =
k 3.585 858 ... =
l
8.3737 ... =
=
c
2
9
=
f
QUESTION 4
a
0.083 33 ... =
QUESTION 5
a
d
g
j
Write the following as recurring decimals.
0.253 53 ... =
QUESTION 6
a
Write the following as recurring decimals.
1
3
3
9
Write the following fractions as recurring decimals.
=
b
=
e
3
11
=
5
110
0.2323 ... =
=
44
© Pascal Press ISBN 978 1 74020 033 2
h
k
2
3
5
9
4
11
1
90
=
i
=
l
=
2
11
5
11
2
90
=
=
=
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Rational numbers
Excel Mathematics Study Guide Year 8
Pages 2–5
UNIT 5: Irrational numbers
QUESTION 1
a
4
7
Write rational, irrational or neither for each number.
b 0.2
2
c
e
d
5
f
52
1
g
17
h
49
i
9+ 3
j
16 + 25
k 0.6!
QUESTION 2
a
c
e
3
k
8
3
7
Write rational, irrational or neither for each number.
81
b
52
8
d
−25
f
0.4
15
17
g
i
l
2.25
h
13
j
22
7
QUESTION 3
l
11
c
0.9
d
e
144
f
a
7
c
e
1
−8
1
16
3 + 17
Which of the following are irrational?
a
QUESTION 4
3
b 12%
33
7
Between which two consecutive integers does each of the following lie?
b
21
72
d
220
32
f
98
Chapter 5: Rational numbers
© Pascal Press ISBN 978 1 74020 033 2
45
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Rational numbers
Excel Mathematics Study Guide Year 8
Pages 176–197
UNIT 6: Equivalent ratios
QUESTION 1
a
Express the following ratios in their simplest form without using the calculator.
6:3 =
b 2:8 =
c
28 : 7 =
d 12 : 36 =
e
15 : 5 =
f
5 : 55 =
g
32 : 4 =
h 3 : 39 =
i
81 : 9 =
j
8 : 48 =
k 64 : 16 =
l
12 : 144 =
QUESTION 2
a
Simplify the following ratios without using the calculator.
35 : 75 =
b 72 : 36 =
c
51 : 17 =
d 20 : 115 =
e
56 : 7 =
f
88 : 12 =
g
63 : 18 =
h 8 : 72 =
i
32 : 6 =
j
8 : 76 =
k 9 : 45 =
l
20 : 45 =
c
12 : 5 =
f
4: 6 =
i
1.2 : 4.8 =
k 3: 8 =
l
3.5 : 4 =
n 5 : 15 : 45 =
o
14 : 28 : 42 =
QUESTION 3
a
Express the following ratios in their simplest form.
3 : 9 : 15 =
b
1
1 1
: =
4 12
1 7
: =
8 8
d 14 : 6 =
e
g
2
5
h 0.7 : 0.9 =
j
1.2 : 5 =
3
: =
5
1
m 2:4:8 =
QUESTION 4
10 cm : 80 cm =
b 30 kg : 75 kg =
c
6 h : 2 days =
d 900 g : 3 kg =
e
30c : 70c =
f
g
60 cm : 3.5 m =
h 80 s : 2 min =
i
5 kg : 1200 g =
j
600 mL : 1 L =
k 8 km : 500 m =
l
20 cm : 160 mm =
m 80 cm : 2 m =
n 40c : $2 =
QUESTION 5
a
40
5
Use a calculator to simplify the following ratios.
a
1
cm : 3 2
1
4 days : 4 weeks =
Use a calculator to express the following ratios in their simplest form.
m=
d 25 min : 2 h =
2
b 800 g : 10 kg =
c
30 min : 2 h =
e
f
54 : 3 =
3 h : 40 min =
5
1
g
33 : 6 =
h 1: 6 =
i
3.5 : 6.5 =
j
3.45 : 4.45 =
k 8.2 : 10 =
l
9.6 : 3 =
46
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Rational numbers
Excel Mathematics Study Guide Year 8
Pages 176–197
UNIT 7: Using ratios
QUESTION 1
a
Divide $560 in the ratio 3 : 4.
b Divide 2 tonnes in the ratio 2 : 3.
c
Divide $720 in the ratio 4 : 5.
d $800 is divided in the ratio 3 : 5. Find the larger part.
e
$3600 is divided in the ratio 1 : 3. Find the smaller part.
QUESTION 2
a
The ratio of girls to boys is 5 : 4. If there are 35 girls, how many boys are there?
b The three angles of a triangle are in the ratio 2 : 3 : 4. Find the size of each angle.
c
of adults and children on the train.
d
e
Georgie and Isabel share $24 000 in the ratio 5 : 3. What is Georgie’s share?
QUESTION 3
a
Two sides of a rectangle are in the ratio 3 : 4. If the longer side is 20 cm, what is the perimeter of the rectangle?
b Find the ratio of the areas of two squares whose sides are 3 cm and 4 cm.
c
The dimensions of a rectangle are 6 cm and 10 cm. What is the ratio of its length to its perimeter?
d Divide $96 000 in the ratio of 4 : 5 : 7.
e
Divide $5400 between two girls in the ratio of their ages, 8 years and 10 years.
Chapter 5: Rational numbers
© Pascal Press ISBN 978 1 74020 033 2
47
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Rational numbers
Excel Mathematics Study Guide Year 8
Pages 176–197
UNIT 8: Rates
QUESTION 1
a
Complete the following sentences.
960 km in 12 hours is a rate of
per hour.
per minute.
b
c
per kg.
8 kg of peas cost $20, which equals
d Angus works for 15 hours and is paid $450, and so his rate of pay is
e
Maddy earns $1250 for a 40-hour week. Her hourly rate of pay is
per hour.
dollars per hour.
QUESTION 2
a
Anna drives 360 km in 4 hours. Find her average speed.
b A car travels at the speed of 25 m/s. How many kilometres does it travel in 1 hour?
c
A car uses petrol at the rate of 12.5 L/100 km. How many litres would be used to travel 850 km?
QUESTION 3
a
1
A tree grows to a height of 13.75 m over a period of 5 2 years. What is the average annual growth rate
in metres per year?
b In a cricket match, runs were scored at a rate of 5.4 runs per over. How many overs did it take to score
270 runs?
c
Change 120 km/h to km/min.
48
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Rational numbers
Excel Mathematics Study Guide Year 8
Pages 176–197
UNIT 9: Conversion of rates
QUESTION 1
Complete the equivalent rates.
a
90 km/h =
km/min
b 60 L/h =
L/day
c
30 m/min =
m/h
d $2/min =
$/h
e
40 mL/min =
g
500 mm/s =
i
12.5 t/week =
mL/h
cm/s
kg/week
kL/min
k 315 L/min =
QUESTION 2
a
f
30°/min =
°/s
h 8.5 ha/day =
j
0.85 m/s =
l
100 km/h =
m2/day
cm/h
km/day
A speed of 46 metres per second is how many:
metres per minute?
b metres per hour?
c
kilometres per hour?
QUESTION 3
A car is travelling at 120 km/h. How many metres does it travel in one second?
QUESTION 4
A flow rate of 25 millilitres per second is how many:
a
millilitres per minute?
QUESTION 5
a
b millilitres per hour?
c
litres per hour?
Change the following.
82 km/h to m/s
b 20 m/s to km/h
Chapter 5: Rational numbers
© Pascal Press ISBN 978 1 74020 033 2
49
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Rational numbers
Excel Mathematics Study Guide Year 8
Pages 176–197
UNIT 10: Scale drawing
QUESTION 1
a
Write each of the following scales in the ratio form.
1 mm to 1 m
b 1 cm to 1 m
c
1 cm to 100 m
d 10 cm to 1 km
e
4 mm to 1 m
f
5 cm to 1 m
g
h 20 cm to 1 m
i
1 mm to 6 m
1 mm to 20 m
QUESTION 2
a
Using a scale of 1 : 100 what length is represented by each of the following?
1 cm
d 8 mm
QUESTION 3
a
d 9.5 cm
a
d 80 m
a
5 cm
e
f
12 m
6 mm
b 5 cm
c
6m
e
f
63.25 m
8.3 m
The distance between two points in real life is given. What will be the distance between
these points on a scale drawing with a scale of 1 cm to 100 m?
500 m
QUESTION 5
c
Using a scale of 1 : 1000 find the real length represented by the following.
8 mm
QUESTION 4
b 3 cm
b 400 m
c
1260 m
e
f
2835 m
3000 m
A drawing of a block of land along with the proposed building has been drawn using a
scale of 1 : 500. Measure the plan and answer the questions using metres.
How wide is the block of land?
N
b How deep is the block of land?
c
Find the area of the block of
land in square metres.
d How far is the proposed building
from the southern boundary?
e
Find the area of the proposed
building in square metres.
50
© Pascal Press ISBN 978 1 74020 033 2
Proposed building
Area I
Area II
Scale 1 : 500
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Rational numbers
Excel Mathematics Study Guide Year 8
Pages 176–197
UNIT 11: Problem solving
1
In a class of 30 students, there are 18 boys. What is the ratio of:
a boys to girls?
b girls to boys?
2
Michael delivered 480 bottles of milk every morning between 6:00 am and 9 : 00 am.
Find his hourly rate of delivery.
3
Tony buys a pen for $30 and sells it for $40. What is the ratio of the:
a
cost price to the selling price?
b selling price to the cost price?
4
John drives 240 km in 4 hours.
Find his average speed.
6
Two angles of a triangle are 40 and 60 . What is the ratio of the:
a
third angle to the angle sum of
the triangle?
5
Divide $300 in the ratio 2 : 3.
b smallest angle to the largest angle?
7
A car travels at 450 km in 5 hours. What is the speed of the car per hour?
8
If a 20-kg box of oranges cost $15, calculate the price of 1 kg of oranges.
9
A man wishes to divide $120 000 in the ratio of 3 : 7 to give to his son and his wife respectively.
How much will each one get?
10
quantity of each needed to make 50 cubic metres of concrete.
Chapter 5: Rational numbers
© Pascal Press ISBN 978 1 74020 033 2
51
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Rational numbers
TOPIC TEST
PART A
Instructions • This part consists of 12 multiple-choice questions.
• Fill in only ONE CIRCLE for each question.
• Each question is worth 1 mark.
Time allowed: 15 minutes
Total marks: 12
Marks
1
What is 218 625 396 rounded off to the nearest million?
218 000 000
2
3
6
7
1
17.99
18.00
1
1:8
1:3
3:1
1
0.85
0.72
0.625
1
5
6
6
7
1
$7200
1
75 km/h
1
17.90
What is the ratio of 8 hours to 1 day?
5
8
as a decimal equals:
0.58
0.6! as a fraction in simplest form is:
3
5
2
3
Leo and Ben share $12 000 in the ratio 2 : 3. What is Ben’s share?
$4800
$6000
What is the average speed if a car travels 245 km in 3½ hours?
60 km/h
9
0.785
3
If 17.895 is rounded off to two decimal places the result is:
$2400
8
25
2
3
8:1
5
1
218 700 000
Which of the following is irrational?
17.89
4
219 000 000
218 600 000
65 km/h
70 km/h
The ratio of cows to sheep on a farm is 3 : 8. If there are 240 cows on the farm, how
many sheep are there?
90
150
640
880
1
200
1
10 A rate of 7.2 litres per hour is how many millilitres per second?
0.2
2
20
11 Using a scale of 1:100 000 what is the real length represented by a distance on a map of 5 cm?
5 km
500 m
50 m
12 When expressed as a decimal, which of these is not a recurring decimal?
4
5
4
7
4
9
5m
1
4
11
1
Total marks achieved for PART A
52
© Pascal Press ISBN 978 1 74020 033 2
12
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Rational numbers
TOPIC TEST
PART B
Instructions • This part consists of 11 questions.
• Answer each question in the space provided.
Time allowed: 20 minutes
Total marks: 15
Marks
1
Write 13.238 correct to one decimal place.
2
Find 100 + 10 as a decimal.
1
3
Write 0.3! as a fraction in simplest form.
1
4
Express these ratios in simplest form.
7
a
1
3
2
b 0.7 : 2
12 : 4
5
Divide 84 in the ratio 3 : 4.
6
On a journey of 300 km the average speed was 75 km/h. How long did the journey take?
1
1
7
Sally is paid $752.50 for working 35 hours. What is her hourly rate of pay?
1
8
A map will be drawn using a scale of 1 : 1000.
a What length on the map will represent a
real distance of 8 m?
b A length on the map of 13 cm would
represent what actual distance?
2
9
1
Change 15 m/s to km/h.
10 The ratio of boys to girls in a class is 5 : 3. If there are 15 girls, how many boys are in the class?
1
11 Determine whether each number is rational or irrational.
a
7
b
3
5
c
.
0. 7
Total marks achieved for PART B
Chapter 5: Rational numbers
© Pascal Press ISBN 978 1 74020 033 2
3
15
53
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Chapter 6
Basic algebra
Excel Mathematics Study Guide Year 8
Pages 43–64
UNIT 1: Algebraic expressions
QUESTION 1
a
Write an expression for each of the following.
The sum of 5x and 6y =
b 15 less than m =
c
The double of 3a =
d The difference between a and b =
e
Two-thirds of y =
QUESTION 2
a
Write an algebraic expression for each of the following.
Six times the number n minus 5 =
b The sum of 5a and 32 =
c
The sum of x, 2y and 5z =
d The product of 4a and 3b =
e
The average of 5a and 7a =
QUESTION 3
a
If x represents any number, write an algebraic expression for each of the following.
Three times the number plus 9 =
b
c
The sum of the number and 20 =
d The difference between the number and 8 =
e
Seven more than the number =
QUESTION 4
a
Show the sum of each of the following.
17 and a =
b 6m and 7n =
c
3a, 4b and 5c =
d 9x, 11y and 2z =
e
8m, 10n and 7p =
QUESTION 5
a
Write an algebraic expression for each of the following.
To the sum of 6a and 5b, add 7c =
b From the product of 4x and 5y, take away 10 =
c
Divide 3a by 4b and then add 15 =
d Divide the sum of a and b by 10 =
e
18 plus x, all divided by 6 =
54
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Basic algebra
Excel Mathematics Study Guide Year 8
Pages 43–64
UNIT 2: Simplifying algebraic expressions
QUESTION 1
Write down the coefficient for each of the following terms.
a
6x
b 19m
c
16t
d 24x
e
14y
f
54n
g
96q
h 35y
i
32a
j
41p
k 15l
QUESTION 2
a
l
31n
Circle the like terms.
3a, 4b, 10a
b 5x, 6y, 9x
c
7m, 3n, 8x
d 5c, 8d, 9c
e
f
5l, 4m, 6l
g
h 12, 5a, 6a
i
18y, y, 3x
b y+y+y+y=
c
m+m+m+m+m=
d x+x+x+x=
e
f
d+d+d=
g
h 7k + 5k + k =
i
4a + 15a =
b 28b – 17b =
c
35x – 12x =
d 20a – 3a =
e
49x – 6x =
f
18a – 5a =
g
h 14c – 8c =
i
21y – 2y =
b 5×a×b=
c
x×y×z=
d 6×x×y=
e
42 × m × n × l =
f
8×m×n=
g
h 4×5×m×n=
i
14 × a × d × e =
3a, 4c, 5c
QUESTION 3
a
a
20d + 5d =
12y – 5y =
Simplify the following.
9×a=
a × b × 10 =
QUESTION 6
a+a+a+a+a=
Simplify the following expressions.
16x – 3x =
QUESTION 5
a
Simplify the following.
5a + 7a =
QUESTION 4
14y, 8a, 6y
Write the following expressions in expanded form.
a
28ab =
b 8abc =
c
7xy =
d 7mn =
e
9abc =
f
g
2xyz =
h 9a2b =
i
14mnp =
j
8a3 =
k 5ace =
l
17a2b2 =
m 16x =
n 28x2y3 =
18m2 =
Chapter 6: Basic algebra
© Pascal Press ISBN 978 1 74020 033 2
55
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Basic algebra
Excel Mathematics Study Guide Year 8
Pages 43–64
UNIT 3: Collecting like terms
QUESTION 1
Collect like terms to simplify the following.
a
a+a+a+a=
b x+x+x+y+y+y+y=
c
x+x+x+x+y=
d l+l+l+l+l+m=
e
m+m+m+n+n=
f
QUESTION 2
k+k+k+m+m+m=
Simplify the following by collecting like terms.
a
5x + 7y + 9x =
b 14a + 17 + 5a + 12 =
c
2a + 5b + 3a + 7b =
d 7x + 3y + 8y =
e
6m + 4n + 8m + 3n =
f
QUESTION 3
3a + 4b + 8a + 11b =
Simplify the following.
a
16x – 9x – 3x + 2y =
b 10x + 9y – 8x + 7y =
c
9p + 3l + 8p – l =
d 9m – 4n + 12m + 6n =
e
15y + 31x + 4y =
f
g
20a – 9a + 6b + 10b + b =
h 9a + 8b + 5a – 5b – 2b =
QUESTION 4
18xyz – 14xyz =
Simplify the following.
a
10m – 2m – m =
b 8p – 5p + 3p =
c
9y2 + 7y2 – 8y2 =
d 12x – 7x – 3x =
e
9a – 7b + 3a – a =
f
g
10x + 5x + 2x =
h 11d – d – 5d – 3d =
QUESTION 5
y + 5y – 2y =
Simplify the following.
a
9x – x – 4x =
b a2 – 7a – a + 15 =
c
7y – 3x – y =
d p3 + 3p2 – p2 – 10 =
e
15a + 2b – b – 7a =
f
g
ab + 4b + 3ab =
h 2xy + 4x – xy + 2x =
QUESTION 6
5x + 10y + 9x – 2y =
Collect like terms and simplify.
a
xy + yz – xy – yz + xy =
b 15m2n – 6mn2 + 7mn2 + 3m2n =
c
5a2 + 15a2 – 4a2 =
d 18xyz + 8x + 5xyz – 4x =
e
20xyz + 12xyz – 5xyz =
f
g
9x2y2 + 8x + 2x2y2 + 9x =
h 9a3 + 7a3 – 4b3 + 8b3 =
56
© Pascal Press ISBN 978 1 74020 033 2
25x2 + 17y2 – 19x2 =
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Basic algebra
Excel Mathematics Study Guide Year 8
Pages 43–64
UNIT 4: Algebraic abbreviations
QUESTION 1
a
Write 8 × y in a shorter way.
b Write 2 × 4 × a in a shorter way.
c
Write 5 × m × m × m in another way.
d Write 7ab, showing multiplication signs.
e
What is the difference between 24y and 2 × 4 × y?
QUESTION 2
a
Write the following expressions without multiplication or division signs.
3×5×a=
b 5×n×7=
c
a+7×b=
d 4 × (x + 16) =
e
3x ÷ 5 =
f
a×b×c=
g
7×a×6=
h 8a × b × b =
i
4×m×5×n=
j
2×m+5=
k 9+4×x=
l
3×a+4×b=
m 23 ÷ x =
n 6a ÷ 11 =
o
m ÷ 10 =
p (m + n) ÷ 5 =
q 5x ÷ (3a + 2) =
r
(8x + 3) ÷ 2a =
QUESTION 3
a
Write the following expressions by showing all multiplication or division signs.
9a =
b 3y =
c
12a =
d 4x – 5 =
e
8m + 3 =
f
60 – 3x =
g
ab + 3 =
h 2x – 3y =
i
a3b2 =
j
14xyz =
k 7m2 + 4 =
l
x2 – y2 =
QUESTION 4
Write the following in a shortened form.
a
6×a×a×a×b=
b 12 × a × a × b × b =
c
5 × (x + 9) =
d 5 × (m – 5) =
e
7 × a × (c + 2) =
f
g
m × n × (p + 3) =
h 6 × (5 × a + 9) =
i
8 + (4 × 5 + 4 × m) =
j
8 × (6 × a – 2 × b) =
k 3a + 4 × a + 5 =
l
4a + 5 × 2a – 5 =
m n×n×7×n=
n 6×a×a×a×3=
o
p 3×m–6+5×m–3=
x×x×x×y×y=
q a + 3 × 5a + 7 =
r
4 × 7 × (x – 2) =
a – 3 + 4a – 7 =
Chapter 6: Basic algebra
© Pascal Press ISBN 978 1 74020 033 2
57
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Basic algebra
Excel Mathematics Study Guide Year 8
Pages 43–64
UNIT 5: Substitution (1)
QUESTION 1
a
If a = 3, find the value of each expression.
7a =
d a2 =
b 9a + 1 =
c
9a – 1 =
5a2 =
f
a(a + 1) =
e
g
a3 =
h a2 – 2a =
i
(2a + 7) × 3a =
j
7a – 12 =
k 180 – 6a =
l
(a – 2) ÷ 15 =
QUESTION 2
If a = 1, b = 3, c = 5 and d = 10, find the value of each of the following expressions.
b a+b+c+d=
c
abc – d 2 =
d abc =
e
f
3b + 5c – d =
g
16bc =
h 8c – d =
i
8d ÷ b =
j
5a – a2 =
k (c + d) – a2 =
l
b 2 + d 2 – abc =
c
m = 5l – 2
a
a+b=
QUESTION 3
a
Complete each table of values.
b = 3a + 2
a
b
0
b y = 4x – 2
1
2
3
4
x
y
d y = 6x – 1
x
y
0
2a + 3b + 4c =
1
QUESTION 4
e
2
3
4
5
6
1
2
3
4
l
m
p = 2q + 3
q
p
1
f
2
3
4
0
1
2
3
3
4
4
v = 9u – 7
u
v
0
1
2
5
6
Complete the following table.
x
y
a
5
1
b
8
3
c
6
2
d
7
5
e
9
4
f
4
2
g
10
3
h
7
4
i
8
1
x+y
58
© Pascal Press ISBN 978 1 74020 033 2
x–y
xy
x2
y2
4x + 5y
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Basic algebra
Excel Mathematics Study Guide Year 8
Pages 43–64
UNIT 6: Substitution (2)
QUESTION 1
If a = 2, b = 3, c = 4 and d = 5, evaluate the following.
a
abc
b a+b+c–d
c
ab + bc
d a2 + b2 + c2
e
bc ÷ a
f
abcd
g
b2 + c2 – ad
h b2 + 10
i
3ab + 2cd
j
3a2c – d
k 5c2 – 12
QUESTION 2
l
a3 + b3
If x = 5, find the value of the following expressions.
a
3x + 2
b 65 – 4x
c
4(x + 3)
d (2x – 7)2
e
6x – x2
f
2x (x – 3)
g
(x + 2)2
h (x – 3)2
i
x3
j
(2x)2
k
21 – x
m (x – 3)3
QUESTION 3
n (x + 2) (x – 2)
o
l
2x2
x2 – 7
If x = 6.5, y = 2.4 and z = 5.8, find correct to one decimal place the value of the
following expressions.
a
x+y
b x+y+z
e
xyz
f
i
yz
m (x + y)2
c
x+y–z
d xy
x2
g
x 2 + z2
h y3
j
(x – z) + 3
k x÷y
n
x+y+z
o
3
l
(x + y) ÷ z
x+y+z
Chapter 6: Basic algebra
© Pascal Press ISBN 978 1 74020 033 2
59
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Basic algebra
Excel Mathematics Study Guide Year 8
UNIT 7: Addition and subtraction of like terms (1)
QUESTION 1
Simplify the following expressions by collecting like terms.
a
2x + 3x =
b 5x – 2x =
c
5a + 4a =
d 9y – 6y =
e
3y + 7y =
f
g
8m + 6m =
h 9a – a =
i
2b + 15b =
j
8t – 2t =
k 7n + 5n =
l
5mn + 3mn =
m 8p – 5p =
n 8xy + 7xy =
o
p 18x2 – 12x2 =
7p – 3p =
QUESTION 2
4q – 3q =
Simplify the following.
a
5p + 6p – 3p =
b 8m – 3m – 2m + 7m =
c
8x – 5x + 7x =
d 4xy + 6xy – 3xy – 2xy =
e
12y – 4y + 5y =
f
g
8xy + 2xy + 5xy =
h 9a + 2a + 3a – 7a =
i
6m – 3m + 10m =
j
11p + 5p – 7p =
k 5a + 7a + 3a + 6a =
l
6ab – 3ab – ab + 2ab =
m 8x2 + 7x2 – 6x2 – 3x2 =
n 6a2 + 7a2 + 8a2 – 10a2 =
o
p 11y – 6y – 3y – y =
4x – 2x + 9x – 6x =
QUESTION 3
Pages 43–64
8k + 4k + 2k – 5k =
Simplify by collecting like terms.
a
4x + 3x + 2y + 7y =
b 11a + 7b – 3a =
c
3m + 7m + 8n + 9m =
d 9c – 6c – 2c + 3d =
e
8a + 7a – 2m – 3m =
f
g
3x + 2y + 5x =
h 12mn – 6mn + 3mn =
i
8y + 7x – 3x – 2x =
j
5x + 7y – 4y – 2x =
k 8m + 2n + 9n + 2n =
l
5t + 17 – 2t – 8 =
m 7y + 6y – 3x + 7x =
n 6a + 9 – 3a =
o
p 9m + 7mn – 6m – 2mn =
12 – 3x – 2x =
q 10m + 5n + 3n + 4m =
60
© Pascal Press ISBN 978 1 74020 033 2
r
9x2 – x2 – 3x2 =
5x + 3y – 2x – 2y =
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Basic algebra
Excel Mathematics Study Guide Year 8
UNIT 8: Addition and subtraction of like terms (2)
QUESTION 1
Simplify the following expressions by collecting like terms.
a
3a – 7a =
b –2x + 3x =
c
6y – 9y =
d –2p – 3p =
e
8a + –3a =
f
g
–2m2 + 5m2 =
h –8n – n =
i
3x – 11x =
j
–6p – 2p =
k –y + y =
l
–10x + 4x =
m 6a – 8a =
n –5t – t =
o
p 2k – 14k =
x – 5x =
QUESTION 2
9x – –2x =
Simplify the following by collecting like terms.
a
5n + –2n =
b –y – y – y =
c
–4a – –6a =
d –k + 2k – 3k =
e
8y – –3y =
f
g
5x – 7x =
h –8n + 15 – 2n =
i
–6m – –10m =
j
3a – 2a2 + 7a2 =
k –x – 2x – 3x =
l
–3y + 4x – 7y =
m 9 – 7t + 12 =
n –3k2 – 2k2 + 9k =
o
p 8xy – 25 – 10xy =
x – 5x + 3y =
QUESTION 3
Pages 43–64
–3p + 6p + 3p =
Simplify by collecting like terms.
a
2x + 3x – y – 5y =
b 3n + 2p – 7n =
c
8a + 9b – 3a + 2b =
d 6n – 3p – 10n + p =
e
2a – 3b – 2a – 3b =
f
g
–7x + 15 + 7x =
h 8m2 – 7m + 3a2 + m =
i
9y – 3 – 2y – 2 =
j
6a – 3b – 9a – b =
k 7k + 5 – 4k + 12 =
l
7xy + 9x – 2x + xy =
m 4m – 7 + 6m – 8 =
n 4a – 5b – 3a =
o
p 6ab – 3b + ab – 9ab =
a – 8t + 2a – t =
q y – 5y + 7 – 18 =
r
a–b–a+a=
–6y2 – 3y – y + 2y2 =
Chapter 6: Basic algebra
© Pascal Press ISBN 978 1 74020 033 2
61
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Basic algebra
Excel Mathematics Study Guide Year 8
UNIT 9: Multiplication of pronumerals
QUESTION 1
Find the products of the following.
a
7 × 3a =
b 4a × 9b =
c
4m × 5n =
d ab × a =
e
–2x × 5 =
f
g
4a × –3a =
h –9m × –3 =
i
8 × 3b × b =
j
–5x × –x =
k –2a × –3b =
l
3a × 4am =
m 4mn × 3m × 2n =
n –2p × 5 × –5p =
o
p –6m × –5mn =
6ab × 5 =
QUESTION 2
–8m × –2m =
Work out the following products.
a
3 × 2 × 5a × b =
b 7a × 2a =
c
8b × –3b =
d –6a × 3 =
e
2m × 3mn =
f
g
ab × bc =
h –9t × 5t =
i
7mn × 8np =
j
–3k × –2k =
k xy × yz =
l
–6 × –5x =
m 2mn × np × 3n =
n –a × 5b =
o
p –2a × –2b =
4ab × –3bc =
q –7a × 2ab × c =
QUESTION 3
Pages 43–64
r
8x × –5 =
–6y × –7y =
Simplify the following.
a
–2x × 4 × –5x =
b –2x × –5 × –8y =
c
3a × 5 × –4y =
d 6m × –5m =
e
–6 × –4a =
f
g
–9x × –2y =
h –3n × –2n × –5n =
i
–8p × 5p =
j
xy × 3xy × –5xy =
k 5 × –2x × 3y =
l
–x × –y × –z =
m –a × 7ab =
n –4a × –5b =
o
p –2m × 10 × –5m =
–m × –2m × –3n =
q –5a × –a =
62
© Pascal Press ISBN 978 1 74020 033 2
r
4n × –15m =
–2ab × –5bc × –3cd =
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Basic algebra
Excel Mathematics Study Guide Year 8
Pages 43–64
UNIT 10: Division of pronumerals
QUESTION 1
a
c
10 x
=
2x
27 mn
=
9m
Simplify the following.
b
30 ab
=
5a
d 36xy ÷ 9xy =
12m2 ÷ 4m =
e
15abc ÷ 5ab =
f
g
9y ÷ y =
h abc ÷ ac =
i
28a ÷ 7a =
j
mk ÷ k =
k 32xy ÷ 8y =
l
8n2 ÷ 4n =
m 9y2 ÷ 9y =
n 60abc ÷ 10ac =
o
25m2 ÷ 5m =
QUESTION 2
a
c
12 a
=
4
2
10 a b
=
5a2
p 72x2 ÷ 12x =
Work out the following divisions.
b
16 m
=
2m
d 25m ÷ 5m =
e
12a ÷ –6 =
f
g
–32a ÷ –8a =
h –48xy ÷ –16x =
i
50ab ÷ 25ab =
j
–9xy ÷ xy =
k 5x ÷ –5 =
l
60m ÷ –10m =
m 18xy ÷ xy =
n –18a ÷ 6a =
o
p 9ab ÷ 3a =
abc ÷ ab =
q 5m ÷ 4m =
QUESTION 3
a
−18 a
=
6
–10pq ÷ 5p =
r
–36mn ÷ –9m =
b
90 abc
=
−10 a
Simplify the following.
c
− xyz
=
− xy
d
−33y
=
−11y
e
–20t ÷ –t =
f
–30ab ÷ –10a =
g
–50ab ÷ –5b =
h a2bc ÷ abc =
i
x2y ÷ xy =
j
m2n ÷ mn2 =
k 27ab2 ÷ 9a2b =
l
–24a2 ÷ 8a =
m 48x2 ÷ –8x =
n 49ab ÷ –7a =
o
p –42a2 ÷ 6a =
–16pqr ÷ 8pr =
q –9y2 ÷ –9y =
r
–27mn ÷ –9m =
Chapter 6: Basic algebra
© Pascal Press ISBN 978 1 74020 033 2
63
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Basic algebra
Excel Mathematics Study Guide Year 8
Pages 43–64
UNIT 11: Algebraic expressions and the order
of operations
QUESTION 1
Simplify the following.
a
2x × 5x × 4 =
b 6a × 12ab ÷ a2b =
c
7mn × 5m ÷ n =
d 3a × 2a × 5b =
e
–4a × 8a × –3 =
f
g
12x × 7 ÷ 4x =
h 20 × 3m ÷ 5 =
i
12 × 8mn ÷ 4n =
j
QUESTION 2
20xyz ÷ 5xy ÷ z =
15a ÷ 3a × 5 =
Find answers to the following.
a
(9x)2 ÷ 3x × 2 =
b –5 × –3x × 8 =
c
81ab ÷ 9a ÷ 3b =
d 21ab ÷ –21ab =
e
(4ab)2 ÷ 16a2b =
f
g
–5a × 3b × –4ab =
h 28xy ÷ 7x ÷ 4y =
QUESTION 3
a
9m × –5 × –2m =
Simplify the following.
(18y ÷ 6) – 2y
b 8x + (6 × 3x)
c
(5 × 8p) – (35p ÷ 7)
d (–5x × 8) – 4x – 3x
e
f
(16a ÷ 2) – (42a ÷ 7)
g
h 5x + 8 × 3x – 4x
i
20a – (15a ÷ 3) – 7a
9a ÷ (8a – 5a)
QUESTION 4
Simplify the following.
85t – (8 × 4t) – 2t
a
26 x + 16 x
=
2x × 3
b
64 a ÷ 16
=
18 a 2 ÷ 9 a
c
35 x 2 ÷ 7 x
=
2 x + 3x
d
8y × 6y
=
12 y 2 ÷ 2 y
e
8n × 5n
=
( 2 n )2
f
8 a − 24 a
=
3a + 5 a
64
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Basic algebra
Excel Mathematics Study Guide Year 8
Pages 43–64
UNIT 12: Applying the distributive law to expand
algebraic expressions
QUESTION 1
Expand the following expressions.
a 5(a + 3) =
b 6(x – 7) =
c –2(6 + a) =
d –5(x + 7) =
e 9(2a + 5) =
f
3(5x – 9) =
g 2a(6 + 3a) =
h x(2x – 5) =
i
m(6m + 3) =
j
5x(x – 3) =
k 7n(2n – 3) =
l
–3a(a – 2) =
m –2(a + 5) =
n –7(3p – 4) =
o 5a(a – 1) =
p –3x(2x – 2) =
q –(x + 9) =
r –(4y – 7) =
QUESTION 2 Expand and simplify by collecting like terms.
b 6(a – 5) – 5a =
a 3(x + 5) + 6x =
c 4(m – 3) + 2m =
d 2(x – 3) + 3x + 7 =
e 6y(y + 4) – 2y2 =
f
6(m – 2) – 3m =
g 5x + 3(10 – x) =
h 9x + 3(x – 2) =
i
6m – 2(m + 1) =
QUESTION 3
Expand and simplify.
a 3(x + 2) + 4(x – 2) =
b 8(m – 3) + 3(m – 2) =
c 5(p – 7) + 3(p + 2) =
d 8(x + 3) + 2(x – 1) =
e 4(x + 3) – 2(x + 1) =
f
x(x + 1) – (x – 3) =
g 5(p – 6) – 2(p – 1) =
h p(5p + 6) – 3(2p – 3) =
i
2m + 3(m – 3) + 7 =
Chapter 6: Basic algebra
© Pascal Press ISBN 978 1 74020 033 2
65
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Basic algebra
Excel Mathematics Study Guide Year 8
Pages 43–64
UNIT 13: Common factors
QUESTION 1
Factorise the following by taking out the highest common factor.
a 5a + 5 =
b 8x – 8 =
c
3y – 3 =
d 2x + 2 =
e
6m + 6 =
f
7m + 7 =
g 3p + 6 =
h 4q + 8 =
i
6x – 9y =
j
k 9b – 18 =
l
5a + 20 =
m 2a + 6 =
n 3m + 12 =
o
6n – 24 =
p 8x – 32 =
q 3a + 15 =
r
2a + 14 =
4x – 16 =
QUESTION 2 Factorise by taking the common factor out.
b 5m + 5n =
a 3a + 3b =
c 6p – 6q =
d 7a + 14b =
e 3l – 9m =
f
m2 + 7m =
g y2 + 6y =
h 9x – 18y =
i
3a – 24b =
j
k mp – 3p =
l
8x – 32y =
m 6x – 36 =
n 3m + 12m2 =
o 5y – y2 =
p 9x – 6 =
q 8m – 8n =
r 6x – 3x2 =
s
4x + 4y =
2x2 – 4x =
t
6pq – 12p2 =
QUESTION 3 Factorise the following.
b –5x + 10 =
a –3x + 6 =
u 10x – 10y =
c –4x + 8 =
d –6x + 18 =
e –2x + x2 =
f
–6a + 24 =
g –3a + 12 =
h –4a + 16 =
i
–6a – 12 =
j
k –2x – 10 =
l
–8y – 4x =
m –3p – 9q =
n –5x – 25 =
o –x – 5 =
QUESTION 4 Factorise.
a 7a + 7b =
b 4a – 20 =
c 9x – 9y =
d 3m + 15 =
e 6 – 6t =
f
m2 – 4m =
g 5ab – a2 =
h 7m – 14n =
i
8ab – 6a2b =
j
k –3 – 15p =
l
–3m – 6n =
n –4a – 20a2 =
o –x – 7 =
–4y – 8 =
–4 – 12a =
m 9m – 36 =
66
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Basic algebra
Excel Mathematics Study Guide Year 8
Pages 43–64
UNIT 14: Problem solving and algebra
1
Write the sum of 2x and 3y.
