# collins review

```Cambridge Lower Secondary
Maths
STAGE 8: STUDENT’S BOOK
REVIEW UNITS
All the questions and answers in this material have been written by the authors.
This material has not been through the Cambridge International endorsement process.
Review units
Review 1A Chapters 1–4
Chapter 1 Negative numbers
1
Problem solving
Ramesh has these number cards.
–4
–9
8
–8
5
Show how Ramesh can use his cards to complete these number statements.
+
a)
2
=1
b)
–
=1
Find the missing number in each statement.
a) 9 &times; –3 = …………
b) –66 &divide; –6 = …………
c) 60 &divide; ………… = –15
d) 3 &times; –2 = ………… &divide; 4
Chapter 2 Place value and rounding
1
Here are four powers of 10.
104
107
106
103
Use these powers of 10 each exactly once to complete these sentences.
………….. is equal to ten thousand
………….. is greater than one million
………….. is smaller than ……………
2
3
Work out
a) 250 &times; 0.01
b) 0.042 &divide; 0.1
c) 450 &divide; 0.01
d) 0.32 &times; 0.1
e) 5.6 &times; 0.01
f) 1.9 &divide; 0.1
Use these numbers to complete these number statements. Use each number exactly once.
0.045
0.54
0.0554
0.102
…………. &lt; 0.12
0.036 &lt; …………. &lt; …………. &lt; 0.06
0.504 ≠ …………..
Online resources
1
4
Round each number to the accuracy shown.
a) 457 476 to the nearest thousand
b) 10.104 to the nearest whole number
c) 2.154 to 1 decimal place
d) 0.3476 to 2 decimal places
Chapter 3 Fractions, decimals and percentages
1
Maria has some money.
She spends
44% of her money on a coat
22.5% of her money on some shoes
3
200
of her money on some socks.
a) Write 44% as a fraction in its simplest form.
b) Write 22.5% as a decimal.
c) Write
2
as a percentage.
Use division to convert these fractions to recurring decimals.
a)
3
3
200
8
9
b)
2
15
c)
1
18
Write each set of fractions in order of size starting with the smallest.
a)
2
3
17
27
5
9 b)
3
16
1
6
5
24
Chapter 4 Mental methods
1
2
Given that 21 &times; 28 = 588, work out:
a) 21 &times; 14 ………..
b) 42 &times; 28 ………..
c) 22 &times; 28 ………..
d) 588 &divide; 21 ………..
Decide if these statements are true or false.
a)
3
2
13
25
= 0.56 b) 1.3 = 103% c) 2 54 = 280%
Use the numbers
statements:
1
1
1000 , 10 ,
180, 1000 and 10 000 each exactly once to complete these
a) 1 kg = ……….. g
b) 1 mm = ………. cm
d) 1 millilitre = ………….. litre
e) half turn = ………… &deg;
Stage 8: Review units
c) 1 m2 = ……….. cm2
Review 1B Chapters 5–8
Chapter 5 Expressions
1
Here are four cards.
A
Perimeter 2a 2b
C
3m n 1
B
3x x 12
n
D
2n 1
a) Which card shows a function?
b) Which card shows a formula?
c) Which card shows an equation?
2
Simplify each of these expressions using powers.
a) t &times; t &times; t b) t &times; t &times; t &times; t &times; t c) 6 &times; t &times; t
3
Write down if each statement is true or false. Correct any statement which is false.
a) 3n − 8m + 1 − n + 5m = 2n + 13m +1 b) 6n &times; 4n = 24n2 c) 4t (2t+ 3) = 6t2 + 7t
4
Noor has n dollars.
Omar has 6 dollars less than Noor.
Preema has 4 times as much money as Omar.
Write down an expression in terms of n for the amount of money that
a) Preema has b) the three people have in total.
Chapter 6 Sequences and functions
1
Find the position-to-term rule and the 40th term for each of these sequences.
a) 9, 15, 21, 27, …. b) –2, 3, 8, 13, …
c) The sequence with first term 14 and term-to-term rule ‘add 3’.
