CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 1 TEST ANSWERS
Stage 9 End of unit 1
The tests and mark schemes have been written by the authors. These may not fully reflect the approach of Cambridge Assessment International
Education.
Answers
1
27 and
2 ×7
(−1 mark for each error or omission)
2 a The product is 10. This can be shown by using a calculator.
b Any valid answer, e.g.
2 and 4 − 2
3 a 1
[1]
[1]
[1]
b 256
c
[2]
1
or 0.0625
16
[1]
[1]
4 Any valid answers. For example:
a
2
[1]
b
90
[1]
5 a
b
6.32 ×106
[1]
1.29 × 10 −5
[1]
6 a 350 000
b y, z, x
7 a True. 172 = 289 and 182 = 324
[1]
[1]
[1]
b False. 73 = 343 > 300
(A reason is required for the mark)
[1]
8 a
25
[1]
b
20
[1]
c
2 −3
[1]
57
[1]
6 −2
[1]
9 a
b
[Total: 20 marks]
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
1
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 2 TEST ANSWERS
Stage 9 End of unit 2
The tests and mark schemes have been written by the authors. These may not fully reflect the approach of Cambridge Assessment International
Education.
Answers
1 a 45
[2]
b 0
c
[2]
72
[2]
2 a 6x + 2
b 2x2 + x
[2]
[2]
3 a p12
[1]
b q6
[1]
r 15
[1]
d 6t 5
[1]
4 a B 12x5
[1]
b C 10 y 6
[1]
c
c
A
d C
e D
1 8
k
2
2 7
m
3
3 −4
n
2
5 a y2 + 8y + 15
b m2 − m − 2
c
p2 − 8p + 15
[1]
[1]
[1]
[1]
[1]
[1]
d n2 − 16n + 64
[1]
e x2 − 4
[1]
3x
5
y
b
6
6 a
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
[1]
[1]
1
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 2 TEST ANSWERS
c
2a + b
8
[1]
d
4 a + 3b
18
[1]
e
3x + 9
[1]
7 a T = 30
[2]
b i
p=
T
x
ii p = 6
8 a B x=
y−c
3
[1]
[2]
[1]
b C x = 4( y + 2k )
[1]
A x = 4ay – b
[1]
c
9 a A = 4x2 + yz
b A = 64
c
x=
A − yz
4
d x=4
[2]
[2]
[2]
[2]
[Total: 45 marks]
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
2
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 3 TEST ANSWERS
Stage 9 End of unit 3
The tests and mark schemes have been written by the authors. These may not fully reflect the approach of Cambridge Assessment International
Education.
Answers
1 a 1500
[1]
b 32 500
[1]
19
[1]
d 0.6
[1]
e 0.045
[1]
c
f
0.27
[1]
g
13
[1]
h 0.0045
[1]
2 a B 4.5
[1]
b C 8.5
[1]
c
A 60 000
3 a 2.4
[1]
[1]
b −4.5
[1]
0.32
[1]
d −4.8
[1]
e 0.006
[1]
c
f
0.0035
4 a 30
[1]
[1]
b −110
[1]
80
[1]
d −400
[1]
e 4
[1]
c
f
1600
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
[1]
1
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 3 TEST ANSWERS
5 200
[2]
6 a 211.2
[2]
b 27
[2]
7 a A 0.88
[1]
b C 1.05
[1]
8 a i 800 × 1.05
ii 800 × 1.052
iii 800 × 1.053
b The population of the village after 4 years.
c
The population of the village after 10 years.
[3]
[1]
[1]
d 13 years
[2]
e 800 × 1.05n
[1]
9 a 55, 56, 57, 58, 59, 60, 61, 62, 63, 64
[1]
b 55
[1]
c
64
[1]
10 a
25
[1]
x < 35
b
455 x < 465
[1]
11 a
650 x < 750
[1]
3450
[1]
b
x < 3550
12 a i 177.5 cm
b
177.5
ii 178.5 cm
x < 178.5
[2]
[2]
[Total: 50 marks]
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
2
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 4 TEST ANSWERS
Stage 9 End of unit 4
The tests and mark schemes have been written by the authors. These may not fully reflect the approach of Cambridge Assessment International
Education.