2
Write the product of m and n.
3
Write the average of 2x, y and 3z.
4
Find the expression 3 more than 2x.
6
Find the area of a square with side length x metres.
Find the perimeter of a square with side length a cm.
5
x, write the next
consecutive integer.
7
Increase 5x by 2.
8
9
Find the volume of a cube with side length y cm.
10 Find the number x less than 3x + 4y.
11 Write the perimeter of a rectangle of length
12 Your pocket money is $x per week. How much do
15 cm and width x cm.
you earn in 7 weeks?
13 Write the perimeter of the following shapes.
a
b
3x
x
x
x
c
5x
2x
2x + 3
8x
2x + 5
14 Find the area of the following shapes.
a
b
c
x
2x
x
2x – 3
15 If I bought p pens and 3q pencils and my sister
bought 5p pens and 2q pencils, how many pens
and pencils do we have altogether?
16 Three different types of sweets cost 5y, 3y and 2y
cents each. If I buy 4 of each type, what would be the
total cost?
Chapter 6: Basic algebra
© Pascal Press ISBN 978 1 74020 033 2
8x + 4
67
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Basic algebra
TOPIC TEST
PART A
Instructions • This part consists of 12 multiple-choice questions.
• Fill in only ONE CIRCLE for each question.
• Each question is worth 1 mark.
Time allowed: 15 minutes
Total marks: 12
Marks
1
2
8x – 3x – x equals:
4x
6x
8x – 3
5
1
a9
2a3
2a6
1
5xy2 equals:
3×x×y×2
5 × xy × xy
5xy × 5xy
5×x×y×y
1
–4x + 5x equals:
x
9x
–45x2
–20x2
1
2(x – 7) + x equals:
3x – 7
3x – 14
x–7
x – 14
1
–7a × 4 equals:
28a
74a
–74a
–28a
1
–9x × –4y equals:
–36y
–94xy
36xy
94xy
1
b is a factor of ab + bc. What is the other factor?
a
a + bc
ac
a+c
1
–30ab ÷ 10a equals:
–3b
3b
–3a2b
3a2b
1
x2 – 5x
–4x
–5x2
1
6n
600n
150n
1
1200
3600
1
a3 + a3 equals:
a6
3
4
5
6
7
8
9
10 x(x – 5) equals:
x2 – 5
11 30 × 2n ÷ 10 equals:
60n
12 If a = 4 and b = 5 then 3ab2 equals:
120
300
Total marks achieved for PART A
68
© Pascal Press ISBN 978 1 74020 033 2
12
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Basic algebra
TOPIC TEST
PART B
Instructions • This part consists of 15 questions.
• Each question is worth 1 mark.
• Answer each question in the space provided.
Time allowed: 20 minutes
Total marks: 15
Marks
1
Simplify – 5a + 6a + 3a
1
2
Simplify (3ab)2
1
3
Simplify 1 ab × 32b2
1
4
Simplify 5ab + 3a × 2b
1
5
Expand and simplify 5a + 3(2 – a)
1
6
Simplify –9x × –2x
1
7
Expand and simplify x(2x – 1) – 2(x2 – x)
1
8
Factorise 2p2q + 4pq2
1
9
Expand and simplify 3(x + 5) + 4(x + 3) – 6(3x – 2)
2
1
10 Expand and simplify y – 2 + 7(2y + 5)
1
11 Simplify 5a – 7b – 8b + b
1
12 If x = 5 and y = –7, what is the value of 2x – y?
1
13 Simplify 64ab ÷ 8b
1
14 Expand and simplify 4(x + 5) – 2(3x – 1)
1
15 Factorise –7x – 21
1
Total marks achieved for PART B
Chapter 6: Basic algebra
© Pascal Press ISBN 978 1 74020 033 2
15
69
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Chapter 7
Length, mass and time
Excel Mathematics Study Guide Year 8
Pages 152–154
UNIT
QUESTION 1
a
Complete the following table by writing the symbol for the name of the unit.
Quantity
Name of unit
Length
metre
m
b
millimetre
c
centimetre
d
kilometre
e
Mass
gram
f
milligram
g
kilogram
h
tonne
i
Symbol
Time
second
j
minute
k
hour
l
day
QUESTION 2 Complete the following table by
writing the symbol of the prefix.
Symbol
QUESTION 3 State the most appropriate unit
(kilometres, metres or centimetres) for the
following.
Meaning
a
a
mega
b
kilo
c
hecto
100
d
deca
10
e
deci
1
10
f
centi
1
100
g
milli
1
1000
h
micro
70
© Pascal Press ISBN 978 1 74020 033 2
Length of a basketball court
1 000 000
1 000
b Height of a door
c
Distance between Sydney
and Brisbane
d Length of a pen
1
1000 000
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Length, mass and time
Excel Mathematics Study Guide Year 8
Pages 152–154
UNIT 2: Units of measurement
QUESTION 1
a
1 cm =
c
1m=
e
Complete the following.
mm
b 1m=
cm
mm
d 1 km =
m
1g=
mg
f 1 kg =
g
1t=
kg
h 1 min =
s
i
1h=
min
j 1 day =
h
QUESTION 2
g
Complete the following.
a
1 normal year =
days
c
1 year =
months
d 1 year =
e
1 year =
weeks
f 1 fortnight =
g
1 decade =
i
1 millennium =
years
years
b 1 leap year =
fortnights
h 1 century =
j 1 year =
weeks
years
seasons
k noon = 12 o’clock in the
l
m am = from midnight to
n pm = from midday to
QUESTION 3
days
midnight = 12 o’clock in the
Complete the table for the number of days in each month. (Assume it is not a leap year.)
Month
Days
Month
a January
g July
b February
h August
c March
i
September
d April
j
October
e May
k November
f
l
June
December
Chapter 7: Length, mass and time
© Pascal Press ISBN 978 1 74020 033 2
Days
71
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Length, mass and time
Excel Mathematics Study Guide Year 8
Pages 152–154
UNIT 3: Conversion of units of length
QUESTION 1
Convert the following to centimetres (cm).
a
1m=
b 4m=
c
2m=
d 4.1 m =
e
3m=
f
6m=
g
3.5 m =
h 8m=
i
5m=
j
7m=
k 2.25 m =
l
o
700 mm =
p 167 mm =
m 10 mm =
QUESTION 2
n 80 mm =
5.34 m =
Convert the following to metres (m).
a
200 cm =
b 1200 cm =
c
90 cm =
d 60 cm =
e
500 cm =
f
2500 cm =
g
150 cm =
h 20 cm =
i
8000 cm =
j
4000 cm =
k 560 cm =
l
o
p 20.07 km =
m 1 km =
QUESTION 3
n 15 km =
4.75 km =
1570 cm =
Convert each of the following lengths to millimetres (mm).
a
1m=
b 3.5 m =
c
2.25 m =
d 10 m =
e
6m=
f
12 m =
g
6.5 m =
h 7.9 m =
i
8m=
j
5m=
k 9.52 m =
l
o
p 50.1 cm =
m 20 cm =
QUESTION 4
n 80 cm =
Convert the following measurements to the units shown.
a
5m=
cm
b 4000 mm =
e
7m=
mm
f
i
9m=
cm
j
m 6 km =
QUESTION 5
a
0.8 m =
e
0.006 km =
i
0.009 m =
m 0.02 m =
25.5 cm =
5.5 m =
m
m
c
4.5 km =
m
d 640 mm =
463 mm =
cm
g
6.35 cm =
mm
h 2.3 km =
800 cm =
mm
n 5.3 m =
cm
k 60 cm =
mm
l
o
m
p 2.31 m =
8560 mm =
18 m =
cm
m
cm
cm
Complete the following conversions.
cm
b 4 km =
cm
c
0.3 m =
mm
d 3.7 m =
m
f
0.04 m =
cm
g
0.002 m =
mm
h 12.69 m =
mm
j
0.007 m =
cm
k 85 m =
mm
n 9 mm =
km
o
72
© Pascal Press ISBN 978 1 74020 033 2
0.05 km =
cm
l
m
58 cm =
p 365 mm =
cm
mm
mm
cm
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Length, mass and time
Excel Mathematics Study Guide Year 8
Pages 152–154
UNIT 4: Pythagoras’ theorem (1)
QUESTION 1
a
If c > 0, find c when:
2
b c2 = 225
c = 16
d c2 = 16 + 9
QUESTION 2
a
e
c2 = 25 + 144
c
c2 = 81
f
c2 = 225 + 64
Find the length of the hypotenuse in these right-angled triangles.
40 m
b
7 cm
c
9m
77 mm
36 mm
24 cm
QUESTION 3
Find the length of the missing side correct to 1 decimal place.
a
b
5 cm
19 mm
22 mm
c
7.5 cm
6.8 cm
8 cm
QUESTION 4
a
Use Pythagoras’ theorem to test if the following triangles are right-angled.
8
7
b
8
15
10
6
4.1
c
0.9
Chapter 7: Length, mass and time
© Pascal Press ISBN 978 1 74020 033 2
4
73
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Length, mass and time
Excel Mathematics Study Guide Year 8
Pages 152–154
UNIT 5: Pythagoras’ theorem (2)
QUESTION 1
a
If a > 0, find a when:
2
b 289 = a2 + 225
25 = a + 16
QUESTION 2
a
x
QUESTION 3
6 cm
QUESTION 4
625 = 576 + a2
Find the length of the unknown side in these right-angled triangles.
3 mm
b
5 mm
12 m
y
a
c
17 cm
8 cm
13 m
Find the value of x correct to 1 decimal place.
16 cm
a
c
x
b
x
c
5 mm
x
2 mm
10 m
A tree 6 m tall casts a shadow 1.1 m long. What is the distance
from the tip of the shadow to the top of the tree?
d
QUESTION 5
A right-angled triangle is drawn inside a circle, using the diameter
as the hypotenuse. If the diameter of the circle is 15 cm long and
the shortest side of the triangle is 9 cm, what is the perimeter
of the triangle?
74
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Length, mass and time
Excel Mathematics Study Guide Year 8
Pages 152–154
UNIT 6: Perimeter of plane shapes
QUESTION 1
a
d
b
d
c
7cm
cm 7 cm 8 cm
7 cm8 cm 8 cm
7 cm
cm
7 cm 787cm
8 cm 13 cm
8cm
cm8 cm 1213
cm
7 cm7 cm 777cm
7 cm
13 cm
cm
8 cm8 cm 813
12 cm
cm
cm 8 cm
8 cm8 7cm
cm
77cm
13cm
cm 13 12
13 cm
8 cm
8 cm
12cm
cm 1212cm
12
cm
13
cm
cm
12 cm cm
7 cm
7
cm
7 cm
7 7cm
8
cm
8
cm
cm
7
cm
8
cm
7
cm
7
cm
8
cm
8
13
cm
13
cm
8 cm
7 cm
7 cm
8 cm
8 cm8 cm
13 cm 12 cm1213cm
12
cm
7 cm
8 cm
8 cm
13cm
cm
12 cm
7 cm 7 cm
7 cm 8 cm
cm
8 cm 13 cm 1312
8 cm
cmcm 1212
cm
7 cm 7 7cm
7
cm
7 cm
8
cm
8
cm
8
cm
8
cm
6
cm
5
cm
5
cm
6
cm
13
13
cm
cm
7
cm
6
cm
5
cm
6
cm
5
cm
8
12
cm13 5cm
8 cm 6 cm 5 cm5 cm 512cm
7 cm
6 cm6 cm 6 cm
7 cm
cmcm 12 cm
cm 7 7cm
7 cm7 cm 77cm
cm
6
cm
5
cm
6
cm
5
cm
6
cm
5
cm
6
cm
5 cm
7 cm 7 cm
7 cm
6 cm
5 cm
76cm
cm
5 cm
7 cm
6 cm
5 cm
7 cm
7 cm
6 cm
5 cm 53cm
6 cm
53 cm
cm
cm
3 cm
7 cm 7 cm
7 cm
cm
cm 3 3cm
36cm
cm 7 cm 7 cm
3cm
cm 737cm
7 cm
7
cm
cm
7
cm
7
7
cm
7
cm
9
cm
9
cm
7
cm
7
cm
9 cm
9
cm
11
cm
11
cm
3
cm
cm
7 cm
11 cm 3 cm7 cm 3 cm3 cm
9 cm9 cm 6 9cmcm 9 cm611
7 cm
3 cm7 cm
116 cm
11ecm
f
cm
cm
6
cm
11
cm
11
cm
3
cm
7
cm
7
cm
cm6 cm 6 cm 6 cm 7 cm
7 cm cm
7 cm
3 cm7 cm
7 cm7 cm
9 6cm
9 cm
11
cm11 cm 7 cm7 11
11 cm
9 cm
cm
711cm
7.5
cm
7.5
cmcm 73 cm
cm
96cm
cm
3 7.5
cm
77.5
cmcm 7.5 cm
cm
6 cm1169 cm
cm
7
cm
9 cm
7.5
cm
3
cm
6
cm
6
cm
6
cm
7.5
cm
9
cm
7.5 cm 7 cm
6 cm 6 cm
7 cm 7 cm
6 cm 67 cm
6 11
cm6cm
4 cm
cm
7 cm
cm
4 cm49 cm
6cm
cm 4 cm11 cm
cm
9cm
cm4 4cm
cm 446cm
7.5 cm
cmcm
11 cm 11 cm6 cm 77.5
7.5 cm
7.5 cm
9cm
7.5
cm
6
cm
6
cm
6
cm
6
cm
7.5
cm
6 cm 7.5 cm
4 cm 4 cm
4 cm
66cm
6 cm6 cm
4
cm
cm
4
cm
4 cm
6 cm
7.5 cm 7.5 cm 7.5 cm
4 cm
6 cm 6 cm
6 cm
4 cm 4 cm
4 cm
QUESTION 2
a
Find the perimeter of each of the following triangles.
Find the perimeter of the following squares and rectangles.
12 m 12 m
12 m
12 12
m m
30 cm 30 cm
30 cm
30 30
cmcm
c12 m 12 m 12 m
30 cm 30 cm 30 cm b
12 m 12 m
12 m
12 m
30 cm30 cm
30 cm
12 m
30 cm
9m
12
9 6m9cm
cm
77mm 7 m
6cm
cm
712
m7mm
30 cm 3030
m 9 m 99mm 9 9mm
cm 6 6cm
6 cm6 cm 66cm
cm
7m
7
m
12 m 12
12 m
30
cm 30 cm
30 cm
9m 9m
9m
6 cm 6 cm
7m 7m
6 cm
7m
9
m
9
m
6
cm
6
cm
7
m
9m
6 cm
7m
9m
6 cm
7m
9m
9m
6 cm 6 cm
7m
6 cm
7m
9m
7m
20 m 20 m
20 m
20 20
m m
20 m 20 m 20 m
20 m 20 m
20 m
20 m
20 m
2012
m m 820
mm
88mm 8 m
12
m
m
12 12
m m
12
m
12
m
8
8m
12
m
20
20 m
8 m 20 m
12 m
e
8m 8m
12 m 12 m
8m
12 m
12
m
8m
12 m
8m
12 m
8m
12 m
8m
8m
12 m 12 m
12 m
8m
8m8m
8 m 8 m 88mm 8 8mm
8m 8m
8m 8m
8m
8m
8m
8m
8m
8m
f
7m
7m
8m
8m
33cm
3 cm
6 cm
6 cm
cm 3 3cm
cm 6 6cm
6 cm6 cm 66cm
cm
cm
9 cm9 cm 9 cm 9 cm
3
cm
3 cm
6 cm 6 cm
3 cm66 cm
cm
b
ccm 64cm
3 cm3 cm
6 cm 6 cm 4 cm 46 cm
9 cm 9 cm
9 cm
6 cm
3 cm
66cm
cm
4 cm
9 cm
cm
6 cm6 cm
3 cm
6
cm
9 cm
4
cm4 cm 4 cm 4 cm
6
cm
7
cm
7
cm
7
cm
7
cm
9 cm 5 cm
5
cm
5
cm
7
cm
7 cm
3
cm
3
cm
59 cm5 cm 5 cm 5 5cm
6
cm
6
cm
736cm
7
cm
6
cm
cm
cm
cm
6
cm
6
cm
4 cm 6 cm4 cm 4 cm
9 cm 9 cm
9 cm
6 cm
4 cm
7 cm 7 cm 6 cm 7 6cm
7 cm
4 cm
5 cm 5 cm
5 cm
4 cm
cm
cm
7 cm
5 cm
5 cm
4 cm 10 cm
7 cm
10
10 10
cm
10
cm
5 cm
7
cm
10
cm
cm
6
cm
6
cm
5 cm
10 cm 4 cm 4 cm
10 cm 6 cm 4 cm
7 cm 7 cm
7 cm
5 cm 5 cm
5 cm
10 cm10 cm
10 cm
10 cm
10
cm
10 cm 10 cm
10 cm 10
10
cm
7m
7m
m cm7 7mm
7 m 7 m 77m
6
m
6
m
6 m6 m
7m 7m
7m
6 m 6 6mm
7m
7m
6m
7m
55mm 5 m
5m
5 m5 m
7m
6m 6m
6m
6m
5m
5m
7m
7m
6m
6m
e
f
7m
6m
5m 5m
5m
5
m
5
m
6m
6m
5
m
5m
6m
5m
5m
5m
3 cm
QUESTION 39 cm Find the
perimeter
of
the following.
3 cm3 cm
9 cm
9 cm
9 cm
a
d
Chapter 7: Length, mass and time
© Pascal Press ISBN 978 1 74020 033 2
75
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Length, mass and time
Excel Mathematics Study Guide Year 8
UNIT 7: Perimeter of irregular shapes
9
9
10
10
14
14
Find
the perimeter of the following. (All10measurements are in centimetres.)
14
9
2
2
3
3
14
101010
141414
9 9 99 39
10 103
14
4
2 14
2
10
9
4
2
3
a
b
c
3
33
1010
3
2 2 22 214 4
10
3
23 3 3
3 3 33 3
42
3 33 339 3
2
12
2
33
3
4 4 4442 42 2
12
3
10
3
3
3
6
6
2
2
2
2
4
4
6 3 3 36 3 3 3 3
2
10
12
101010
10
8 4 48 4
73 272 22 2
10
33 3
6 33 3 6
4
12
12
2
4
4
12
2
1212
4
8 12
7
6 6366 6 6 6 66 6
3
10
8
2
6
8 8 12
4
7 7 77 7
8
8
3 6
8
36
8 8
6
7
6
6
8
3
8
7
6
8 8 88 8
3 3 33 3
6 6 66 6
8
3
6
12
15
12
8
3 15
6
12
4
15
4 4
3
4
3
12
121212
151515
12
3
15 15
4
6
3
12
4
3
15
9
6
9 d 9
9
4
4
e
f
4
3
3
4
3
4
4
312
15 9
6
44 4
444 4
9
63 333 3 3
4
4
6
6
6
5
4
9 9 99 9 5
33 3
9 9 99 9
44
6 66
4
3
4
6
9
9
3 363
4
44
4
3 6
5
4 4 442 4
6
63
2 4 4
3
6
4
9
6
6
4
2
2
5
4
4
5 5
5
5
6
44 4
5
12
3 3 333 3
2
2
4 4 54454554444 4
12
4
6
33 3
3
5
5
4
4
4
2 2 224 2 4 2 2 22 2
33
5
12
3
5
5
5
5
3
2
2
5
4 55 455
121212
12 12
55 5
4
12 3
2
24
5
5
4 4
12
44 4
4
3
3
QUESTION 1
9
Pages 152–154
3
QUESTION 2
Find 28
the missing lengths of the following shapes and then
find the perimeter of each.
8
8
28
(All measurements
are in centimetres.)
8
28
4
28
8 8 88 8
4
282828
28
8
8
28
8
4
a 12
b
12
12
12
8
8
28
4 4 44 4
12
12
8 8 8 8
4
8
8
8
12
121212
8
121212
12
12 12
4
8
12
12
88
8
8
12
12
88 8
20
24
8 24
20
20
24
202020
24
242424
20 20
24
20
24
4 20
24
4
12
12
4
c
d
12
4 4 44 4
6
6
4
121212
12 12
12
6
4
6 6 6612 6
16
6
16
6
6
6
16
6
6
6
161616
16 16
6
6 6 66 6 6
16
6 6
6 6 66 6
16
4
6
6
6
4
6
6
12
6
6
4
12
66 6
4 4 44 4
12
6
4
121212
12 12
12
4
QUESTION 3
12
a
If the perimeter of a square is 72 metres,
b A room is measured 8.64 metres long and 5.36 metres
width in metres.
76
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Length, mass and time
Excel Mathematics Study Guide Year 8
Pages 152–154
UNIT 8: Conversion of units of mass
QUESTION 1
a
Convert the following to kilograms.
b 3.5 t =
c
9.35 t =
d 8t=
e
8.32 t =
f
4.9 t =
g
12 t =
h 1.25 t =
i
5.1 t =
j
4t=
k 7.5 t =
l
8.392 t =
m 5000 g =
n 500 g =
o
3600 g =
p 8000 g =
q 750 g =
r
5675 g =
QUESTION 2
Change the following to grams.
b 1t=
c
8000 mg =
d 7 kg =
e
12 kg =
f
6.357 kg =
g
3.25 kg =
h 15.35 kg =
i
2t=
j
9 mg =
k 3.875 kg =
l
2.508 kg =
m 8 kg =
n 50 mg =
o
6.07 kg =
p 300 mg =
q 6.5 kg =
r
9.008 kg =
c
6.5 g =
f
25 000 mg =
a
3t=
5 kg =
QUESTION 3
a
Convert the following to the units shown.
7000 g =
kg
b 38.3 t =
t
d 15 000 kg =
e
3500 g =
kg
mg
g
h 635 g =
kg
i
8.9 t =
kg
k 9000 kg
t
l
8605 kg =
t
m 1.75 g =
mg
n 2.25 t =
kg
o
3.205 t =
kg
p 450 g =
kg
q 4368 mg =
r
8900 kg =
t
QUESTION 4
Complete the following.
c
5.1 t =
f
3t =
g
i
9t =
mg
g
890 g =
j
2000 g =
a
kg
kg
1 000 000 mg =
kg
b 11 000 kg =
d 2.1 g =
mg
e
g
kg
h 9500 kg =
600 g =
g
1000 g =
t
t
t
Chapter 7: Length, mass and time
© Pascal Press ISBN 978 1 74020 033 2
kg
kg
77
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Length, mass and time
Excel Mathematics Study Guide Year 8
Pages 152–154
UNIT 9: Applications of mass
QUESTION 1
a
A ship has a mass of 36 500 000 kg. What
is this in tonnes?
b A packet of sugar weighs 800 g. How many
of these packets would weigh 1 tonne?
average mass is 42.5 kg. What is the total mass?
d A truck and its load have a mass of 33 t 600 kg.
The mass of the truck is one-third of this. What
is the mass of the load?
c
e
Find the mass of the container of a product if
its gross mass is 4.5 kg and net mass is 2540 g.
f
Find the net mass (mass of contents) if the gross
mass of a package is 980 g and the container’s
mass is 160 g.
QUESTION 2
a
Arrange the following masses in ascending
order (from smallest to largest).
380 g, 23.5 t, 18.8 kg, 3600 g, 1.9 kg, 4.2 t
c
b A truck weighing 2.5 t is carrying a load of
1635 kg. What is the total weight of the truck
and the load? Give your answer in tonnes.
d Penny’s cat weighed 2.5 kg in March and by
in kilograms in August?
78
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Length, mass and time
Excel Mathematics Study Guide Year 8
Pages 152–154
UNIT 10: Conversion of units of time
QUESTION 1
Complete the following table.
1 minute (min) =
seconds (s)
c
1 day =
e
1 fortnight =
g
1 year =
weeks
h 1 year =
i
1 year =
days
j
1 leap year =
l
1 century =
hours (h)
f
years
days
weeks
1 month =
months
days
years
years
m 1 millennium =
QUESTION 2
minutes (min)
d 1 week =
weeks
k 1 decade =
a
b 1 hour (h) =
a
Which unit would be the best to use to measure the time:
to travel from home to school?
b to travel from India to Australia by plane?
c
to swim a distance of 100 metres?
d to play a hockey match?
e
to drive from Sydney to Canberra?
QUESTION 3
Complete the following.
a
4 decades =
years
c
3 centuries =
years
e
9 minutes =
seconds
g
7 weeks =
i
72 months =
years
j
96 hours =
k 156 weeks =
years
l
10 minutes =
days
b 480 minutes =
d 2 years =
f
5 minutes =
h 2 hours =
hours
days
seconds
minutes
days
seconds
Chapter 7: Length, mass and time
© Pascal Press ISBN 978 1 74020 033 2
79
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Length, mass and time
Excel Mathematics Study Guide Year 8
Pages 152–154
UNIT 11: Addition and subtraction of time
QUESTION 1
a
h min
6
20
+ 5
18
b
h
12
+ 9
min
46
12
c
h
9
+ 6
min
28
18
d
h min
5
34
+ 3
37
e
h
9
+ 3
min
41
52
f
h
15
– 7
min
40
16
g
h min
19
47
– 6
38
h
h
10
– 8
min
53
48
i
h
6
– 4
min
23
41
QUESTION 2
a
Add 4 days, 6 hours and 32 minutes to 7 days, 9 hours and 45 minutes.
b From 19 h 36 min take away 7 h 23 min.
c
How many hours are there from Friday noon to 10 pm (the same day)?
d How many hours are there from 9.00 am to 3 pm the same day?
QUESTION 3
What will be the time:
a
20 minutes after 10:20 am?
b 15 minutes after 5:40 am?
c
50 minutes after 2:15 pm?
d 25 minutes after 6:30 am?
e
15 minutes after 4:51 pm?
f
g
10 minutes after 8:57 am?
h 17 minutes after 6:30 am?
i
35 minutes after 6:09 pm?
j
QUESTION 4
32 minutes after 5:43 pm?
3 hours after 9:10 pm?
What is the length of time between:
a
10 am and 11 am?
b 3:30 am and 5:40 am?
c
5 pm and 9 pm?
d 3:25 am and 7:45 am?
e
6 am and 11 am?
f
80
© Pascal Press ISBN 978 1 74020 033 2
5:10 am and 10:30 am?
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Length, mass and time
Excel Mathematics Study Guide Year 8
Pages 152–154
UNIT 12: Clocks and times
QUESTION 1
a
11
Write in two different ways the time shown on the clocks below. Write your answers
in words.
12
11
1
1
11
2
10
2
10
12
4
8
7
4
8
5
6
7
6
d
5
11
1
10
10
12
2
9
39
39
9
b 12
4
7
7
10
6
5
6
12
11
2
1
12
1
10
7
2
6
11
1 12
c
10
5
4
7
3
8
6 7
5
b 8 o’clock
c
a quarter past ten
d midnight
e
midday
f
3
3
9
4
4
8
5
7
6
5
twenty past ten
Write the following times using am or pm.
a
7 in the morning
b 10:20 at night
c
6:40 in the afternoon
d 3 hours after 8 am
e
8:30 in the morning
f
2 hours before noon
Convert the following 24-hour times to 12-hour time (using am or pm).
a
0700
b 2317
c
1825
d 1921
e
0625
f
QUESTION 5
2
Change the following to digital times.
half past four
QUESTION 4
1
f
a
QUESTION 3
6
12
10
2
4
e
QUESTION 2
11
1
2
39
8
84
5
6
12
11
9
3
9
4
8
5 7
11
10 2
3
39
8
8
1
0900
Convert the following 12-hour times to 24-hour time.
a
6 am
b 2:45 pm
c
4:30 pm
d 6:30 am
e
3:25 am
f
g
7:48 pm
h 9:10 pm
10:20 am
Chapter 7: Length, mass and time
© Pascal Press ISBN 978 1 74020 033 2
81
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Length, mass and time
Excel Mathematics Study Guide Year 8
Pages 152–154
UNIT 13: Problem solving using 12– and
24-hour time
1
Write the plane arrival times in 12-hour time. State whether each time is am or pm.
a
0835 hours
d 1520 hours
2
11
12
1
11
12
9
9
84
7
6
5
b
12
11
12
1
3
9
84
8 4 8
7
6
5
7
2
3
9
7
6
5 7
5
6
morning
e
f
2340 hours
2036 hours
1212
12
11
1111 1
1 11
21010
10
3
9
93
9
4
6
3
48 8
8
57
6
66
33
9
84 4
4
77 5
11
102 2
2
55
7
12
c111
12
12 12
1
11 111
2
102 10
10
9
9
3
3
9
75
6
afternoon
6
7 57
6
2
3
9
4
84 8
8
84
6
5
12
1 11
102
5 7
111
3
12
57
6
d1
2
11
2
3
4 8
8
6
111
3
9
9
4
12
2 10
10
3
4
75
1
2
3
9
4
4
8
5
6
12
10
morning
7
6
5
night
Write the times in 24-hour notation for the following digital clocks.
a
b
c
d
Work out the time in hours and minutes between:
a
5
1025 hours
12
1 11
102
10 2 10
3
9
8
11
1
102
10
4
c
Write the following times in 24-hour notation.
a
3
b 0943 hours
1130 hours and 1750 hours
b 0820 hours and 1320 hours
Write the time in 24-hour notation.
a
15 minutes after 1630 hours
b 20 minutes before 2300 hours
6
Write 2120 h in 12-hour time.
7
How long is it between 1800 h and 1955 h?
8
Convert the following times into 12-hour time indicating whether the time is am or pm.
a
1610
b 0935
c
2330
c
10:40 pm
9 Convert the following 12-hour times into 24-hour time.
a
5:30 am
b 3:20 pm
10
Give the time in 24-hour time.
82
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Length, mass and time
Excel Mathematics Study Guide Year 8
UNIT 14: Problem solving with length, mass
and time
Pages 152–154
1
A room is measured as 10.34 m long and 6.58 m
wide. Calculate the difference between the
length and breadth in metres.
2
An equilateral triangle has a side of 9 cm. What is the
perimeter of the shape in centimetres?
3
I walked 5.347 km in the morning and 5283
metres in the evening. How many kilometres
did I walk altogether?
4
Find the perimeter of a square whose side
length is 8.25 cm.
5
Find the perimeter of a rectangular block of
land which is 150 m long and 70 m wide.
6
A ship has a mass of 45 960 000 kg. What is this
in tonnes?
7
Find the mass of the load if the mass of a
loaded truck is 25.64 tonnes and the mass of
the empty truck is 12.63 tonnes.
8
Jill needs 3 tonnes of salt. If a packet of salt weighs
600 g how many packets does she need?
9
There are 11 members in a team and the average
mass is 55 kg. What is the total mass?
10 Find the mass of a container of a product if the
11 If a pulse beats 75 times a minute, how
product’s gross mass is 2.75 kg and the net
mass is 2125 g.
12 How many hours are there in two weeks?
many beats would there be in 30 minutes?
Chapter 7: Length, mass and time
© Pascal Press ISBN 978 1 74020 033 2
83
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Length, mass and time
TOPIC TEST
PART A
Instructions • This part consists of 12 multiple-choice questions.
• Fill in only ONE CIRCLE for each question.
• Each question is worth 1 mark.
Time allowed: 15 minutes
Total marks: 12
Marks
1
2
3
4
5
6
7
8
9
9 m equals:
90 mm
9000 cm
1
How many 4-m lengths can be made from a piece 28 m long?
6
5
7
9
1
What is the perimeter of a rectangle 30 cm long and 14 cm wide?
88 cm
60 cm
64 cm
56 cm
1
The height of a door would be closest to:
2m
10 m
0.4 m
90 cm
1
What is the cost of 4 kg of beans at $2.99 per kg?
$8.97
$10.94
$11.96
$12.63
1
23
kg
4
5125 g
1
What is the most suitable unit to use to measure the mass of a lamb?
metre
gram
tonne
kilogram
1
What is the number of grams in 6.25 kg?
625
62.5
6200
6250
1
1930 h is the same as:
9:30 am
9:30 pm
7:30 am
7:30 pm
1
11:35 am
11:30 am
11:05 am
1
60
1
2:10 pm
1
900 mm
900 cm
1
5 4 kg can be written as:
5.005 kg
5250 g
1
10 If a 1 2
10:05 am
1
11 A tap drips every 1 2 seconds. How many times will it drip in 2 minutes?
90
80
70
12 A plane due at 3 pm arrived 28 minutes early. When did it arrive?
2:28 pm
2:32 pm
2:15 pm
Total marks achieved for PART A
84
© Pascal Press ISBN 978 1 74020 033 2
12
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Length, mass and time
TOPIC TEST
PART B
Instructions • This part consists of 15 questions.
• Each question is worth 1 mark.
• Answer each question in the space provided.
Time allowed: 20 minutes
Total marks: 15
Marks
1
2
3
Find the perimeter of a square whose side
length is 7 metres.
