YEAR
8
Mathematics
Revision & Exam
Workbook
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AS Kalra
Chapter 9
Circles
UNIT 1: Parts of circles
Question 1
a
Name the part of the circle indicated.
b c
O
d e f
a lo n g thlo n
a g
nc e
s
t
a
s
st
j
k l
Di
c e a lo n g th e
Di
an
bo
st
e
a ry
un d
bo
a ry
un d
b o d a ry
un
b o d a ry
un
Di
Di
Di
h i s ta a nctaenacleo nngec teh ea ltoh en g th
bo
g
un d
a ry
Question 2
Find the fraction of the circle given in the following diagrams.
abcd
120°
45°
© Pascal Press ISBN 978 1 74020 033 2
270°
Question 3
a
If the diameter of a circle is b If the radius of a circle is 12 cm, what is
18 cm, find its radius. its diameter?
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
103
Circles
UNIT 2: Circumference of circles
Question 1
a
Calculate the circumference of the following circles correct to one decimal place.
b
c
4 cm
6c
m
3
cm
d e f
32
cm
cm
cm
h i
10
cm
2
g
15
26 cm
© Pascal Press ISBN 978 1 74020 033 2
a
22
y using
B
as the value of π, find the approximate length of the circumference for
7
these circles.
b
7
cm
Question 3
a
9
cm
Question 2
c
m
49 c
21 cm
Find, to one decimal place, the circumference of a circle with:
radius 11 km
b diameter 57 m
d diameter 94 cm
104
e
diameter 78 mm
c
radius 23 cm
f
radius 19 m
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
12 cm
12 cm
14 cm
12 cm
14 cm
Circles
12 cm
20 cm
14 cm
20 cm
UNIT 3: Applications
of circumference
14 cm
20 cm
12 cm
20 cm
20
cm
12
cm
Calculate
the total perimeter
14 of
cm the following semicircles correct to one decimal place.
cm
15.814cm
20.7 cm 20 cm
21 cm
12
cm
b
c
1520
cmcm
14
17cm
15.8 cm
20.7
cm
13.5 cm
cm
15.8
cm
20.7
Question 1
15.8 cm
20.7 cm
15.8 cm
15.8
13.5
cmcm
7 cm
15.8
cm
18.3
cm
13.5 cm
Question 2
a
20.7 cm
20.7 cm
7 cm
20.7
17.9cm
cm
Find the total perimeter of these quadrants.
21 cm
14.2 cm
15.4 cm
15.4 cm
15.4
35.7
cm
20
cmcm
14 cm
21 cm
21 cm
21.7 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
14 cm 21 cm
21.7 cm
c
21.7 cm
21 cm
15.4 cm
14.2 cm
21.7 cm
b
20 cm
18
cm
20
15cm
cm
18 cm
1
14.2 cm
14.2 cm
c
15 cm
5 cm
5 cm
15 cm
15 cm
7 cm
1
14
21 cm
cm
15 cm
15 cm
14.2
Find18the
correct
to one decimal
14.7 cm
cm place.
cm perimeter of each of these figures
18 cm
2018
cmcm
20 cm
g
13.5
24.6 cm
cm
21 cm
77cm
cm
15.4 cm
Question 3
d
7 cm
b
15.4 cm
14.2 cm
15 cm
13.5 cm
13.5 cm
7 cm
14 cm
15 cm
7 cm
14 cm 15.4 cm
a
13.5 cm
7 cm
20 cm
5 cm
5 cm
5 cm
5 cm
85
20 cm cm
20
cm
7 cm
51
cm
54 cm
54 cm
14.7 cm
cm
cm
5.3
cm
20
cm
28
cm
68 cm
85 cm
5.3 cm
5.3 cm
51 cm
e f
85 cm
68 cm 85 cm
7 cm
85 cm
51 cm
5.3
cm
7
cm
51
cm
51 cm
40 85
cm
8 cm
14
cmcm
68
cm
cm
714cm
51 cm 68 cm
cm6885cm
5.3
cm
51 cm 8 cm
8 cm5.3 cm
26 cm
14 cm
14
68cm
cm
20 cm
40 cm
68 cm
5.3
6.7cm
cm
5 cm
5 18
cmcm
18 cm
7 cm20 cm
5 cm
5 cm
20 cm
7 cm
8 cm
40 cm
8 cm
40 cm 8 cm
15 cm
14 cm
14 cm
14 cm
20 cm
h
89cm
cm
18 cm
i
14cm
cm
14
20 cm
5 cm
20 cm
15 cm
5 cm
18 cm
18 cm
18 cm
36
cm
18 cm
9 cm
18 cm
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
40 cm
40 cm
18 cm
40 cm
40 cm
20 cm
20 cm
20 cm
cm
2020cm
105
© Pascal Press ISBN 978 1 74020 033 2
a
Circles
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 π.
b
c
m
m
3c
5c
m
9c
d e f
13
g
cm
17
cm
19
h i
cm
22
8
cm
10
cm
22
as the value of π, find the approximate area of these circles.