Answers
1 a x = −13
[2]
b y=5
[2]
x=3
[2]
c
2 x = 11
[3]
3 Correct working to show that all equations solve to give y = 8
[6]
4 a 3(x + 16) + 9x − 4 + 2(23 − x) = 180
or 3x + 48 + 9x − 4 + 46 − 2x = 180
or 10x + 90 = 180
[1]
b x=9
c
[3]
75 º, 77 º, 28 º
[3]
5 x = 3, y = 15
6 a
y = 2x + 4
[3]
x
0
2
4
y
4
8
12
y=x+6
x
0
2
4
y
6
8
10
[2]
b
[2]
x = 2, y = 8
[1]
7 a x = 3, y = 2
[3]
b x = 4, y = 3
[3]
c
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1
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 4 TEST ANSWERS
8 a
[2]
b
[2]
c
[2]
9 a 4x − 11 > 3x − 7
b x>4
[1]
[2]
[Total: 45 marks]
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
2
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 5 TEST ANSWERS
Stage 9 End of unit 5
The tests and mark schemes have been written by the authors. These may not fully reflect the approach of Cambridge Assessment International
Education.
Answers
1 Show a hexagon divided into 4 triangles.
[2]
4 × 180 = 720 °
2 a
[2]
6 × 180 = 1080 °
b 135 ° (allow follow through from incorrect answer to part a)
[1]
3 360 − (52 + 55 + 58 + 61 + 64) = 360 − 290 = 70 °
[2]
4 a 35 °
[1]
b 120 °
[1]
5
132 − 122 = 5 (1 mark for 5 if no method shown)
[2]
6
4.52 + 7.52 = 76.5 = 8.7 or 8.75 m
[2]
7 a Use of compasses to draw sides seen.
Sides correct to within 2 mm.
[2]
b Use of compasses to construct perpendicular bisector of the 8.5 cm side.
Two parts of line are between 4.2 and 4.3 cm and angle is between 88 ° and 92 °.
[2]
8 Evidence of construction of 90 °, bisection to give 45 ° and bisection of 45 °.
Error less than 2 °.
[3]
[Total: 20 marks]
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1
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 6 TEST ANSWERS
Stage 9 End of unit 6
The tests and mark schemes have been written by the authors. These may not fully reflect the approach of Cambridge Assessment International
Education.
Answers
The answers given here are examples. Usually there are alternative possible answers.
1 a Gender and estimates of masses of a range of items for each person.
[2]
b It will enable you to look at ability to estimate heavy and light objects and relate
this to gender.
[2]
Give each person several objects to estimate the mass. Record gender and results
in a table or in a spreadsheet so that they can be processed.
[2]
c
(1 mark for a partial answer in each section)
2 a People might not know their height and just guess. People might be embarrassed and
give an incorrect answer.
[1]
b People might be wearing shoes with heels, in which case the height recorded will
be too large.
[1]
c
You might not make accurate or consistent guesses.
[1]
3 Method 1: Yes, because longer words are usually harder to read than shorter words.
There could be bias if some articles are on a familiar subject and other articles are not.
Method 2: Yes, because longer articles require more concentration. There could be bias if
different readers are used because there is a difference between reading speed that is not
connected to ability to understand.
[4]
(1 mark for a partial answer in each section)
4 a Women stay longer in the supermarket than men.
Younger people spend more than older people.
[2]
b Collect data on different days and at different times of day.
Include specific numbers of men and women.
Choose a range of ages of customers.
[3]
5 Not all customers will reply.
Customers might be more likely to reply if they are dissatisfied.