1
Find the perimeter of a rectangle whose
length is 20 cm and width 12 cm.
1
Find the perimeter of a rectangular block
of land 50 m long and 30 m wide.
1
1
4
How many metres are in 3 2 km?
1
5
What fraction of 4 metres is 25 cm?
1
6
Jack needs half a tonne of sugar. If a packet of sugar weighs
800 g how many packets does he need?
1
7
Convert 3000 kg to tonnes.
1
8
A carton has a mass of 12 kg. If it contains
30 cans of beans, what is the mass of each
can (ignoring the weight of the carton)?
1
9
1
The weight of a dog is 5 2 kg and he then
puts on 640 g in 6 months. What is
his weight now?
1
10 A cruise ship has a mass of
1
35 000 000 kg. What is this in tonnes?
11 How many minutes are there from
2:00 am to 5:00 am?
1
12 Express 5 days in hours.
1
13 How many hours are in a year?
1
14 Change 160 seconds into minutes and seconds.
1
15 Add 5 days, 7 hours and 45 minutes
1
to 3 days, 8 hours and 25 minutes.
Total marks achieved for PART B
Chapter 7: Length, mass and time
© Pascal Press ISBN 978 1 74020 033 2
15
85
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Chapter 8
Area, volume and capacity
Pages 137–174
UNIT 1: Units of measurement
QUESTION 1
Complete the following.
2
mm2
b 1 m2 =
cm2
d 1 km2 =
m2
a
1 cm =
c
1 ha =
e
1 km2 =
ha
g
1 m3 =
cm2
h 1L=
i
1 kL =
L
j
1 cm3 =
k 1 m3 =
L
l
1 m3 =
QUESTION 2
Excel Mathematics Study Guide Year 8
m2
f
1 cm3 =
mm3
mL
mL
kL
Complete the following table.
Capacity/water
a
Volume
Mass
1 mL
b
1g
10 cm3
10 mL
c
100 mL
100 g
d
500 cm3
e
600 cm3
600 mL
f
800 mL
g
800 g
1 000 cm3
1L
QUESTION 3
500 g
Complete the following.
a
7 cm2 =
c
9 m2 =
cm2
d 350 ha =
km2
e
5 ha =
m2
f
230 m2 =
cm2
g
6 cm3 =
i
15 000 mm3 =
k 8 m3 =
mm2
b 80 000 m2 =
mm3
h 5 000 000 cm3 =
cm3
kL
86
© Pascal Press ISBN 978 1 74020 033 2
ha
j
49 cm3 =
l
50 000 L =
m3
mm3
m3
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Area, volume and capacity
Excel Mathematics Study Guide Year 8
UNIT 2: Formulae for plane shapes and solids
Pages 137–174
Complete the following table by writing the formulae of the given plane shapes and solids.
Name
Diagram
Formula
Area =
h
1 Parallelogram
b
a
2 Trapezium
Area =
h
b
Area =
d
3 Rhombus
D
Area =
d
4 Kite
D
Area =
r
5 Circle
Circumference =
Volume =
6 Cube
x
l
Volume =
b
7 Rectangular prism
h
Volume =
r
8 Cylinder
h
Volume =
9 Triangular prism
A
h
Chapter 8: Area, volume and capacity
© Pascal Press ISBN 978 1 74020 033 2
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
87
Area, volume and capacity
Excel Mathematics Study Guide Year 8
Pages 137–174
UNIT 3: Area of parallelograms
QUESTION 1
6 cm
a
Find the area of each parallelogram.
8 cm
b
8 cm
6 cm
6 cm
10 cm
6 cm
8 cm14 cm
14 cm
10 cm
10 cm
10 cm
14 cm
14 cm
c
8 cm
d
9 cm
8 cm
9 cm
9 cm
9 cm
16
cm
Base
5 cm
16 cm
16 cm
QUESTION 2
5 cm
16 cm
5 cm
Use the formula A = bh to find the
area of each parallelogram given in
the table below.
Height
QUESTION 3
Area
Base
8 cm
8 cm
8 cm
5 cm
Complete the following table for the
area of parallelograms.
Height
160 m2
a
12 m
5m
a
b
24 cm
9 cm
b
c
16 cm
21 cm
c
8 mm
11 mm
d
14 m
9m
d
22 cm
15 cm
e
7 cm
18 cm
e
16 m
f
12 m
10 m
f
10 mm
g
6 cm
19 cm
g
h
14 m
12 m
h
i
32 cm
10 cm
i
j
15 mm
20 mm
j
88
© Pascal Press ISBN 978 1 74020 033 2
8m
20 cm
180 cm2
128 m2
17 mm
12 cm
108 cm2
432 m2
24 m
23 cm
28 cm
Area
253 cm2
15 cm
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Area, volume and capacity
Excel Mathematics Study Guide Year 8
Pages 137–174
UNIT 4: Area of trapeziums
QUESTION 1
Find the area of each trapezium.
a
10 m
9 cm
b
5 cm
12 m
22 m
18 cm
27 m
e
f
9 cm
11 m
7 km
15 km
4 cm
6 cm
19 m
57 cm
g
10 cm
15 cm
10 km
d
8 cm
c
1.2 m
h
39 cm
3.8 m
5.4 m
91.7 m
i
52.5 m
59.5 m
87 cm
63.7 m
2m
QUESTION 2
a
Find the shaded area.
10 m
8m
26 m (not to scale)
b
Chapter 8: Area, volume and capacity
© Pascal Press ISBN 978 1 74020 033 2
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
89
Area, volume and capacity
Excel Mathematics Study Guide Year 8
Pages 137–174
UNIT 5: Area of rhombuses
QUESTION 1
Find the area of each rhombus. All measurements are in centimetres.
a
5
b
3
3
3
53
5
5
3
35
3
3
20
5
5
5
c
20
20
20
15
15
15
15
12
8
d
e
11
QUESTION 2
10
7
10
10
7
QUESTION 3
Height
Area
9 cm
7 cm
a
6m
b
12 cm
3 cm
b
8 cm
c
14 m
5m
c
18 cm
d
11 mm
6 mm
d
12 cm
Diagonal 2
(d2)
Diagonal 1
(d1)
Area
e
10 m
6m
e
13 m
f
15 cm
8 cm
f
14 cm
g
25 mm
6 mm
g
90
© Pascal Press ISBN 978 1 74020 033 2
Complete the following for the area
of each rhombus.
Base
a
Diagonal 1
(d1)
18
11
11
11
Find the area of each of the
following rhombuses.
Base
8
8
8
f
18
18
18
18
12
12
12
Height
Area
5m
32 cm2
4 cm
84 cm2
Diagonal 2
(d2)
Area
65 m2
8 cm
9 cm
99 cm2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Area, volume and capacity
Excel Mathematics Study Guide Year 8
Pages 137–174
UNIT 6: Area of kites
QUESTION 1
Find the area of the following kites. All measurements are in centimetres.
a
3
b
3
54
54
34
4
5 94 9
c
2
4
2 3
3
23 3 8
9
e
5
6
6
QUESTION 2
5
8
5
5
5 2
2
5
3
32
2
2
3
6
4
7
3
4
7
4
7
3
7
6
4
6
7
12
12
7
12
2
Find the area of each of the
following kites.
Diagonal 1
(d1)
f
8
4
11
8
8
3
6
11
11
8
3
d
6
6
3
4
6
Diagonal 2
(d2)
QUESTION 3
Complete the following for the area
of each kite.
Diagonal 1
(d1)
Area
Diagonal 2
(d2)
Area
a
9 cm
7 cm
a
6m
5m
b
14 m
5m
b
18 cm
4 cm
c
11 mm
6 mm
c
12 cm
84 cm2
d
10 m
6m
d
13 m
65 m2
e
15 cm
8 cm
e
14 cm
f
25 mm
6 mm
f
8 cm
9 cm
Chapter 8: Area, volume and capacity
© Pascal Press ISBN 978 1 74020 033 2
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
99 cm2
91
Area, volume and capacity
Excel Mathematics Study Guide Year 8
Pages 137–174
UNIT 7: Area of plane shapes
QUESTION 1
Find the area of the following shapes. All measurements are in centimetres.
a
b
c
4.8
5.2
12.6
d
31.5
7
e
57.2
f
13
15
4
10
7
h
8
10
i
6
15
13
7
12
13
k
17
15
12
9
15
65.3
g
j
6.8
9.4
l
11
21
92
© Pascal Press ISBN 978 1 74020 033 2
11.8
25.6
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Area, volume and capacity
UNIT 8: Problem solving with area
Excel Mathematics Study Guide Year 8
Pages 137–174
1
Calculate the number of square centimetres (cm2) in a square metre (m2).
2
Calculate the number of square metres (m2) in a square kilometre (km2).
3
Calculate the number of square metres (m2) in a hectare.
4
A rectangular playground measures 150 m by 250 m. Find its area in hectares (ha).
5
A garden is in the shape of a parallelogram with the base 30 m and the height 16 m. What is the cost of top
dressing the garden at $28 per square metre?
6
In a hotel, a reception area is in the form of a rhombus with its base length 50 m and height 20 m.
a Calculate its area in square metres.
b
7
The area of a parallelogram is the same as the area of a square with side length 30 cm. Calculate the height of
the parallelogram if its base is 45 cm.
8
A farm has an area of 180 km2. Calculate this area in hectares.
9
Another farm has an area of 320 ha (hectares). Calculate its area in:
a m2
b
km2 (square kilometres)
10 A rectangular mirror measures 190 cm by 20 cm and is surrounded by a frame of width 5 cm. Calculate the:
a
area of the mirror
b
area of the frame
c
total area
Chapter 8: Area, volume and capacity
© Pascal Press ISBN 978 1 74020 033 2
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
93
Area, volume and capacity
Excel Mathematics Study Guide Year 8
Pages 137–174
UNIT 9: Volume of cubes
QUESTION 1
a
Calculate the volume of each of the following cubes whose side length is given.
2 cm
b 3 cm
c
10 cm
d 1.2 m
e
3.4 m
f
12 m
g
h 4.1 m
i
1.8 m
9 cm
QUESTION 2
Find the volume of each cube. (All measurements are in metres.)
a
b
c
7
7
11
9
7
9
9
11
11
d
e
f
15
15
QUESTION 3
a
15
13
14
13
13
14
14
Find the side length of the cube with given volume.
3
512 cm
94
© Pascal Press ISBN 978 1 74020 033 2
b 1728 cm3
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Area, volume and capacity
Excel Mathematics Study Guide Year 8
Pages 137–174
UNIT 10: Volume of rectangular prisms
QUESTION 1
Find the volume of each rectangular prism whose dimensions are given below.
(All measurements are in centimetres.)
Length
Breadth
Height
a
8
6
4
b
7
5
c
20
8
QUESTION 2
Volume
Length
Breadth
Height
d
14
7
8
3
e
12
5
7
9
f
9
6
4
Volume
Insert the missing measurements in the table for the volume of various rectangular
prisms. (All measurements are in centimetres.)
Length
Breadth
Height
a
8
5
7
d
b
10
6
5
e
12
c
7
4
f
15
QUESTION 3
Volume
Length
140 cm3
Breadth
Height
Volume
6
9
594 cm3
8
384 cm3
6
9
Find the volume of each rectangular prism. (All measurements are in centimetres.)
a
b
c
6
12
3
8
6
7
d
5
4
10
e
f
9
9
8
3
11
12
4
4
Chapter 8: Area, volume and capacity
© Pascal Press ISBN 978 1 74020 033 2
4
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
95
Area, volume and capacity
Excel Mathematics Study Guide Year 8
Pages 137–174
UNIT 11: Volume of triangular prisms
QUESTION 1
Find the volume of the following triangular prisms. All lengths are in centimetres and
areas in square centimetres.
a
b
c
15
A = 34
A = 25
15
A = 34
d
12
A = 42
8
4
18
25
e
15
f
33
3
12
5
8
4
18
15
25
12
QUESTION 2
A = 42
10
A = 25
5
12
10
33
3
Find the volume of each of the
following triangular prisms whose
dimensions are given below.
Cross-sectional
area
Height
QUESTION 3
Cross-sectional
area
Volume
a
64 cm2
10 cm
a
b
45 m2
8m
b
c
80 cm2
9 cm
c
25 m2
d
32 cm2
6 cm
d
42 m2
e
88 m2
12 m
e
96
© Pascal Press ISBN 978 1 74020 033 2
Complete the following table for
triangular prisms with these
dimensions.
36 m2
Height
Volume
8m
11 cm
286 cm3
9m
756 m3
12 cm
276 cm3
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Area, volume and capacity
Excel Mathematics Study Guide Year 8
Pages 137–174
UNIT 12: Volume of prisms—miscellaneous
QUESTION 1
Find the volume of the following prisms. All lengths are in centimetres and areas in
square centimetres.
a
b
c
11
12
11
11
11
18
11
11
9
d
e
11
15
11
15
A = 96
3
5
12
a
29
A = 84
12
21
A = 84
12
18 cm 21
15 cm
15 cm
12 cm
10 cm
QUESTION 2
29
f
A = 96
3
12
12
9
18
5
For the given solid:
18 cm
cm
26
24 cm
10 cm
9 cm
divide it into a rectangular prism and a triangular prism
24 cm
12 cm
b
8 cm
9 cm
8 cm
26 cm
c
d
QUESTION 3
For the given solid:
a
b
9 cm
5 cm
c
16 cm
8 cm
48 cm
16 cm
d
Chapter 8: Area, volume and capacity
© Pascal Press ISBN 978 1 74020 033 2
8 cm
16 cm8
Excel Essential Skills Mathematics Revision & Exam Workbook Year
16 cm
5 cm
27 cm
10 cm
10 cm
8 cm
3 cm
27 cm
9 cm
3 cm97
8 cm
Area, volume and capacity
UNIT 13: Problem solving with volume
Excel Mathematics Study Guide Year 8
Pages 137–174
1
Calculate the volume of a rectangular prism with base area of 120 cm2 and height of 25 cm.
2
Find the side length of a cube whose volume is 343 cm3.
3
A rectangular prism has dimensions 60 mm × 100 mm × 140 mm. Calculate the volume of the prism in:
a
4
cubic millimetres
b cubic centimetres
A small cube has dimensions 3 cm × 3 cm × 3 cm.
a
Calculate the volume of one small cube.
b Calculate the volume of 30 small cubes.
c
18 cm × 20 cm × 30 cm.
5
If the side lengths of a cube are doubled, how many times greater is the volume of the prism.
6
The cross-sectional area of a triangular prism is 280 cm2 and its height is 30 cm. What is its volume?
7
A triangular prism has a volume of 900 cm3 and a height of 15 cm. Find its cross-sectional area.
8
A prism has its side face in the form of a parallelogram, with its base 20 cm and height 8 cm.
98
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Area, volume and capacity
Excel Mathematics Study Guide Year 8
Pages 137–174
UNIT 14: Capacity and volume
QUESTION 1
a
Convert the following to the units given.
50 000 mL =
L
mL
d 18.5 L =
4 kL =
j
9350 mL =
QUESTION 2
a
e
L
g
b 10.253 L =
L
mL
8.3 kL =
L
c
9.6 kL =
L
f
18.35 L =
mL
L
h 9863 mL =
L
i
2384 mL =
k 12.78 L =
mL
l
8.8 kL =
c
2648 cm3 =
L
cm3
f
19 000 cm3 =
L
L
i
9530 mm3 =
cm3
cm3
l
7685 L =
L
Convert the following to the units given.
9000 mm3 =
cm3
kL
d 20 000 L =
g
3000 cm3 =
j
5 000 000 cm3 =
cm3
b 4 mL =
e
6000 mm3 =
h 15 000 cm3 =
L
m3
k 9875 mL =
cm3
QUESTION 3
a
A jug has a volume of 18 000 cm3. How many litres of water can it hold?
b A swimming pool holds 35 000 L of water. How many kilolitres is this?
c
A bottle contains
QUESTION 4
a
5
of a litre of drink. How many millilitres is this?
8
A fish tank measures 85 cm × 60 cm × 40 cm.
Find the volume of the tank in cubic centimetres.
b How many litres of water will the tank hold?
QUESTION 5
Find the volume of the following prisms and then find how many millilitres of liquid
each would hold.
a
b
c
14 cm
14 cm
9 cm
14 cm
18 cm
12 cm
50 cm
A = 70 cm2
Chapter 8: Area, volume and capacity
© Pascal Press ISBN 978 1 74020 033 2
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
99
Area, volume and capacity
UNIT 15: Problem solving with area, volume
and capacity
Excel Mathematics Study Guide Year 8
Pages 137–174
1
How much water will it hold?
2
A dripping tap loses 10 mL of water every 45 seconds. How much water will be lost in 6 hours?
3
Find the side length of a cube that has a volume of 6859 cm3.
4
Madeleine drank
7
of a litre of milk. How many millilitres is this?
8
5
was this?
6
A rectangular prism has dimensions 12 cm × 10 cm × 20 cm.
a What is its volume?
b What would be its volume if all the dimensions
were doubled?
7
Find the area of a photograph that is 70 cm long and 40 cm wide.
8
The perimeter of a square is 60 cm. Find its area.
9
A triangle has an area of 1750 cm2
10 Jasbir drank 1.250 litres of milk. How many millilitres is this?
11 One of the faces of a cube has an area of 256 cm2. What is the volume of the cube?
12 Find the total area of the four walls of a room 14 m long, 8 m wide and 5 m high.
100
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Area, volume and capacity
TOPIC TEST
PART A
Instructions • This part consists of 11 multiple-choice questions.
• Fill in only ONE CIRCLE for each question.
• Each question is worth 1 mark.
Time allowed: 15 minutes
Total marks: 11
Marks
1
A = 1 bh
A = bh
A = 1 (a + b)h
A = 2(a + b)h
1
250
2500
5000
40
1
2
2
2
3
4
A rhombus has diagonals of lengths 14 cm and 18 cm. What is the area of the rhombus?
63 cm2
126 cm2
252 cm2
504 cm2
What is the area of this shape?
80 m2
112 m2
14 m
140 m2
8m
There is not enough information to determine the area.
5
6
7
8
1
10 m
A triangular prism has perpendicular height 12 cm. The area of the triangular face is
15 cm2. What is the volume of the prism?
45 cm3
60 cm3
90 cm3
180 cm3
1
If the volume of cube is 125 cm3, what is its side length?
15 cm
5 cm
25 cm
12.5 cm
1
How many square millimetres are in 5 cm2?
5 mm2
50 mm2
5000 mm2
1
500 mm2
11 cm
What is the area of this trapezium?
246 cm2
266.5 cm2
2
20 cm
2
330 cm
9
1
410 cm
How many cubic centimetres are in 7 m3?
7000 cm3
70 000 cm3
12 cm
13 cm
1
30 cm
7 000 000 cm3
1
480 cm3
80 cm3
1
3500 mL
35 000 mL
1
700 000 cm3
10 The volume of a rectangular prism 6 cm × 8 cm × 10 cm equals:
4.8 cm3
48 cm3
11 Which is the capacity of a glass closest to?
35 mL
350 mL
Total marks achieved for PART A
Chapter 8: Area, volume and capacity
© Pascal Press ISBN 978 1 74020 033 2
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
11
101
Area, volume and capacity
TOPIC TEST
PART B
Instructions • This part consists of 6 questions.
• Answer each question in the space provided.
Time allowed: 20 minutes
Total marks: 12
Marks
1
Find the area of the following shapes.
a
b
20 cm
15 cm
90 cm
c
13 cm
2.1 m
25 cm
7 cm
1
1
1
d
8 cm
10 cm
4m
e
5m
15 cm
f
3m
9 cm
12 cm
8m
1
1
1
2
Find the volume of these prisms.
a
b
5m
4m
3m
70 cm2
2m
5 cm
1
1
3
Find the volume of a cube with sides 7 cm.
1
4
Find the volume of a rectangular prism
8 cm × 10 cm × 12 cm.
1
5
How many cubic centimetres are in one cubic metre?
1
6
A jug has a volume of 5000 cm3.
How many litres of water can it hold?
1
Total marks achieved for PART B
102
© Pascal Press ISBN 978 1 74020 033 2
12
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Chapter 9
Circles
Excel Mathematics Study Guide Year 8
Pages 142–151
UNIT 1: Parts of circles
QUESTION 1
Name the part of the circle indicated.
a
b
c
d
e
f
g
h
a ng
n
i s ta a nctaenacleo nngec teh ea ltoh en g th
t s
e
j
k
O
c e a lo n g thlo
Di
Di
Di
Di
c e a lo n g th e
Di
an
bo
st
a
a ry
un d
bo
a ry
un d
b o d a ry
un
b o d a ry
un
l
st
bo
s
un d
a ry
QUESTION 2
Find the fraction of the circle given in the following diagrams.
a
b
c
270°
d
45°
120°
QUESTION 3
a
If the diameter of a circle is
b If the radius of a circle is 12 cm, what is
Chapter 9: Circles
© Pascal Press ISBN 978 1 74020 033 2
103
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Circles
Excel Mathematics Study Guide Year 8
Pages 142–151
UNIT 2: Circumference of circles
QUESTION 1
Calculate the circumference of the following circles correct to one decimal place.
a
b
c
6c
m
4 cm
3
cm
d
e
f
15
h
cm
i
10
cm
2
cm
g
32
cm
26 cm
a
By using
as the value of , find the approximate length of the circumference for
7
these circles.
b
7c
m
QUESTION 3
a
9
cm
22
QUESTION 2
c
m
49 c
21 cm
Find, to one decimal place, the circumference of a circle with:
radius 11 km
d diameter 94 cm
104
© Pascal Press ISBN 978 1 74020 033 2
b diameter 57 m
c
radius 23 cm
e
f
radius 19 m
diameter 78 mm
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
12 cm
12 cm
Circles
UNIT
cm
3:12Applications
12 cm
20
cm
12
cm
Calculate
QUESTION 1
a
12
cm
1520
cmcm
15.8 cm
b
14
17cm
20.7
cm
15.8
cm
20.7 cm
20.7 cm
7 cm
20.7
17.9cm
cm
13.5 cm
13.5 cm
13.5
24.6 cm
cm
7 cm
b
14 cm
21 cm
21 cm
21.7 cm
15.4
35.7
cm
20
cmcm
21.7 cm
14.2 cm
14.2 cm
14.2 cm
b
c
15 cm
18
cm
20
15cm
cm
18 cm
5 cm
5 18
cmcm
18 cm
7 cm20 cm
5 cm
5 cm
20 cm
7 cm
e
18 cm
f
5.3 cm
8 cm
5.3 cm
8 cm5.3 cm
14 cm
5.3
6.7cm
cm
68 cm
89cm
cm
14.7 cm
5.3 cm
7 cm
85 cm
7 cm
51
cm
cm
714cm
cm6885cm
51 cm
8 cm
8 cm
40 cm
8 cm
40 cm 8 cm
5 cm
15 cm
7 cm
14 cm
20 cm
20 cm
18 cm
h
14 cm
14 cm
i
14cm
cm
14
9 cm
5 cm
5 cm
15 cm
15 cm
7 cm
15 cm
20 cm
20 cm
15 cm
5 cm
5 cm
5 cm
5 cm
5 cm
85
20 cm cm
20
cm
51 cm 54 cm
54 cm
cm
cm
5.3 cm
20
cm
28
68 cm
cm
85 cm
5.3 cm
51 cm
85 cm
68 cm 85 cm
51 cm
51 cm
cm
40
85
14cm
cmcm
68
51 cm 68 cm
26 cm
14
68cm
cm
20 cm
40 cm
40 cm
40 cm
18 cm
40 cm
40 cm
18 cm
18 cm
18 cm
36cm
cm
18
Chapter 9: Circles
© Pascal Press ISBN 978 1 74020 033 2
14.2 cm
14
21 cm
cm
15 cm
14.2
Find18the
correct
to one decimal
14.7 cm
cm place.
cm perimeter of each of these figures
18 cm
20 cm
14.2 cm
14.2 cm 14 cm
14 cm
21
14cm
cm
21.7 cm
21.7 cm
20 cm
21.7
cm
28 cm
2018
cmcm
15.4 cm
15.4 cm
14 cm 21 cm
21.7 cm
c
15.4 cm
21.7 cm
21 cm
15.4 cm
2018
cmcm
20 cm
g
1
21 cm
77cm
cm
15.4 cm
14.2 cm
1
13.5 cm
7 cm
Find the total perimeter of these quadrants.
21 cm
7 cm
QUESTION 3
d
20.7 cm 20 cm
21 cm
13.5
cm
20.7 cm
7 cm
14.2 cm
15 cm
20 cm
c
15.8 cm
15.8
13.5
cmcm
7 cm
15.8
cm
18.3
cm
13.5 cm
14 cm
15 cm
Pages 142–151
20 cm
cm
15.814cm
14 cm 15.4 cm
a
Excel Mathematics Study Guide Year 8
20 cm
the total perimeter
14 of
cm the following semicircles correct to one decimal place.
20.7 cm
a
20 cm
14 cm
of circumference
14 cm
15.8 cm
QUESTION 2
14 cm
12 cm
14 cm
20 cm
20 cm
20 cm
cm
2020cm
105
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
5
5
Circles
Excel Mathematics Study Guide Year 8
Pages 142–151
UNIT 4: Area of circles
QUESTION 1
a
Calculate the area of the following circles correct to one decimal place using the
calculator value of .
b
m
3c
c
m
d
e
13
cm
f
17
g
h
cm
19
22
cm
cm
By using
a
22
as the value of , find the approximate area of these circles.
7
b
c
m
35
7c
QUESTION 3
a
cm
i
m
c
10
8
QUESTION 2
m
9c
5c
cm
14
cm
Find the area, to one decimal place, of a circle with:
radius 25 km
d radius 73 cm
106
© Pascal Press ISBN 978 1 74020 033 2
b radius 1.8 m
c
diameter 37 mm
e
f
diameter 13.9 cm
diameter 400 km
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
15 cm
17 cm
15 cm
Circles
15 cm
15 cm
17 cm
21 cm
17 cm
Excel 21
Mathematics
Study Guide Year 8
cm
17 cm
Pages 142–151
UNIT 5: Applications of area
15 cm
21 cm
QUESTION 18.3
1 cmCalculate
15cm
cm
15
a
15 cm
18.3 cm
15 cm
the area of the
b
18.3 cm
7 cm
18.3 cm
24.6 cm
cm
18.37cm
cm
18.3
18.3 cm
7 cm
18.3 cm
QUESTION 2
a
17 cm
17.9
following
semicircles
18.3cm
cm
c
21cm
cm
21
21 cm
24.6 cm 21 cm
24.6 cm
24.6 cm
24.6cm
cm
24.6
24.6 cm
24.6 cm 21 cm 14 cm
14 cm
Find the area of these quadrants correct to one decimal place.
7 cm
b
35.7 cm
7
cm
7 cm
7 cm
7 cm35.7 cm
18 cm
cm
35.7
cm
35.7
35.7
cm
15 cmthe area
Find
35.7 cm
1518
cmcm
14.7 cm
QUESTION 3
a
14 cm28 cm
35.7 cm
14 cm
28 cm
14 cm
28 cm
14
cm
2814
cmcm
14 cm
14 cm 15 cm
28cm
cm
28
28 cm18 cm
18 cm
15cm
cm
14 cm
15
15
cm
4 cm
4 cm
18cm
cm
15 cm 18
28 cm 18 cm
14 cm
18 cm
14 cm
14 cm
b
14 cm
6.7 cm
6.7 cm
14 cm 9 cm
6.7 cm
14 cm
40 cm
9 cm
20 cm
936
cmcm
h
14.7 cm
1
21 cm
21cm
cm
21
21 cm
14.7 cm21 cm
14.7 cm
4 cm
4 cm
14.7cm
cm
14.7
28 cm
c 14.7 cm
14.7 cm
4 cm
4 cm
14.7 cm
28 cm
14.7 cm
4 cm
4 cm
28 cm
14.7 cm
4 cm
4 cm
28 cm 26 cm
14.7cm
cm
cm
cm
6.7
cm
14.7
44cm
44cm
14.7 cm
4 cm 28 cm 4 cm
cm
2628cm
14.7 cm
4 cm
4cm
cm
4028
cm
28 cm
f
26 cm
40 cm
9 cm
14cm
cm
14
14 cm
14 cm
9 cm
9 cm
cm
99cm
9 cm
i
14.7 cm
m
726c cm
114
4020
cmcm
cm
40 cm
26cm
cm 9 cm
26
40 cm 26
36 cmcm20 cm
26 cm
40 cm
20 cm
36 cm
40cm
cm
20 cm
40
36 cm40 cm
40 cm
20cm
cm
20
36 cm
20 cm
20 cm
36cm
cm
36
36 cm
36 cm
Chapter 9: Circles
© Pascal Press ISBN 978 1 74020 033 2
28 cm
cm
14.721cm
6.7cm
cm
6.7
6.7 cm
14 cm
9 cm
6.7 cm
14 cm 9 cm
9 cm
cm
99cm
9 cm
6.7 cm
e
9 cm
26
cm
14
cm
14 cm
14 cm
14 cm 9 cm
g
21 cm
c
cm
28 cm
of these shapes correct
to one decimal 14.7
place.
1815cm
cm
cm
24.6
cm
correct to one decimal
17.9place.
cm
7 cm
17.9cm
cm
17.9
17.9 cm
17.9 cm
35.7 cm
15 cm
d
21 cm
17cm
cm
17
17 cm
17.9 cm
17 cm
17.9 cm
17.9 cm
35.7 cm
21 cm
14.7 cm
21 cm
107
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Circles
Excel Mathematics Study Guide Year 8
Pages 142–151
UNIT 6: Miscellaneous questions
QUESTION 1
Calculate the circumference of each circle correct to one decimal place.
b
c
11
cm
a
QUESTION 2
a
77
cm
12
Calculate the area of each circle correct to two decimal places.
9
b
cm
c
7
m
cm
c
54
QUESTION 3
a
cm
Calculate the perimeter of the following shapes correct to three significant figures.
7 cm
7 cm
b
18 cm
c
7 cm
12 cm
8 cm
5 cm
7 cm
5c
cm
20 cm
9 cm
5
cm
Calculate
the shaded area of the following shapes correct to two decimal places.
6
8 8cm
8cm
cm
cm
8 cm
5c
5 cm
5 cm
10 cm
m5 cm
8 cm
8 cm
8 cm
8 cm5
b
8 cm
10 cm
15 cm
15 cm
15 cm
15 cm
15 cm
108
© Pascal Press ISBN 978 1 74020 033 2
cm
10 cm
10 cm
10 cm
10 cm
15 cm
6
cm
20 cm
12 cm
18
e
12 cm
18cm
cm
12
12 12
cm cm
12 cm
18 18
cm cm
18 cm
18 cm
20 cm
9 cm
9 cm
9 cm
5 cm
20 cm
20 cm
20 cm
20 cm
9 cm
10 cm
5 cm
c
d
9 cm
12 cm
6
10 cm
cm
158cm
c
cmcmcm
66 6 m
8 cm
a
8 cm
8 cm
QUESTION 4
9 cm
6
m
5 cm
f
5 cm10 cm
5 cm10 cm
5 cm
5 cm
10 cm
10 cm
10 cm
10 cm
18 cm
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Circles
Excel Mathematics Study Guide Year 8
UNIT 7: Problem solving with circles
Pages 142–151
1
A circular track has a radius of 28 metres. Calculate the distance round the track.
2
Calculate the area of the circle formed by the circular track in Question 1.
3
Calculate the radius of a circle with a circumference of 220 cm.
4
Find the area of the top of a can 16 cm in diameter and with 12 cm height to one decimal place.
5
The circumference of a circle is 200 cm. Find the area of the circle.
6
Find the circumference of a circle with diameter equal to 18 cm.
7
What distance do you ride in one turn of a merry-go-round when you sit 6.3 metres from the centre?
8
The wheel of a bicycle has a radius of 25 cm. How far does the bicycle travel when its
wheels make one complete turn?
9
What is the cooking area of a circular barbecue grill having a radius of 18 cm?
10 A revolving sprinkler sprays a lawn for a distance of 14 metres in all directions. How much area does the
sprinkler water in one revolution?
11 Two cylindrical cans are both 25 cm high. One can has a base with a radius of 10 cm, and the other has a
radius of 20 cm. Find the ratio of the area of their bases.
12 Find the circumference of a circle with diameter of 68 cm.
13 Find the area of a round tablecloth if its diameter is 3 metres.
14 A circular ring has a radius of 1.5 metres. What is the perimeter of the ring?
Chapter 9: Circles
© Pascal Press ISBN 978 1 74020 033 2
109
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Circles
TOPIC TEST
PART A
Instructions • This part consists of 12 multiple-choice questions.
• Fill in only ONE CIRCLE for each question.
• Each question is worth 1 mark.
Time allowed: 15 minutes
Total marks: 12
Marks
1
What is the formula for the circumference of a circle?
C = 2π
C = 2π
C
What is the formula for the area of a circle?
A
r2
A
d2
A = π2
A = π2
1
22
7
none of these
1
What is the relationship between the diameter and radius of a circle?
d = 2r
r = 2d
rd = 2
none of these
1
Which of these is a name for part of the circumference of a circle?
arc
radius
sector
segment
1
The circumference of a circle of radius 7 cm is closest to:
44 cm
24 cm
22 cm
14 cm
1
The area of a circle of diameter 28 cm is closest to:
88 cm2
616 cm2
2463 cm2
1
The area of a quadrant with a radius 10 cm is closest to:
157.1 cm2
31.4 cm2
78.5 cm2
314.2 cm2
1
The radius of a circle is 12 cm. Its diameter equals:
6 cm
12 cm
12 cm
1
none of these
1
r
2
3
4
5
6
7
8
9
What is the exact value of ?
3.14
d
r
r
3.142
1232 cm2
24 cm
C
d
d
1
10 The area of a circle of radius 3 cm is approximately equal to:
27 cm2
28 cm2
29 cm2
11 The circumference of a circle is 154 cm. Which is closest to the length of the diameter?
24 cm
49 cm
98 cm
242 cm
1
0
1
12 In how many places does a chord meet the circumference?
1
2
3
Total marks achieved for PART A
110
© Pascal Press ISBN 978 1 74020 033 2
12
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Circles
TOPIC TEST
PART B
Instructions • This part consists of 7 questions.
• Answer each question in the space provided
Time allowed: 20 minutes
Total marks: 13
Marks
1
If the diameter of a circle is 24 cm, what is its radius?