7
b
c
Question 2
a
By using
m
35
© Pascal Press ISBN 978 1 74020 033 2
7c
Question 3
a
cm
cm
14
Find the area, to one decimal place, of a circle with:
radius 25 km
b radius 1.8 m
d radius 73 cm
106
cm
e
diameter 400 km
c
diameter 37 mm
f
diameter 13.9 cm
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
15 cm
17 cm
15 cm
Circles
15 cm
15 cm
17 cm
21 cm
21 cm
17 cm
21 cm
17 cm
UNIT 5: Applications of area
21 cm
15 cm
17 cm
21 cm
17.9
24.6
cm
Question 18.3
1 cmCalculate the area of the following
semicircles correct to one decimal
18.3cm
cm
17.9place.
cm
21cm
cm
15
cm
21
15
cm
a b
c
21
cm
17
cm
15 cm
17 cm
17 cm
18.3 cm
17.9 cm
24.6 cm 21 cm
15 cm
17 cm
18.3 cm
17.9 cm
24.6 cm
18.3 cm
24.6 cm
cm
18.37cm
cm
18.3
18.3 cm
7 cm
18.3 cm
Question 2
a
7 cm
7 cm
17.9 cm
17.9cm
cm
17.9
17.9 cm
17.9 cm
24.6 cm
14 cm
24.6cm
cm
24.6
24.6 cm
24.6 cm 21 cm 14 cm
Find the area of these quadrants correct to one decimal place.
7 cm
14 cm28 cm
b
35.7 cm
cm
77cm
7 cm
7 cm35.7 cm
35.7 cm
21 cm
35.7 cm
15 cm
14 cm
28 cm
c
35.7 cm
14
cm
2814
cmcm
14 cm
14 cm 15 cm
28cm
cm
28
28 cm18 cm
28 cm
cm
14.721cm
14 cm
28 cm
21 cm
14.7 cm
21 cm
21cm
cm
21
21 cm
14.7 cm21 cm
14.7 cm
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
© Pascal Press ISBN 978 1 74020 033 2
18 cm
cm
35.7
cm
35.7
cm
4 cm
4 cm
35.7
cm
14.7 cm
15
cm
28 cm
Question 3 Find the area of these shapes correct
to one decimal 14.7
place.
14.7cm
cm
14.7
28 cm
35.7 cm
a b
c 14.7 cm
1518
cmcm
14.7 cm
4 cm
4 cm
14.7 cm
1815cm
cm
28 cm
14.7 cm
4 cm
4 cm
18 cm
28 cm
15cm
cm
14.7 cm
4 cm
4 cm
14 cm
15
14 cm
cm
14.7 cm
4 cm
415cm
28
cm
26
cm
18cm
cm
15 cm 18
28 cm 18 cm
14.7
cm
4
cm
cm
6.7
cm
cm
6.7
cm
14.7
4 cm
44cm
14 cm
14.7 cm
4 cm 28 cm 4 cm
18 cm
28
cm
26 cm
14.7 cm
4 cm
4 cm
14 cm
4028
cmcm
6.7
cm
28 cm
d e f
26 cm
40 cm
14 cm
6.7 cm
mcm
9 cm
726ccm
14 cm 9 cm
114
4020
cmcm
14cm
cm 26 cm
6.7 cm
40 cm
14
14 cm
9 cm
26cm
cm 9 cm
26
40 cm 26
14 cm 9 cm
14
cm
cm
6.7cm
cm
36 cm 20 cm
6.7
26 cm
6.7 cm
9 cm
14 cm
9 cm
40 cm
20 cm
6.7 cm
40 cm
36
cm
9 cm
14 cm 9 cm
40cm
cm
20 cm
40
g h i
36 cm40 cm
20 cm
9 cm
cm
99cm
14cm
cm
40 cm
14
20cm
cm
9 cm
20
36 cm
14 cm
20 cm
936
cmcm
9
cm
14 cm
9 cm
20 cm
9 cm
36cm
cm
36
9 cm
36 cm
36 cm
14.7 cm
107
Circles
UNIT 6: Miscellaneous questions
Question 1
b
11
cm
a
Calculate the circumference of each circle correct to one decimal place.