2
These three patterns are made from circular tiles. They are the first three terms in a
&shy;sequence of patterns.
Pattern 1
Pattern 2
Pattern 3
Online resources
3
a) Draw Pattern 4 in this sequence.
b) Find the position-to-term rule to find the number of counters needed to make any
pattern.
c) Find the number of counters needed to make Pattern 20.
d) Ollie has 30 counters. What is the largest pattern in this sequence he can make?
3
a) Here is a function.
x  2x − 9 .
Complete this number machine to match the function.
x
……
……
2x 9
b) Here is a number machine.
5
2
Complete this function to match the number machine.
x  ……….
Chapter 7 Shapes
1
These two triangles are congruent.
3.2 cm
c
129&deg;
4 cm
b cm
6.5 cm
29&deg;
a cm
4 cm
Not to scale
Write down the values of a, b and c.
2
Which of these triangles has a hypotenuse measuring 20 cm?
16 cm
15 cm
25 cm
12 cm
20 cm
4 cm
7.5 cm
20 cm
Triangle A
8.5 cm
Triangle B
Triangle C
Not to scale
4
Stage 8: Review units
3
Problem solving
a) The diagonals of a quadrilateral measure 5 cm and 6 cm.
The acute angle between the diagonals is 80&deg;.
Samira says that the quadrilateral could be a rectangle.
Explain how you can tell that she is wrong.
b) The diagonals of a different quadrilateral both measure 11 cm.
The diagonals meet at right angles.
Tom says the quadrilateral must be a square.
4
Decide if these statements are true or false.
Diagram
Statement
The two shaded angles are alternate angles.
The two shaded angles are corresponding angles.
The two shaded angles are equal.
Chapter 8 Midpoints
1
Find the midpoint of the line segment joining these points.
a) (3, 2) and (11, 20)
b) (–3, 11) and (9, 2)
c) (–5, 9) and (1, –3)
d) (0, 5) and (–7, –10)
Online resources
5
Review 1C Chapters 9–12
Chapter 9 Scale drawing and measures
1
Ella makes a scale drawing of her bedroom. She uses a scale of 1:50.
a) If her bed is 2m long, how long will it be on her scale drawing?
b) She calculates that the width of her bedroom will need to be 12 cm. How wide is her
bedroom?
2
3
Match the object to the units that would be used to measure it:
Length of a car
m2
Area of a football pitch
cm2
Volume of a swimming pool
km2
Area of a piece of paper
m3
Volume of a box of chocolates
m
Area of a forest
cm3
Some people take part in a race.
a) The race is 8 laps of a track that is 400m metres long. How many kilometres is the race?
b) Rosa has 5 litres of water. She pours it into cups to give to the people in the race. If
each cup can hold 180 ml of water, how many complete cups can she fill?
Chapter 10 Data collection
1
Josi wants to find out if older students exercise more than younger students at her school.
a) Which two of the following would it be most useful to collect data about
The age
of the
student
The name
of the
student
The number of hours
the student exercises
each week
The football
team the student
supports
b) Josi decides to write a questionnaire and hand it out in the school sports clubs.
Give one disadvantage of this approach.
2
Sayed is collecting data about the books in a library. Decide if each of the following
types of data are discrete or continuous:
The number of words in the title
The number of pages in each book
The width of each book
The mass of each book
6
Stage 8: Review units
3
Barry does an experiment to find out how long (in minutes) it takes students to solve
some mathematical problems. His results are:
5 min
4 min
8 min
6 min
12 min
3 min
6 min
9 min
5 min
7 min
15 min
11 min
14 min
19 min
7 min
5 min
9 min
9 min
18 min
11 min
a) Copy and complete the frequency table
for this data, filling in the missing class
interval as well as the data.
b) What is the modal class?
c) How many students had a time of more
than 10 minutes?