2
What name is given to the shaded part of each circle?
a
b
O
O
1
O
O
1
1
3
a
circumference
b area
1
1
4
a
area
b circumference
1
1
5
A semicircle has radius 48 cm. Find the:
a perimeter to the nearest centimetre
b area to the nearest square centimetre
1
1
6
A quadrant has radius 9 cm. Find, to one decimal place, the:
a area
b perimeter
1
1
7
Find the shaded area to the nearest square centimetre.
a
b
16 cm
12 cm
20 cm
16 cm
12 cm
20 cm
1
Total marks achieved for PART B
Chapter 9: Circles
© Pascal Press ISBN 978 1 74020 033 2
1
13
111
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Linear relationships
Chapter 10
Excel Mathematics Study Guide Year 8
Pages 66–86
UNIT 1: The number plane
QUESTION 1
Write the letter used to name the following points.
a
(0, 0)
b (1, 1)
c
(2, 2)
d (3, 3)
e
(4, 4)
f
g
(0, 2)
h (0, 3)
i
(0, 4)
j
(1, 0)
k (2, 0)
l
(3, 0)
m (4, 0)
n (2, 1)
o
p (2, 4)
(2, 3)
q (1, 2)
r
(1, 3)
s
(1, 4)
t
(3, 1)
u (3, 2)
v
(3, 4)
w (4, 1)
QUESTION 2
a
D
E
F
C
S
T
U
I
B
R
Y
V
J
A
Q
X
W
K
O
P
N
M
L
4
(0, 1)
3
2
1
0
(4, 2)
1
C
f
F
g
G
I
j
J
E
B
A
K
G
4
3
2
S
L
T
–4
–5
–6
D
C
2
–2
–3
J
I
H
N
O
–x –7 –6 –5 –4 –3 –2 –1 0 1
–1
U
Y
X
m M
R
3
V
P
Z
4
5
6
7
x
W
Q
–7
n N
o
6
1
k K
l
4
7
5
F
h H
i
L
M
d D
E
3
y
A
e
2
H
Write down the coordinates of the following points shown in the number plane.
b B
c
G
–y
O
p P
q Q
r
R
s
S
u U
v
V
w
W
y
z
Z
Y
112
© Pascal Press ISBN 978 1 74020 033 2
t
T
X
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Linear relationships
Excel Mathematics Study Guide Year 8
Pages 66–86
UNIT 2: Tables of values
QUESTION 1
a
Complete each table of values.
y=x
b y = 2x
x
0
1
2
3
x
y
c
–2 –1
0
1
x
f
–2 –1
0
1
–1
0
1
2
q
0
1
2
–1
0
1
2
–1
1
2
3
0
1
2
d m = 3n + 2
0
1
2
n
0
m
s = 4t – 3
t
–1
p
c
e
2
b p = 2q – 1
c = 2d + 3
d
1
Complete each table of values and list the coordinates of the points.
y = 2x + 1
y
c
0
y
QUESTION 2
x
–1
y=x–3
x
y
a
2
y
y=x+2
x
1
d y = –x
y
e
0
y
y = 3x
x
–1
–1
f
0
1
2
s
a = 3b – 2
b
–1
a
Chapter 10: Linear relationships
© Pascal Press ISBN 978 1 74020 033 2
113
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Linear relationships
Excel Mathematics Study Guide Year 8
Pages 66–86
UNIT 3: Graphing straight lines
QUESTION 1
a
Complete each table of values and then graph the equation on the number plane.
y=x+2
x
b y=x–1
–1
0
1
2
x
y
c
–1
0
1
2
QUESTION 2
y
x
0
x
1
2
3
c
0
1
2
y=x
3
x
y
0
1
2
3
y
y
y
x
x
x
On the same number plane, graph the following equations by first completing the tables
of values. Find their point of intersection.
y=x
y = –x
–1
2
y
b y=3
y
x
1
Complete each table of values and then graph the equation on the number plane.
x
a
0
x
x=2
QUESTION 3
–1
y
x
y
x
y
y
a
y = –x + 3
0
1
2
x
y
b y=x+2
–1
0
y
1
2
x
–1
y = 2x + 1
0
1
2
x
y
Point of intersection
–1
0
1
2
y
Point of intersection
y
y
x
114
© Pascal Press ISBN 978 1 74020 033 2
x
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Linear relationships
Excel Mathematics Study Guide Year 8
UNIT 4: Using the intercept method to graph lines
QUESTION 1
Pages 66–86
Find the x-intercept for each equation.
a
x+y=2
b x–y=4
c
2x + y = 6
d 2x – y = 8
e
x – 3y = 6
f
QUESTION 2
2x – 3y = 12
Find the y-intercept for each equation.
a
x – 2y = 4
b x–y=8
c
2x + y = 6
d 2x – y = 3
e
3x – 4y = 12
f
3x – y = 3
QUESTION 3
a
Draw the graph of each equation, given the x-intercept and the y-intercept:
x-intercept = 3, y-intercept = 2
b x-intercept = –1, y-intercept = 3
y
y
x
QUESTION 4
a
y = –2x + 3
x
For each equation, find the x-intercept and the y-intercept and then draw its graph.
b x+y–5=0
y
x
y
0
y
x
0
0
y
0
x
c
4
y = 2x – 3
x
y
x
d y = 3x – 1
y
0
x
0
y
y
0
0
x
Chapter 10: Linear relationships
© Pascal Press ISBN 978 1 74020 033 2
x
115
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Linear relationships
Excel Mathematics Study Guide Year 8
UNIT 5: Intersection of two lines
QUESTION 1
a
Pages 66–86
Graph each pair of lines on the same number plane and find their point of intersection.
x = 1; y = 3
x=1
y=3
x
x
y
y
y
x
b x = 3; y = –2
x=3
y = –2
x
x
y
y
y
x
QUESTION 2
a
y = 2x – 1; y = –x + 2
y = 2x – 1
y = –x + 2
x
x
y
y
y
x
b y = 3x – 1; y = x – 3
y = 3x – 1
y=x–3
x
x
y
y
y
x
116
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Linear relationships
Excel Mathematics Study Guide Year 8
UNIT 6: Determining whether or not a point lies
on a line
QUESTION 1
Pages 66–86
Which of the following points lie on the line 3x + 4y = 12?
b (0, 0)
a
(0, 3)
c
(–4, 6)
d (4, 3)
e
(4, 0)
f
(8, –3)
QUESTION 2
a
Which of the following lines pass through the origin, (0, 0)?
b 2y = 3x
2x – y + 2 = 0
c
x – 5y = 0
d 2x + 3y = 6
e
y = –2x
f
y = 5x – 4
QUESTION 3
a
Does the given point lie on the given line?
b x + y = 2 (0, 2)
x + 2y = 3 (3, 0)
c
2x + 3y = 6 (3, –2)
d y = 5x – 3 (1, 2)
e
y = –x + 7 (4, 3)
f
2x + y = 5 (2, –1)
QUESTION 4
A straight line y = mx + 8 passes through the point (–2, 2). Find the value of m.
QUESTION 5
If the point (–3, –6) is on the line ax – 4y – 9 = 0, what is the value of a?
QUESTION 6
a
(0,
)
Find the missing coordinates to make each of the following points satisfy the equation
y = 3x – 2.
b (
, 4)
c
(1,
)
d (5,
e
(
, –5)
f
(
)
, –8)
Chapter 10: Linear relationships
© Pascal Press ISBN 978 1 74020 033 2
117
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Linear relationships
Excel Mathematics Study Guide Year 8
Pages 66–86
UNIT 7: Using graphs to solve linear equations
1
Use the graph of y = x + 1 on the right to write the x-value, when:
a
y=3
b y = –2
x=
x=
c
y=x+1
y
y=5
4
x=
2
–4
0
–2
2
x
4
–2
–4
2
3
Use your answers from Question 1 to solve the following equations.
a x+1=3
b x + 1 = –2
c
x +1=5
The graph of y = 2x – 3 is drawn opposite. Use the graph to solve each of the
following equations.
a 2x – 3 = 3
b 2x – 3 = –4
y
10
8
6
4
y = 2x – 3
2
c
2x – 3 = 1
d 2x – 3 = 5
0
–2
2
4
8x
6
–2
4
The graph of y = 3x + 2 is drawn opposite. Use the graph to solve each of the
following linear equations.
a 3x + 2 = –1
b 3x + 2 = 5
y
4
2
c
3x + 2 = –4
–4
d 3x + 2 = 8
y = 3x + 2
0
–2
2
4
x
–2
–4
QUESTION 5
a
The graph of y = –x + 2 is drawn opposite. Use the graph to
solve each of the following equations.
–x + 2 = 3
10
y
8
b –x + 2 = 6
6
4
y = –x + 2
2
c
–x + 2 = –2
d –x + 2 = 0
0
–2
2
4
6
8x
–2
118
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Linear relationships
TOPIC TEST
PART A
Instructions • This part consists of 12 multiple-choice questions.
• Fill in only ONE CIRCLE for each question.
• Each question is worth 1 mark.
Time allowed: 15 minutes
Total marks: 12
Marks
1
2
The straight line y = 2x – 1 passes through one of the following points. Which one?
(0, 2)
(0, –2)
(0, 1)
(0, –1)
1
Which graph best represents y = x?
asd y
1
x
3
4
5
6
7
8
9
y
y
y
x
x
The equation of the line l is:
x = –3
x=3
y = –3
y=3
x
y
l
0
3
x
1
If the x-coordinate of a point on the line y = 8 – 2x is 1, what is the y-coordinate?
3
4
5
6
1
If the y-coordinate of a point on the line y = 5 + 3x is 20, what is the x-coordinate?
5
4
3
2
1
Which one of the following points lies on the y-axis?
(2, 3)
(3, 2)
(0, 6)
(6, 0)
1
Which linear rule states that y is always 3 less than x?
y=3–x
y=x–3
y = –x – 3
y=3+x
1
On which of the following lines does the point (5, 1) lie?
4x + 5y = 15
5x – 4y = 15
4x – 5y = 15
5x + 4y = 15
1
Which one of the following points lies on the line 2x – y = 4?
(1, –4)
(2, 0)
(–1, 6)
(–2, 3)
1
2
–2
1
3
–3
1
(3, –5)
1
10 What is the x-intercept of the line x + 2y = 4?
4
–4
11 What is the y-intercept of the line 2x – 3y = 6?
2
–2
12 The coordinates of the point of intersection of the lines x = 3 and y = –5 are:
(–5, 3)
(5, –3)
(–3, 5)
Total marks achieved for PART A
Chapter 10: Linear relationships
© Pascal Press ISBN 978 1 74020 033 2
12
119
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Linear relationships
TOPIC TEST
PART B
Instructions • This part consists of 3 questions.
• Answer each question in the space provided.
Time allowed: 20 minutes
Total marks: 15
Marks
1
Match each table of values with an equation.
a
x –2 –1 0 1
c
e
y
–5 –3 –1
1
x
–2 –1
0
1
y
–4 –2
0
2
x
–2 –1
0
1
y
9
5
3
i
2 a
7
b
d
f
y = 2x
ii y =
x
3
iv y = 5 – 2x
v
vi y = –3x
x = –3
ii
a
–3 –2 –1
0
1
y
–2
1
4
7
x
–3
0
3
6
y
–1
0
1
2
x
–3
0
3
6
y
9
0
–9 –18
1
1
1
1
1
1
x
y=1
Complete the table of values below for the
equation y = x + 2.
x
y
1
2
b Write the coordinates of the point of intersection
of the lines x = –3 and y = 1.
3
0
0
On the same number plane, draw
the graphs of the following lines.
i
–2 –1
y
iii y = 2x – 1
y = 3x + 4
x
2
y
1
0
x
1
3
1
b Draw the graph of y = x + 2.
c
1
What is the value of y when x = –7?
d Where does the graph cut the x-axis?
1
e
Where does this graph cut the y-axis?
1
f
Using the graph, solve x + 2 = –3.
1
Total marks achieved for PART B
120
© Pascal Press ISBN 978 1 74020 033 2
15
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Equations
Chapter 11
Excel Mathematics Study Guide Year 8
Pages 88–108
UNIT 1: Solving equations by inspection
QUESTION 1
a x+2=5
Solve the following one-step equations by inspection and then check by substitution.
b a+3=7
c m–4=8
d b+1=7
e a + 2 = 10
f
n + 5 = 12
g x–2=4
h x+3=9
i
y + 8 = 14
j
k t–2=8
l
a–9=3
n x – 4 = –6
o 8 + x = 12
p–3=7
m y – 2 = –7
QUESTION 2 Solve the following equations by inspection and then check by substitution.
b x + 2 = 12
c 3 + y = 15
a m+1=9
d 9 + n = –3
e x–4=7
f
x – 2 = 16
g m+5=9
h y – 3 = 18
i
a+6=8
j
m–3=7
k n – 6 = 10
l
a – 4 = 11
m y – 5 = –3
n t – 2 = –4
o 15 + a = 21
Chapter 11: Equations
© Pascal Press ISBN 978 1 74020 033 2
121
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Equations
Excel Mathematics Study Guide Year 8
Pages 88–108
UNIT 2: One-step equations (addition and
subtraction)
QUESTION 1
a x+5=9
Solve the following one-step equations.
b a + 7 = 15
c m–3=4
d b + 3 = 11
e a + 4 = 10
f
n + 9 = 12
g x – 3 = 12
h x + 5 = 16
i
y + 8 = 20
j
k t–4=1
l
a–9=9
n x – 5 = –6
o 5 + x = 20
p – 2 = 10
m y – 2 = –3
QUESTION 2 Solve the following equations. Check your solutions by substitution.
b x+3=1
c 9 + y = 14
a m+7=2
d 12 + n = 18
e x – 10 = 12
f
x–1=8
g m + 15 = 30
h y – 12 = 27
i
a + 5 = 13
j
k n – 12 = 19
l
a–7=1
n t – 6 = –3
o 10 + a = 14
m – 4 = 11
m y – 5 = –5
122
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Equations
Excel Mathematics Study Guide Year 8
Pages 88–108
UNIT 3: One-step equations (multiplication and
division)
QUESTION 1
a 4a = 16
Solve the following one-step equations.
x
b
=3
2
c 5y = 15
y
=6
5
f
8x = –32
g 6m = –18
h 2x = 6
i
t
= –5
4
j
2p = –8
k
y
= –4
5
l
7t = 28
m
a
=9
2
n 3a = 24
o
x
= –3
7
d
x
=7
3
QUESTION 2
a
x
=5
6
d
e
Solve the following equations. Check your solutions by substitution.
b
x
= –2
6
c
x
=6
7
a
= –20
3
e
a
= –2
9
f
b
=9
8
g
m
= 12
3
h
x
=9
3
i
y
= –14
2
j
3a = 18
k –2b = –10
l
–3x = –12
n 8x = 48
o 7x = 49
m 5x = 35
Chapter 11: Equations
© Pascal Press ISBN 978 1 74020 033 2
123
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Equations
Excel Mathematics Study Guide Year 8
Pages 88–108
UNIT 4: Two-step equations
QUESTION 1 Solve the following two-step equations.
b 18 = 3x – 6
a 2x + 1 = 3
d
5m
3 = 10
e
g
x
2 –1=7
j
8x – 7 = 33
m 7y – 5 = 9
x–3
4 =5
c 10 = 5y – 15
f
2a + 9 = 19
h 3x + 5 = 11
i
a–2
7 =3
k 5x + 3 = 28
l
6t – 3 = 39
n
m
3 –4=6
o 2k + 3 = 21
QUESTION 2 Solve the following equations. Verify your solutions by substitution.
a 3x – 3 = 9
b
m
2 +6=9
c
x–5
7 =4
x–2
6 =8
e 5x – 9 = 26
f
5m
6 = 10
g 10 – 2m = 0
h 3y – 9 = 21
i
7y + 4 = –3
j
k 8x – 7 = 17
l
9x – 7 = 56
d
2x + 8 = 14
m 3a – 2.3 = 7
124
© Pascal Press ISBN 978 1 74020 033 2
1
1
n 6a – 1 2 = 4 2
o 8p + 0.3 = 2.7
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Equations
Excel Mathematics Study Guide Year 8
Pages 88–108
UNIT 5: Three-step equations
QUESTION 1
Solve the following three-step equations.
a
4x + 9 = 3x – 12
b
2x – 7 = x – 3
c
6t – 10 = 4t + 12
d
11m – 6 = 7m + 14
e
9m – 3 = 7m + 9
f
4a – 3 = 3a + 9
g
10y – 6 = 5y + 19
h
6x – 4 = 2x + 16
i
7y – 3 = 4y + 15
j
5x – 1 = 6x – 9
k
3a + 5 = 21 – a
l
12p – 3 = 7p + 32
QUESTION 2
Solve the following equations. Check your solutions by substitution.
a
6x – 20 = 4x + 48
b
2x – 6 = 3 – x
c
6x – 2 = 3x – 6
d
7y – 14 = 5y
e
2x – 14 = x – 12
f
5x + 17 = 3 – 4x
g
3m – 2 = 2m + 7
h
6x – 21 = 2x – 2
i
3y + 1 = 2y + 7
j
6m + 7 = 7m + 10
k
2x
l
4y – 3 = 2y + 11
3=x–9
Chapter 11: Equations
© Pascal Press ISBN 978 1 74020 033 2
20
125
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Equations
Excel Mathematics Study Guide Year 8
Pages 88–108
UNIT 6: Equations with grouping symbols
QUESTION 1 Solve the following equations.
b 2(m + 1) = 5
a 3(x + 4) = 18
c
6(m – 1) = 24
d
2(x + 5) = 18
e
3(a – 3) = 10
f
4(n – 3) = 36
g
5(2n – 1) = 25
h
2(3p – 1) = 22
i
5(2x + 3) = 45
j
4(a – 4) = 8
k
3(m + 2) = m + 14
l
2(3x + 2) = 16
QUESTION 2 Solve the following equations.
b 3(x – 5) = 2(x + 4)
a 5(a + 4) = 4(a – 3)
c
4(y – 3) = 3(y
d
7(x – 8) = 6(x + 2)
e
8(3 – x) = 7(x – 6)
f
2(a + 1) + a + 3 = 0
g
3(x + 7) + x + 3 = 18
h
5(a + 3) = 4(a + 9)
i
3(3a – 2) = 4(4 – a)
j
2(a + 1) – a + 7 = 9
k
3(a – 3) – 2a + 9 = 15 l
m
6(a + 7) = 5(a – 3)
n
8(2a + 7) = 5(3a – 8)
o
9(3a – 4) = 13(2a – 1)
126
© Pascal Press ISBN 978 1 74020 033 2
2)
2(5a – 10) – 9a + 6 = 0
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Equations
Excel Mathematics Study Guide Year 8
Pages 88–108
UNIT 7: Formulae
QUESTION 1 Given the formula V = Ah, find V if:
b A = 15, h = 5
a A = 10, h = 3
c A = 9, h = 4
QUESTION 2 Given the formula P = 2L + 2B, find P if:
b L = 12, B = 5
a L = 18, B = 10
c L = 9, B = 4
QUESTION 3 If y = mx + b, find y for the given values of m, x and b.
1
b m = 2, x = 6, b = 3
c m = 2 , x = 8, b = 4
a m = 1, x = 3, b = 2
QUESTION 4 If A =
a b = 4, h = 3
QUESTION 5
a
bh, find A for the given values of b and h.
b b = 6, h = 4
c b = 9, h = 6
If C = 2 r, find the value of C to one decimal place when:
r=8
QUESTION 6
a
1
2
b r = 37
If A =
1
2
c
r = 63.5
c
h = 23, a = 35 and b = 44
h(a + b), find A when:
h = 6, a = 8 and b = 10
b h = 17, a = 13 and b = 19
Chapter 11: Equations
© Pascal Press ISBN 978 1 74020 033 2
127
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Equations
Excel Mathematics Study Guide Year 8
Pages 88–108
UNIT 8: Problem solving with equations
In the following questions, suppose the unknown number is represented by x. Write the statement as
an equation and find the value of x.
1
The sum of a number
and 8 is 24.
2
Multiply a number by 3 and
then take away 9. The answer
is 21.
3
I think of a number and
add 12. The result is 26.
4
A number increased by 9
is 27.
5
The difference between
5 times a number and 3 is 7.
6
I think of a number, double it,
and the result is 30.
7
I think of a number, double it
and add 12. The result is 48.
8
I think of a number, divide it
by 4, subtract 2 and the
result is 7.
9
The difference between
7 times a number and 6 is 29.
In the following questions, write an equation using the pronumeral x for the unknown number and
then find the value of x.
10 A rectangle is 5 cm longer than it is wide.
11 If the perimeter of an equilateral triangle is 36 cm,
length of the rectangle.
12 The length of a rectangle is 8 cm and its
13 If I subtract 29 from a certain number the result is 23.
14 Find x if the sum of 3, 5, 8, x is 28.
15 I think of a number, add 3 to it, multiply this sum
by 7 and then subtract 9. The result is 47.
128
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Equations
Excel Mathematics Study Guide Year 8
Pages 88–108
UNIT 9: Simple equations with one fraction
QUESTION 1 Solve the following equations.
a
x
=9
4
b
a
=8
3
c
y
=7
6
d
m
= 10
3
e
m
=7
4
f
x
=9
6
g
a+3
=2
7
h
3x
=9
4
i
5x – 4
=7
3
j
x
=2
3
k
x+2
=6
2
l
m+5
=9
3
QUESTION 2 Solve the following equations. Check your solutions by substitution.
a
2x = 8
5
b
3y – 1
2 = 10
c
t–5
2 =5
d
m–7
3 =4
e
2a + 8
4 =6
f
3p – 5
2 =8
g
3x + 1 = 7
4
h
4x – 2 = 3
5
i
3x + 4
2 =2
j
3m – 1
4 =8
k
5 – 3x = 1
2
l
2m + 9 = 4
6
n
6p
5 +3=9
o
3a + 4
2 = 14
m 3x = –2
5
Chapter 11: Equations
© Pascal Press ISBN 978 1 74020 033 2
129
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Equations
TOPIC TEST
PART A
Instructions • This part consists of 12 multiple-choice questions.
• Fill in only ONE CIRCLE for each question.
• Each question is worth 1 mark.
Time allowed: 15 minutes
Total marks: 12
Marks
1
2
3
4
5
6
7
8
9
n
If 3 = 7, n equals:
7
11
17
21
1
If x – 10 = –2, x equals:
–12
–8
8
12
1
13
26
1
3
9
18
1
If 2p – 5 = 23, then p equals:
8
9
14
28
1
If n + 3 = –4 then n equals:
–7
–1
1
7
1
Solve for x: 5x + 3 = 2(x + 12).
x=3
x=5
x=9
x=7
1
If 2(t + 3) = t – 4 then t equals:
–10
2
8
none of these
1
If 2(7 – x) = 3 then x equals:
11
82
If 2x – 5 = 21, what is the value of x
6
8
m
If 3
m.
2
1
17
10 2(x – 3) = 3(2x + 4) then x equals:
1
12
1
4
1
1
52
1
3
–4 2
–3 4
1
49
1849
1
567
1
11 If y = ax2 what is the value of y when a = 4 and x
36
144
1
12 If A = 2 h(a + b) and h = 12, a = 9 and b = 21, what is the value of A
90
180
36
Total marks achieved for PART A
130
© Pascal Press ISBN 978 1 74020 033 2
12
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Equations
TOPIC TEST
PART B
Instructions • This part consists of 2 questions.
• Answer each question in the space provided.
Time allowed: 20 minutes
Total marks: 15
Marks
Solve the following equations.
1
a
c
x – 7 = 30
7n = 147
b m + 9 = 15
d
x
12 = 96
1
1
1
1
e
2x – 3 = 5
f
5a + 17 = –3
1
g
x–2
3 = 10
h
x
2
=
4
3
1
1
1
i
3(x – 1) = 9
j
4(p + 7) = 30
1
1
k 3x + 10 = 5x – 2
l
4x – 3 = 2x + 9
1
1
m 4(2x – 5) = 0
n 3(x + 4) = x + 19
1
1
2
I think of a number, double it, add 8 and the result is 42. Find the number.
1
Total marks achieved for PART B
Chapter 11: Equations
© Pascal Press ISBN 978 1 74020 033 2
15
131
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Chapter 12
Reasoning in geometry
Excel Mathematics Study Guide Year 8
Pages 199–230
UNIT 1: Angles and the value of the pronumerals
QUESTION 1
Find the value of the pronumeral(s) in each of the following.
a
b
c
n
m
50
y
a
d
75
e
k
m
20
m
30
110
QUESTION 2
f
40
130
50
Find the value of the pronumeral(s).
a
b
c
y
t
15
70
20
d
f
50
115
65
m
x
82
p
Find the value of the pronumeral.
a
b
a
n
85
155
70
y
a
70
40
e
QUESTION 3
60
2a
a
132
© Pascal Press ISBN 978 1 74020 033 2
80
30
n
c
a
a
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
76°
76°
76°
n°nGuide
°
Excel Mathematics Study
Year 8
Pages 199–230 n°
76°
76°76°
nn°°
n°
76°
n°
76°
76° n°
n°
Reasoning in geometry
60°
60°
mm
° °
60°
a
°a°
m
°
UNITa2:
Parallel lines and angles
°
120°
120°
60°
m
120°
m°°min° each60°
QUESTION a1° Find the value of the pronumeral
of60°the following.
a° a°
120°
a
b
c
60°
120°
m°
120°
a°
60°
m°
120°
60°
a°
m°
a° 120°
50°
d
120°
50°
50°
25°
y°y°
50°
50°50°
y°
x°
e
yy°° 50°
y°
y°
y°
25°25°
25°
25°
x°
x°
QUESTION 3
Find the value of each
a
a°a°
a°
b
aa°°
a°
a°
a°
a°
20°
f
20°
20°
75°
75°
x°
xx°°
20°
45°
20°20° 45°
x°
45°
x°
45°
45°
20° 45°x°
x°
20°
45°
20°
y°
y°y°
yy°°
y°
y°
y°
Chapter 12: Reasoning
in geometry
45°
45°
125°
125°
125°
pronumeral.
y°
© Pascal Press ISBN 978 1 74020 033 2
x°
125°
x°
125°
125°
x°
x°
40°
40°
40°
x°
x°x°
xx°°
yx°y°
d°d°
d°110° b°b°
110°
ba° °a°
110°
a°d° c°c°
dc°°d°
110°
b°
110°
aa°° b° b°
110°
d° acc°°°
b°c°
110°
da°°
110° d° cb°°
110° a° b°
a° c°
c°
c
x°x°
xx°°
x°
125°
125°
125°
e
x°x°
75°
nn75°
°
° n°
75°n°
75°75°
n°
75°n°
QUESTION 2 Find the value of each pronumeral.
a°a° y°y° x°x°
120°
120°
a
b
a° yb°°b° x°
y120°
°y°x°x°
120°
120°
y° x° mm
b° 120° x°
° °
aa°° yy°° x°
m° 120°
x
°
120°
y°
yy°° xx°° 120°
bba°°° 120°
120°
ym
° ° x°
x°
a° b°y° 120°
m120°
°m°
y° x°
b
° 120° x°
a° y° x°
m120°
°
a° y°
y
°
x120°
°
b° 120°
y° m
x°°
b° 120°
m°
d
75°
25°
x°
n°n°
n°
x°x°25°
xx°°
x°
50°
50°
y°
25°
25°
110°
c
a°
110°
110°
a110°
°a°
110°
110°
aa°° 110°
a°
a°
110°
110°
a°
a°
f
30°
30°
30°
60°
60°
60°
a°
a°a°
b°b60°
°
y°30°
30°
30°
60°60°
40°
30°30°b°
40°40°
x°
30°
aa°°
a°
yy°°
bb°° 60°
30°
40° 30° x° y°
30°30°x°
b°
a°
60°
y°
30°
40°
b° 60° a°
30°
40° 30°
a°
y°
b°
30° y°
b°
30°
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
133
x° xx°°
110°
110°
110°
Reasoning
in geometry
50°50°
50°
a° aa°°
Excel Mathematics Study Guide Year 8
Pages 199–230
UNIT
3:
The20°angle
sum of a trianglea° aa°°
65°65°
65°
20°
20°
110°
QUESTION
in each of the following.
50° 110°
110°110°
a°a°1 Find the value of the pronumeral
110°
50°
50°
50°
110°
a
°
°
50°
a
b
c
a°
50°110°
a°a°
65° a°
20°
50°
a
°
a
°
65°
20°
65°
20°
a°a°°
65°65°
20°20°
65°
20°
a°
65°
20°
x° xx°°
60°60°
60°y° yy°°
b° bb°°
b65°
°
65°65°
b°
b°b°°
b°
d
bx°° xx°°
x°
65°
65° 65° x°°
x°x°
65°65°
65°
x°
65°
e
x°
QUESTION 2
x° xx°°
a
35°
35° 35°
35°35°
35°
x°x35°
°
x°x°° x°
x°
x°x°
x° ° x°
60° x°y°
60°x60°
° y°° y°
y°
60°60°
60° y° 50°50°
50° 50°
60° y° 50°50°
f
a° aa°°
x° xx°120°
° 120°
120°
Find the value of each pronumeral.
30°30°
30°
y° yy°°
b
x°x°120° a°a°° a°
x° 120°
a°a°
120°
120°
x°x°°120°
120° a°
30° x° 120°
y° °
30° 30°
y
°
30°30°
y
°
30°
y°y°
30°
y°
c° c°
a° aba°°°bb°°c°
QUESTION 3 Find the value of each pronumeral.
50°50°
50°
a
b
c°
x° xxy°°° yy°°
75°75°
75°
a°ab°° c°c°° c°
60°
60°
a
°
60°
°
a°ab°°b°° cc°°b°
a° bb°°
50°
75° x° y°
50°
50° 50°
°° y
75° x
x°° y°
50°
60°
50°
x°x75°
75°75°
60°
60°
°y° y°
75°
60°
50°
60°60°
75° x° y°
60°60°
60°
50°
50°
50° 50°
50°50°
50°
y° yy°°
145°
145°
145°
145°
145°
145°145°
145°
145°
145°
80°80°
80°
y° yy°°
x° xx°°
80°
80° 80°
80°80°
80°
y°80°
y°
y°yx°° ° y°° x°
yx° °xx°°
x°
134
© Pascal Press ISBN 978 1 74020 033 2
e
a° aa°°
c° cc°°
60°
35°35°
35°
30°30°
30°
c
a° aa°n° ° nn°°
35°
m°mm
35° 35°
°°35°
35°
30°
30° 30°
30°30°
30°
30°
35°
35°
a° °n°
° an°° n°
m°ma°°a
am°n° °n°°
°
m°m° a° n°
m°
m°mm°°
c
m°m°
m°m°° m°
m°
60°
d
60°
60° 60°
60°
x°60°
xx60°
°°
y°y°
y°y°° y°
x°yx°°
x°x°° x°
x°
50°
35°35°
35°
45°
45° 45°
45°45°
45°
45°
50°50°
50°
50°50°
50°
x°x°
x°x°° x°
x°
45°45°
45°
f
a° aa°°
b° bb°°
85°85°
85°
c° c°
130°
130°
50°50°
50°
130°
b°abb°°°
40° c°
a°a° 40°85°
40°
a
°
85°
b
°
85°
°
a°
85°85°
ba°° °ab°°
a°ca°°°c°°a°c°
85°
b
°
b° a°
ca°°c°
85°
b°
c
°
c
°
130° b°
50°
40°
c° c°
130°
b°° b° 50°50°
40°
130°130°
50° 50°
° c°°
40°c40°
130°
b
°
40°
130° b°
50°
40° c°
130° b°
50°
40°
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Reasoning in geometry
Excel Mathematics Study Guide Year 8
Pages 199–230
UNIT 4: Triangles and the value of the pronumerals
QUESTION 1
a
Find the value of each pronumeral.
b
63
x
65
d
c
x
65
y
65
e
35
y
x
y
f
a
30
a
QUESTION 2
140
20
Find the value of each pronumeral.
a
b
y
58
115
QUESTION 3
110
62
45
a
x
c
105
Find the value of each pronumeral.
a
b
x
c
100
x
a
118
d
e
55
35
130
f
80
a
35
m
x
x
y
a
88 110
65
Chapter 12: Reasoning in geometry
© Pascal Press ISBN 978 1 74020 033 2
75
135
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Reasoning in geometry
m°mm°°
Excel
80°
80°
80°
80°80°
80°
110°
110° angle sum of a quadrilateral
UNIT 5:110°
The
m°
80°
m°°
145°
145°
145°
80°
80°
mm
°
n° nn°°
110°
aa°° value of each pronumeral.
QUESTION
1
70°
70°70°
110° Finda°the
110°
mm° °
110°
a 145°
b
145° 110°
n° m °
145°
a°
70°
145°
n°
a°°
70° 110°
a
70°
n°n°
a°
70° 145°110°
145°
70°
nn° °
145°
aa° °
70°
n°
a°
70°
130°
130°
130°
d
120°
120°
120°m
°m
m°°
130°
130°
130°
130°
120° m° 130°
120° m
m°°
120°
120° m° 130°
130°
120° m°
120° m°
120° m°
n° nn°°
n° 55°55°
55°
n°
n°n°
°
nn°55°
55°
n°55°55°
f
a°
a°°
140°
a°a140°
140°
140°a°
a°
a140°
°
140°
a
d
m°mm°°
30°
30°30°
m°
m°°
mm
°
30°
30° °
30°
30° mm
°
m
°
30°
30°
30°
130°
130°
130°
130°
130°
130°
130°
140°
b a°
a°
a°a°
aa° °
a°
b° bb°°
b°
b°
b°b°
bb° °
b°
60°
60°
60°
n° n60°
n°°
60°
60°
60°
n°
n°
n°n°
nn° °
n°
136
© Pascal Press ISBN 978 1 74020 033 2
e
145°
145°
145°
c
145°
145°
145°
145°
145°
145°
145°
c
2a°
°
2a°° 3a3a
3a°
2a2a
°
3a° °
2a° °
3a° °
2a
3a
2a°
3a°
60°60°
60°
60°
60°
60°
60°
60°
60°
60°
n°
m°
n°
m°° 110°
110° n°n° p° pp°°
mm
° 110°
m° °
npn°°°
m
110°
n° pp°°
m°110°
110°
p°
110°
110°
pp° °
110°
p°
110°
p° pp°n° ° nn°°
70°70°
70°
70°
70°
70°
70°
70°
70°
70°
f
2a2a
°2a°° 3a3a
°3a°°
a° b°b°
a°
a°a° b°b°
aa° ° bb° °
a° b°
n° nn°°
m°mm°°
87°87°
87°
60°60°
60°
a° aa°°b° bb°°
x° xx°°
x°
x°
x°x°
x°x°
x°
2a2a
°2a°°
Find the value of the following pronumerals.
a87°
° aa°°
50°50°
50°
b
87°
87°
2a°
3a3a
°3a°°
20°20°
20° 87°
2a°°
2a
2a
° 4a4a
a° 87°50°
°
4a
°
°
a° aa°°
a° 87° 50°
2a° ° 3a°
a°a° 87° 50°50°
20°
2a
3a°°
3a
20°
20°
a
°
4a
2a
° ° 3a°
50°
20°
a°
a°
50°
4a
°
4a
°
a°
4a°
3a° °
50°
a°a°
20° a°
3a
20°
4a° °3a°
20°
4a
aa° °
4a
°
a°
QUESTION 3
80°
80° 140°
80°
80°
140°
140°
140°
80°
80°
140°
140°
80°
140°
130°
130°
130°
140°
140°
140°
e
a° aa°°
m°mm°°
135°
135°x° x
Q135°
UESTION
2x°° Find the unknown
angles.
a
c
a° aa°°
55°
55°
55°
m°
135° x°xx°°
y° yy°° 120°
120°
120°
m°°
135°
135°
mm
°
135° x° 220°
220°
220°
m° °
135° x° y°
135° x°
yy°° 120°
120° m
120°
x
°
m
°
y
°
135° 220°
120°
220°
220°
220°
120°
y°y° 120°
220° y°
120°
220°
220°
80°p° pp°°
80°
80°
p°80°
p°
p°p°
pp° °
p°
Mathematics Study Guide Year 8
140°
140°
140°
Pages 199–230
p° n° m°mm°°
p°
p°p° n°nn°°
° °
pp° m
n°mn°°°°
p° mm
n°
mm° °
m°
100°
100°
100°
100°
100°
100°
100°
3a
3a
°3a°°
100°
100°
3a° 100°
3a°°
3a3a
°
3a° °
3a
3a°
3a3a
°3a°°
3a°
3a
°°
4a3a
4a
3a
°°4a°°
3a°
4a° 3a°
4a3a
°° °
4a4a
°
4a° °
4a
4a°
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Reasoning in geometry
Excel Mathematics Study Guide Year 8
Pages 199–230
UNIT 6: Transformations
QUESTION 1
a
Complete the following sentences.