[2]
[Total: 20 marks]
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1
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 7 TEST ANSWERS
Stage 9 End of unit 7
The tests and mark schemes have been written by the authors. These may not fully reflect the approach of Cambridge Assessment International
Education.
Answers
1 a 154 m2
[2]
b 531 cm2
[2]
2 a 56.5 cm2
[2]
b 30.8 cm
[3]
3 3.66 cm
[3]
4 a 28.8 cm2
[3]
b 14.6 m2
[3]
5 233 cm2
[5]
6 a 5 nanolitres, 5 microlitres, 5 millilitres, 5 centilitres, 5 litres, 5 kilolitres
[4]
7
b 5 nL, 5 μL, 5 mL, 5 cL, 5 L, 5 kL
[1]
D 512 KB, B 256 MB, A 32 GB, C 2 TB
[2]
[Total: 30 marks]
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
1
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 8 TEST ANSWERS
Stage 9 End of unit 8
The tests and mark schemes have been written by the authors. These may not fully reflect the approach of Cambridge Assessment International
Education.
Answers
1 a B, D and E
[2]
b A and C
[2]
2 a
3
1
2
[2]
b
5
11
18
[2]
c
5
1
8
[2]
2
3 a
b
3
1
1 3
 3
 3
 1  + 1 × 2 or 1 + 2  × 1
4
2
2 4
 4
 4
7
7
m2
16
[2]
[2]
4 a 119
[2]
2
3
[2]
b
14
c
8
[2]
1
2
5 a
27
[2]
b
4
5
[2]
c
3
8
[2]
6
3
78 cm3 or 78.75 cm
4
[2]
7
2 m2
[2]
[Total: 30 marks]
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
1
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 9 TEST ANSWERS
Stage 9 End of unit 9
The tests and mark schemes have been written by the authors. These may not fully reflect the approach of Cambridge Assessment International
Education.
Answers
1 a 1st term: 1, 2nd term: 3, 3rd term: 11, 4th term: 123
[2]
b 1st term: 6, 2nd term: 9, 3rd term: 36, 4th term: 1089
[2]
1st term: 4, 2nd term: 5, 3rd term: 8, 4th term: 13
[2]
d 1st term: 22, 2nd term: 20, 3rd term: 16, 4th term: 10
[2]
c
3
5
1
5
4
5
2
5
2 a 2, 3 , 5 , 6 , 8 , 10, 11
3
5
[2]
b 25.6, 22.4, 19.2, 16, 12.8, 9.6, 6.4, 3.2
[2]
3 4
[3]
4 a 1st term: −2, 2nd term: 1, 3rd term: 4, 10th term: 25
[2]
1
4
1
2
3
4
b 1st term: 2 , 2nd term: 2 , 3rd term: 2 , 10th term: 4
c
1
2
1st term: 6, 2nd term: 13, 3rd term: 32, 10th term: 1005
[2]
[2]
5 a nth term is: n2 + 5
[2]
b nth term is: n2 − 7
[2]
6 a A term:
9 3
6 2
15 5
= ; B term: = ; C term: =
12 4
9 3
18 6
b B, A, C or
2 3 5
, ,
3 4 6
[1]
7
Yes, 15th term is 152 − 21 = 225 − 21 = 204
8
a i
x
1
y
6
[3]
1
2
1
7
4
1
±3
14
1
2
1
25
4
[2]
±4
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[2]
1
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 9 TEST ANSWERS
ii
x
−1
2
5
10
y
−9
0
117
992
[2]
y = x2 + 5
ii
y = x3 − 8
[2]
y = x2 + 2
ii
x = ± y −2
[2]
b i
y = (x − 5)2
ii
x = ± y +5
[2]
c
y = (3x)3
ii
x=
y
3
[2]
ii
x = ±4 y
[2]
b i
9 a
i
3
i
d i
x
y = 
4
2
[Total: 45 marks]
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
2
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 10 TEST ANSWERS
Stage 9 End of unit 10
The tests and mark schemes have been written by the authors. These may not fully reflect the approach of Cambridge Assessment International
Education.