4
Time (minutes)
0&lt;t≤5
5 &lt; t ≤ 10
Tally
Frequency
15 &lt; t ≤ 20
Total
The two-way table gives information about the number of left handed and right
&shy;handed students in two classes. Fill in the missing numbers
Boys
Girls
Total
Right Handed
16
34
Left Handed
9
16
Total
23
27
a) How many students were asked altogether?
b) How many boys are left handed?
c) What fraction of the girls are right handed?
1
Pete has an apple tree in his garden. He weighed some of the apples he picked from the
tree. Here are his results to the nearest gram.
86 g 78 g 80 g 86 g 111 g 93 g 92 g 99 g 94 g 94 g 100 g 91 g
88 g 103 g
What is
94 g
a) the mode b) the median c) the mean d) the range?
d) Which average would he use if he wanted to show off how big his apples are?
Chapter 12 Probability
1
If the probability that Ernest will get homework tomorrow is 35%, what is the probability
that Ernest will not get homework?
2
If you pick a letter at random from the word MATHEMATICAL what is the probability
that you will choose:
a) A vowel
b) A letter that is not a vowel (a consonant)
c) The letter M
d) A letter that is also in the word TEAM
Online resources
7
Review 2A Chapters 13–17
Chapter 13 Types of number
1
Decide if these statements are true or false
a) 1 is a prime number
b) A list of all the factors of 76 is 1, 2, 4, 19, 38, 76
c) The highest common factor of 54 and 72 is 4
d) 112 is a common multiple of 8, 14 and 18
e) The lowest common multiple of 2 &times; 3 &times; 5 and 2 &times; 3 &times; 7 is 210
2
3
Write each number as a product of its prime factors
a) 68
b) 130
c) 270
d) 504
Match each expression in the left-hand column with its answer in the right-hand column
182 − 172 −
12
225
3
400 − 2 11
6 + 132 − 3 1
20
256 − 3 12 + 113
18
Chapter 14 Fractions
1
Ivan has written these fractions.
2 23 1
2 7
8 11
12
3 34
Using these fractions, each exactly once, to complete the following calculations:
a) __ −
c)
2
19
9
1
5
3
=
− __ =
2
5
=
17 &times; 2
5
b) 1 41 &times; 19 =
c) 19 &divide;
8
43
1
3
=
29
= 1__
d) 3__ − __ 23 + 2 56 = __ = __
= 1__
Correct the errors in these calculations
a) 17 &times;
3
b) __ +
7
4
=
6
4
=
36
5
= 7 54
&times; 19 =
26 &times; 7
4
=
6 &times; 19
4
104
7
=
95
5
= 23 24
= 13 67
Work out
a) 4% of 3200 kg
b) 32% of \$1400
c) 61% of 4300 ml
d) 93% of 1250 cm
Stage 8: Review units
4
Tom wrote down these values
250 m \$7500 973 litres 165.5 cm
Find the answers to Tom’s calculations
5
6
a) 250 m increased by 3%
b) 973 litres decreased by 8%
c) \$7500 increased by 45%
d) 165.5 cm decreased by 84%
Match the proportion on the left with an equivalent value on the right
15 out of 165
1
9
27 minutes out of 3 hours
0.125
56 apples out of 504 apples
15%
0.66 cm out of 528m
1
11
Write each set in order of size, starting with the largest
7
8
26 out of 32
83.2%
0.8751
b) 38 minutes out of 1.5 hours
25.3%
65
250
0.294
c) 65.25%
99 cm out of 1.5 m
224
350
0.6552
a)
Chapter 15 Using known facts
1
2
Decide if these statements are true or false
a) 6 &times; 0.9 = 54
b) 0.008 &times; 4 = 0.032
d) 0.0065 &divide; 5 = 0.013
e) 0.0006 &times; 7 = 0.042
c) 7.2 &divide; 9 = 0.8
Work out
a)
1
12
of 84000
c) 4% of 400
b)
5
9
of 63
d) 55% of 8000
Chapter 16 Solving word problems mentally
1
Using each direct proportion, complete the statements
a) 40 pencils cost \$6.
___ pencils cost \$15.
b) Mohammed is paid \$54 for 9 hours work.