Question 2
a
77
c
cm
12
Calculate the area of each circle correct to two decimal places.
b
9
c
c
m
7
cm
cm
54
Question 3
a
cm
Calculate the perimeter of the following shapes correct to three significant figures.
18 cm
b
c
7 cm
7 cm
7 cm
12 cm
8 cm
5 cm
9 cm
5
cm
Calculate
the shaded area of the following shapes correct to two decimal places.
8 8cm
8cm
cm
b
8 cm
6
8 cm
cm
cm
12 cm
18
20 cm
9 cm
9 cm
9 cm
5 cm
20 cm
20 cm
20 cm
20 cm
9 cm
c
© Pascal Press ISBN 978 1 74020 033 2
9 cm
12 cm
6
10 cm
cm
158cm
c
cmcmcm
66 6 m
8 cm
5c
5 cm
5 cm
10 cm
m5 cm
8 cm
8 cm
8 cm
8 cm5
d
9 cm
20 cm
cm
a
7 cm
6
Question 4
8 cm
8 cm
cm
m
6
5c
20 cm
10 cm
5 cm
5 cm10 cm
5 cm
5 cm
10 cm
12 cm
5 cm
10 cm
12 12
cm cm
10
cm
e f
18cm
cm
10 cm
12
15 cm
5 cm10 cm
10 cm
10 cm
10 cm
12 cm
10 cm
18 18
cm cm
10 cm
18 cm
15 cm
15 cm
18 cm
15 cm
15 cm
18 cm
15 cm
108
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Circles
UNIT 7: Problem solving with circles
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
© Pascal Press ISBN 978 1 74020 033 2
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?
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
109
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
A
2
r
B
B 3.142
B
1
C 227
D none of these
1
D none of these
1
D segment
1
D 14 cm
1
2
C
B
C
The area of a circle of diameter 28 cm is closest to:
88 cm2
616 cm2
B
C 1232 cm
D 2463 cm
2
1
C
D 314.2 cm
2
1
C 24 cm
D 12π cm
1
D none of these
1
2
The area of a quadrant with a radius 10 cm is closest to:
157.1 cm2
31.4 cm2
78.5 cm2
A
9
D A = dπ
The circumference of a circle of radius 7 cm is closest to:
44 cm
24 cm
22 cm
A
8
C A = rπ
C
B
A
7
1
Which of these is a name for part of the circumference of a circle?
arc
radius
sector
A
6
D C = 2πd
What is the relationship between the diameter and radius of a circle?
d = 2r
r = 2d
rd = 2
A
5
C C = 2πr
2
What is the exact value of π?
3.14
A
4
d
What is the formula for the area of a circle?
A = πr2
A = πd2
A
3
B
B
The radius of a circle is 12 cm. Its diameter equals:
6 cm
12 cm
A
B
10 The area of a circle of radius 3 cm is approximately equal to:
A 27 cm
© Pascal Press ISBN 978 1 74020 033 2
2
B 28 cm
2
C 29 cm
2
11 The circumference of a circle is 154 cm. Which is closest to the length of the diameter?
A 24 cm
B 49 cm
C 98 cm
D 242 cm
1
D 0
1
12 In how many places does a chord meet the circumference?
A1
B 2
C 3
Total marks achieved for PART A
110
12
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
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
4
5
6
7
1
A circle has radius 21 cm. To one decimal place, find the:
a circumference
b area
1
1
A circular pond has a diameter of 4 m. To one decimal place, find the:
a area
b circumference
1
1
A semicircle has radius 48 cm. Find the:
a perimeter to the nearest centimetre
b area to the nearest square centimetre
1
1
A quadrant has radius 9 cm. Find, to one decimal place, the:
a area
b perimeter
1
1
Find the shaded area to the nearest square centimetre.