Under a
a shape is moved from one position to another.
.
b If the shape is moved by sliding, the transformation is
c
.
d If the shape is moved by turning, the transformation is
.
QUESTION 2
Name the transformation used when each of the following shapes is moved to its new
position.
a
A
B A'
B'
D
C D'
C'
X
c
Y
Z'
P
Y'
R
P'
R'
G
d
Z
Q'
Q
b
H
H'
X'
I
I'
G'
M L'
e
O
f
O'
L
T'
M'
N N'
Q'
S'
A
g
P'
h
C
D
T
Q
S
R
R'
B
F'
P
V'
Y'
W'
X'
V
W
Y
X
E
F
C'
E'
D'
B'
A'
Chapter 12: Reasoning in geometry
© Pascal Press ISBN 978 1 74020 033 2
137
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Reasoning in geometry
Excel Mathematics Study Guide Year 8
Pages 199–230
UNIT 7: Congruence of plane shapes using
transformation
QUESTION 1
a
Complete the following.
The symbol for congruence is
.
shape and the
b Congruent shapes have the
c
other by Ba
B
B
90°
90°
.
D
D
90°
90°
D
size.
90°
d The congruence
statement of a ABC and 90°
a DEF is written as
A
60° 2
QUESTION
A
60°
60°
A
Name
B
a
90°
A
30°
30°
60°
C E C E
the 30°
transformation
has
AC E A60° that D
D
A
D
30°
60°
30°
A
b
60°
B
30°
c
A
60°
A
60°
B
90°
90°
90°C
A
E
60°
30°
30°
60°
C
C
90° D
30°
30°
QUESTION 3
C
For each
A pair
A of congruent
D
D triangles below, write the congruence statement.
A
a
D
P
b
P
B
B
A B
CE
CE
D
CE
F Q
138
B
60°
90° D 90° D
60°
F
90° D
E30°
90°
30°
30°
30°
C
B
60°
60°
F
60°
B
90°
A
F
D
E
60°
BB
90°
F
30°
90°
90°60°
60°
60°
60°90°
90°
B
C
C
E
F
30° E
30°
90°
60°
90°
C
E
FE
E
B
30°
F
30°
60°
C E
30°
30° in each pair of congruent triangles below.
been
D used
F
90° 30°
30°
30°
60°
.
E 1 74020 033F2 Q
© Pascal Press ISBN C
978
F Q
P
L
P
L
L
R M
L
c G
G
R M R M
F Q
G
N GH
J
J
I K
I K
J
N
HN
H
JI K
L
L
L
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
R Skills
M MathematicsNRevision
H & Exam Workbook
I K Year 8
Excel Essential
L
Reasoning in geometry
Excel Mathematics Study Guide Year 8
Pages 199–230
UNIT
QUESTION 1
Complete the following sentences.
a
size and the
shape.
b
i
.
matching sides are
.
ii matching angles are
.
iii matching areas are
c
.
The symbol for congruence is
QUESTION 2
a
Name the congruent faces in each prism.
B
A
P
Q
H
QUESTION 3
B
B
C
C
H
a
R
D
H
I
I
J
N
D
E
E
J
K
L
K
F
F
L
M
M
N
QUESTION 4
U
Name the pairs of congruent figures.
A
G
T
G
E
G
S
D
F
A
b
C
The following pairs of figures are congruent.
Name all pairs of matching angles.
b Name all matching sides.
I
L
O
J
P
M
K
N
Chapter 12: Reasoning in geometry
© Pascal Press ISBN 978 1 74020 033 2
139
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Reasoning in geometry
Excel Mathematics Study Guide Year 8
Pages 199–230
UNIT 9: Recognising congruent triangles
QUESTION 1
Complete the following sentences:
a
Two right-angled triangles are congruent if two
sides and the
one triangle are equal to
b Two right-angled triangles are congruent if three
of the other triangle.
c Two right-angled triangles are congruent if one
triangle are equal to
d Two right-angled triangles are congruent if two
sides and one
are equal to
QUESTION 2
E
D
B
C
F
G
and the h
of one
of the other triangle.
and one
of one triangle
of the other triangle.
V
X
O
N
Y
A
W
A
QUESTION 3
M
K
L
U
R
J
I
H
T
Q
S
a
of
of the other triangle.
of one triangle are equal to
Name the pairs of congruent triangles.
A
P
and the included
R
Z
T
The following pairs of triangles are congruent. Fill in the blanks for the corresponding
P
angles.
X
D
A
b
F
C
B
E
Q
BCA =
P=
QUESTION 4
b
a
B
Y
R=
Z
Q=
Divide each shape into two congruent triangles using a single line.
a
QUESTION 5
R
A
G
C
c
d
There are four pairs of congruent triangles in each shape. Name the different pairs.
b
P
T
F
U
E
D
140
© Pascal Press ISBN 978 1 74020 033 2
Q
S
R
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Reasoning in geometry
Excel Mathematics Study Guide Year 8
Pages 199–230
UNIT 10: Naming congruent triangles
QUESTION 1
Two pairs of congruent triangles are drawn below.
a
b
D
A
45°
B 70°
65°
E 70°
C
13 cm
65°
D
A
Q
F
B 70°
65°
C
EA 70°
65°
i
D
F
B 70°
65°
C
E 70°
65°
iii Write the congruence statement.
E
E
QUESTION 2
13 cm
R
5 cm
T
U
5 cm
S
Which angle corresponds
to QRP
13 cm
13 cm
Q
45°
ii Name these congruent
45° triangles,
giving the vertices in the matching order.
S
12 cm
12 cm
P
45°
Which45°
side corresponds to
AC
i
P
45°
12 cm
12 cm
5 cm
R
T
5 cmP
U
S
ii Name these congruent triangles,
13 cm
13 cm in the
12matching
cm
giving the vertices
order.
Q
F
12 cm
5 cm
R
T
U
5 cm
iii Write the congruence statement.
F
F
H
E
H
G
F
G
Complete the following statements for the parallelogram EFGH:
a
P
EFH =
EHF =
S
bH EF =
FH =
P
Q
HEF =
S
R
QUESTION 3
T
HE =
P
W
R
GEFH
U
U
W
Q
S
c
T
V
V
T
U
W
V
Q
R
Complete the following statements:
a SP =
c
b
SPQ =
PQ =
PSQ =
QS =
PQS =
PQS
Chapter 12: Reasoning in geometry
© Pascal Press ISBN 978 1 74020 033 2
141
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Reasoning in geometry
Excel Mathematics Study Guide Year 8
Pages 199–230
UNIT 11: Tests for congruent triangles
QUESTION 1
a
Complete the following sentences.
Two triangles are congruent if three sides of one triangle are equal to
of the other triangle.
b Two triangles are congruent if two sides and the included angle of one triangle are equal to
of the other triangle.
c
Two triangles are congruent if two angles and a side of one triangle are equal to
of the other triangle.
d Two right-angled triangles are congruent if the hypotenuse and one side of one triangle
of the other triangle.
are equal to
e
.
The symbol for congruence is
QUESTION 2
In each pair of triangles below, write the congruence test that would be used to prove
that the triangles are congruent.
a
b
c
d
A
QUESTION 3
a
Name the common side in
ABC and
ADC.
B
b
Are the triangles congruent?
c
If they are, name the test that you can use to prove it.
142
© Pascal Press ISBN 978 1 74020 033 2
C
D
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Reasoning in geometry
Excel Mathematics Study Guide Year 8
Pages 199–230
UNIT 12: Applying properties to solve numerical
problems
Find the value of the pronumerals
in these quadrilaterals.
c°
120°
QUESTION 1
a
a°
a°
120°
120°
a°
a°
c°
120°
120°
QUESTION 2
b°
120°
95°
b° c°
b°x°
96°
48°
b°120°
b°y°
95°
130°
y°x°
48°
96°
96°
y°
a°120°
48°
a°
y°
a°
a°
a°
95°
x°
QUESTION 3
150°
x° 120° 150°
130°
60° 130°
y°
60°
a°
b°
130°
y°
y°
150°
y°
y°
y°
a°
a°
a°
a°
© Pascal Press ISBN 978 1 74020 033 2
b°
b°
b°
88°
c°
x°
y°
c°
65°
70°
88°
a°
50°
50°
10°
c°
b°
b°
a65°
°
x° 88°
b° c°
50°
65°
x°
88°
b°
c°
125°
88°
x°
c°
b°
c
b125°
°
c°
c°
a°
50°
10°
50°
b°
b°
a°
50°
50° a° 50°
10°
10°
50°
y°
70°
c°
a°
125°
65°
y°
70° x° 88°
125°
a°125°
125°
b°
70°
125°
y°a°
70°
y°
y°
a°
50°
10°
Chapter 12: Reasoning in geometry
c°
cb° °
65°
65°
130°
a°
150°
y°
b
c°
6
y°
c°
a°
a°
150°
150°
x°
Find the value of each pronumeral.
60°150°x° 60°
60°
130°
ax°°
95°
x120°
°
60°
120°
b°
a°
48°
130°
a°
120°
b°
c
a°
a95°
°
95°
a°
48°
96°
y° x°
a°
y°
48°
b
a°
60°
x°
a°
a°
96°
y° x°
c
96°
70°
70° x°
Find the value of each pronumeral in the following quadrilaterals.
a°
x°
96°
48°
c°
a
a
x°
b°
c°
c°
a°
120° a°
a°
95°
c°
a°
b°
120°
a°
b
x°
50°
b°
50°
b°
50°
50°
b°
b°
10° Skills Mathematics
10°
Excel Essential
Revision & Exam Workbook Year 8
143
Reasoning in geometry
Excel Mathematics Study Guide Year 8
Pages 199–230
UNIT 13: More numerical problems
QUESTION 1
For each of the following quadrilaterals, (i) write an equation first
(ii) solve the equation to find the value of the pronumeral (iii) find the size of each angle.
a
x°
x°
6x°
x°
6x°
(10x + 7)°
(8x + 3)°
(8x + 3)°
y°
6x°
6x° 6x°
7)°7)°
(10x (10x
+ (10x
7)°+ +
(8x
++
3)°3)°
(8x +(8x
3)°
6x°
6x°
x°
(10x + 7)°
(10x + 7)°
(8x + 3)° a°
(8x + 3)°
b°
a°
b°
QUESTION
a°
b°
c°c°
2b°c°b° Find
2y°
(x + 40)°
30°
a° x°
x°
x°
c°
30°
b°
c°
a°
a°a°
x°
a°
the value of each pronumeral.
x°
c°
b
a°
e°
a° 35°
c°
d°
e°
144
© Pascal Press ISBN 978 1 74020 033 2
d°
b° d°
e°
35°
35°
e°e° 35°
d°d°
e°
35°
115°
a°
35°
e°
b°
115°
(a + 30)°
(a + 30)°
2a°
c°
80° c°
a°
a°a°
c°
c°
b°
c°c°
c
e°
35°
a°
c°
b°
80°d°
c°
b°
80°
b° b°b° 80°
c°c°80° 80°
c°
a°
a°
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
b°
80°
Exceld°Essential Skills Mathematics
Revision
& Exam Workbook Year 8
c°
d°
115°
a°
a°
a°
a°
b°
c°
35°
a°a°
b°
115°
115° 115°
b°b°
b°
2a°
115°
2a°
115° 2a°
b°
x°
2a°
2a°
2a° 2a°
2a° 2a°
110°
a°
a°
c°
b°
80°
2a°
30)°
(a + 30)°
(a(a
++
30)°
f
c°
30°
2a°
a°a°
2a°
(x + 40)°
a°
x°2a°
x°x°
x°
110°
a°
a°
(x + 40)°
(x + 40)°
x°
x°
110°
110° 110°
40)°
(x + 40)°
(x(x
++
40)°
x°x°
2a° 2y°
a°
(a + 30)°
(a + 30)° 110°
x° a°
2a°
2a° 2a°
2a°
110°
110°
x°x°
x°
y°
2a°
2a° 2a°
(10x + x°
7)°
3y°
2y°
+
(x3)°
+ 40)°
x° (8x2y°
30°
30° 30°
a°a°
30°a°
b°
c°
3y°
x°
30°
c°
a
b°
x°
e
y°2y°
3y°
2y°
2y° 2y°
2y°
6x°
x°
y°
3y°
a°
3y°
3y° 3y°
y°y°
2y°
(10x + 7)°
3y°
a°
2y°
2y° 2y°
y°
a°
2y°
2y°
y°
x°x°
x°
x°
d
2y°
x°
x°x°
x°
c
x°
x°
x°
x°
b
x°
Reasoning in geometry
TOPIC TEST
PART A
Instructions • This part consists of 10 multiple-choice questions.
• Fill in only ONE CIRCLE for each question.
• Each question is worth 1 mark.
Time allowed: 15 minutes
Total marks: 10
Marks
1
Two triangles are congruent if they are the:
same shape only
same size only
same shape and size
none of these
1
sliding
turning
enlarging
1
isosceles
4x°
similar
right-angled
1
2
3
All congruent triangles are:
equilateral
4
5
6
36
40
45
54
4x°
50
55
75
105
2x°
x°
55°
50°
a°
55°
The symbol for congruence is:
1
50°
1
a°
none of these
1
360°
1
congruent
none of these
1
180°
90°
1
none of these
1
=
The angle sum of a triangle is always equal to:
90°
270°
A diagonal of a parallelogram divides it into two triangles that are:
equilateral
9
3x°
What is the value of a
180°
8
2x°
x°
What is the value of x
|||
7
3x°
isosceles
The angle sum of a quadrilateral is always equal to:
360°
270°
10 The longer diagonal of a kite divides it into two triangles that are:
isosceles
equilateral
congruent
Total marks achieved for PART A
Chapter 12: Reasoning in geometry
© Pascal Press ISBN 978 1 74020 033 2
10
145
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Reasoning in geometry
TOPIC TEST
PART B
Instructions • This part consists of 4 questions.
• Answer each question in the space provided.
Time allowed: 20 minutes
Total marks: 15
Marks
1
a
Name the pairs of equal sides.
E
A
1
b Name the pairs of equal angles.
c
C
1
B
Name triangles that are congruent.
D
1
d Name a congruence test.
e
Under what single transformation will
1
1
2
a
P
Name the pairs of equal sides.
1
b
c
Name the pairs of equal angles.
A
Name the triangles that are congruent.
D
QA y°
d
For the parallelogram, drawn opposite:
a
Find the value of x.
4
30°
110° C
B
S x° T
R
30°
1
D
y°
D
30°
B
B
x°
110° C
30°
110° C
Write the congruence statement applying to the
two congruent triangles shown.
B
1
1
C
A
1
D
B
Under what single transformation will
1
A
In the kite drawn opposite, ADC = 96° and DAC = 54°.
Find the size of DCB.
1
110° C
x°A
y°
D
d State the congruence test.
e
A
A
b Find the value of y.
c
1
Name a congruence test.
D
3
B
x°
y°
D
1
A
B
C
D
B
Total marks achieved for PART
B
C
1
15
C
146
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Chapter 13
Probability
Excel Mathematics Study Guide Year 8
Pages 252–268
UNIT 1: The language of probability
QUESTION 1
Using the terms of probability, rate the chance of these events as certain, likely, unlikely,
impossible or even.
a
The sun will rise tomorrow.
b There will be at least one cloud in the sky tomorrow.
c
If a die is rolled, a seven appears.
d
e
g
f
scoring an even number when a die is thrown
QUESTION 2
John will live to the age of 142 years.
h A year will have 460 days.
Select the most appropriate from 0%, 30%, 50%, 70% or 100% to describe the
chance implied by each of the following words.
a
maybe
b
c
perhaps
d sure
e
an outside chance
f
g
against all odds
h probably
QUESTION 3
50–50
Choose from certain, most likely, even chance, unlikely or impossible to best describe
an event which has a probability of:
a
10%
b 0
c
100%
d
7
8
e
1
2
f
95%
g
0.005
h
3
97
i
4
5
j
1
k
1
64
l
75%
Chapter 13: Probability
© Pascal Press ISBN 978 1 74020 033 2
147
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Probability
Excel Mathematics Study Guide Year 8
Pages 252–268
UNIT 2: Sample space
QUESTION 1
a
Write the sample space for each of the following.
choosing a month of the year
b selecting a primary colour
c
choosing a letter that comes before I in the alphabet
d choosing a letter that comes after V in the alphabet
e
choosing a square number less than 50
f
choosing a letter from the word MATHEMATICS
g
choosing a whole number greater than 25 and less than 30
h choosing a season
QUESTION 2
a
The letters of the word CONSCIENTIOUS are written on cards and turned face down. A
card is then selected at random.
Write the sample space.
b
c
How many different
QUESTION 3
a
For each of the following events, write the number of elements in the sample space.
selecting a letter from the alphabet
b selecting a day of the week to visit a relative on
c
selecting a colour from the rainbow (red, orange, yellow, green, blue, indigo, violet)
d selecting a captain from a 15-player soccer team
148
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Probability
Excel Mathematics Study Guide Year 8
Pages 252–268
UNIT 3: Outcomes
QUESTION 1
a
For each of the following, state whether each element of the sample space is equally likely to
occur.
choosing a letter from the word PINEAPPLE
b the weather on a given day
c
the gender of a baby being born
d choosing a whole number between 21 and 30
e
the result of a horse race
QUESTION 2
a
Write the outcomes for each of the following.
selecting a letter from the word HAPPINESS
b selecting a sock from a drawer containing black and grey socks
c
tossing two coins at once
d rolling two dice and adding the numbers together
QUESTION 3
a
For each of the following, state whether each of the possible outcomes is equally likely
to occur.
tossing a coin
b tossing two coins at the same time
c
choosing a letter from the word ELEPHANT
d the result of a football match
e
choosing a card from a standard pack of cards.
QUESTION 4
The season of each Year 8 student’s birthday in a particular school is recorded below.
Boys
Girls
Total
Summer
(Dec.–Feb.)
15
8
23
Autumn
(Mar.–May)
15
20
35
Winter
(June–Aug.)
14
16
30
Spring
(Sept.–Nov.)
18
16
34
Total
62
60
122
How many outcomes are there for each event below?
a
boys born in winter
b girls born in spring or autumn
c
boys or girls born in summer
d girls born in a season beginning with the letter Q
e
boys born in a season beginning with the letter S
Chapter 13: Probability
© Pascal Press ISBN 978 1 74020 033 2
149
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Probability
Excel Mathematics Study Guide Year 8
Pages 252–268
UNIT 4: Theoretical probability
QUESTION 1
a
A card is drawn at random from a normal pack of 52 cards. Find the probability that the
card is:
a club
d not a spade
QUESTION 2
b a black card
c
an ace
e
f
a red card
a black ace
From the letters of the word CHANCE, one letter is selected at random. What is the
probability that the letter is:
a
b
QUESTION 3
c
A die is thrown once. Find the probability that it is:
a
b an odd number
c
a number greater than 2
d zero
e
a prime number
f
QUESTION 4
a square number
A bag contains 6 yellow, 4 blue and 5 red balls. If a ball is drawn at random, find the
probability that it is:
a
yellow
b red
c
blue
d not yellow
e
white
f
QUESTION 5
The numbers 1 to 15 are written on separate cards. One card is chosen at random.
What is the probability that the number is:
a
b
c
d
e
f
QUESTION 6
The numbers from 1 to 7 are written on separate cards. One card is chosen at random.
What is the probability that:
a
b
c
d
e
f
QUESTION 7
either blue or red
A letter is chosen from the word PROBABILITY. What is the probability that the
letter is:
a
b
c
d
e
f
150
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Probability
Excel Mathematics Study Guide Year 8
Pages 252–268
UNIT 5: Complementary events
QUESTION 1
A die is rolled, what is the probability of:
a
b
c
d
QUESTION 2
From a pack of 52 playing cards one card is drawn at random, what is, the probability
that it is not a club?
QUESTION 3
The probability of winning a competition is
QUESTION 4
A coin is tossed once. What is the probability that the result is:
1
. What is the probability of losing?
500
a
b
c
19
QUESTION 5
The probability of a train arriving on time is , what is the probability that it will not
32
arrive on time?
QUESTION 6
The probability of it raining today is , what is the probability of it not raining today?
QUESTION 7
A bag holds only two-dollar coins. If a coin is selected at random from the bag, what is
the probability that it is not a two-dollar coin?
QUESTION 8
There is a 27% chance of winning a game, what is the probability of not winning
the game?
QUESTION 9
The probability of a baby being born with a particular defect is 0.005, what is the
probability of the baby being born without that defect?
1
5
QUESTION 10 As the result of an experiment it is determined that the chance that any motorist at a
particular location is exceeding the speed limit is 1 in 5. If a motorist at that location is
randomly selected, what is the probability that she or he is travelling at, or less than,
the speed limit?
Chapter 13: Probability
© Pascal Press ISBN 978 1 74020 033 2
151
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Probability
Excel Mathematics Study Guide Year 8
Pages 252–268
UNIT 6: Venn diagrams
QUESTION 1
For the Venn diagram shown, fill in the missing words to make the statements true.
There are
students who play both soccer and hockey;
students who play soccer or hockey, but not both;
students who play neither sport;
soccer or hockey or both; and
QUESTION 2
students who play
Sport played by Year 8
Soccer
32
Hockey
12
18
students in Year 8.
23
For the Venn diagram shown, fill in the missing words to make the statements true.
There are
students who study Japanese;
students who study French;
neither language;
students who study
students who study both languages;
Languages studied by Year 8
Japanese
French
27
41
and
students in Year 8.
QUESTION 3
Use the following information to work out the missing values in the Venn diagram
shown.
19
There are 120 students in Year 8, of whom 46 own neither a dog nor a cat.
62 own a dog or a cat but not both, while 35 own cats.
A=
B=
C=
D=
QUESTION 4
a
Pets owned by Year 8
Dog
A
Cat
B
C
D
In a Year 8 class, students play cricket or basketball or both. Eighteen play cricket, 15
play basketball and 6 play both cricket and basketball.
Show this information by drawing a Venn diagram
b
c
d
e
Find the total number of students in class.
152
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Probability
Excel Mathematics Study Guide Year 8
UNIT 7: Using language of ‘at least’, exclusive ‘or’,
inclusive ‘or’ and ‘and’
Pages 252–268
QUESTION 1
In a family of three children, find the probability that there is at least one girl.
QUESTION 2
When a coin is tossed four times, find the probability of getting at least one head.
QUESTION 3
From a pack of cards numbered 1 to 10, one card is selected at random. Find the
probability that the number drawn is:
a
odd
b greater than 5
c
less than 4
d greater than 5 or less than 4
e
odd or greater than 5
f
odd and greater than 5
g
odd and less than 5
h greater than 5 and less than 4
i
less than 5 or divisible by 6
j
less than 5 or divisible by 3
QUESTION 4
a
From a pack of 52 playing cards, one card is drawn at random.
Find the probability that it is:
a black card or a ten
b a black ten or a king
c
a spade or a ten
QUESTION 5
a
Two dice are thrown. Find the probability that the throw gives:
a double or a total of 10
b a double or a total of 15
Chapter 13: Probability
© Pascal Press ISBN 978 1 74020 033 2
153
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Probability
Excel Mathematics Study Guide Year 8
Pages 252–268
UNIT 8: Two-way tables
QUESTION 1
Lachlan takes note of the occupants of cars as they leave a car park. He records whether
the drivers are male or female and whether or not there are passengers. The results are
shown in the two-way table.
Male
Female
Total
a
Passengers
48
X
102
No passengers
36
62
Y
Total
84
116
What is the value of:
i
ii
b
c
d
e
f
g
QUESTION 2
A survey was conducted to see whether students preferred strawberry- or chocolateflavoured milk. The results are shown in the table.
Male
Female
Total
a
Strawberry
98
66
164
Chocolate
52
84
136
Total
150
150
300
What is the probability that a student chosen at random from the group:
i
ii
iii
iv
b What is the probability that:
i
ii
QUESTION 3
a
185 out of 300 boys and 165 out of 250 girls surveyed had seen a particular movie.
Complete the two-way table to display the information.
Seen the movie
Not seen
Total
Boys
Girls
Total
b What is the probability that a person who has seen the movie chosen at random from the surveyed
154
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Probability
TOPIC TEST
PART A
Instructions • This part consists of 12 multiple-choice questions.
• Fill in only ONE CIRCLE for each question.
• Each question is worth 1 mark.
Time allowed: 15 minutes
Total marks: 12
Marks
1
impossible
unlikely
even chance
2 One of these cards is selected at random. What is the probability
3
4
likely
1
1
5
2
5
3
5
4
5
1
2
3
3
4
7
10
9
11
1
impossible
unlikely
likely
certain
5 A card is drawn at random from a standard pack of playing cards. What is the probability that
1
1
1
3
1
0
4
2
4
7 A letter is chosen at random from the word EXCELLENT. How many different elements are
1
1
3
1
6
7
8
9
8 A bag contains 3 white, 2 yellow and 5 black balls. If a ball is drawn at random, the
probability of a white ball is:
1
0
4
2
4
6 A card is drawn at random from a standard pack of playing cards. What is the probability
9
10
1
10
1
3
3
7
This two-way table shows the number and colour of ribbons
won in a competition by some students. What is the probability
3
10
Boys
Girls
Blue
12
20
1
Red
18
10
2
3
2
5
3
8
1
3
1
5
9
5
14
1
2
1
3
1
11 A ticket is chosen at random from a hat. The probability that the ticket is green is
1
5
and the probability that it is blue is . What is the probability that the ticket is neither blue
12
12
1
12
5
12
1
2
7
12
1
5
12
1
2
7
12
5
6
1
12 A number is chosen at random from the whole numbers 1 to 12 inclusive. What is the probability
Total marks achieved for PART A
Chapter 13: Probability
© Pascal Press ISBN 978 1 74020 033 2
12
155
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Probability
TOPIC TEST
PART B
Instructions • This part consists of 4 questions.
• Answer each question in the space provided.
Time allowed: 20 minutes
Total marks: 15
Marks
1
Of a group of 40 students in Year 8, 20 study
Italian, 25 study French and 5 study neither.
a Show this information
on a Venn diagram.
1
b
1
c
1
d What is the probability that a randomly chosen student from the group studies:
1
ii
1
2
3
4
A card is drawn at random from a normal pack
of 52 cards. Find the probability that the card is:
1
1
a
a diamond
b a queen
1
c
black and a heart
d
1
e
not a club
1
Write the complement of the following.
a
tossing a head with a coin
1
b
not winning a cricket match
1
In a normal pack of playing cards, E represents the
a
1
P (E)
b
1
c
1
Total marks achieved for PART B
156
© Pascal Press ISBN 978 1 74020 033 2
15
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Chapter 14
Statistics
Excel Mathematics Study Guide Year 8
Pages 232–250
UNIT 1: Review of basic statistics
QUESTION 1
Some students sat for a quiz. The results are shown in the table.
Score
6
7
8
9
10
Frequency
2
5
9
7
3
a
d Show these results in a frequency histogram.
Frequency (f)
b
c
Score (x)
QUESTION 2
a
A die was rolled many times.
Complete the frequency distribution table.
Score
1
2
3
4
5
6
Tally
|||| ||||
|||| ||
|||| ||||
|||| |
|||| |||
|||| |||| |
Frequency
Cumulative frequency
b
c
d
f
g
h Draw a cumulative frequency histogram.
Cumulative Frequency (f)
e
Score (x)
Chapter 14: Statistics
© Pascal Press ISBN 978 1 74020 033 2
157
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Statistics
Excel Mathematics Study Guide Year 8
Pages 232–250
UNIT 2: Collecting data
QUESTION 1
Complete the following.
a
the process is called
b When each and every member of the population is surveyed it is called a
c
When only a part of the population is surveyed it is called a
QUESTION 2
State whether a census or a sample should be used in each of the following.
a
b the total number of books available for sale in a bookshop
c
the number of students who travel to school by car
d the number of people who bought two tickets for a movie
e
all the students and teachers in a high school who voted for the selection of a new school captain.
f
QUESTION 3
a
State whether a sample or a census is used in the following.
the total number of people working in a hotel
b the number of adults who went to a hall to attend a meeting
c
the total number of students in a high school
d the number of students who were selected to participate in a swimming carnival
e
the number of teachers who work in the state of NSW
f
the number of people who travel to work by bus
158
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Statistics
Excel Mathematics Study Guide Year 8
Pages 232–250
UNIT 3: Types of sampling
QUESTION 1
Complete the following.
a
of selection.
b A systematic random sample is a sample where those chosen for the sample are chosen in a
way.
and a
c
sample is taken from each group.
QUESTION 2
State whether the sample chosen is a random sample, systematic sample or a stratified
sample.
a
b
c
In a high school, there are 500 boys and 400 girls. The sample of students chosen consists of 50 boys and
40 girls to represent the school in a function.
QUESTION 3
a
Which sampling method would be most suitable for each of the following?
A sample of milk bottles is to be inspected to check the quality of the milk.
b
c
to determine what new books the school library needs
d checking the quality of shirts made by the manufacturer
e
Chapter 14: Statistics
© Pascal Press ISBN 978 1 74020 033 2
159
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Statistics
Excel Mathematics Study Guide Year 8
Pages 232–250
UNIT
QUESTION 1
Answer the following questions.
a
b
c
QUESTION 2
a
State whether the data is numerical or categorical.
the heights of horses
b
c
the number of messages sent in a day
d the colour of cars
e
the lengths of newborn babies
f
the type of pet that students have
g
the minimum temperature each day
h the number of students in each class
QUESTION 3
a
State whether the data is discrete or continuous.
the number of children in families
b the lengths of cars
c
the number of days in months
d
e
the heights of buildings
f
the number of biscuits in packets
g
the weights of babies
h the masses of containers
i
the number of marks in tests
j
the diameters of tanks
k the temperatures of patients
160
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Statistics
Excel Mathematics Study Guide Year 8
Pages 232–250
UNIT
QUESTION 1
a
State whether the data is numerical or categorical. If numerical, also state whether it is
discrete or continuous.
the mass of packets of noodles
b the day of the week on which your birthday falls
c
the type of trees growing in a backyard
d favourite colours
e
the number of students in each class at school
f
the heights of buildings
g
the heights of saplings
h the ages of people at a concert
i
the breed of dogs at a dog shelter
j
the number of medals won at Olympic games
k the type of medal (gold, silver or bronze) won at Olympic games
l
m favourite movies
n
o
the weight of babies
QUESTION 2
Determine whether the type of sample is random, systematic or stratified.
a
b selecting a boy and a girl from every class
c
picking names out of a hat
d every 100th name from the telephone book
e
all the members of a club whose membership numbers end in 7
QUESTION 3
Julie wants to conduct a survey of teachers. She knows that quite a few of the teachers
are attending a lunchtime meeting and decides to use these people as her sample.
Explain why this is not a random sample.
QUESTION 4
Greg wants to conduct a survey of the opinion of students about the school uniform. He
decides to select a stratified sample. There are 1250 students at the school, 215 in
Year 7, 200 in Year 8, 210 in Year 9, 220 in Year 10, 225 in Year 11 and 180 in Year 12. If
Greg decides to survey 250 students, how many should he choose from each year?
Chapter 14: Statistics
© Pascal Press ISBN 978 1 74020 033 2
161
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Statistics
Excel Mathematics Study Guide Year 8
Pages 232–250
UNIT 6: Mean
QUESTION 1
a
Find the mean of the following sets of scores.
3, 5, 7
b 4, 7, 8, 12, 13
c
60, 62, 69, 75
d 5, 6, 6, 8, 11, 18
e
0, 1, 3, 4, 6, 7, 7, 8, 9
f
14, 15, 17, 19, 23, 25, 27
g
h 6, 7, 7, 8, 8, 8, 9, 9, 10, 10
i
3, 4, 4, 4, 5, 6, 7, 7, 8, 9, 9
2, 2, 2, 2, 3, 3, 3, 4
QUESTION 2
Find the mean, giving each answer correct to one decimal place.
a
5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7
b 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6
c
11, 12, 14, 14, 16, 17, 17, 17, 20
d 44, 44, 44, 44, 45, 46, 46, 47, 48, 48, 49
QUESTION 3
a
Complete the tables below and calculate the mean.
x
f
1
fx
x
f
5
0
2
8
3
f
11
6
3
1
13
7
5
6
2
14
8
6
4
9
3
12
9
7
5
12
4
10
10
4
QUESTION 4
Total
fx
c
x
Total
a
b
fx
Total
Answer the following questions.