If Mohammed works 31.5 hours he earns ___.
c) Peter can walk 3km in 15 minutes.
In 105 minutes Peter can walk ___.
d) The mass of 4 magazines is 560g.
2.52kg is the mass of ___ magazines.
Online resources
9
Chapter 17 Decimals
1
Work out
a) 35 742 + 84 928
b) 584 294 − 2945 + 211 411
c) 98.42 − 39.548
d) 13.28 − 7.9105 + 4.801
e) 56 543.2 + 456.701 − 4537.28
2
47.4 0.1 0.006 0.66
Using these calculations, write down the non-calculator methods used to find the answers.
0.92 &divide; 7 0.0453 &divide; 8 284.4 &divide; 6 5.943 &divide; 9
Review 2B Chapters 18–21
Chapter 18 Formulae
1
a) Write a formula for the perimeter, P, of this shape.
2a
Use your formula to calculate the perimeter of the shape
when a = 4,
b
b = 2 and c = 2
3b
b) Pierre charges a fixed fee of \$24 + \$25 per hour for each
electrical item he repairs.
3b
Write a formula for the total cost C for a repair that takes h hours.
Use your formula to find the total cost of a repair lasting 4 hours.
c
c
c
2
F = 1.8 + 32C is the formula for converting temperatures given in degrees Celsius (&deg;C), C,
to degrees Fahrenheit (&deg;F), F.
Use the formula to convert the following temperatures from &deg;C into &deg;F.
a) 8&deg;C
3
b) 12&deg;C
c) 45&deg;C
d) 68&deg;C
Using a = 2, b = 3 and c = –4, find the value of v for these formulae
a) v = a + b2 − 3 b) v = 15 − b2 + c2 c) v = a3 + c d) v = 4a2 − 2b + c
10
Stage 8: Review units
Chapter 19 Straight-line graphs
1
a) Match the equation on the left with the correct table of values on the right.
y=x−2
x
y
–2
–1
–1
1
0
3
1
5
y = 2x + 3
x
y
0
2
1
2.5
2
3
3
3.5
y = 4 − 3x
x
y
–2
–4
0
–2
2
0
4
2
1
2
x
y
–4
16
–3
13
–2
10
–1
7
y= x+2
b) Using the correct table of values from question 4, draw the graphs of
y = 2x + 3
2
1
2
y= x+2
y = 4 − 3x
Decide if these statements are true or false
a) The graph of y = 4x is not a straight line
b) Alan draws a curve. He says that the equation of the curve cannot be 2x − 3 = 7.
c) The graph of y = x pass through the point (0, 0)
d) On a set of axes, the co-ordinates (–1, 1) and (0, 3) lie on the line y = 5x
e) The graphs of equations of the form y = mx + c are always straight lines
Chapter 20 Nets and constructions
1 Draw a sketch of the net of each of these shapes.
a)
2
b)
c)
Construct on plain paper
a) The perpendicular bisector of a line segment 8 cm long. Mark the midpoint with the
letter P.
b) The perpendicular bisector of a line segment 6.5 cm long. Mark the midpoint with
the letter Q.
c) The angle bisector of 56&deg;.
d) The angle bisector of 125&deg;.
Online resources
11
Chapter 21 Symmetry and transformations
1
Complete these sentences
a) A square has ___ lines of symmetry.
b) An isosceles triangle has ___ rotational symmetry.
c) A regular hexagon has rotational symmetry of order ___.
d) A parallelogram ___ lines of symmetry.
2
Peter has drawn a translation, reflection and rotation. However, each transformation
has errors. Redraw each one so that it is correct.