Answers
1 a
[1]
8 × 5 + 8 × 10 = 40 + 80 = 120
b 5 f + 10t = 120
[1]
c
9
[1]
d
120 − 7 × 5 = 120 − 35 = 85 which is not a multiple of 10
[1]
2 a
x
0
2
4
6
8
10
y
5
4
3
2
1
0
[2]
(1 mark for 5 correct answers and just 1 error)
b A straight line through (0, 5) and (10, 0).
[2]
c
1
y =5− x
2
d
−
3 a
1
2
[1]
b (0, −2)
[1]
c
[1]
1
2
y=
[1]
1
x−2
2
d Yes, because
[1]
1
× 44 − 2 = 20.
2
[1]
(reason must be given to get the mark)
2
3
2
3
4 a A rearrangement is y = 2 − x and this has a gradient of − .
b (0, 2)
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
[1]
[1]
1
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 10 TEST ANSWERS
5 a A straight line from the origin through (50, 600).
[2]
b
y = 12 x
[1]
c
130 dollars
[1]
[Total: 20 marks]
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
2
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 11 TEST ANSWERS
Stage 9 End of unit 11
The tests and mark schemes have been written by the authors. These may not fully reflect the approach of Cambridge Assessment International
Education.
Answers
1 a $45
[1]
b $81
[2]
2 1.35 litres
[4]
3 0.75 and 1.47
[4]
4 21 : 32 : 37
[4]
5 $5.76
[2]
6 a 24 days
[2]
b 4 men
[2]
7 a 40 minutes
[2]
b 12 km/h
[2]
[Total: 25 marks]
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
1
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 12 TEST ANSWERS
Stage 9 End of unit 12
The tests and mark schemes have been written by the authors. These may not fully reflect the approach of Cambridge Assessment International
Education.
Answers
1 a 0.32
[1]
b 0.47
[1]
2 a
b
7
16
[1]
6
3
or
16
8
[1]
3 a Any reasonable answer. For example: They travel to work together.
b Any reasonable answer. For example: They work in different places.
[1]
[1]
4 a If X happens the number is 2 or 4 and P(Y) = 0.5.
If X does not happen the number is 1 or 3 and P(Y) = 0.5 again.
[2]
b If X happens the number is 2 or 4 and P(Z) = 0.5.
If X does not happen the number is 1 or 3 and P(Z) = 1, which is different.
(Allow any equivalent explanation.) (Award 1 mark for an incomplete answer.)
5 a
b
[2]
3
5
[1]
7
20
[1]
6 a
[2]
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
1
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 12 TEST ANSWERS
b i
ii
3 1 1
× =
4 3 4
[1]
1 1 5
+ =
4 6 12
[1]
7 a
[2]
b
1−
25 11
=
or an equivalent method
36 36
[2]
[Total: 20 marks]
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
2
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 13 TEST ANSWERS
Stage 9 End of unit 13
The tests and mark schemes have been written by the authors. These may not fully reflect the approach of Cambridge Assessment International
Education.
Answers
1 a Correct scale drawing.
[2]
b Answer in the range 47 km to 48 km.
[2]
2 Correct scale drawing.
[4]
3 a Correct scale drawing.
[3]
b Answer in the range 28 km to 30 km.
[2]
Answer in the range 083 º to 085 º.
[1]
c
4 a B (6, 7)
b C (28, 20)
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
[1]
[1]
1
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 13 TEST ANSWERS
5 C (24, 36)
[3]
6 G (8, 11)
[3]
7 a and b
(2 marks for each shape)
[4]
8 a Reflection in the line x = 3.
[1]
 −1 
b Translation   .
 −4 
c
[1]
Rotation 180 º, centre (1, 0)
[1]
d Any correct combined transformation.