a b
16 cm
12 cm
20 cm
16 cm
12 cm
1
20 cm
1
Total marks achieved for PART B
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
13
111
© Pascal Press ISBN 978 1 74020 033 2
3
1
Linear relationships
Chapter 10
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)
x
(4, 2)
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
1
C
f
F
g
G
I
j
J
E
B
A
© Pascal Press ISBN 978 1 74020 033 2
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
t
T
u U
v
V
w
W
x
X
y
z
Z
Y
112
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Linear relationships
UNIT 2: Tables of values
Question 1
a
Complete each table of values.
y = x
b y = 2x
x
0
1
2
3
y
c
–1
0
1
2
y
y = 3x
d y = –x
x
–2 –1
0
1
y
e
x
x
0
1
2
0
1
2
y
y = x + 2
x
–1
–2 –1
0
f
1
y=x–3
x
–1
y
y
Question 2
Complete each table of values and list the coordinates of the points.
a
y = 2x + 1
x
–1
0
1
b p = 2q – 1
2
y
q
–1
0
1
2
1
2
3
0
1
2
p
c
c = 2d + 3 d
–1
0
1
d m = 3n + 2
2
c
n
0
m
e
s = 4t – 3
t
s
–1
0
1
2
f
© Pascal Press ISBN 978 1 74020 033 2
a = 3b – 2
b
–1
a
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
113
Linear relationships
UNIT 3: Graphing straight lines
Question 1
a
Complete each table of values and then graph the equation on the number plane.
b y = x – 1
y = x + 2
x
–1
0
1
2
x
y
–1
0
1
y
b y = 3
x
0
1
2
3
0
1
2
© Pascal Press ISBN 978 1 74020 033 2
y=x
0
x
y
1
2
3
y
y
y
x
x
n the same number plane, graph the following equations by first completing the tables
O
of values. Find their point of intersection.
y=x
b y=x+2
y = –x
0
1
2
x
y
–1
0
y
Point of intersection
1
2
x
–1
y = 2x + 1
0
1
2
x
y
–1
0
1
2
y
Point of intersection
y
y
x
114
c
3
x
–1
x
y
x
2
Complete each table of values and then graph the equation on the number plane.
x
a
1
x
x = 2
Question 3
0
y
y
y
–1
x
x
a
y = –x + 3
2
y
y
Question 2
c
x
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Linear relationships
UNIT 4: Using the intercept method to graph lines
Question 1
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
x
Question 4
a
For each equation, find the x-intercept and the y-intercept and then draw its graph.
y = –2x + 3 b x + y – 5 = 0
y
x
0
0
x
0
y
y
0
y
x
x
c
y = 2x – 3
x
y
y
0
0
4
d y = 3x – 1
x
0
y
0
y
x
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
x
115
© Pascal Press ISBN 978 1 74020 033 2
Linear relationships
UNIT 5: Intersection of two lines
Question 1
a
Graph each pair of lines on the same number plane and find their point of intersection.
x = 1; y = 3
x = 1
x
y
y=3
y
x
y
x
b x = 3; y = –2
x = 3
x
y
y = –2
y
x
y
x
Question 2
a
Graph each pair of lines on the same number plane and find their point of intersection.
y = 2x – 1; y = –x + 2
y = 2x – 1
x
y
y = –x + 2
y
x
y
x
© Pascal Press ISBN 978 1 74020 033 2
b y = 3x – 1; y = x – 3
y = 3x – 1
x
y
y=x–3
y
x
y
x
116
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Linear relationships
UNIT 6: Determining whether or not a point lies on a line
Question 1
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 Which of the following lines pass through the origin, (0, 0)?
a
2x – y + 2 = 0
b 2y = 3x
c
x – 5y = 0
d 2x + 3y = 6
e
y = –2x
f
y = 5x – 4
Question 3 Does the given point lie on the given line?
a
x + 2y = 3 (3, 0)
b x + y = 2 (0, 2)
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.
© Pascal Press ISBN 978 1 74020 033 2
Question 5 If the point (–3, –6) is on the line ax – 4y – 9 = 0, what is the value of a?