Mirror line
Review 2C Chapters 22–25
Chapter 22 Imperial units of measurement
1
Max and Olga are discussing the distance between Moscow and St. Petersburg. Max says
it is 450 miles and Olga says that it’s 688 km.
a) How many miles is 688 km?
b) The actual distance between Moscow and St. Petersburg is 705 km. Whose estimate
Chapter 23 Area, surface area and volume
1
Calculate the areas of the following shapes:
b)
a)
5 cm
5 cm
5
5 cm
cm
8 cm
88 cm
cm
c)
5 cm
5 cm
5 cm
3 cm
3 cm
3 cm
8 cm
d)
9 cm
9 cm
9 cm
5 cm
5 cm
5 cm
9 cm
5 cm
7 cm
7 cm
7 cm
3 cm
3 3cm
cm
Stage 8: Review units
3 cm
3 cm
3 cm
3 cm
7 cm
7 cm
7 cm
7 cm
12
5 cm
5 cm
5 cm
12 cm
12 cm
12
12cm
cm
5 cm
3 cm
4 cm
4 cm
4 4cm
cm
3 cm
7 cm
5 cm
2
Dariya has a cuboid with a length of 6 cm and width of 5 cm.
The volume is 120 cm3.
a) What is the height of the cuboid?
b) What is the surface area of the cuboid?
3
5 cm
6 cm
Here are the nets of two shapes. What is the surface area of each shape?
a)
b)
5 cm
8 cm
6 cm
4 cm
6 cm
5 cm
5 cm
12 cm
Chapter 24 Displaying and interpreting data
1
Jessica measures the thickness of 60 books and gets the result shown in the table below.
Thickness, t (mm)
0≤t&lt;5
5 ≤ t &lt; 10
10 ≤ t &lt; 15
15 ≤ t &lt; 20
20 ≤ t &lt; 25
25 ≤ t &lt; 30
Frequency
5
8
15
17
10
5
60
Draw a frequency diagram to illustrate this data
2
The table and pie chart below show the same data about the favourite sports of 60 people.
Sport
Swimming
Football
Frequency
11
28
Favourite sports of 60 people
168&ordm;
84&ordm;
Tennis
Total
Angle
60
42&ordm;
360&ordm;
Complete the table and the pie chart.
Football
Online resources
13
3
The stem and leaf diagram below shows the heights of 25 statues in a city to the nearest
10 cm.
Stem
1
2
3
4
5
Leaf
7
1
0
0
6
9
4
2
0
7
5 8 8
3 6 6 6 6 9
1 4 5 6 8
9
Key 1| 7 represents 1.7 metres
a) What is the height of the tallest statue?
b) What is the median height of the statues?
c) What the range of the heights of the statues?
4
The frequency diagram below shows time taken for
students to travel to school on a particular day.
Time taken for students
to travel to school
70
a) How many students took part in the survey?
60
b) How many students took more that 30 minutes
to travel to school?
50
Frequency
c) What percentage of students can get to school
in less than 20 minutes?
40
30
20
10
0
0
5
10
20
30
40
Travel time (minutes)
50
Rory collects data on the number of songs on 10 albums recorded by each of two rock
bands.
Median
Mean
Range
Band A
18.5
19.6
5
Band B
18
18.4
8
a) Compare the average number of songs on albums by the two bands.
b) Which band is more consistent in the number of songs on their albums? How do you
know?
14
Stage 8: Review units
Chapter 25 Mutually exclusive outcomes
1
A group of students are on an activity holiday. On a particular day they have the choice
of the following activities. They must choose one morning activity and one afternoon
activity.
Morning
Afternoon:
• Horse Riding (HR)
• Swimming (Sw)
• Climbing (C)
• Kayaking (K)
• Archery (A)
• Sailing (Sa)
List all the possible combinations of activities that they could choose.
Review 3A Chapters 26–29
Chapter 26 Calculations
1
2
Write each set in order of size, starting with the smallest
a) 43 − 49
( − 5)3
13.322
b) 105
33 − 3 −27
5&times;5&times;5&times;5
144
c) 3 &times; 3 &times; 4 &times; 5 &times; 5
36
(–8)2
52 − 3 216
9
Work out
a) 3 + 3 &times; 4 − 5
b) (4 − 3 + 7) &times; 4
d) 33 &divide; 2 &times; 1.5 − 23
e) 2.8 + 145 &divide; 5 − 5 &times; 5
c) 54 &divide; (6 &times; 3) + 42
Chapter 27 Ratio and proportions
1
San has written these numbers
3 1.6 16 750 3 4
Use the numbers to complete these statements
2
a) 64 : __ = 4 : 1
b) 150 : 450 = 1 :__
c) 600 g : 150 g : __ g = __ : 1: 5
d) __ l : 4000 ml : 2.4 l = 2 : 5 : __
Red, green and blue paint are mixed in the ratio 5:3:4. Sanjit uses the three colours to
create 4500ml of the paint.