5
For example: rotation 180 º centre (−2, −2) followed by translation   .
0
[2]
e Any correct combined transformation.
4
For example: reflection in line y = −1, followed by translation   .
2
[2]
9
[2]
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2
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 13 TEST ANSWERS
10 a 48 cm
[1]
b 144 cm2
[2]
11 Shape G is an enlargement of shape F, scale factor 3 and centre of enlargement at (3, 4).
[2]
[Total: 40 marks]
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
3
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 14 TEST ANSWERS
Stage 9 End of unit 14
The tests and mark schemes have been written by the authors. These may not fully reflect the approach of Cambridge Assessment International
Education.
Answers
1
Prism Area of cross-section Length of prism Volume of prism
A
9 cm2
12 cm
108 cm3
B
12 mm2
5 mm
60 mm3
C
4.5 m2
8m
36 m3
[3]
2 252 cm3
[2]
3 4020 mm3
[2]
4 4 cm
[3]
5 12 mm
[3]
6 SA of cylinder = 226.19 cm2 and SA of triangular prism = 228 cm2.
The triangular prism has the greater surface area. 228 > 226.19.
[8]
7 a i three planes of symmetry
ii
[2]
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
1
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 14 TEST ANSWERS
b i two planes of symmetry
ii
[2]
[Total: 25 marks]
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
2
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 15 TEST ANSWERS
Stage 9 End of unit 15
The tests and mark schemes have been written by the authors. These may not fully reflect the approach of Cambridge Assessment International
Education.
Answers
1 a
Age, a (years)
Frequency
Midpoint
20 ⩽ a < 30
6
25
30 ⩽ a < 40
12
35
40 ⩽ a < 50
14
45
50 ⩽ a < 60
8
55
[1]
b 40
c
4
5
d False. Learner’s own explanation. For example: It is impossible to tell how
old the youngest person is. All you know is that the youngest person is in the
age group 20 ⩽ a < 30. You do not know the exact ages of the members.
[1]
[1]
[2]
e
[4]
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1
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 15 TEST ANSWERS
2 a Learner’s choice of class intervals. For example:
[4]
Time, t seconds
Tally
Frequency
Midpoint
0 < t ⩽ 10
llll ll
7
5
10 < t ⩽ 20
llll lll
8
15
20 < t ⩽ 30
llll
5
25
30 < t ⩽ 40
llll
4
35
b Correct frequency polygon for their class intervals. For example:
[4]
3 a
[4]
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
2
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 15 TEST ANSWERS
b Positive
c
[1]
Learner’s own line of best fit.
[1]
d Correct answer for learner’s line of best fit.
[1]
4 a
[4]
b
Location
c
Mode
Median
Range
Newgale beach
42
41
21
Solva car park
24
37
36
[3]
Learner’s own answers. For example:
At Solva car park the number of burgers sold each day was more varied than
at Newgale beach. Using the median and mode you can say that on average
the number of burgers sold each day was greater at Newgale beach than at
Solva car park.
[3]
d Learner’s own answers. For example:
I agree because the median and mode are both greater at Newgale beach than
at Solva car park.
5 a 40
[2]
[1]
b
Station Modal class interval
Class interval where
the median lies
Estimate of mean
Ashton
0 ⩽ t < 10
10 ⩽ t < 20
15.75
Burton
0 ⩽ t < 10
0 ⩽ t < 10
17.5
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
[4]
3
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END OF UNIT 15 TEST ANSWERS
c
Learner’s own answers. For example:
The median delay is less at Burton station than at Ashton station. However,
the mean delay is less at Ashton station than at Burton station. The modal class
interval is the same for both stations.
(Answers must be supported by the data to get the marks)
[2]
d Learner’s own answers. For example:
I would rather go to Ashton station because the mean delay is less. Also,
Ashton station had less than half the number of trains delayed between
30 and 40 minutes compared to Burton station.
[2]
[Total: 45 marks]
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4