Find the sum of the scores if the mean of 50 scores is 78.6.
b
c
162
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Statistics
Excel Mathematics Study Guide Year 8
Pages 232–250
UNIT 7: Median and mode
QUESTION 1
Find the median of each set of scores.
a
12, 13, 15, 17, 20
b 5, 5, 6, 7, 7, 8, 8, 8, 9, 9
c
73, 81, 76, 79, 80, 74, 70, 84, 74
d 29, 26, 30, 22, 29, 24, 30, 27, 22, 29
e
121, 108, 112, 123, 102, 120, 123, 105
f
QUESTION 2
56, 60, 68, 49, 66, 87, 67, 56
Find the mode of each set of scores.
a
2, 2, 3, 4, 4, 5, 5, 6, 5, 6
b 4, 8, 8, 9, 9, 9, 9, 9
c
2, 3, 3, 2, 4, 2, 5, 6, 5, 3, 3
d 52, 17, 18, 52, 53, 54, 52, 52, 53, 52
e
8, 9, 10, 8, 11, 8, 9, 8, 10, 8, 6, 8
f
QUESTION 3
a
c
Score
1
2
3
4
5
6
5, 6, 5, 5, 7, 6, 6, 7, 6, 5
Complete the table, then find the mode and median.
Frequency Cumulative frequency
3
6
8
7
5
4
b
Score
5
6
7
8
9
10
mode =
mode =
median =
median =
Score
Frequency Cumulative frequency
d
Score
Frequency Cumulative frequency
12
19
18
15
10
13
Frequency Cumulative frequency
16
8
16
5
17
6
17
7
18
7
18
8
19
10
19
14
20
5
20
6
mode =
mode =
median =
median =
Chapter 14: Statistics
© Pascal Press ISBN 978 1 74020 033 2
163
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Statistics
Excel Mathematics Study Guide Year 8
Pages 232–250
UNIT 8: Using the mean, mode and median
QUESTION 1
a
A foreign language class has just 6 students. The class sat for a test and the following
marks resulted: 7, 93, 95, 96, 96, 99.
Find the:
i
median
ii mean
iii mode
b Barry scored 93. ‘I did well in the test,’ Barry told his mother. ‘I was way above average.’ Do you agree with
QUESTION 2
When talking about real estate, people in the industry and the media refer to the
median house price. Why is the median a better means of describing the data than the
mean or mode?
QUESTION 3
A shop sells women’s clothes. The table shows the number of each size of dress sold
over the previous month.
Size
Number sold
a
8
2
10
13
12
28
14
42
16
35
18
26
20
23
22
19
24
21
Find the mean dress size.
b
c
d
164
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Statistics
Excel Mathematics Study Guide Year 8
Pages 232–250
UNIT 9: Range
QUESTION 1
Find the range of the following sets of scores.
a
3, 5, 8, 12, 17
b 1, 4, 9, 12
c
0, 5, 9, 11, 13, 18
d 56, 59, 65, 69, 77, 78, 84, 84, 91
e
23, 28, 35, 38, 44, 46
f
g
12, 9, 10, 17, 22, 9, 8
h 11, 13, 8, 21, 7, 24
i
7, 9, 6, 13, 15, 11, 9
j
30, 26, 24, 13, 3, 17, 35, 17, 21, 16, 7
l
69, 47, 53, 80, 37, 55, 64, 71, 83, 81
k 109, 107, 123, 110, 101, 107, 105
QUESTION 2
Find the range for the scores in each dot plot.
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
5
6
7
8
9
10
a
QUESTION 3
a
4
5
6
7
8
9
6
4
2
0
1
0
8
5
3
4
5
QUESTION 4
6, 23, 34, 49, 51, 68, 70
b
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
0
1
2
3
4
5
6
7
8
9
Find the range for the scores in each stem-and-leaf plot.
9
5
3
4
6
b
6
3
5
9
7 7
6 8 9
7 8
9
13
14
15
16
17
18
8
0
1
0
1
2
9
5
2
3
4
7 9
2 5 7 8
4 6 8 9
5
Answer the following questions.
a
b
Chapter 14: Statistics
© Pascal Press ISBN 978 1 74020 033 2
165
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Statistics
TOPIC TEST
PART A
Instructions • This part consists of 9 multiple-choice questions.
• Fill in only ONE CIRCLE for each question.
• Each question is worth 1 mark.
Time allowed: 15 minutes
Total marks: 9
Marks
1
Niamh wanted to test a theory that older students preferred a different type of music to younger
students. She chose the youngest person from each Year 7 class and the oldest person from each
random
systematic
census
1
2
over a month. This data is
categorical.
numerical continuous.
numerical discrete.
1
none of these.
For Questions 3, 4, 5 consider the scores 5, 7, 3, 3, 8, 2, 6, 3, 9 and answer the questions.
3
3
5
7
8
1
3
5
7
8
1
3
5
7
8
1
4
5
6
Which of the following is not
values of cards chosen from a standard pack
weights of children
number of visitors to a theme park
1
7
8
Score
5
6
7
8
9
Frequency
13
22
35
26
11
the mean
the median
the mode
The mean, mode and median are all equal.
1
30% of a country’s population is aged over 60. How many people aged over 60 should be
30
50
60
75
1
12
12.5
13
13.5
1
9
Total marks achieved for PART A
166
© Pascal Press ISBN 978 1 74020 033 2
9
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Statistics
TOPIC TEST
PART B
Instructions • This part consists of 4 questions.
• Answer each question in the space provided.
Time allowed: 20 minutes
Total marks: 11
Marks
1
off each of the buses as they arrived back at school to answer his questions.
a
1
b
1
2
40 people were randomly selected at a concert and asked their age.
The results were recorded in the table below.
Age
12 13 14 15 16 17 18 19
Frequency
3
7
6
9
a
8
4
2
1
b
1
1
c
Find the mean.
d
1
1
e
1
3
A high school has 500 girls and 700 boys.
a
1
b
1
4
The range of a set of 12 scores is 19. The lowest score is 8 and the mean is 11.
a
b
1
1
Total marks achieved for PART B
Chapter 14: Statistics
© Pascal Press ISBN 978 1 74020 033 2
11
167
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Exam Paper 1
Instructions for all parts •
Time allowed: 1 hour
Attempt all questions.
Part A: Allow about 10 minutes for this part.
Part B: Allow about 20 minutes for this part.
Part C: Allow about 30 minutes for this part.
Total marks: 50
EXAM PAPER 1
PART A
Fill in only one circle for each question.
Fill in only one circle for each question.
1
6
50
Marks
is equivalent to:
3%
2
3
1
6%
8 3%
12%
8
12
If x – 10 = –2, then x equals:
48
2× 4
6
8
18
48
28
18
24
21
–12
1
17
x2 – 2x
–x
–2x2
20
–15
36
5
The mode is 3.
The mean is 3.
The median is 3.
The range is 3.
16 mm
160 mm
1600 mm
16 000 mm
1
4
1
3
1
2
2
3
0.02
0.2
0.5
5
36 cm2
144 cm2
–7 + 2
1
1
–4 equals:
8
9
1
x(x – 2) equals:
x2 – 2
7
1
(–3)2 + (–2)3 equals:
–17
6
1
equals:
4
5
1
1
1
1.6 m equals:
10
11
12 The area of a quadrant with radius 12 cm is:
6 cm2
24 cm2
Total marks achieved for PART A
168
© Pascal Press ISBN 978 1 74020 033 2
1
1
1
1
12
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
EXAM PAPER 1
PART B
Answer each question in the space provided.
Marks
1
1
Calculate 80 635 – 43 419.
2
Complete the table of values for y = 3x
x
y
–1
0
1
1
2
1
3
4
Simplify 8ab + 2ba.
1
5
Simplify 22 × 24 × 25.
1
1
6
1
7
Find 5 of 3.8 tonnes.
1
8
Write 48% as a fraction in its simplest form.
1
9
Simplify 4 – 2(a + 1).
1
1
10 Edwina draws a sketch of a building using a scale of 1 cm to 2 metre.
1
7m
1
11
10 m
12 Find the value of a
13 Calculate
2
1
b when a =12 and b = 9.
14 m
1
256 × 53 × .
1
4
135°
14 Find the value of x.
15 A rectangular prism measures 8 cm
3 cm
x°
5 cm. Find its volume.
1
1
16
1
17
1
18 Factorise 6ab – 3b2 + 12a2b.
1
19
1
20 On a sports afternoon, half of Year 8 went swimming, a third of
Year 8 played basketball and the rest stayed at school. If 52
Total marks achieved for PART B
Exam Papers
© Pascal Press ISBN 978 1 74020 033 2
1
20
169
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
EXAM PAPER 1
PART C
Show all working for each question.
Marks
1
a
ABC
EFD D
B
E
3 cm
4 cm
3 cm
A
b Find the area
of the
parallelogram
ABCD
4 cm
F
7 cm
C
15 cm
i
Name the side in
EFD that matches to BC.
1
ii Name the angle in
1
EFD that matches to ABC.
1
2
a
Simplify:
3a + 2a 4
b
x
3)
c
Factorise: 3x
1
24
5a
1
1
3
Peta surveyed the staff and students at her
high school to see how many wore glasses and Staff
how many didn’t wear glasses. Her results are
Students
partly displayed in the table below
Total
a
Glasses
30
(b)
180
No glasses
(a)
480
520
Total
70
630
700
1
b
1
If one person is selected at random from Peta’s school, what is the probability that he or she is:
c
d
1
1
4
Calculate the time:
a 35 minutes after 11:43 am b 24 minutes before 8:15 pm
c
1
1 hour and 52 minutes
before 1:17 am
1
1
5
a
Find the value of the pronumeral in each of the following.
b
c
x
50 15
3x
130
75
72
y
1
4
65
2
0
–4 –2
6
a
y = x + 1.
b Where does this line cut the x
1
2
4
© Pascal Press ISBN 978 1 74020 033 2
1
–2
1
–4
1
Total marks achieved for PART C
170
x
18
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Exam Paper 2
Instructions for all parts •
Time allowed: 1 hour
Attempt all questions.
Part A: Allow about 10 minutes for this part.
Part B: Allow about 20 minutes for this part.
Part C: Allow about 30 minutes for this part.
Total marks: 47
EXAM PAPER 2
PART A
Fill in only one circle for each question.
1
Marks
(0.3)2 equals:
0.09
2
0.9
9.0
0.03
40 m 2 n 2
3
10 m 2 n 2
3
10 m 2
3n 2
10 m 2
3n 6
20%
12.5%
25%
37.5%
1
3
4
7x – 7
4x – 5
4x – 10
(5m2 × 8n4) ÷ (4m0 × 3n2) =
3
4
$24
$80
$120
1
176 L
1760 L
176 000 L
$50
$60
1
If $80 is divided in the ratio 5:3, the bigger amount is:
$30
9
1
What is the capacity of an animal water trough in the shape of a rectangular prism with
1.76 L
8
1
The interest on $500 for 3 years at an interest rate of 8% per annum is:
$40
7
1
x + 3 + 2 (3x – 5) equals:
7x + 13
6
1
If x = 3 and y = 2, the value of x2 – xy is:
0
5
1
$40
1
The sum of the smallest and the largest of the numbers 0.519, 0.9, 0.89 and 0.289 is:
1.189
0.8019
1.319
1.519
y
y + xz
yz
y+z
10
100
360
3600
a16
2a4
2a8
10 x is a factor of xy + xz
11
12 a4 + a4 equals:
a8
Total marks achieved for PART A
Exam Papers
© Pascal Press ISBN 978 1 74020 033 2
1
1
1
1
12
171
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
EXAM PAPER 2
PART B
Answer each question in the space provided.
Marks
1
Write 4:35 pm in 24-hour time.
1
2
Evaluate 4.2 − 2.54 .
1
3
Factorise 8a – 8.
1
4
Find the third angle in a triangle if the other two angles measure 53° and 42°.
5
Calculate the area of the kite where AC = 32 mm and BD = 18 mm.
15.6
1
D
A
E
B
6
1
C
1
2x
8
1
7
Solve 3 = 6 .
8
Simplify 3 4 – 1 5 .
3
2
1
1
9
10
1
x – 3(x + 2).
11 Find the mean of the set of scores: 8, 6, 4, 6, 5, 6, 10
1
1
1
12 The area of a square is 20 4 cm2
13 If A = 4b2 and A
b (b
2
1
14 Find 3 of 1.5 litres.
1
15
1
16 If the bill at a restaurant for three people came to $129.90, how much
17
7
9
1
as a recurring decimal.
18 If m
1
m – 1)3.
19 Increase $100 by 10% and then decrease this amount by 10%.
20 Three parcels weigh 5.3 kg, 8.7 kg and 3.7 kg.
© Pascal Press ISBN 978 1 74020 033 2
1
1
Total marks achieved for PART B
172
1
20
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
EXAM PAPER 2
PART C
Show all working for each question.
1
Marks
Correctly name the feature of the circle shown below.
a
b
Q
P
A
c
B
1
PQ is a
AB is a
The shaded region is a
1
1
2
Solve the following equations.
a x – 5 = 31
b
3x + 10 = 5x – 6
c
4(a – 8) = 48
1
1
1
3
For the following scores — 10, 15, 11, 9, 14, 14, 12, 10, 10, 15 — state the:
a mode
b median
2
c range
d mean
2
1
4
5
Find the length of the missing side.
a
1.5 m
x
b
6 cm
7
1
6.5 cm
2m
6
y
1
It is known that the wheels of a toy truck rotate 100 times per minute. If the radius of the
22
wheels is 70 mm, calculate, using = 7 , how far the truck will travel in 10 minutes.
The diagram shows a quadrilateral and a semicircle.
Find the value of x.
1
15 cm
x
1
10 cm
Total marks achieved for PART C
Exam Papers
© Pascal Press ISBN 978 1 74020 033 2
15
173
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Exam Paper 3
Instructions for all parts •
Time allowed: 1 hour
Attempt all questions.
Part A: Allow about 10 minutes for this part.
Part B: Allow about 20 minutes for this part.
Part C: Allow about 30 minutes for this part.
Total marks: 44
EXAM PAPER 3
PART A
Fill in only one circle for each question.
Fill in only one circle for each question.
Marks
1
12 cm
16 cm
24 cm
32 cm
7000
6800
6850
6900
0.65
6.5
65
650
0.65
0.62
0.062
0.065
5%
10%
20%
45%
5a × 5a × b
5ab × 5ab
5×a×a×b
3
4
1
4
1
13
26
2
3
4
(23)2 ÷ (22)3 equals:
4
8
1
1
1
1
If 3x – 8 = 31, what is the value of x
6
9
1
5a2b equals:
5×a×2×b
7
1
1
Write 6 2 % as a decimal.
5
6
1
8
1
A letter is chosen at random from the word MATHEMATICS. How many different elements are
8
9
10
11
$1500
$4500
$6200
$6000
1 : 250
1:4
10
11 The ratio of 12 grams to 3 kilograms is
3 : 250
4:1
12 Find in square metres the area of a rectangle 3 m long and 90 cm wide.
0.27 m2
2.7 m2
27 m2
270 m2
Total marks achieved for PART A
174
© Pascal Press ISBN 978 1 74020 033 2
1
1
1
1
12
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
EXAM PAPER 3
PART B
Answer each question in the space provided.
Marks
2
1
1
Write 9 as a recurring decimal.
2
A man’s wage is $250. If he spends 40% of this on rent and 35% on
3
Solve for x: 12(x – 1) = 2(5x + 4).
1
1
4
1
5
A road map is drawn to a scale of 50 mm to 1 km. How far apart
6
Simplify 8x + 6y
7
Calculate the mean of 34, 37, 42, 45 and 48.
1
8
Simplify 5x + (5x)0.
1
9
Factorise fully 9m
1
1
x + 2y.
1
3m2.
120
10 Find the value of x.
x
3
1
1
11 Change 8 to a decimal.
12 The numbers 1 to 12 are written on separate cards and placed face down on a table.
If one card is chosen at random, what is the probability of selecting a number
1
13
1
14 Simplify 105 × 102 × 100.
1
15 If the volume of a cube is 729 cm3
1
16 Solve 4x
5 = 2x + 7.
1
17 Convert 3 hours 20 minutes to minutes.
1
18 A car travels at an average speed of 80 km/h. How long will it take
19 Kate earns $90.80 for 20 hours babysitting. How much
1
1
20 Calculate the area correct to
1
one decimal place.
15 cm
Total marks achieved for PART B
Exam Papers
© Pascal Press ISBN 978 1 74020 033 2
20
175
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
EXAM PAPER 3
PART C
Show all working for each question.
1
a
Marks
Calculate the area of the following shapes.
b
c
14 cm
6 cm
8 cm
1
20 cm
15 cm
1
1
2
Calculate the volume of the following prism.
5 cm
3
4
1
20 cm
12 cm
A swimming club has 40 members and an athletics club has 55 members. There are 16 people
who are in both clubs.
a Draw a Venn diagram to
show this information.
b
How many people are in either the swimming
club or the athletics club or both.
a
Complete the table of values for y = 2x – 1.
x
y
–3 –2 –1
0
1
2
1
y
1
3
0
b Draw the graph of y = 2x – 1.
c
x
1
1
What is the y
1
d For what value of x does y
5
1
A pair of congruent triangles is drawn below.
a Write all pairs of matching sides
A
1
b Write the congruence statement.
1
C
M
B
Total marks achieved for PART C
176
© Pascal Press ISBN 978 1 74020 033 2
12
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Exam Paper 4
Instructions for all parts •
Time allowed: 1 hour
•
Attempt all questions.
Calculators are NOT allowed for Part A.
Part A: Allow about 10 minutes for this part.
Part B: Allow about 20 minutes for this part.
Part C: Allow about 30 minutes for this part.
Total marks: 50
EXAM PAPER 4
PART A
Fill in only one circle for each question.
1
4
25
Marks
is equivalent to:
4%
8%
16%
20%
1
1
2
12
1
11
2
10
3
9
4
8
3
0.125
4
0.0125
$50
0.0625
0.625
$80
$120
The area of this triangle is:
15 cm2
2
9 cm
6
5
6
4 cm
18 cm2
5 cm
3 cm
22.5 cm
6 cm
(–1)2 – (–1)3 equals:
–2
2
1
–1
3
14
32
38
12x + 1
5x + 8
5x + 12
$216
$320
9600
9700
10 000
a + 7b
ab
a+b
3:2
3 : 200
3 : 2000
1
1
7 + 5(x + 1) equals:
5x + 6
9
1
1
2
7
8
1
If $200 is divided in the ratio 2:3, the smaller amount is:
$40
5
7
(0.25)2 equals:
1
Interest on $800 for 3 years at 9% per annum is:
$72
$24
10 The number 9659 rounded to the nearest hundred is:
9500
11 If 7 is a factor of 7a + 7b
a
12 The ratio of 30 mL to 2 L is:
30 : 2
Total marks achieved for PART A
Exam Papers
© Pascal Press ISBN 978 1 74020 033 2
1
1
1
1
12
177
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
EXAM PAPER 4
PART B
Answer each question in the space provided.
Marks
1
Decrease $720 by 5%.
1
2
Find the value of
1
ab + ac
abc if a = 2, b = 3 and c = 4.
y
3
1
y = 2x
4
What is the point of intersection for the lines y = 2x and y = 3 – x
0
5
Write 84% as a fraction in its simplest form.
6
Simplify 8y2 ÷ 8y2.
7
A bicycle wheel has a diameter of 65 cm. How far, correct to the nearest metre, will
8
Find the size of a quantity if 20% of it is 30 metres.
x
y=3–x
1
1
1
1
1
1
9
10
1
98
11 What is the value of x
x
140
1
1
12 Write 500 minutes as hours and minutes.
13 What is the area (to the nearest whole number) of a circular speed limit sign with
1
14 Factorise 8m – 10.
1
15
1
16 A cube has a volume of 216 cm3
1
17
1
x(3x – 5) + 2x(5 – 3x).
18 Calculate the circumference of a wheel with a diameter of 42 cm.
1
Answer to the nearest centimetre.
19 If v = u + at
62
v when u = 10, a = 6 and t = 5.6.
20 Find the value of the pronumeral
in the given diagram.
x
Total marks achieved for PART B
178
© Pascal Press ISBN 978 1 74020 033 2
1
1
20
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
EXAM PAPER 4
PART C
Show all working for each question.
1
a
Marks
Find the value of the pronumeral, giving reasons.
b
R
S
A
Q
2x
67
c
3x
B
104
128
45
P
P
T
a
C
Q
R
92
71
D
1
S
1
1
2
Find the area of the following plane shapes.
a
b
7 cm
A
B
ABCD is a
rhombus.
AC = 19 cm,
BD = 15 cm
9 cm
12.5 cm
D
C
1
1
3
Find the volume of the given solid.
12 mm
47 mm
1
62 mm
4
a
In the rectangle given opposite, a diagonal is drawn
to divide it into two congruent triangles. Write:
all pairs of equal sides
48 mm
A
B
1
b all pairs of equal angles
1
c
1
the congruence statement
D
C
Continued on the next page
Exam Papers
© Pascal Press ISBN 978 1 74020 033 2
179
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
EXAM PAPER 4
PART C
Show all working for each question.
Marks
5
Nine students did a short test. The results are recorded below.
6, 7, 4, 7, 8, 7, 7, 3, 9
a
Determine the range.
1
1
b
1
c
1
d
6
Solve the following.
a
2
3
9= y
b
a−2
= 10
4
1
1
7
Find the value of the pronumeral in each of the following.
a
b
c
120
50
x
25
x
3x
1
1
1
Total marks achieved for PART C
180
© Pascal Press ISBN 978 1 74020 033 2
18
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Answers
Chapter 1 – Basic arithmetic and the calculator
Page 1 1 a 40 b 70 c 90 d 30 e 160 f 230 g 630 h 830 i 390 j 5670 k 9650 l 6380 2 a 800 b 500 c 200 d 2400
e 5400 f 6300 g 8900 h 6400 i 8500 j 500 k 900 l 600 3 a 3.6 b 0.8 c 9.7 d 31.6 e 0.2 f 16.1 g 18.4 h 91.5 i 62.9 j 43.2
k 83.3 l 55.1 4 a 5.67 b 8.94 c 9.62 d 33.26 e 41.67 f 83.19 g 52.37 h 81.29 i 63.14 j 59.33 k 129.64 l 538.63 5 a 50 b 3
c 90 d 9 e 0.007 f 0.05 6 a 84 b 240 c 8.9 d 92 e 330 f 82 g 250 h 0.000 65 i 0.0076
Page 2
1 a 17 b 46 c 48 d 59 e 45 f 100 g 360 h 112 i 20 j 23 k 11 l 29 m 32 n 109 o 11 2 a 244.52 b 678.804
3
11
4
4
c 121.7 d 38.1 e 114.632 f 223.1 g 27.62 h 22.35 i 11.02 j 59.94 k 25.346 l 114.53 3 a 9 4 b 1215 c 515 d 17 e
6
7
6
36
1
16
173
39 f 1175
11
212
4 a 100.15 b 10.98 c 72 d 2363.75 e 8.122 f 5.2 g 4754.65 h 498.015 i 158 5 a 118 b 2 35 c 35 d 2125 e 13 8 f
Page 3 1 a 25 b 36 c 225 d 1521 e 4225 f 7921 g 12.25 h 4.41 i 44.89 j 232.5625 k 265.69 l 14 713.69 2 a 512
b 64 c 125 d 216 e 32 f 2401 g 3125 h 512 i 243 j 1.728 k 13.824 l 1296 m 5.0625 n 0.343 o 13.0321 3 a 104.86 b 4.91
1
27
9
c 571.79 d 753.57 e 2138.14 f 3442.95 g 39 283.24 h 3763.82 i 20 730.72 j 6512.49 k 316.84 l 2766.76 4 a 2 4 b 125 c 116
4
24
1
5
7
1
13
93
4
d 28 9 e 40 25 f 72 4 g 15 8 h 42 8 i 41016 j 3 81 k 2125 l 5 9
Page 4 1 a 3 b 5 c 6 d 11 e 13 f 15 g 9 h 14 i 8 j 5 k 2 l 2 m 7 n 36 o 2 2 a 2 b 4 c 3 d 9 e 7 f 6 g 13 h 8 i 2
j 33 k 40 l 1.2 3 a 7.5 b 1.5 c 1.4 d 2.4 e 4.2 f 0.2 g 5.8 h 4.4 i 2.1 4 a 2.50 b 0.88 c 2.92 d 2.48 e 2.05 f 3.09 g 1.60
h 7.31 i 0.34 j 2.77 k 7.61 l 2.09 m 1.71 n 2.34 o 1.13
Page 5 1 16.8 cm 2 148.877 cm3 3 1219.68 cm3 4 17 cm 5 85 000 6 50 7 $830.40 8 $148.75 9 $111.88 10 24 11 48.54
1
12 $1891 13 6.06 14 2 2 15 2.38 16 159 17 $30.49 18 132.01 19 32.939 20 $1375
Page 6 1 C 2 A 3 B 4 C 5 A 6 C 7 A 8 A 9 A 10 A 11 D 12 C
Page 7 1 558.13 2 4700 3 0.50 4 2.38 5 1436.03 6 21.95 7 0.61 8 20.9 9 11.1 10 2 11 66.0 12 0.1 13 20.5 14 6.9 15 5.0
Chapter 2 – Percentages
Page 8 1 a 100 b 100 c 100 d 100 e %, 100 2 a 48% b 52% 3 a 35% b 42% c 97% 4 a 75% b 80% c 90% d 33%
e 11% f 49% g 36% h 22% i 91% 5 a 68% b 53% c 9% d 31% e 63% f 23% 6 a 77% b 85% c 77% d 81% 7 a 88% b 14%
Page 9
7
e 200 f
i
2
3
17
11
40
1
2
3
1
1
169
201
5
1
g 200 h 500 i 8 j 200 k
11
1
21
51
j 200 k 200 l 8 m 200 n 200 o
21
11
3
7
1
3
17
17
9
19
49
19
23
1
41
9
73
4 j 4 k 20 l 1 m 100 n 10 o 20 p 100 q 100 r 100 2 a 40 b 500 c 200 d 200
1
21
17
183
37
81
131
1
1
1
1
9
21
11
1
l 125 m 200 n 200 o 1000 p 400 q 200 r 200 3 a 200 b 300 c 400 d 800 e 40 f 40 g 200 h 3
171
31
81
19
14
31
19
49
13
19
43
6
37
69
13
p 200 q 200 r 400 4 a 50 b 25 c 50 d 75 e 400 f 400 g 200 h 500 i 125 j 1000 k 1000 l 250
1 a 2 b 5 c 10 d 10 e 5 f 5 g 10 h
18
9
40
71
200
4
5
i
m 50 n 20 o 25
Page 10 1 a 30% b 50% c 80% d 40% e 43% f 84% g 62% h 39% i 56% j 25% k 16% l 72% 2 a 50% b 160%
1
2
1
1
c 70% d 80% e 30% f 18% g 36% h 28% i 14% 3 a 75% b 6 4 % c 65% d 11 3% e 25% f 17 2 % g 15% h 60% i 17 2 %
1
5
1
7
2
1
4 a 37 2 % b 55 9 % c 62 2 % d 6311% e 41 3% f 33 3%
Page 11 1 a 0.1 b 0.8 c 0.3 d 0.5 e 0.4 f 0.6 g 0.2 h 0.7 i 0.9 j 1 k 0.15 l 0.65 2 a 0.16 b 0.19 c 0.39 d 0.12
e 0.61 f 0.56 g 0.14 h 0.73 i 0.67 j 0.98 k 0.81 l 0.78 m 0.62 n 0.43 o 0.49 3 a 0.05 b 0.02 c 0.08 d 0.09 e 0.06 f 0.07
g 0.03 h 0.01 i 0.04 j 0.015 k 0.025 l 0.033 m 0.021 n 0.017 o 0.049 4 a 0.455 b 0.892 c 0.574 d 0.639 e 0.632 f 0.365
•
•
•
•
g 0.538 h 0.927 i 0.697 j 0.237 k 0.158 l 0.213 5 a 0. 3 b 0.0083 c 0.003 75 d 0.015 e 0. 6 f 0.125 g 0.0925 h 0.2075 i 0.007
Page 12 1 a 15% b 25% c 35% d 95% e 14% f 85% g 18% h 55% i 17% j 45% k 67% l 65% m 91% n 75% o 72%
2 a 80% b 60% c 10% d 50% e 90% f 20% g 70% h 40% i 30% j 1% k 2% l 5% m 4% n 6% o 3% 3 a 12.3% b 62.5%
c 53.7% d 18.9% e 42.7% f 13.9% g 83.5% h 56.7% i 68.3% j 12.9% k 81.6% l 92.7% m 68.7% n 25.7% o 36.9 %
4 a 0.1% b 91% c 0.6% d 0.7% e 0.2% f 0.9% g 81% h 3.7% i 2.1% j 0.4% k 0.5% l 0.3% m 5.7% n 8.9% o 6.5%
5 a 120% b 250% c 360% d 256% e 131% f 357% g 825% h 341% i 563% j 284% k 534% l 813% m 527% n 803% o 206%
Page 13 1 a 30 b 1000 c 270 d 252 e 290 f 630 g 92.5 h 50.4 i 10.5 j 135 k 623 l 79 m 56.25 n 664 o 313.65 p 650
2 a 0.48 b 8.84 c 0.9 d 7.82 e 5.727 f 207.936 g 2.365 h 677.875 i 556.25 j 302.95 k 11 l 105 m 45 n 516.6 o 60 p 46.8
3 a 85 b $224 c 6.03 d 67.71 days e 46.2 f $2 g $18 h 1.2 kg i 80c j 120 k 200 g l $203 m $60 n $170.40 o 45 p 68
Page 14 1 a $58.50 b $9200 c $116 d $4800 e $420 f $1012.50 g 1260 g h 1 hour i 640 kg j 360 L k 72 h l 140 t m $810
n $372.13 o $209.95 p $168.64 q 96 ha r 1020 cm 2 a $51.03 b $57.12 c 2.6 m d 197.6 L e $837 f $5083.20 g $100.50 h $402.50
i $789.23 j $121.90 k 36 h l $252 m $310.25 n $528 o $57.60 p $12.10 q $676.80 r $403 3 a $414 000 b $1800 c $24 000 d $97.50
1
5
4
1
Page 15 1 a 10% b 40% c 57 7 % d 35 7 % e 3611% 2 a 25% b 25% c 40% d 25% e 50% f 33 3% g 12.5% h 90%
1
2
2
1
1
i 25% j 5% k 8 3% l 63% m 66 3% n 7.5% 3 a 12.5% b 16 3% c 13 3% d 2% e 20% f 25% g 33 3% h 25% i 30% j 10%
1
2
1
5
1
1
1
1
k 25% l 40% m 4% n 1.6% o 83 3% p 6 3% 4 a 8 3% b 25% c 15 9 % d 12 2 % e 16 4 % f 87 2 % g 20% h 333 3% i 2% j 25%
Answers
© Pascal Press ISBN 978 1 74020 033 2
181
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Answers
Page 66 1 a 5(a + 1) b 8(x – 1) c 3(y – 1) d 2(x + 1) e 6(m + 1) f 7(m + 1) g 3(p + 2) h 4(q + 2) i 3(2x – 3y)
j 4(x – 4) k 9(b – 2) l 5(a + 4) m 2(a + 3) n 3(m + 4) o 6(n – 4) p 8(x – 4) q 3(a + 5) r 2(a + 7) 2 a 3(a + b) b 5(m + n)
c 6(p – q) d 7(a + 2b) e 3(l – 3m) f m(m + 7) g y(y + 6) h 9(x – 2y) i 3(a – 8b) j 4(x + y) k p(m – 3) l 8(x – 4y) m 6(x – 6)
n 3m(1 + 4m) o y(5 – y) p 3(3x – 2) q 8(m – n) r 3x(2 – x) s 2x(x – 2) t 6p(q – 2p) u 10(x – y) 3 a –3(x – 2) b –5(x – 2)
c –4(x – 2) d –6(x – 3) e –x(2 – x) f –6(a – 4) g –3(a – 4) h –4(a – 4) i –6(a + 2) j –4(y + 2) k –2(x + 5) l –4(2y + x)
m –3(p + 3q) n –5(x + 5) o –(x + 5) 4 a 7(a + b) b 4(a – 5) c 9(x – y) d 3(m + 5) e 6(1 – t) f m(m – 4) g a(5b – a)
h 7(m – 2n) i 2ab(4 – 3a) j –4(1 + 3a) k –3(1 + 5p) l –3(m + 2n) m 9(m – 4) n –4a(1 + 5a) o –(x + 7)
2 x + y + 3z
Page 67 1 2x + 3y 2 mn 3
4 2x + 3 5 x + 1 6 x2 7 5x + 2 8 4a cm 9 y3 cm3 10 2x + 4y 11 2x + 30 cm
3
12 $7x 13 a 6x + 10 b 6x + 3 c 16x 14 a 4x2 b 2x2 – 3x c x (4x + 2) 15 6p + 5q 16 40y cents
Page 68 1 A 2 C 3 D 4 A 5 B 6 D 7 C 8 D 9 A 10 B 11 B 12 B
Page 69 1 4a 2 9a2b2 3 16ab3 4 11ab 5 2a + 6 6 18x2 7 x 8 2pq(p + 2q) 9 –11x + 39 10 15y + 33 11 5a – 14b 12 17 13 8a
14 –2x + 22 15 –7(x + 3)
Chapter 7 – Length, mass and time
Page 70 1 a m b mm c cm d km e g f mg g kg h t i s j min k h l d 2 a M b k c h d da e d f c g m h µ
3 a m b m c km d cm
Page 71 1 a 10 b 100 c 1000 d 1000 e 1000 f 1000 g 1000 h 60 i 60 j 24 2 a 365 b 366 c 12 d 26 e 52 f 2 g 10