Sanjit uses this method to find how much he needs of each colour.
Find and correct the errors in his method.
4500 &divide; 10 = 375
Red = 5 &times; 375 = 2625 ml
Green = 4 &times; 375 = 1125 ml
Blue = 4 &times; 370 = 1500 ml
Online resources
15
3
a) 8 tins of meat cost \$6.80
Find the cost of 14 tins of meat.
b) Pierre mixes butter, sugar and flour in the ratio 2 : 1 : 3. He uses 130g of butter.
How much sugar and flour does Sanjit use in the mixture?
Chapter 28 Mental calculations with fractions and integers
1
Work out
a) 30 &times;
d)
2
1
4
&times;
b)
1
6
3
5
2
6
&times; 90
e) 4 &divide;
1
5
c)
1
2
&times;
1
5
f) 2 &divide;
1
5
Match the calculation on the left with the correct answer on the right
9 + 2050 + 951 + 650
5
7
&times;
( 81 + 43 )
8
5
&times;
1
4
21 &times;
+5−
1
4
2
5
&divide;2
Chapter 29 Calculations with decimals
1
Decide if these statements are true or false
a) 25.2 &times; 0.7 = 176.4
b) 0.06 &times; 2.88 = 0.1728
c) 0.024 g &divide; 0.03 g = 0.0008 g
d) 99.045 &times; 0.04 = 3.9618
e) \$38.42 &divide; 0.17 = 226
Review 3B Chapters 30–32
Chapter 30 Equations
1
For each problem, construct an equation to solve it.
a) Peter’s age is 7. When you multiply Ann’s age by 5 and subtract the result from 45
you get Peter’s age.
Find Ann’s age.
b) The area of a rectangle is 28 cm2. The length of the rectangle is
(3x − 4)cm and the width of the rectangle is 8 cm.
What is the value of x?
16
Stage 8: Review units
c) Tim thinks of a number. He multiples it by 14 then adds 2.
Pierre thinks of the same number. He multiples it by 2 and then subtracts the result
from 4. He gets the same answer as Tim.
What is the number Tim and Pierre had chosen?
d) The lengths of two adjacent sides of a square are 2(x − 4) and 7(3 + 2x).
Find the value of x.
Chapter 31 nth term of sequences
1
Write an expression for the number of squares in Pattern n of each sequence.
a)
Pattern 1
Pattern 3
Pattern 2
b)
Pattern 1
Pattern 2
Pattern 3
c)
Pattern 1
Pattern 2
Pattern 3
d)
Pattern 1
Pattern 2
Pattern 3
Online resources
17
Chapter 32 Geometrical reasoning and proof
1
Dot has written three geometrical proofs but each of them contains errors.
Correct each proof.
a) A proof to show that the sum of the angles in the
triangle is 180&ordm;
d&deg; c&deg;
e&deg;
a = d because of corresponding angles
b = c because of alternate angles
a&deg;
The sum of the angles in the triangle
b&deg;
=a+b+c
=d+c+c
= 180&ordm;
b) A proof to show that the sum of the angles in the
q&deg;
The sum of the angles in the quadrilateral is:
c&deg; r&deg;
=p+q+r+s
d&deg;
= (a + d) + q + (d + s) + c
a&deg;
=a+q+d+b+s+c
p&deg;
b&deg;
s&deg;
= 180&ordm; + 170&ordm;
= 360&ordm;
c) A proof to show that the exterior angle of a triangle is equal to the sum of the two
interior opposite angles.