Question 6 Find the missing coord inates to make each of the following points satisfy the equation
y = 3x – 2.
a
(0,
)
b (
, 4)
c
(1,
)
d (5,
)
e
(
, –5)
f
(
, –8)
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
117
Linear relationships
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
x=
b y = –2
x =
c
y=x+1
y
y=5
4
x=
2
–4
0
–2
2
x
4
–2
–4
2
Use your answers from Question 1 to solve the following equations.
a x+1=3
b x + 1 = –2
3
2x – 3 = 1
y
10
8
6
4
y = 2x – 3
2
d 2x – 3 = 5
4
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
c
0
–2
3x + 2 = –4
Question 5
a
4
2
–4
c
10
118
4
x
y
8
b –x + 2 = 6
6
4
y = –x + 2
2
d –x + 2 = 0
2
–4
0
–2
–2
–x + 2 = –2
y = 3x + 2
0
–2
8x
6
y
he graph of y = –x + 2 is drawn opposite. Use the graph to
T
solve each of the following equations.
–x + 2 = 3
4
–2
d 3x + 2 = 8
2
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
c
© Pascal Press ISBN 978 1 74020 033 2
c
2
4
6
8x
–2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
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
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
A
2
B
A
B
C
x
3
l
0
3
x
1
1
Which one of the following points lies on the y-axis?
(2, 3)
(3, 2)
D (6, 0)
1
D y=3+x
1
D 5x + 4y = 15
1
C
D (–2, 3)
1
C 2
D –2
1
C 3
D –3
1
D (3, –5)
1
B
B
B
C
C
C (0, 6)
Which linear rule states that y is always 3 less than x?
y=3–x
y=x–3
B
C y = –x – 3
On which of the following lines does the point (5, 1) lie?
4x + 5y = 15
5x – 4y = 15
4x – 5y = 15
A
9
y
D
A
8
B
D
x
If the y-coordinate of a point on the line y = 5 + 3x is 20, what is the x-coordinate?
5
4
3
2
A
7
x
x
1
A
6
y
D
If the x-coordinate of a point on the line y = 8 – 2x is 1, what is the y-coordinate?
3
4
5
6
A
5
y
The equation of the line l is:
x = –3
x=3
y = –3
y=3
A
C
4
C
y
D
B
C
Which one of the following points lies on the line 2x – y = 4?
(1, –4)
(2, 0)
(–1, 6)
A
B
D
A 4
B –4
11 What is the y-intercept of the line 2x – 3y = 6?
A 2
B –2
12 The coordinates of the point of intersection of the lines x = 3 and y = –5 are:
A (–5, 3)
B (5, –3)
C (–3, 5)
Total marks achieved for PART A
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
12
119
© Pascal Press ISBN 978 1 74020 033 2
10 What is the x-intercept of the line x + 2y = 4?
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
–2 –1
0
1
1
1
y
i
–4 –2
9
7
0
1
1
1
y –1 0 1 2
f
x –2 –1 0 1
x –3 0 3 6
y
e
x
y –2 1 4 7
d
x –2 –1 0 1
x –3 0 3 6
y
–5 –3 –1
b
5
2
3
y 9
x
1
–9 –18
y
ii y = 3
y = 2x
0
1
iii y = 2x – 1iv y = 5 – 2x
v
2 a
vi y = –3x
y = 3x + 4
2
0
n the same number plane, draw
O
the graphs of the following lines.
i
ii
x = –3
y=1
b Write the coordinates of the point of intersection
of the lines x = –3 and y = 1.
3
aComplete the table of values below for the
equation y = x + 2.
© Pascal Press ISBN 978 1 74020 033 2
x
–3 –2 –1
0
1
x
2
y
1
0
x
3
1
y
b Draw the graph of y = x + 2.
c
1
What is the value of y when x = –7?
1
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
15
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Chapter 11
Equations
UNIT 1: Solving equations by inspection
Question 1 Solve the following one-step equations by inspection and then check by substitution.
a x + 2 = 5 b a + 3 = 7 c m – 4 = 8
d b + 1 = 7
f
n + 5 = 12
g x – 2 = 4
j
e a + 2 = 10
h x + 3 = 9
i
y + 8 = 14
p – 3 = 7
k t – 2 = 8
l
a–9=3
m y – 2 = –7
n x – 4 = –6
o 8 + x = 12
Question 2 Solve the following equations by inspection and then check by substitution.
a m + 1 = 9 b x + 2 = 12 c 3 + y = 15
f
x – 2 = 16
g m + 5 = 9
j
e x – 4 = 7
h y – 3 = 18
i
a+6=8
m – 3 = 7
k n – 6 = 10
l
a – 4 = 11
m y – 5 = –3
n t – 2 = –4
o 15 + a = 21
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
© Pascal Press ISBN 978 1 74020 033 2
d 9 + n = –3
121
Equations
UNIT 2: One-step equations (addition and subtraction)
Question 1 Solve the following one-step equations.