h 100 i 1000 j 4 k day l night m midday n midnight 3 a 31 b 28 c 31 d 30 e 31 f 30 g 31 h 31 i 30 j 31 k 30 l 31
Page 72 1 a 100 b 400 c 200 d 410 e 300 f 600 g 350 h 800 i 500 j 700 k 225 l 534 m 1 n 8 o 70 p 16.7 2 a 2
b 12 c 0.9 d 0.6 e 5 f 25 g 1.5 h 0.2 i 80 j 40 k 5.6 l 15.7 m 1000 n 15 000 o 4750 p 20 070 3 a 1000 b 3500 c 2250
d 10 000 e 6000 f 12 000 g 6500 h 7900 i 8000 j 5000 k 9520 l 5500 m 200 n 800 o 255 p 501 4 a 500 b 4 c 4500 d 64
e 7000 f 46.3 g 63.5 h 2300 i 900 j 8000 k 600 l 1800 m 6000 n 530 o 8.56 p 231 5 a 80 b 400 000 c 300 d 370
e 6 f 4 g 2 h 12 690 i 9 j 0.7 k 8500 l 580 m 20 n 0.000 009 o 50 p 36.5
Page 73 1 a c = 4 b c = 15 c c = 9 d c = 5 e c = 13 f 17 2 a 25 cm b 41 m c 85 mm 3 a 9.4 cm b 29.1 mm c 10.1 cm
4 a No b Yes c Yes
Page 74 1 a a = 3 b a = 8 c a = 7 2 a x = 4 mm b y = 5 m c a = 15 cm 3 a x = 14.8 cm b x = 7.1 m c x = 4.6 mm
4 6.1 m 5 36 cm
Page 75 1 a 21 cm b 22 cm c 30 cm d 19 cm e 24 cm f 17.5 cm 2 a 72 cm b 36 m c 38 m d 48 m e 56 m f 32 m
3 a 28 cm b 20 cm c 26 cm d 24 m e 25 m f 42 m
Page 76 1 a 36 b 40 c 52 d 56 e 48 f 24 2 a 80 b 88 c 56 d 60 3 a 18 m b 3.28 m
Page 77 1 a 3000 b 3500 c 9350 d 8000 e 8320 f 4900 g 12 000 h 1250 i 5100 j 4000 k 7500 l 8392 m 5 n 0.5 o 3.6
p 8 q 0.75 r 5.675 2 a 5000 b 1 000 000 c 8 d 7000 e 12 000 f 6357 g 3250 h 15 350 i 2 000 000 j 0.009 k 3875 l 2508
m 8000 n 0.05 o 6070 p 0.3 q 6500 r 9008 3 a 7 b 38 300 c 6500 d 15 e 3.5 f 25 g 0.89 h 0.635 i 8900 j 2 k 9 l 8.605
m 1750 n 2250 o 3205 p 0.45 q 4.368 r 8.9 4 a 1 b 11 c 5100 d 2100 e 0.001 f 3 000 000 g 0.6 h 9.5 i 9 000 000 000
Page 78 1 a 36 500 t b 1250 c 212.5 kg d 22.4 t e 1.96 kg f 820 g 2 a 380 g, 1.9 kg, 3600 g, 18.8 kg, 4.2 t, 23.5 t
b 4.135 t c 3140 g d 2.8 kg
Page 79 1 a 60 b 60 c 24 d 7 e 2 f 4 g 52 h 12 i 365 j 366 k 10 l 100 m 1000 2 a min b h c s d min e h 3 a 40 b 8
c 300 d 730 e 540 f 300 g 49 h 120 i 6 j 4 k 3 l 600
Page 80 1 a 11 h 38 min b 21 h 58 min c 15 h 46 min d 9 h 11 min e 13 h 33 min f 8 h 24 min g 13 h 9 min h 2 h 5 min
i 1 h 42 min 2 a 11 d 16 h 17 min b 12 h 13 min c 10 h d 6 h 3 a 10:40 am b 5:55 am c 3:05 pm d 6:55 am e 5:06 pm f 6:15 pm
g 9:07 am h 6:47 am i 6:44 pm j 12:10 am 4 a 1 h b 2 h 10 min c 4 h d 4 h 20 min e 5 h f 5 h 20 min
Page 81 1 a
b half past eight; eight thirty c
d ten past eleven; eleven ten e
f twenty past seven; seven twenty 2 a 4:30 b 8:00 c 10:15
d 12:00 e 12:00 f 10:20 3 a 7:00 am b 10:20 pm c 6:40 pm d 11:00 am e 8:30 am f 10:00 am 4 a 7:00 am
b 11:17 pm c 6:25 pm d 7:21 pm e 6:25 am f 9:00 am 5 a 0600 b 1445 c 1630 d 0630 e 0325 f 1020 g 1948 h 2110
Page 82 1 a 8:35 am b 9:43 am c 10:25 am d 3:20 pm e 8:36 pm f 11:40 pm 2 a 0900 b 1230 c 0440 d 2310 3 a 0530
b 1445 c 2320 d 0215 4 a 6 h 20 min b 5 hours 5 a 1645 b 2240 6 9:20 pm 7 1 h 55 min 8 a 4:10 pm b 9:35 am
c 11:30 pm 9 a 0530 b 1520 c 2240 10 2020
Page 83 1 3.76 m 2 27 cm 3 10.63 km 4 33 cm 5 440 m 6 45 960 t 7 13.01 t 8 5000 9 605 kg 10 625 g 11 2250 12 336 h
Page 84 1 C 2 C 3 A 4 A 5 C 6 B 7 D 8 D 9 D 10 D 11 B 12 B
1
Page 85 1 28 m 2 64 cm 3 160 m 4 3500 m 5 16 6 625 7 3 t 8 400 g 9 6.14 kg 10 35 000 t 11 180 min 12 120 h
13 8760 h 14 2 min 40 s 15 8 d 16 h 10 min
Chapter 8 – Area, volume and capacity
Page 86 1 a 100 b 10 000 c 10 000 d 1 000 000 e 100 f 1000 g 1 000 000 h 1000 i 1000 j 1 k 1000 l 1 2 a 1 cm3 b 10 g
Answers
© Pascal Press ISBN 978 1 74020 033 2
185
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Answers
5
1
k 55 9 % l 30% m 7 2 % n 25%
Page 16 1 a 64 b $150 c 50 d 40 2 a 160 b 630 c 2400 d 700 3 a 200 b 460 c 480 d 400 e 140 f 600 g 1660
•
h 264. 4 i 4700 j 425 k 287.5 l 1840 4 a 27 b $21 500 c $575 d $168 000 e $550 f $54.17 g 5000
Page 17 1 $2430 2 a $2700 b $4400 3 a $4125 b $4475 4 $15 800 5 a $733.75 b $8400
Page 18 1 2$56, $504; $9, $36; $5.12, $58.88; $6.50, $123.50; $142.50, $807.50; $35, $105 2 a $81.60 b $598.40
3 a $300 b 21 3% 4 a $31 b $217 5 a $209.41 b $31.41 6 a $1520 b $684
Page 19 1 a $660 b 25.98% c 20.63% 2 a $12 360 b $18 540 3 a $5.16 b $51.64 4 $600
Page 20 1 44% 2 36 3 318 4 85% 5 500 kg 6 $495 7 20% 8 $2950 9 $190 10 $881.10 11 $969.50 12 3 13 $110.50
1
14 a 144 b 56 4 %
Page 21 1 D 2 D 3 A 4 D 5 C 6 D 7 A 8 D 9 B 10 C 11 D 12 D
1
Page 22 1 $111 2 257.40 kg 3 58.33% 4 $933.33 5 $106.67 6 33 3% 7 7 8 $72 9 12.5% 10 245 11 $50 714.29
12 28.78% 13 $2000 14 $2880 15 $2100
Chapter 3 – Four operations with integers
Page 23 1 a 11 b 5 c 11 d 9 e 13 f –1 g 14 h 8 i 26 2 a 13 b 4 c 31 d 4 e 24 f 13 g 12 h –2 i 54 3 a 5 b 3 c 19
d –5 e 30 f 2 g 27 h – 2 i 9 4 a 24 b –5 c 15 d 7 e 36 f –14 g 12 h –11 i 8 5 a 11 b 8 c 15 d –5 e 8 f –13 g 0 h –17
i 3 6 a 9 b 15 c 6 d – 15 e 4 f –15 g 14 h –12 i 20
Page 24 1 a 4 b 11 c 3 d 10 e 12 f 28 g –7 h 22 i 17 2 a 11 b 31 c 5 d 18 e 14 f 87 g 15 h 58 i 9 3 a – 21 b –6
c –13 d –12 e –10 f –6 g –17 h –4 i –28 4 a –17 b –2 c –17 d –4 e –23 f –5 g –32 h –2 i –25 5 a –26 b –14 c 43 d –8
e –46 f –3 g –24 h –10 i –40 6 a –4 b –7 c –12 d 14 e –14 f –2 g –18 h –17 i –9
Page 25 1 a 10 b –84 c 150 d –24 e 12 f –96 g 54 h –90 i 52 2 a 6 b –15 c 189 d –120 e 44 f –42 g 27 h –63 i 360
3 a –36 b 12 c –55 d 45 e –6 f 140 g –24 h 27 i –20 4 a –21 b 24 c –32 d 24 e –45 f 60 g –60 h 32 i –48 5 a 64 b 18
c –350 d 36 e 60 f –24 g –48 h –210 i 30
6 a
b
c
7
11
–4
–5
–9
8
12
–25
–100
×
×
×
3
21
33
–12
7
–35
–63
56
–4
–48
100
400
–7
–49
–77
28
–10
50
90
–80
12
144
–300
–1200
Page 26 1 a 6 b –7 c 6 d –4 e 4 f –7 g 2 h –11 i 6 2 a 6 b –3 c 3 d –5 e 9 f –4 g 2 h –12 i 7 3 a –9 b 4 c 3 d 3
e –9 f –1 g –3 h 12 i 9 4 a 6 b –2 c –3 d –1 e –16 f 3 g –1 h 2 i –3 5 a 6 b –5 c –9 d 35 e –7 f –80 g 6 h –24 i –1
6 a –5 b 4 c –5 d 3 e –5 f –1 g –2 h 5 i –1
Page 27 1 a –6 b –1 c 7 d –4 e 10 f –2 g –1 h –12 i 7 2 a –32 b 2 c –9 d –21 e –77 f –8 g 90 h 25 i –72 3 a –8
b 15 c –5 d 12 e –28 f 3 g 11 h 0 i –64 4 a –14 b –5 c –16 d –2 e –4 f –18 g 0 h 49 i –4 5 a –2 b –42 c 1 d 50 e –5
f 8 g –9 h –9 i –8 6 a +
3
–7 –9 12 –15 b
×
–4
5
–10
8
–9
–1
2
–8
–10
11
–16
–5
20
–25
50
–40
45
6
9
–1
–3
18
–9
11
–44
55
–110
88
–99
–8
–5
–15 –17
4
–23
–6
24
–30
60
–48
54
Page 28 1 a 8 b 25 c –27 d 9 e 16 f 1 g 125 h 64 i –1 j 64 k –8 l 1 m 32 n 81 o 16 p 81 q –25 r –125 2 a 1 b 625
c –125 d –1 e –32 f 32 g –1 h –1000 i 64 j –216 k 64 l 108 m 81 n 343 o 100 p –64 q 81 r 162 3 a –72 b 85 c –63
d 41 e 125 f 2 g –28 h –49 i –150 j 4 k 56 l –288 m 441 n 208 o 100 p –4 q –11 r –16 4 a –5 b 1 c –1 d 21 e 2500
f 8 g 2100 h –15 i –100 000 j –6000 k 24 l –116 m 63 n 176 o –241 p 19 q –964 r 5000
Page 29 1 a 17 b –3 c 4 d 0 e 11 f 3 g –1 h 1 i –25 j 3 k –5 l –1 2 a 6 b 12 c –10 d –60 e 64 f –2 g –1 h –4 i –25
3 a –24 b 81 c –55 d –18 e 7 f 19 g 0 h 26 i –6 4 a (5 + 7) 6 = 2 b (–3 + 5) –1 = –2 c 5 (4 – 6) 3 = –30
d (6 + 3 5) –7 = –3 e (–4 + 7 – 9) 2 = –12 f 54 –9 – (2 + 7) = –15 g (–4 7 – 5) –2 = 66 h (7 – 10) (3 – 8) = 15
i 10 – (7 + 4 –3 12) = 4
Page 30 1 4 2 3 km east 3 70 4 –4 5 –1 kg 6 –3 7 a $1750 b $2545 8 loss of $3000 9 –3 and –5 10 5 cm 11 $575
12 fall of 13 degrees 13 –2 and 6 14 –5 15 –42
Page 31 1 C 2 D 3 B 4 B 5 A 6 A 7 C 8 D 9 C 10 A 11 D 12 A
Page 32 1 –11 2 13 3 –18 4 –15 5 8 6 11 7 5 8 –1000 9 –10 10 –29 11 –76 12 –60 13 28 14 –12 15 12 C
Chapter 4 – Indices
Page 33 1 a 2 2 2 2 b 5 5 c 7 7 7 d 6 6 6 6 6 e 10 10 10 10 10 10
f 3 3 3 3 3 3 3 3 3 g 2 2 2 2 2 2 2 h 7 7 7 7 7 7 7 7 2 a 26 b 75 c 57 d 38 e 104 f 65
g 123 h 29 3 a 16 b 27 c 121 d 125 e 169 f 100 000 g 216 h 64 i 81 4 a 52 b 23 c 104 d 62 e 25 f 72 g 107 h 32 i 63
182
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Answers
5 a2 2 2 3 3 b6 6 7 7 7 7 c5 5 5 2 2 2 2 d3 3 3 3 3 5 e7 7 7 2 2
f 3 3 3 3 2 2 2 5 5 6 a 23 5 b 24 3 c 23 32 d 32 52 e 22 34 f 2 35 g 25 72 h 22 3 52
Page 34 1 a 28 b 39 c 510 d 711 e 211 f 109 g 69 h 114 i 512 j 316 k 222 l 717 2 a 65 b 59 c 38 d 76 e 28 f 511 g 237 h 1018
i 153 j 310 k 1224 l 55 3 a 45 b 512 c 511 d 214 e 49 f 812 g 312 h 712 i 314 j 210 k 321 l 232 4 a 55 b 99 c 411 d 811 e 211 f 510
g 35 47 h 310 i 65 j 65 k 78 l 810 5 a 55 b 38 c 65 d 76 e 55 f 712 g 414 h 815 i 410 j 64 k 29 l 315 6 a 53 b 53 c 77 d 82 e 43
f 8 g 37 h 3 i 94 j 66 k 73 l 72
Page 35 1 a 73 b 22 c 36 d 53 e 25 f 64 g 108 h 72 i 310 j 29 k 116 l 5 2 a 5 b 9 c 2 d 49 e 125 f 3 g 36 h 16
i 5 j 1 000 000 k 27 l 8 3 a 212 b 515 c 742 d 312 e 24 f 56 g 6 h 314 i 215 j 108 k 730 l 1212 4 a 38 b 96 c 55
d 56 e 29 f 76 g 78 h 415 i 912 j 87 k 614 l 1026 5 a 33 b 57 c 8 d 95 e 123 f 9 g 23 h 75 i 53 46 j 82 33 k 22 35 l 25 3
6 a 55 b 56 c 85 d 37 e 73 f 33 g 84 h 69 i 42 j 2 32 k 58 l 23 36
Page 36 1 a 210 b 318 c 516 d 715 e 228 f 618 g 550 h 316 i 114 j 1018 k 560 l 336 2 a 6561 b 1024 c 4 035 607 d 1 048 576
e 244 140 625 f 1 679 616 g 4 782 969 h 262 144 i 2401 j 4096 k 1 771 561 l 14 348 907 3 a 321 b 220 c 614 d 536 e 76 f 1121
g 2100 h 1010 i 612 j 128 k 749 l 230 4 a 415 b 335 c 840 d 5144 e 290 f 584 g 718 h 480 i 266 j 948 k 763 l 3126 5 a 64 b (23)3, 29
c (34)2, 38 d (53)2, 56 e (72)4, 78 f (25)3, 215 6 a 212 b 236 c 340 d 396 e 1116 f 330 g 512 h 1045 i 240 j 372
Page 37 1 a 1 b 8, 8, 1 c 10 000, 10 000, 1 d 125, 125, 1 e 49, 49, 1 f 32, 32, 1 2 a 30 b 20 c 100 d 50 e 70 f 20 3 1
4 a 1 b 1 c 1 d 1 e 1 f 1 g 1 h 1 i 1 5 a 2 b 0 c 1 d 7 e 8 f –1 g –1 h 15 i 6 j 2 k 1 l 10 6 a 1 b 1 c 1 d 2 e 3
f 5 g 1 h 1 i 1 j 1 k 1 l p m 10 n 8 o 6
Page 38 1 a 79 b 27 c 78 d 412 e 39 f 86 g 85 h 55 i 63 2 a 43 b 23 c 62 d 52 e 43 f 32 g 34 h 52 i 43 3 a 36 b 26 c 76
d 412 e 610 f 88 g 522 h 330 i 512 4 a 4 b 1 c 8 d 5 e 64 f 1 g 1 h 1 i 81 5 a 85 b 611 c 220 d 56 e 52 f 54 g 26 66 h 4 32
i 33 j 9 k 72 42 l 44
Page 39 1 C 2 A 3 C 4 B 5 B 6 D 7 C 8 C 9 B 10 D 11 B 12 B
Page 40 1 66 2 52 3 86 4 6 5 312 6 314 7 94 8 72 52 9 36 10 9 11 314 12 34 13 1 14 3 15 58 × 236
Chapter 5 – Rational numbers
Page 41 1 a 8 b 12 c 15 d 9 e 7 f 8 g 6 h 35 i 23 2 a 70 b 50 c 90 d 400 e 70 f 80 g 150 h 380 i 570 3 a 200 b 600
c 400 d 700 e 800 f 1000 g 300 h 300 i 2500 4 a 6000 b 8000 c 8000 d 5000 e 2000 f 3000 g 5000 h 6000 i 6000 j 9000
5 a 20 000 b 90 000 c 30 000 d 50 000 e 50 000 f 60 000 g 70 000 h 80 000 i 50 000 j 20 000 6 a 3 000 000 b 6 000 000
c 8 000 000 d 6 000 000 e 29 000 000 f 32 000 000 g 48 000 000 h 92 000 000 i 9 000 000 j 31 000 000
Page 42 1 a 2.3 b 8.9 c 30.6 d 81.1 e 92.8 f 41.4 g 89.5 h 32.1 i 54.2 j 53.3 k 91.8 l 39.4 2 a 81.3 b 32.1 c 36.5 d 41.9
e 62.5 f 92.4 g 51.3 h 39.6 i 42.8 j 28.5 k 58.7 l 73.9 3 a 7.81 b 19.63 c 21.54 d 63.83 e 51.37 f 72.12 g 84.35 h 63.84
i 41.64 j 64.84 k 75.61 l 81.14 4 a 7.42 b 15.63 c 28.14 d 0.94 e 33.46 f 47.44 g 53.24 h 64.83 i 78.36 j 81.89 k 92.64
l 125.84 5 a 5.678 b 25.831 c 19.716 d 37.840 e 42.839 f 59.235 g 63.615 h 72.819 i 81.342 j 93.145 k 120.616 l 92.184
6 a 88.615 b 63.341 c 230.361 d 95.649 e 94.833 f 512.158 g 120.158 h 134.643 i 832.325 j 435.235 k 437.130 l 531.641
Page 43 1 a 0.3 b 0.9 c 0.7 d 4.3 e 0.07 f 0.12 g 0.93 h 2.39 i 0.783 j 0.549 k 0.6342 l 0.0764 2 a 5.3 b 8.9 c 15.07
d 28.05 e 16.01 f 94.7 g 123.03 h 128.8 i 532.37 j 81.3 k 58.7 l 94.19 3 a 0.1 b 0.6 c 0.03 d 0.17 e 0.063 f 0.0415 g 0.6
h 0.14 i 0.375 j 0.25 k 0.064 l 0.875 4 a 0.1 b 0.18 c 0.2 d 2.49 e 0.068 f 2.8 g 1.26 h 3.04 i 0.935 j 0.018 k 0.044 l 0.24
5 a 0.003 b 0.0114 c 0.625 d 0.4 e 0.3 f 0.74 g 0.206 h 0.135 i 1.28 j 0.275 k 0.322 l 0.056
Page 44 1 a terminating b recurring c terminating d recurring
e terminating f recurring g recurring h terminating
! !
0.936
! ! f 0.26! g 0.43
! ! h 0.12
! ! i 0.81
! ! j 0.6!
i terminating j terminating k terminating l terminating 2 a
b 0.7! c 0.53! d 0.8! e 0.27
!
!
!
!
k 0.428 571 l 0.08 3 a 4.333 ... b 8.666 ... c 0.111 ... d 0.3131 ... e 0.7777 ... f 2.222 ... g 1.7272 ... h 0.227 272 7 ...
! ! e 1.63
! ! f 5.123
! ! g 6.230
! 69! h 5.06! i 3.25!
i 1.2424 ... j 0.708333 ... k 0.555 ... l 0.1515 ... 4 a 0.083! b 0.2! c 1.4! d 1.6892
! ! b 0.3! c 0.6! d 0.38! e 0.23
! ! l 8.37
! ! k 2.1! l 0.936
! ! f 0.153! g 1.72
! ! h 0.4! i 1.7! j 0.002! k 3.58
! ! 6 a 0.3!
! ! 5 a 0.253
j 0.456
! ! j 0.045
! ! k 0.01! l 0.02!
! ! g 0.27
! ! h 0.36
! ! i 0.45
b 0.6! c 0.2! d 0.3! e 0.5! f 0.18
Page 45 1 a rational b rational c irrational d irrational e irrational f rational g rational h rational i irrational j rational
k rational l irrational 2 a rational b rational c rational d neither e rational f irrational g rational h rational i irrational
j rational k rational l irrational 3 a irrational b rational c irrational d rational e rational f irrational 4 a 2 and 3 b 4 and 5
c 8 and 9 d 14 and 15 e 5 and 6 f 9 and 10
Page 46 1 a 2 : 1 b 1 : 4 c 4 : 1 d 1 : 3 e 3 : 1 f 1 : 11 g 8 : 1 h 1 : 13 i 9 : 1 j 1 : 6 k 4 : 1 l 1 : 12 2 a 7 : 15 b 2 : 1 c 3 : 1
d 4 : 23 e 8 : 1 f 22 : 3 g 7 : 2 h 1 : 9 i 16 : 3 j 2 : 19 k 1 : 5 l 4 : 9 3 a 1 : 3 : 5 b 3 : 1 c 3 : 10 d 5 : 24 e 1 : 7 f 24 : 5 g 2 : 3 h 7 : 9
i 1 : 4 j 6 : 25 k 24 : 1 l 7 : 8 m 1 : 2 : 4 n 1 : 3 : 9 o 1 : 2 : 3 4 a 1 : 8 b 2 : 5 c 1 : 8 d 3 : 10 e 3 : 7 f 1 : 7 g 6 : 35 h 2 : 3 i 25 : 6
j 3 : 5 k 16 : 1 l 5 : 4 m 2 : 5 n 1 : 5 5 a 4 : 35 b 2 : 25 c 1 : 4 d 5 : 24 e 9 : 2 f 7 : 4 g 11 : 18 h 6 : 5 i 7 : 13 j 69 : 89 k 41 : 50 l 16 : 5
Page 47 1 a $240 and $320 b 800 kg and 1200 kg c $320 and $400 d $500 e $900 2 a 28 boys b 40°, 60°, 80°
c adults = 480, children = 320 d 80 g e $15 000 3 a 70 cm b 9 : 16 c 5 : 16 d $24 000, $30 000 and $42 000 e $2400 and $3000
Page 48 1 a 80 km b 5 litres c $2.50 d $30 e $31.25 2 a 90 km/h b 90 km c 106.25 L 3 a 2.5 m/year b 50 c 2 km/min
Page 49 1 a 1.5 b 1440 c 1800 d 120 e 2400 f 0.5 g 50 h 85 000 i 12 500 j 306 000 k 0.315 l 2400 2 a 2760 b 165 600
c 165.6 3 33.3 m/s 4 a 1500 b 90 000 c 90 5 a 22.8 m/s b 72 km/h
Page 50 1 a 1 : 1000 b 1 : 100 c 1 : 10 000 d 1 : 10 000 e 1 : 250 f 1 : 20 g 1 : 20 000 h 1 : 5 i 1 : 6000 2 a 1 m b 3 m c 5 m
Answers
© Pascal Press ISBN 978 1 74020 033 2
183
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Answers
d 0.8 m e 0.6 m f 1200 m 3 a 8 m b 50 m c 6000 m d 95 m e 8300 m f 63.25 km 4 a 5 cm b 4 cm c 12.6 cm d 8 mm
e 30 cm f 28.35 cm 5 a 35 m b 15 m c 525 m2 d 2.5 m e 150 m2
Page 51 1 a 3 : 2 b 2 : 3 2 160 bottles/h 3 a 3 : 4 b 4 : 3 4 60 km/h 5 $120, $180 6 a 4 : 9 b 1 : 2 7 90 km/h 8 75 cents
9 $36 000, $84 000 10 metal 25 m3, sand 15 m3, cement 10 m3
Page 52 1 D 2 B 3 B 4 C 5 D 6 B 7 D 8 C 9 C 10 B 11 A 12 A
1
Page 53 1 13.2 2 0.37 3 3 4 a 3 : 1 b 7 : 20 5 36, 48 6 4 h 7 $21.50 per hour 8 a 8 mm b 130 m 9 54 km/h 10 25
11 a irrational b rational c rational
Chapter 6 – Basic algebra
Page 54 1 a 5x + 6y b m – 15 c 6a d a – b e
2y
3
x
2 a 6n – 5 b 5a + 32 c x + 2y + 5z d 12ab e 6a 3 a 3x + 9 b 5 + 8
c x + 20 d x – 8 e x + 7 4 a a + 17 b 6m + 7n c 3a + 4b + 5c d 9x + 11y + 2z e 8m + 10n + 7p 5 a 6a + 5b + 7c b 20xy – 10
3a
a +b
18 + x
c 4 b + 15 d 10 e 6
Page 55 1 a 6 b 19 c 16 d 24 e 14 f 54 g 96 h 35 i 32 j 41 k 15 l 31 2 a 3a, 10a b 5x, 9x c none d 5c, 9c e 14y, 6y
f 5l, 6l g 4c, 5c h 5a, 6a i 18y, y 3 a 12a b 4y c 5m d 4x e 5a f 3d g 25d h 13k i 19a 4 a 13x b 11b c 23x d 17a e 43x
f 13a g 7y h 6c i 19y 5 a 9a b 5ab c xyz d 6xy e 42mnl f 8mn g 10ab h 20mn i 14ade 6 a 28 × a × b b 8 × a × b × c
c 7 × x × y d 7 × m × n e 9 × a × b × c f 18 × m × m g 2 × x × y × z h 9 × a × a × b i 14 × m × n × p j 8 × a × a × a
k 5 × a × c × e l 17 × a × a × b × b m 16 × x n 28 × x × x × y × y × y
Page 56 1 a 4a b 3x + 4y c 4x + y d 5l + m e 3m + 2n f 3k + 3m 2 a 14x + 7y b 19a + 29 c 5a + 12b d 7x + 11y
e 14m + 7n f 11a + 15b 3 a 4x + 2y b 2x + 16y c 17p + 2l d 21m + 2n e 19y + 31x f 4xyz g 11a + 17b h 14a + b 4 a 7m
b 6p c 8y2 d 2x e 11a – 7b f 4y g 17x h 2d 5 a 4x b a2 – 8a + 15 c 6y – 3x d p3 + 2p2 – 10 e 8a + b f 14x + 8y g 4ab + 4b
h xy + 6x 6 a xy b 18m2n + mn2 c 16a2 d 23xyz + 4x e 27xyz f 6x2 + 17y2 g 11x2y2 + 17x h 16a3 + 4b3
Page 57 1 a 8y b 8a c 5m3 d 7 × a × b e 16y 2 a 15a b 35n c a + 7b d 4x + 64 e
23
6a
m
m +n
5x
8x + 3
3x
5
f abc g 42a h 8ab2 i 20mn
j 2m + 5 k 9 + 4x l 3a + 4b m x n 11 o 10 p 5 q 3a + 2 r 2 a 3 a 9 × a b 3 × y c 12 × a d 4 × x – 5 e 8 × m + 3
f 60 – 3 × x g a × b + 3 h 2 × x – 3 × y i a × a × a × b × b j 14 × x × y × z k 7 × m × m + 4 l x × x – y × y 4 a 6a3b b 12a2b2
c 5(x + 9) d 5(m – 5) e 7a(c + 2) f 28(x – 2) g mn(p + 3) h 6(5a + 9) i 8 + (20 + 4m) j 8(6a – 2b) k 7a + 5 l 14a – 5
m 7n3 n 18a3 o x3y2 p 8m – 9 q 16a + 7 r 5a – 10
1
2
Page 58 1 a 21 b 28 c 26 d 9 e 45 f 12 g 27 h 3 i 117 j 9 k 162 l 15 2 a 4 b 19 c –85 d 15 e 31 f 24 g 240 h 30 i 26 3
j 4 k 14 l 94 3 a 2, 5, 8, 11, 14 b 2, 6, 10, 14 c –2, 3, 8, 13, 18 d –1, 5, 11, 17, 23, 29, 35 e 5, 7, 9, 11
f –7, 2, 11, 20, 29, 38, 47 4 a 6, 4, 5, 25, 1, 25 b 11, 5, 24, 64, 9, 47 c 8, 4, 12, 36, 4, 34 d 12, 2, 35, 49, 25, 53
e 13, 5, 36, 81, 16, 56 f 6, 2, 8, 16, 4, 26 g 13, 7, 30, 100, 9, 55 h 11, 3, 28, 49, 16, 48 i 9, 7, 8, 64, 1, 37
Page 59 1 a 24 b 4 c 18 d 29 e 6 f 120 g 15 h 19 i 58 j 43 k 68 l 35 2 a 17 b 45 c 32 d 9 e 5 f 20 g 49 h 4 i 125
j 100 k 4 l 50 m 8 n 21 o 18 3 a 8.9 b 14.7 c 3.1 d 15.6 e 90.5 f 42.3 g 75.9 h 13.8 i 3.7 j 3.7 k 2.7 l 1.5 m 79.2
n 3.8 o 2.4
Page 60 1 a 5x b 3x c 9a d 3y e 10y f q g 14m h 8a i 17b j 6t k 12n l 8mn m 3p n 15xy o 4p p 6x2 2 a 8p b 10m
c 10x d 5xy e 13y f 9k g 15xy h 7a i 13m j 9p k 21a l 4ab m 6x2 n 11a2 o 5x p y 3 a 7x + 9y b 8a + 7b c 19m + 8n
d c + 3d e 15a – 5m f 5x2 g 8x + 2y h 9mn i 8y + 2x j 3x + 3y k 8m + 13n l 3t + 9 m 13y + 4x n 3a + 9 o 12 – 5x
p 3m + 5mn q 14m + 8n r 3x + y
Page 61 1 a –4a b x c –3y d –5p e 5a f 11x g 3m2 h –9n i –8x j –8p k 0 l –6x m –2a n –6t o –4x p –12k
2 a 3n b –3y c 2a d –2k e 11y f 6p g –2x h –10n + 15 i 4m j 5a2 + 3a k –6x l 4x – 10y m –7t + 21 n –5k2 + 9k o –4x + 3y
p –2xy – 25 3 a 5x – 6y b 2p – 4n c 5a + 11b d –4n – 2p e –6b f a – b g 15 h 8m2 + 3a2 – 6m i 7y – 5 j –3a – 4b
k 3k + 17 l 8xy + 7x m 10m – 15 n a – 5b o 3a – 9t p –2ab – 3b q –4y – 11 r –4y2 – 4y
Page 62 1 a 21a b 36ab c 20mn d a2b e –10x f 16m2 g –12a2 h 27m i 24b2 j 5x2 k 6ab l 12a2m m 24m2n2 n 50p2
o 30ab p 30m2n 2 a 30ab b 14a2 c –24b2 d –18a e 6m2n f –40x g ab2c h –45t2 i 56mn2p j 6k2 k xy2z l 30x m 6mn3p
n –5ab o –12ab2c p 4ab q –14a2bc r 42y2 3 a 40x2 b –80xy c –60ay d –30m2 e 24a f –60mn g 18xy h –30n3
i –40p2 j –15x3y3 k –30xy l –xyz m –7a2b n 20ab o –6m2n p 100m2 q 5a2 r –30ab2c2d
Page 63 1 a 5 b 6b c 3n d 4 e 3c f 3m g 9 h b i 4 j m k 4x l 2n m y n 6b o 5m p 6x 2 a 3a b 8 c 2b d 5 e –2a
5
m
3b
f –2q g 4 h 3y i 2 j –9 k –x l –6 m 18 n –3 o c p 3b q 4 r 4n 3 a –3a b –9bc c z d 3 e 20 f 3b g 10a h a i x j n k a
l –3a m –6x n –7b o –2q p –7a q y r 3n
Page 64 1 a 40x2 b 72 c 35m2 d 30a2b e 96a2 f 4 g 21 h 12m i 24m j 25 2 a 54x b 120x c 3 d –1 e b f 90m2 g 60a2b2
h 1 3 a y b 26x c 35p d –47x e 51t f 2a g 3 h 25x i 8a 4 a 7 b 2 c 1 d 8y e 10 f –2
Page 65 1 a 5a + 15 b 6x – 42 c –12 – 2a d –5x – 35 e 18a + 45 f 15x – 27 g 12a + 6a2 h 2x2 – 5x i 6m2 + 3m j 5x2 – 15x
k 14n2 – 21n l –3a2 + 6a m –2a – 10 n –21p + 28 o 5a2 – 5a p –6x2 + 6x q –x – 9 r –4y + 7 2 a 9x + 15 b a – 30 c 6m – 12
d 5x + 1 e 4y2 + 24y f 3m – 12 g 2x + 30 h 12x – 6 i 4m – 2 3 a 7x – 2 b 11m – 30 c 8p – 29 d 10x + 22 e 2x + 10 f x2 + 3
g 3p – 28 h 5p2 + 9 i 5m – 2
184
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Answers
c 100 cm3 d 500 mL e 600 g f 800 cm3 g 1 kg 3 a 700 b 8 c 90 000 d 3.5 e 50 000 f 2 300 000 g 6000 h 5 i 15 j 49 000
k 8 l 50
1
1
1
Page 87 1 A = b × h 2 A = 2 h (a + b) 3 A = 2 dD 4 A = 2 dD 5 A
r2, C
r 6 V = x3 7 V = lbh 8 V
r2h
9 V = Area of triangular face × length of the prism (V = Ah)
Page 88 1 a 60 cm2 b 112 cm2 c 144 cm2 d 40 cm2 2 a 60 m2 b 216 cm2 c 336 cm2 d 126 m2 e 126 cm2 f 120 m2 g 114 cm2
h 168 m2 i 320 cm2 j 300 mm2 3 a 20 m b 9 cm c 88 mm2 d 330 cm2 e 8 m f 170 mm2 g 9 cm h 18 m i 11 cm j 420 cm2
Page 89 1 a 192 m2 b 60 cm2 c 130 cm2 d 87.5 km2 e 253 m2 f 30 cm2 g 2808 cm2 h 5.52 m2 i 4079.25 m2 2 a 64 m2
b
Page 90 1 a 30 cm2 b 150 cm2 c 96 cm2 d 198 cm2 e 140 cm2 f 90 cm2 2 a 63 cm2 b 36 cm2 c 70 m2 d 66 mm2
e 30 m2 f 60 cm2 g 75 mm2 3 a 30 m2 b 4 cm c 72 cm2 d 7 cm e 10 m f 56 cm2 g 22 cm
Page 91 1 a 48 cm2 b 30 cm2 c 90 cm2 d 40 cm2 e 30 cm2 f 112 cm2 2 a 31.5 cm2 b 35 m2 c 33 mm2 d 30 m2 e 60 cm2
f 75 mm2 3 a 15 m2 b 36 cm2 c 14 cm d 10 m e 56 cm2 f 22 cm
Page 92 1 a 30.24 cm2 b 48.88 cm2 c 46.24 cm2 d 900.9 cm2 e 195 cm2 f 24 cm2 g 120 cm2 h 57 cm2 i 45.5 cm2
j 255 cm2 k 380.1 cm2
l 151.04 cm2
Page 93 1 10 000 cm2 2 1 000 000 m2 3 10 000 m2 4 3.75 ha 5 $13 440 6 a 1000 m2 b $130,000 7 20 cm 8 18 000 ha
9 a 3 200 000 m2 b 3.2 km2 10 a 3800 cm2 b 2200 cm2 c 6000 cm2
Page 94 1 a 8 cm3 b 27 cm3 c 1000 cm3 d 1.728 m3 e 39.304 m3 f 1728 m3 g 729 cm3 h 68.921 m3 i 5.832 m3
2 a 343 m3 b 729 m3 c 1331 m3 d 3375 m3 e 2197 m3 f 2744 m3 3 a 8 cm b 12 cm
Page 95 1 a 192 cm3 b 105 cm3 c 1440 cm3 d 784 cm3 e 420 cm3 f 216 cm3 2 a 280 cm3 b 300 cm3 c 5 cm d 11 cm
e 4 cm f 810 cm3 3 a 144 cm3 b 420 cm3 c 240 cm3 d 324 cm3 e 352 cm3 f 144 cm3
Page 96 1 a 510 cm3 b 250 cm3 c 504 cm3 d 540 cm3 e 150 cm3 f 1980 cm3 2 a 640 cm3 b 360 m3 c 720 cm3 d 192 cm3
e 1056 m3 3 a 288 m3 b 26 cm c 225 cm3 d 18 m e 23 cm2
Page 97 1 a 1331 cm3 b 1944 cm3 c 870 cm3 d 247.5 cm3 e 1152 cm3 f 1764 cm3 2 a
b 1728 cm3 c 384 cm3 d 2112 cm3 3 a 1296 cm2 b 144 cm2 c 1152 cm2 d 9216 cm3
Page 98 1 a 3000 cm3 2 7 cm 3 a 840 000 mm3 b 840 cm3 4 a 27 cm3 b 810 cm3 c 360 5 8 times 6 8400 cm3 7 60 cm2
8 5600 cm3
Page 99 1 a 50 b 10 253 c 9600 d 18 500 e 8300 f 18 350 g 4000 h 9.863 i 2.384 j 9.35 k 12 780 l 18 800 2 a 9 b 4
c 2.648 d 20 e 6 f 19 g 3 h 15 i 9.53 j 5 k 9875 l 7 685 000 3 a 18 L b 35 kL c 625 mL 4 a 204 000 cm3 b 204 L
5 a 2744 cm3; 2744 mL b 1944 cm3; 1944 mL c 3500 cm3; 3500 mL
Page 100 1 312 L 2 4.8 L 3 19 cm 4 875 mL 5 19.5 L 6 a 2400 cm3 b 19 200 cm3 7 2800 cm2 8 225 cm2 9 50 cm
10 1250 mL 11 4096 cm3 12 220 m2
Page 101 1 C 2 A 3 B 4 B 5 D 6 B 7 C 8 A 9 D 10 C 11 B
Page 102 1 a 150 cm2 b 1.89 m2 (or 18 900 cm2) c 45.5 cm2 d 120 cm2 e 18 m2 f 108 cm2 2 a 12 m3 b 350 cm3 3 343 cm3
4 960 cm3 5 1 000 000 cm3 6 5 L
Chapter 9 – Circles
Page 103 1 a centre b
1
4
3
4
c
1
8
1
3
d arc e
f semicircle g minor segment h major segment i sector j tangent
k secant l circumference 2 a b c d 3 a 9 cm b 24 cm
Page 104 1 a 25.1 cm b 18.8 cm c 37.7 cm d 81.7 cm e 47.1 cm f 100.5 cm g 12.6 cm h 62.8 cm i 56.5 cm
2 a 44 cm b 154 cm c 132 cm 3 a 69.1 km b 179.1 m c 144.5 cm d 295.3 cm e 245.0 mm f 119.4 m
Page 105 1 a 51.4 cm b 40.6 cm c 34.7 cm 2 a 50 cm b 55 cm c 77.5 cm 3 a 96.5 cm b 68.6 cm c 57.1 cm d 40.0 cm
e 35.6 cm f 320.4 cm g 57.1 cm h 50.0 cm i 140.5 cm
Page 106 1 a 28.3 cm2 b 78.5 cm2 c 254.5 cm2 d 132.7 cm2 e 227.0 cm2 f 283.5 cm2 g 201.1 cm2 h 314.2 cm2 i 380.1 cm2
2 a 154 cm2 b 3850 cm2 c 154 cm2 3 a 1963.5 km2 b 10.2 m2 c 1075.2 mm2 d 16 741.5 cm2 e 125 663.7 km2 f 151.7 cm2
Page 107 1 a 88.4 cm2 b 113.5 cm2 c 237.6 cm2 2 a 346.4 cm2 b 1001.0 cm2 c 169.7 cm2 3 a 524.5 cm2 b 300.9 cm2
c 150.8 cm2 d 384.8 cm2 e 105.8 cm2 f 692.1 cm2 g 127.2 cm3 h 140.0 cm2 i 291.1 cm2
Page 108 1 a 69.1 cm b 241.9 cm c 75.4 cm 2 a 254.47 cm2 b 2290.22 cm2 c 153.94 cm2 3 a 40.0 cm b 73.7 cm
c 35.0 cm 4 a 46.54 cm2 b 41.10 cm2 c 202.08 cm2 d 98.17 cm2 e 210.90 cm2 f 289.16 cm2
Page 109 1 175.9 m 2 2463 m2 3 35 cm 4 201.1 cm2 5 3183.1 cm2 6 56.55 cm 7 39.58 m 8 157.1 cm 9 1017.88 cm2
10 615.75 m2 11 1 : 4 12 213.6 cm 13 7.07 m2 14 9.42 m
Page 110 1 C 2 A 3 D 4 A 5 A 6 A 7 B 8 C 9 C 10 B 11 B 12 B
Page 111 1 12 cm 2 a (minor) segment b sector 3 a 131.9 cm b 1385.4 cm2 4 a 12.6 m2 b 12.6 m 5 a 247 cm
b 3619 cm2 6 a 63.6 cm2 b 32.1 cm 7 a 55 cm2 b 201 cm2
186
© Pascal Press ISBN 978 1 74020 033 2
Chapter Answers_2015 updates for future reprint.indd 186
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
12/08/2015 3:15 pm
Answers
Chapter 10 – Linear relationships
Page 112 1 a O b Q c Y d U e H f A g B h C i D j P k N l M m L n X o T p F q R r S s E t W u V v G w K x J
2 a (–6, 1) b (–4, 1) c (1, 1) d (4, 2) e (–3, 2) f (–5, 3) g (–2, 3) h (0, 3) i (2, 3) j (4, 4) k (2, 5) l (–2, 6) m (–6, 5) n (–2, 0)
o (0, 0) p (3, 0) q (1, –5) r (1, –4) s (–3, –4) t (–2, –3) u (–4, –2) v (2, –2) w (5, –2) x (–5, –1) y (–2, –1) z (3, –1)
Page 113 1 a 0, 1, 2, 3 b –2, 0, 2, 4 c –6, –3, 0, 3 d 1, 0, –1, –2 e 0, 1, 2, 3 f –4, –3, –2, –1 2 a –1, 1, 3, 5
b –3, –1, 1, 3 c 1, 3, 5, 7 d 2, 5, 8, 11 e –7, –3, 1, 5 f –5, –2, 1, 4
Page 114
1 a
b
c
x –1 0
1
2
x –1 0
1
2
x –1 0
1
2
y
1
2
3
4
y
–2
y
–1
0
1
y
4
3
2
1
y
y
y = –x + 3
y=x+2
x
2 a
x
2
y
0
2
2
2
1
2
3
y=x–1
b
x
0
y
3
y
1
2
3
3
3
3
y
0
0
0
1
1
1
2
3
1
2
3
y=x
x
b
–1
0
y=3
3 ay=x
y
x
y
x
–1
c
y
x=2
x
x
x
2
y
2
y = –x
y=x+2
x
–1
0
1
2
y
1
2
3
4
y = 2x + 1
x
–1
0
1
2
y
1
0
–1
–2
Their point of intersection
is (0, 0).