c = 170 − a − b
b&deg;
d = 190 − c
c&deg;
d = 190 − (170 − a − b)
d = 190 − 170 + c + b
d=a+b
18
Stage 8: Review units
a&deg;
d&deg;
2
Find the size of each of the lettered angles marked below, stating the geometrical
reason for each step of your working out.
b)
a)
95&deg;
27&deg;
s
p
40&deg;
r
q
c)
d)
35&deg;
75&deg;
105&deg;
45&deg;
s
t
65&deg;
a
80&deg;
85&deg;
Review 3C Chapters 33–36
Chapter 33 Circles
1
Using plain paper
a) Draw a circle with radius 4cm.
b) Construct a triangle with sides measuring 7.4 cm, 6.5 cm, 4.9 cm
c) Construct a triangle PQR with PQR = 90˚, QR = 4.7 cm, PR = 7.2 cm
2
Liam wrote down these names for the parts of a circle
segment
chord
diameter
sector arc
semicircle
circumference
Using words from Liam’s list, add labels to this circle.
Online resources
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3
Work out, correct to 1 decimal place
a) The circumference of a circle with radius = 4.8 cm
b) The area of a circle with diameter = 52 mm
c) The circumference and area of a circle with radius = 0.85 cm
d) The area of the shaded part of this diagram
5 cm
5 cm
2.5 cm
4
Andrew drew these two pie charts comparing the transport used by students to get to
school.
Car
Walk
Bus
Cycle
200 students
300 students
a) Which school has about a quarter of its students cycling to school.
b) Just over half of the students at Silverstone Academy walk to school. About what
proportion of students walk to school at Benbridge Academy?
c) Compare the proportion of students in each school who use a car.
d) Andrew says that the same number of students, at each school, use the bus. Explain
why he is incorrect.
20
Stage 8: Review units
Chapter 34 Enlargement
1
Three shapes are drawn onto cm squared paper.
A
B
C
a) Pierre says that shape B is an enlargement of shape A by a scale factor of 2. Explain
why he is incorrect.
b) Copy shape A on to cm squared paper.
Enlarge shape A by a scale factor of 2.
c) What is the scale factor of the enlargement which maps shape A onto shape C?
2
Copy each shape onto cm squared paper.
Enlarge each shape by the given scale factor from the centre of enlargement O.
b)
a)
c)
O
O
O
Scale factor 2
O
O
O
O
O
Scale factor
3 factor 2
Scale factor
2 factor
Scale factor
2 factor
Scale
3 factor
Scale
Scale
3
Scale
2
O
Scale factor 2
Online resources
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Chapter 35 Real-life graphs
1
Claire drives from Town A to Town B, a journey of 300 km. She stops twice on the journey.
300
Distance (km)
250
200
150
100
50
0
13:00
14:00
15:00
Time
16:00
17:00
a) How long does Claire stop altogether during the journey?
b) What is the distance between the first and second stops?
c) Claire arrives at Town B at 17:00. Complete the distance-time graph for her journey.
d) Which part of the journey did Claire drive slower? Give a reason for your answer.
2
A student cycles from Town A to Town B.
Another student runs for 10km away from Town B
20
Distance (km)
Town A
Runner
10
Cyclist
0
Town B
14:00
14:30
15:00
Time
a) What is the distance between Town A and Town B?
b) At what time did the two students pass each other?
c) Explain why the cyclist travels at a faster speed?
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Stage 8: Review units
Chapter 36 Experimental probability
1
Sanjit throws a fair die 100 times. He obtains the following results
Number
Number of times thrown
1
25
2
5
3
25
4
15
5
20
6
10
Alan throws the same die 250 times. He obtains the following results.
Number
Number of times thrown
1
40
2
30
3
35
4
45
5
50
6
50
a) For Sanjit’s experiment, calculate the experimental probability of throwing a 6.
b) For Alan’s experiment, calculate the experimental probability of throwing a 3.
c) What is the theoretical probability of throwing any number on a fair die? Give a