a x + 5 = 9 b a + 7 = 15
d b + 3 = 11
e a + 4 = 10
f
n + 9 = 12
g x – 3 = 12
j
c m–3=4
h x + 5 = 16
i
y + 8 = 20
p – 2 = 10
k t – 4 = 1
l
a–9=9
m y – 2 = –3
n x – 5 = –6
o 5 + x = 20
Question 2 Solve the following equations. Check your solutions by substitution.
a m + 7 = 2 b x + 3 = 1 c 9 + y = 14
d 12 + n = 18
© Pascal Press ISBN 978 1 74020 033 2
x–1=8
h y – 12 = 27
i
a + 5 = 13
m – 4 = 11
k n – 12 = 19
l
a–7=1
m y – 5 = –5
122
f
g m + 15 = 30
j
e x – 10 = 12
n t – 6 = –3
o 10 + a = 14
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Equations
UNIT 3: One-step equations (multiplication and division)
Question 1 Solve the following one-step equations.
x
a 4a = 16 b
= 3
2
d
c 5y = 15
x
y
= 7 e
= 6 f 8x = –32
3
5
g
t
6m = –18 h 2x = 6 i
= –5
4
j
y
2p = –8 k
= –4 l 7t = 28
5
a
x
m
= 9 n 3a = 24 o
= –3
2
7
Solve the following equations. Check your solutions by substitution.
a
x
x
x
= 5 b
= –2
c
=6
6
6
7
d
a
a
b
= –20
e
= –2
f
=9
9
3
8
g
m
x
y
= 12
h
= 9
i
= –14
3
3
2
j
3a = 18
k –2b = –10
l
–3x = –12
m 5x = 35
n 8x = 48
o 7x = 49
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
© Pascal Press ISBN 978 1 74020 033 2
Question 2
123
Equations
UNIT 4: Two-step equations
Question 1 Solve the following two-step equations.
a 2x + 1 = 3 b 18 = 3x – 6
d
g
5m
3 = 10
x
2 –1=7
x–3
e
4 =5
f 2a + 9 = 19
a–2
h 3x + 5 = 11 i
7 =3
j
c 10 = 5y – 15
8x – 7 = 33
k 5x + 3 = 28
l
6t – 3 = 39
m
m 7y – 5 = 9 n 3 – 4 = 6
o 2k + 3 = 21
Question 2 Solve the following equations. Verify your solutions by substitution.
m
2 +6=9
a 3x – 3 = 9
d
x–2
6 =8
b
5m
e 5x – 9 = 26 f 6 = 10
© Pascal Press ISBN 978 1 74020 033 2
g 10 – 2m = 0
j
h 3y – 9 = 21
i
7y + 4 = –3
2x + 8 = 14
k 8x – 7 = 17
l
9x – 7 = 56
m 3a – 2.3 = 7
124
x–5
c
7 =4
n
1
1
6a – 1 2 = 4 2
o 8p + 0.3 = 2.7
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Equations
UNIT 5: Three-step equations
a
e
i
4x + 9 = 3x – 12
9m – 3 = 7m + 9
7y – 3 = 4y + 15
Question 2
a
e
i
Solve the following three-step equations.
b
2x – 7 = x – 3
c
6t – 10 = 4t + 12
d
f
g
4a – 3 = 3a + 9
10y – 6 = 5y + 19
h
j
k
5x – 1 = 6x – 9
3a + 5 = 21 – a
l
11m – 6 = 7m + 14
6x – 4 = 2x + 16
12p – 3 = 7p + 32
Solve the following equations. Check your solutions by substitution.
6x – 20 = 4x + 48
2x – 14 = x – 12
3y + 1 = 2y + 7
b
2x – 6 = 3 – x
c
6x – 2 = 3x – 6
d
f
g
5x + 17 = 3 – 4x
3m – 2 = 2m + 7
h
j
k
6m + 7 = 7m + 10
2x + 3 = x – 9
l
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
7y – 14 = 5y + 20
6x – 21 = 2x – 2
4y – 3 = 2y + 11
125
© Pascal Press ISBN 978 1 74020 033 2
Question 1
Equations
UNIT 6: Equations with grouping symbols
Question 1 Solve the following equations.