y=x
y = –x
x
y
y=x+2
x
–1
0
1
2
y
–1
1
3
5
y = 2x + 1
x
Their point of intersection
is (1, 3)
Answers
© Pascal Press ISBN 978 1 74020 033 2
x
187
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Answers
Page 115 1 a x = 2 b x = 4 c x = 3 d x = 4 e x = 6 f x = 6 2 a y = –2 b y = –8 c y = 6 d y = –3 e y = –3 f y = –3
3 a
b
4 a
y
y
y
x
b
x
0
5
y
5
0
x
c
x
0
3
2
y
–3
0
y
d
b
y
1
1
1
y
–2 –1
0
1
2
y=3
(1, 3)
y=3
x
–2 –1
0
1
2
3
3
3
3
3
x=1
2 a y = 2x – 1
b
x
–1
0
1
2
y
–3
–1
1
3
y
y = –x + 2
x
y
–1
3
3
0
x
0
3
4
y
–1
0
x
x=3
y
x
3
3
3
3
3
y
–2 –1
0
1
2
x=3
2
(3, –2)
y = –2
x
y
y
x
Page 116
1 ax=1
1
3
2
y
x
1
0
x
y
x
x
x
x
–2 –1
y
–2 –2 –2 –2 –2
0
1
y = –2
y = 3x – 1
x
–1
0
1
2
y
–4
–1
2
5
y
y = 3x – 1
y=x–3
0
2
1
1
(1, 1)
2
0
x
y = 2x – 1
Their point of intersection
is (1, 1).
y = –x + 2
x
–1
0
1
2
y
–4
–3
–2
–1
Their point of intersection
is (–1, –4).
x
y=x–3
(–1, –4)
Page 117 1 a (0, 3) c (–4, 6) e (4, 0) f (8, –3) 2 b 2y = 3x c x – 5y = 0 e y = –2x 3 a yes b yes c no d yes e yes f no 4 m = 3
5 a = 5 6 a (0, –2) b (2, 4) c (1, 1) d (5, 13) e (–1, –5) f (–2, –8)
1
Page 118 1 a x = 2 b x = –3 c x = 4 2 a 2 + 1 = 3; 3 = 3 b –3 + 1 = –2; –2 = –2 c 4 + 1 = 5; 5 = 5 3 a x = 3 b x = – 2
c x = 2 d x = 4 4 a x = –1 b x = 1 c x = –2 d x = 2 5 a x = –1 b x = –4 c x = 4 d x = 2
Page 119 1 D 2 A 3 B 4 D 5 A 6 C 7 B 8 C 9 B 10 A 11 B 12 D
188
© Pascal Press ISBN 978 1 74020 033 2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Answers
Page 120 1 a and iii, b and v, c and i, d and ii, e and iv, f and vi 2 a
y
b (–3, 1)
(–3, 1)
–3
•
y=1
x
x = –3
3 ay=x+2
b
x
–3
–2
–1
0
1
2
3
y
–1
0
1
2
3
4
5
y
c –5 d (–2, 0) e (0, 2) f x = –5
x
Chapter 11 – Equations
Page 121 1 a x = 3 b a = 4 c m = 12 d b = 6 e a = 8 f n = 7 g x = 6 h x = 6 i y = 6 j p = 10 k t = 10 l a = 12 m y = –5
n x = –2 o x = 4 2 a m = 8 b x = 10 c y = 12 d n = –12 e x = 11 f x = 18 g m = 4 h y = 21 i a = 2 j m = 10 k n = 16 l a = 15
m y = 2 n t = –2 o a = 6
Page 122 1 a x = 4 b a = 8 c m = 7 d b = 8 e a = 6 f n = 3 g x = 15 h x = 11 i y = 12 j p = 12 k t = 5 l a = 18
m y = –1 n x = –1 o x = 15 2 a m = –5 b x = –2 c y = 5 d n = 6 e x = 22 f x = 9 g m = 15 h y = 39 i a = 8 j m = 15
k n = 31 l a = 8 m y = 0 n t = 3 o a = 4
Page 123 1 a a = 4 b x = 6 c y = 3 d x = 21 e y = 30 f x = –4 g m = –3 h x = 3 i t = –20 j p = –4 k y = –20 l t = 4
m a = 18 n a = 8 o x = –21 2 a x = 30 b x = –12 c x = 42 d a = –60 e a = –18 f b = 72 g m = 36 h x = 27 i y = –28 j a = 6
kb=5 lx=4 mx=7 nx=6 ox=7
Page 124 1 a x = 1 b x = 8 c y = 5 d m = 6 e x = 23 f a = 5 g x = 16 h x = 2 i a = 23 j x = 5 k x = 5 l t = 7
m y = 2 n m = 30 o k = 9 2 a x = 4 b m = 6 c x = 33 d x = 50 e x = 7 f m = 12 g m = 5 h y = 10 i y = –1 j x = 3 k x = 3
l x = 7 m a = 3.1 n a = 1 o p = 0.3
Page 125 1 a x = –21 b x = 4 c t = 11 d m = 5 e m = 6 f a = 12 g y = 5 h x = 5 i y = 6 j x = 8 k a = 4 l p = 7
4
14
3
2 a x = 34 b x = 3 c x = – 3 d y = 17 e x = 2 f x = – 9 g m = 9 h x = 4 4 i y = 6 j m = –3 k x = –12 l y = 7
3
1
Page 126 1 a x = 2 b m = 2 c m = 5 d x = 4 e a = 6 3 f n = 12 g n = 3 h p = 4 i x = 3 j a = 6 k m = 4 l x = 2 2 a a = –32
2
5
3
22
b x = 23 c y = 18 d x = 68 e x = 4 5 f a = – 3 g x = – 2 h a = 21 i a = 13 j a = 0 k a = 15 l a = 14 m a = –57 n a = –96 o a = 23
Page 127 1 a 30 b 75 c 36 2 a 56 b 34 c 26 3 a 5 b 15 c 8 4 a 6 b 12 c 27 5 a 50.3 b 232.5 c 399.0
6 a 54 b 272 c 908.5
Page 128 1 16 2 10 3 14 4 18 5 2 6 15 7 18 8 36 9 5 10 width = 4 cm, length = 9 cm 11 12 cm 12 3 cm 13 52
14 x = 12 15 5
Page 129 1 a x = 36 b a = 24 c y = 42 d m = 30 e m = 28 f x = 54 g a = 11 h x = 12 i x = 5 j x = 6 k x = 10 l m = 22
1
1
1
2 a x = 20 b y = 7 c t = 15 d m = 19 e a = 8 f p = 7 g x = 8 h x = 6 4 i x = 0 j m = 11 k x = 1 l m = 7 2 m x = –3 3
np=5 oa=8
Page 130 1 D 2 C 3 C 4 D 5 C 6 A 7 D 8 A 9 D 10 C 11 A 12 B
Page 131 1 a x = 37 b m = 6 c n = 21 d x = 1152 e x = 4 f a = –4 g x = 32 h x =
1
8
3
1
1
i x = 4 j p = 2 k x = 6 l x = 6 m x = 22
n x = 3 2 2 17
Answers
© Pascal Press ISBN 978 1 74020 033 2
189
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Answers
Chapter 12 – Reasoning in geometry
Page 132 1 a y = 40 b a = 105 c m = 50, n = 130 d k = 120 e m = 70 f m = 40 2 a t = 90 b y = 35 c a = 20
d y = 35 e x = 55 f m = 82, n = 98, p = 98 3 a a = 45 b n = 70 c a = 90
Page 133 1 a a = 120 b m = 60 c n = 104 d y = 50 e x = 25 f n = 105 2 a a = 120, b = 60, y = 60, x = 120
b x = 60, y = 120, m = 120 c a = 70, b = 110, d = 70, c = 110 3 a a = 60 b x = 55 c a = 70 d x = 45, y = 20
e x = 30, y = 40 f a = 30, b = 60
Page 134 1 a a = 95 b a = 20 c x = 45 d x = 65, b = 50 e x = 70, y = 50 f x = 70, y = 70 2 a x = 35,
y = 55 b x = 30, a = 30 c a = 115, m = 35, n = 30 3 a b = 70, a = 60, c = 50 b x = 75, y = 105 c m = 120 d y = 65, x = 115
e b = 50, c = 80, a = 100 f a = 40, b = 55, c = 55
Page 135 1 a x = 52 b x = 50 c y = 60 d a = 55 e x = 20 f a = 60 2 a a = 70 b y = 120 c x = 35 3 a x = 56
b a = 50 c x = 65 d x = 35, y = 55 e a = 35, m = 123 f a = 40, x = 75
Page 136 1 a a = 35 b m = 100, n = 80, p = 100 c a = 50, b = 130 d m = 60, n = 115 e a = 140 f x = 100
2 a x = 45, y = 140, m = 55 b a = 90, b = 145 c m = 70, n = 110, p = 70 3 a a = 203 b a = 36 c m = 90,
p = 110, n = 70 d m = 150, n = 60 e a = 36 f a = 26
Page 137 1 a transformation b translation c
d rotation 2 a translation b
c rotation d
e rotation f translation g rotation h
Page 138 1 a
b same, same c transformation d ABC
DEF 2 a translation b
c rotation
3 a ABC
DEF b PQR
LMN c GHI
JKL
Page 139 1 a same, same b i equal ii equal iii equal c
2 a ABCD and EFGH, ABFE and DCGH, ADHE and BCGF
b PQR and STU 3 A and M, B and F, C and L, D and I, E and G, H and J, K and N 4 a L and P, I and M, J and N, K and O
b LI = PM, IJ = MN, JK = NO, KL = OP
Page 140 1 a sides, angle, two, included angle b sides, three sides c side, hypotenuse, one side and the hypotenuse
d sides, angle, two, angle 2 ABC and ZYX, DEF and AWV, HGI and ATR, JKL and PQR, MNO and SUT
3 a EFD b P = X, R = Z, Q = Y 4 a
b
d
c
5 a ACF and AEB; BGC and FGE; BCE and FEC; CGE and CDE
b RPS and RTQ; PQS and TSQ; PQU and TSU; PQT and TSP
Page 141 1 a i DF ii ABC and DEF iii ABC DEF b i TUS ii PQR and STU iii PQR
STU
2 a EFH = GHF; HEF = FGH b EF = GH; FH = HF; HE = FQ c EFH
GHF 3 a SP = SR; PQ = RQ; QS = QS
b SPQ = SRQ; PSQ = RSQ; PQS = RQS c PQS
RQS
Page 142 1 a three matching sides b two matching sides and the included angle c two matching angles and the matching side
d the hypotenuse and one matching side e
2 a SSS = SSS b RHS = RHS c SAS = SAS d AAS = AAS 3 a AC b yes c RHS
Page 143 1 a a = 60, b = 120, c = 60 b x = 108, y = 108 c a = 90, b = 90, c = 90 2 a a = 55 b a = 50
c x = 92, y = 133 3 a x = 120, y = 30 b a = 55 b = 125, c = 55 c a = 40, b = 80
Page 144 1 a x = 90 b y = 45, 45, 90, 90, 135 c a = 60, 60, 60, 120, 120 d x = 14, 14, 84, 147, 115
e x = 70, 70, 70, 110, 110 f a = 55, 55, 110, 110, 85 2 a = 90, b = 30, c = 60 b a = 65, b = 115, c = 65 c a = 80,
b = 65, c = 35, d = 80, e = 65
Page 145 1 C 2 B 3 C 4 A 5 C 6 B 7 A 8 C 9 A 10 C
Page 146 1 a AB = ED, AC = EC, BC = DC b A = E, B = D, ACB = ECD c ABC
EDC
d SSS or SAS or AAS e
2 a QR = ST, PQ = PT, PR = PS b QPR = SPT, PQR = PTS, PRQ = PST
c PQR
PTS d SSS or SAS or AAS 3 a 30 b 110 c ABD
CDB d AAS e rotation 4 60°
Chapter 13 – Probability
Page 147 1 a certain b likely c impossible d unlikely e impossible f impossible g even chance h impossible
2 a 30% b 100% c 30% d 100% e 0% f 50% g 0% h 70% 3 a unlikely b impossible c certain d most likely e even chance
f most likely g unlikely h unlikely i most likely j certain k unlikely l most likely
Page 148 1 a January, February, March, April, May, June, July, August, September, October, November, December
b red, blue, yellow c A, B, C, D, E, F, G, H d W, X, Y, Z e 1, 4, 9, 16, 25, 36, 49 f A, A, C, E, H, I, M, M, S, T, T
g 26, 27, 28, 29 h spring, summer, autumn, winter 2 a C, C, E, I, I, N, N, O, O, S, S, T, U b 13 c 8 3 a 26 b 7 c 7 d 15
Page 149 1 a no b no c yes d yes e no 2 a A, E, H, I, N, P, S b black, grey c two heads, one head and one tail, two tails
d 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 3 a yes b no c no d no e yes 4 a 14 b 36 c 23 d 0 e 33
1
4
1
1
1
4
d3 e5 f3 6 a7
5
Page 151 1 a 6
Page 150 1 a
1
1
b 2 c 13 d
3
7
5
b6
b
1
7
2
c3
c
3
4
1
1
e 26 f 2 2 a
4
7
1
3
2 2 4
2
7
d0 e
f
d
3
190
© Pascal Press ISBN 978 1 74020 033 2
1
3
2
3
1
3
2
11
1
1
c
3 a6 b2 c
7 a 11 b 11 c
d 11 e 0 f 11
4
499
500
1
b
7
3
4 a2 b0 c1 5
13
32
1
6
4
5
2
3
1
d0 e2 f
1
3
2
4 a5 b
1
3
4
3
3
7
8
4
c 15 d 5 e 0 f 5 5 a 15 b 15 c 15
7 0 8 73% 9 0.995 10 4 in 5
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Answers
Page 152 1 There are 12 students who play both soccer and hockey; 50 students who play soccer or hockey, but not both; 23
students who play neither sport; 62 students who play soccer or hockey or both; and 85 students in Year 8. 2 There are 27 students
who study Japanese; 41 students who study French; 19 students who study neither language; 0 students who study both languages;
and 87 students in Year 8. 3 A = 39 B = 12 C = 23 D = 46 4 a
b 12 c 9 d 21 e 27
C
B E
12 6
9
Page 153 1
7
8
15
1
1
3
2 16 3 a 2 b 2 c 10 d
Page 154 1 a i 54 ii 98 b 200 c
3 a
Boys
29
50
4
5
d
e
4
7
4
5
1
1
1
3
7
6
1
27
Seen the movie
Not seen
Total
185
115
300
Girls
165
85
250
350
200
550
41
7
75 iii 25
33
b 70
Page 155 1 B 2 D 3 B 4 D 5 A 6 D 7 A 8 D 9 B 10 B 11 C 12 C
5
1
b 10 c 25 d i 8 ii 4 2 a
I
F
10 10 15
4
e 49% f 25 g 58 2 a i 2 ii
Total
Page 156 1 a
3
2
1
f 5 g 5 h 0 i 2 j 5 4 a 13 b 26 c 13 5 a 9 b 6
1
4
1
2
b 13 c 0 d 13 e
5
1
3 a tossing a tail with a coin b winning a cricket match 4 a P(E) = 2 b
101
iv 150 b i
49
75
ii
49
82
3
4
1
2
c
Chapter 14 – Statistics
10
2 a Frequency: 9, 7, 9, 6, 8, 11;
cumulative frequency 9, 16, 25, 31, 39, 50 b 6 c 5
d 50 e 25 f 31 g 34
50
h
Frequency (f)
8
6
4
2
6
7
8
Score (x)
9
10
Cumulative Frequency (f)
Page 157 1 a 5 b 9 c 26 d
40
30
20
10
1
2
3
Score (x)
4
5
6
Page 158 1 a census b census c sample 2 a sample b census c sample d sample e census f census 3 a census b sample
c census d sample e census f sample
Page 159 1 a chance b systematic c strata 2 a systematic b random c
3 a systematic b
c
d systematic e random sample
Page 160 1 a In a census the whole population is surveyed, whereas in a sample only part of the population is surveyed.
b Categorical data is data that can be placed in categories or sorted by types. Categorical data cannot be measured. Numerical data
has number values. Calculations can be made with numerical data. c
2 a numerical b numerical
c numerical d categorical e numerical f categorical g numerical h numerical 3 a discrete b continuous c discrete
d discrete e continuous f discrete g continuous h continuous i discrete j continuous k continuous
Page 161 1 a numerical, discrete b categorical c categorical d categorical e numerical, discrete f numerical, continuous
g numerical, continuous h numerical, discrete i categorical j numerical, discrete k categorical l numerical, continuous
m categorical n categorical o numerical, continuous 2 a systematic b
c random d systematic e systematic
3 The meeting may be an English teachers’ meeting, so the views of teachers in other faculties would not be obtained.
4 Year 7, 43; Year 8, 40; Year 9, 42; Year 10, 44; Year 11, 45; Year 12, 36
Answers
© Pascal Press ISBN 978 1 74020 033 2
191
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Answers
Page 162 1 a 5 b 8.8 c 66.5 d 9 e 5 f 20 g 2.625 h 8.2 i 6 2 a 5.9 b 3.9 c 15.3 d 45.9
3 a
x
f
fx mean = 3.375 b x
f
fx mean = 1.95 c x
f
1
5
5
0
11
0
6
3
2
8
16
1
13
13
7
5
3
6
18
2
14
28
8
6
4
9
36
3
12
36
9
7
5
12
60
4
10
40
10
4
Total 40
135
Total 60
117
Total 25
fx
18
35
48
63
40
204
mean = 8.16
4 a 3930 b 12.3 c 91%
Page 163 1 a 15 b 7.5 c 76 d 28 e 116 f 63 2 a 5 b 9 c 3 d 52 e 8 f 5 and 6 3 a cumulative frequency: 3, 9, 17, 24, 29, 33;
mode = 3 median = 3 b cumulative frequency: 12, 31, 49, 64, 74, 87; mode = 6 median = 7 c cumulative frequency: 8, 14, 21, 31, 36;
mode = 19 median = 18 d cumulative frequency: 5, 12, 20, 34, 40 mode = 19 median = 18.5
Page 164 1 a i 95.5 ii 81 iii 96 b Barry was above the average but he did not do well, he was second lowest in the class.
When data includes atypical scores, the median should be used as the measure of ‘the middle’.
2
would be unaffected by the few high prices. 3 a 16.7 b 14 c 16 d The shop owner would sell more of this size and so would need to
stock more of the modal size.
Page 165 1 a 14 b 11 c 18 d 35 e 23 f 64 g 14 h 17 i 9 j 32 k 22 l 46 2 a 5 b 9 3 a 44 b 44 4 a 38 b 77
Page 166 1 C 2 C 3 B 4 C 5 A 6 A 7 D 8 D 9 A
Page 167 1 a It is not random because each student on the bus does not have an equal chance of being selected.
3
b He would need to survey every student. 2 a 15 b 15 c 14.9 d 7 e 8 3 a 75 b 180 4 a 27 b 132
Exam Papers
Page 168 1 D 2 C 3 A 4 B 5 C 6 B 7 B 8 D 9 C 10 C 11 B 12 C
Page 169 1 37 216 2
x
–1
0
1
2
y
–5
–2
1
4
12
3 3.645 L 4 10ab 5 211 6 3000 7 760 kg 8 25 9 2 – 2a 10 24 cm
2
11 105 m 12 432 13 212 14 x = 45 15 120 cm3 16 950 m 17 90º 18 3b(2a – b + 4a2) 19 $7.90 20 312
3
Page 170 1 a i FD ii EFD b 105 cm3 2 a 6a b 10x – 6 c 3(x – 8) 3 a 40 b 150 c 14 d
b 7:51 pm c 11:25 pm 5 a x = 105 b x = 205 c x = 31 6 a
y
26
35
4 a 12:18 pm
b (-1,0)
y=x+1
x
Page 171 1 A 2 B 3 B 4 C 5 B 6 D 7 C 8 C 9 A 10 D 11 B 12 C
7
5
Page 172 1 1635 h 2 9.4 3 8(a – 1) 4 85º 5 288 mm2 6 34 cents 7 x = 2 8 2 20 9 6 10 5x – 6 11 6.43 12 18 cm 13
•
•
14 1 L 15 35.83% 16 $43.30 17 0. 7 18 8 19 $99 20 5.9 kg
•
Page 173 1 a diameter b tangent c minor segment 2 a x = 36 b x = 8 c a = 20 3 a 10 b 11.5 c 6 d 12 4 66. 6 m
5 a x = 2.5 m b y = 2.5 cm 6 440 m 7 10 cm
192
© Pascal Press ISBN 978 1 74020 033 2
5
2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Answers
Page 174 1 C 2 B 3 C 4 D 5 B 6 D 7 D 8 C 9 A 10 D 11 C 12 B
1
1
Page 175 1 0.2! 2 $62.50 3 x = 10 4 37 2 % 5 5.5 km 6 7x + 8y 7 41.2 8 5x + 1 9 3m(3 – m) 10 150º 11 0.375 12 6
13 alternate angles 14 107 15 9 cm 16 x = 6 17 200 minutes 18 5 hours 19 $204.30 20 88.4 cm2
Page 176 1 a 90 cm2 b 80 cm2 c 461.8 cm2 2 600 cm3 3 a
b 79 4 a –7, –5, –3, –1, 1, 3, 5
S
A
24 16 39
y
b
c –1 d x = 4 5 a AC = AB, CM = BM, AM = AM b
ACM
ABM
x
y = 2x – 1
Page 177 1 C 2 B 3 C 4 C 5 C 6 B 7 B 8 D 9 C 10 C 11 D 12 C
7
21
1
Page 178 1 $684 2 12 3 3500 4 (1, 2) 5 25 6 1 7 408 m 8 150 m 9 3 10 1400 g 11 42° 12 8 h 20 min
13 962 cm2 14 2(4m – 5) 15 25 cm2 16 6 cm 17 –3x2 + 5x 18 132 cm 19 43.6 20 x = 59
Page 179 1 a x = 34 (angles in a straight line) b a = 52 (cointerior angles) c x = 31° (angle sum of a quadrilateral)
2 a 87.5 cm2 b 142.5 cm2 3 157 728 mm3 4 a AB = CD, AD = CB, BD = DB b A = C, ABD = CDB, ADB = CBD
c ABD
CDB
Page 180 5 a 6 b 7 c 7 d 6.44 6 a y = 13.5 b a = 42 7 a x = 60 b x = 20 c x = 75
Answers
© Pascal Press ISBN 978 1 74020 033 2
193
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Notes
© Pascal Press ISBN 978 1 74020 033 2
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Topic Test Feedback Chart
Percentage Score
Your score
x 100%)
(
Marks available
Your Score
(Part A + Part B)
Chapter Topic Test
1
Basic arithmetic
and the calculator
+
=
2
Percentages
+
=
3
Four operations
with integers
+
=
4
Indices
+
=
5
Rational numbers
+
=
6
Basic algebra
+
=
7
Length, mass and
time
+
=
8
Area, volume and
capacity
+
=
9
Circles
+
=
10
Linear
relationships
+
=
11
Equations
+
=
12
Reasoning in
geometry
+
=
13
Probability
+
=
14
Statistics
+
=
27
27
27
27
27
27
27
23
25
27
27
25
27
20
x 100% =
%
x 100% =
%
x 100% =
%
x 100% =
%
x 100% =
%
x 100% =
%
x 100% =
%
x 100% =
%
x 100% =
%
x 100% =
%
x 100% =
%
x 100% =
%
x 100% =
%
x 100% =
%
Exam Paper Feedback Chart
Exam
Paper
Percentage Score
Your score
x 100%)
(
Marks available
Your Score
(Part A + Part B + Part C)
1
+
+
=
50
x 100% =
%
2
+
+
=
47
x 100% =
%
3
+
+
=
44
x 100% =
%
4
+
+
=
50
x 100% =
%
© Pascal Press ISBN 978 1 74020 033 2
Excel Essential Skills Mathematics Revision & Exam Workbook Year 8
Excel
Excel
Get the Results You Want!
Year 8 Mathematics
Revision & Exam Workbook
This is a revised and extended edition with over fifty extra pages of work for students to complete.
In this book you will find:
Topics covering the complete Year 8 Australian Curriculum Mathematics course
Over 170 pages of practice exercises
Fourteen topic tests
Four practice exams
E S S E N TI AL S KIL L S
This book is suitable for students of all abilities studying
Year 8 Mathematics. It has been specifically written to help
students revise their work and succeed in all their class tests,
half-yearly and yearly exams.
Answers to all questions
AS Kalra is the author of many successful Mathematics books, including the Excel Essential Skills
Mathematics Revision & Exam Workbook series for Years 7–10 (eight titles), and Excel Essential
Skills The Complete Fractions Workbook Year 7.
Your own checklist for Excel books for Year 8 students:
Bookseller reference
Books
Level
✓
English books:
978-1-74125-411-2
Excel Essential Skills Grammar and Punctuation Workbook
Years 7–8
978-1-74125-408-2
Excel Essential Skills Reading and Vocabulary Workbook
Years 7–8
978-1-74125-414-3
Excel Essential Skills Writing and Spelling Workbook
Years 7–8
978-1-74020-037-0
Excel Essential Skills English Workbook
Year 8
Mathematics books:
978-1-74020-040-3
Excel Essential Skills Step-by-Step Algebra 1 Workbook
Years 7– 8
978-1-74020-316-6
Excel Essential Skills Mathematics Extension Revision & Exam Workbook
Year 8
978-1-74125-435-8
Excel Essential Skills Problem Solving Workbook
Year 8
978-1-74125-474-7
Excel SmartStudy Mathematics
Year 8
978-1-74125-007-7
Excel Mathematics Study Guide
Year 8
978-1-74020-041-7
Excel Essential Skills Step-by-Step Algebra 2 Workbook
Years 8 –10
Science books:
978-1-74125-421-1
Excel SmartStudy Science
Year 8
978-1-74125-392-4
Excel Science Study Guide
Year 8
Year 8 Mathematics Revision & Exam Workbook AS Kalra
About the author
YEAR
8
Mathematics
Revision & Exam
Workbook
Updated Edition for the
Australian Curriculum
Over 100 Units of Work
Fourteen Topic Tests and
four Exams
Get the Results You Want!
ISBN 978-1-74020-033-2
Visit our website for more information at www.pascalpress.com.au
Our address is Pascal Press PO Box 250 Glebe NSW 2037 (02) 8585 4044
9781740200332_ESS Maths RandE WB Yr8 2015 spine 11mm.indd All Pages
9 781740 200332
AS Kalra
8/07/15 12:15 PM