a 3(x + 4) = 18
b 2(m + 1) = 5
e
i
3(a – 3) = 10
5(2x + 3) = 45
c
f
g
4(n – 3) = 36
© Pascal Press ISBN 978 1 74020 033 2
i
m
126
8(3 – x) = 7(x – 6)
3(3a – 2) = 4(4 – a)
6(a + 7) = 5(a – 3)
h
5(2n – 1) = 25
j
k
4(a – 4) = 8
l
3(m + 2) = m + 14
Question 2 Solve the following equations.
a 5(a + 4) = 4(a – 3)
b 3(x – 5) = 2(x + 4)
e
d
6(m – 1) = 24
c
d
4(y – 3) = 3(y + 2)
f
g
2(a + 1) + a + 3 = 0
3(x + 7) + x + 3 = 18
h
j
k
2(a + 1) – a + 7 = 9
3(a – 3) – 2a + 9 = 15 l
n
o
8(2a + 7) = 5(3a – 8)
2(x + 5) = 18
2(3p – 1) = 22
2(3x + 2) = 16
7(x – 8) = 6(x + 2)
5(a + 3) = 4(a + 9)
2(5a – 10) – 9a + 6 = 0
9(3a – 4) = 13(2a – 1)
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Equations
UNIT 7: Formulae
Question 1 Given the formula V = Ah, find V if:
a A = 10, h = 3 b A = 15, h = 5
c A = 9, h = 4
Question 2 Given the formula P = 2L + 2B, find P if:
a L = 18, B = 10 b L = 12, B = 5
c L = 9, B = 4
Question 3 If y = mx + b, find y for the given values of m, x and b.
1
a m = 1, x = 3, b = 2 b m = 2, x = 6, b = 3 c m = 2 , x = 8, b = 4
Question 4 If A = 12 bh, find A for the given values of b and h.
a b = 4, h = 3 b b = 6, h = 4
c b = 9, h = 6
Question 6 If A = 12 h(a + b), find A when:
a h = 6, a = 8 and b = 10 b h = 17, a = 13 and b = 19
c
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
© Pascal Press ISBN 978 1 74020 033 2
Question 5 If C = 2πr, find the value of C to one decimal place when:
a r = 8 b r = 37 c r = 63.5
h = 23, a = 35 and b = 44
127
Equations
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 2 Multiply a number by 3 and 3 I think of a number and
and 8 is 24. then take away 9. The answer add 12. The result is 26.
is 21.
4
A number increased by 9 5 The difference between 6 I think of a number, double it,
is 27. 5 times a number and 3 is 7. and the result is 30.
7
I think of a number, double it 8 I think of a number, divide it 9 The difference between
and add 12. The result is 48. by 4, subtract 2 and the 7 times a number and 6 is 29.
result is 7.
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,
If its perimeter is 26 cm, find the width and the length of the rectangle.
what is the length of each side?
© Pascal Press ISBN 978 1 74020 033 2
12 The length of a rectangle is 8 cm and its 13 If I subtract 29 from a certain number the result is 23.
perimeter is 22 cm. Find its width.
What is the number?
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.
What is the number?
128
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Equations
UNIT 9: Simple equations with one fraction
Question 1 Solve the following equations.
a
x
a
y
= 9 b
= 8 c
=7
4
3
6
d
m
m
x
= 10 e
= 7 f
=9
3
4
6
g
a+3
3x
5x – 4
= 2 h
= 9 i
=7
7
4
3
j
x
x+2
m+5
= 2 k
= 6 l
=9
3
2
3
3y – 1
b
2 = 10
t–5
c
2 =5
m–7
3 =4
2a + 8
e
4 =6
3p – 5
f
2 =8
3x + 1 = 7
4
h 4x – 2 = 3
5
3x + 4
i
2 =2
3m – 1
4 =8
k 5 – 3x = 1
2
l 2m + 9 = 4
6
6p
n
5 +3=9
3a + 4
o
2 = 14
a
2x = 8
5
d
g
j
m 3x = –2
5
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
© Pascal Press ISBN 978 1 74020 033 2
Question 2 Solve the following equations. Check your solutions by substitution.
129
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
n
If 3 = 7, n equals:
7
A
2
If x – 10 = –2, x equals:
–12
A
3
m
D 12
1
C 13
D 26
1
C 9
D 18
1
C 14
D 28
1
C 1
D 7
1
C x=9
D x=7
1
C 8
D none of these
1
B 9
If n + 3 = –4 then n equals:
–7
B –1
Solve for x: 5x + 3 = 2(x + 12).
x=3
x=5
B
If 2(t + 3) = t – 4 then t equals:
–10
2
A
9
C 8
If 2p – 5 = 23, then p equals:
8
A
8
B –8
B 3
A
7
1
If 3 = 6, find the value of m.
2
A
6
D 21
B
A
5
C 17
If 2x – 5 = 21, what is the value of x?
6
8
A
4
B 11
B
If 2(7 – x) = 3 then x equals:
11
A
B 17
1
10 2(x – 3) = 3(2x + 4) then x equals:
© Pascal Press ISBN 978 1 74020 033 2
1
A 12
1
B 4
1
C 82
D 52
1
C –4 2
1
3
D –3 4
1
D 1849
1
D 567
1
11 If y = ax2 what is the value of y when a = 4 and x = 3?
A 36
B 144
C 49
1
12 If A = 2 h(a + b) and h = 12, a = 9 and b = 21, what is the value of A?
A 90
B 180
C 36
Total marks achieved for PART A
130
12
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
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
x – 7 = 30 b m + 9 = 15
c
7n = 147 d
x
12 = 96
e
g
i
1
1
1
1
2x – 3 = 5 f 5a + 17 = –3
1
1
1
1
x–2
x
2
h 4 = 3
3 = 10 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
2
1
1
I think of a number, double it, add 8 and the result is 42. Find the number.
1
Total marks achieved for PART B
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
15
131
© Pascal Press ISBN 978 1 74020 033 2
Answers
Chapter 9 – Circles
Page 103 1 a centre b diameter c radius d arc e chord f semicircle g minor segment h major segment i sector j tangent
1
3
1
1
k secant l circumference 2 a 4 b 4 c 8 d 3 3 a 96.5 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 64.0 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
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
1
2
1
2
1
2
x –1 0
x –1 0
x –1 0
y
1
2
3
4
y –2
y
–1
0
1
4
y
y
3
2
1
y
y = –x + 3
y=x+2
x
y=x–1
x
2 a
2
x
y
0
2
2
2
1
2
3
b
3
y
© Pascal Press ISBN 978 1 74020 033 2
y
0
x
1
2
3
3
3
3
c
x
0
0
y
y
1
2
3
1
2
3
y
y=3
x=2
x
y=x
x
3 a y = xb
186
x
x
y=x+2
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Answers
1
2
1
2
3
y
y = –xy = 2x + 1
4
x
–1
0
1
2
y
–1
0
1
2
x
–1
0
1
2
x
–1
0
y
y=x
x
–1
0
y
y=x+2
1
y = 2x + 1
2
x
y = –x
3
5
y –1 1
Their point of intersection
Their point of intersection
is (0, 0).
is (1, 3)
1
y
0
–1
x
–2
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
x
b
0
5
x
5
y
cx
3
2
y
3
0
d
x
3
4
0
y –3 0
y –1 0
0
y
y
y
x
x
1
1
1
y
–2 –1
0
1
2
x
–2 –1
0
1
2
y
3
3
3
3
x=3
y
3
3
y –2 –1 0 1
(1, 3)
y = 3y = –2
2
x=3
2
(3, –2)
x
x
y=3
3
3
3
x
3
x
–2 –1
0
1
x
x=1
y –2 –2 –2 –2 –2
2 a y = 2x – 1b
y = –2
© Pascal Press ISBN 978 1 74020 033 2
1
x
Page 116
1 a x = 1b
y
1
0
x
3
2
0
x
y = 3x – 1
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
187
Answers
1
2
y –4 –1 2
y = –x + 2y = x – 3
5
x
–1
0
1
2
y
–3
–1
1
3
x
–1
0
1
2
2
1
–1
0
(1, 1)
x
–1
0
1
y
y = 3x – 1
2
x
y –4 –3 –2 –1
y = 2x – 1
Their point of intersection
Their point of intersection
y = –x + 2
is (1, 1).
is (–1, –4).
y
3
x
y
0
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
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
© Pascal Press ISBN 978 1 74020 033 2
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
188
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
Answers
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
8
1
1
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 = 3 i x = 4 j p = 2 k x = 6 l x = 6 m x = 2 2
1
© Pascal Press ISBN 978 1 74020 033 2
n x = 3 2 2 17
Excel ESSENTIAL SKILLS Year 8 Mathematics Revision & Exam Workbook
189