RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
1 Integers, powers and roots
F Exercise 1.1 Directed numbers
1 a −3.3
b −8.7
c 13.3
d −13.3
2 a 12
b 12.3
c −1.9
d 1.9
3 a 3.7
b −20.5
c 20.5
d −3.7
5 a N = −7
b N = −8.5
c N = −10.8
6 a −6.8
b 1.2
c −27.6
d −3.5
c 14.8
d −3.7
4 −4.4 °C
7
×
−1.2
3
−1.1
1.32
−3.3
−0.5
0.6
−1.5
8 a 7.4
b 9.4
e −2
9 A and B are 6 and −6 so A − B is either 12 or −12.
F Exercise 1.2 Square roots and cube roots
1 a 7
b 12
c 19
d 7
d 3 < 3 55.5 < 4
2 a 92 = 81 < 95 and 102 = 100 > 95 so 9 < 95 < 10
b 43 = 64 < 95 and 53 = 125 > 95 so 4 < 3 95 < 5
3 a 19 < 385 < 20
b 7 < 3 500 < 8
c 8 < 69.8 < 9
4 a 12 < N < 15
b 10 < M < 20
c 0< 3R <5
5 a 26
6
3
b 25.5
c 26.5
200 < 6 because 6 = 216. 200 > 14 because 14 = 196. 6 is less than half of 14.
3
2
7 a 802 = 6400 < 7500
b 203 = 8000 > 7500
8 a 5.5
b 21
c 29
d 7.4
e 13.2
9 a 2.45
b 7.75
c 24.49
d 6.53
e 1.56
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Unit 1 Answers to Practice Book exercises
F Exercise 1.3 Indices
1 a 625
b 243
2 a 0.125
b 0.25
3 1 , 12 , 6 , 2 and 4 (the same), 3
12
1
2
6
3
d 1
e 1
c 0.25
d 0.333…
e 0.001
c
1
36
8
4
4 3−3, 2−4 and 4−2 (the same), 5−1, 1−5
5 a 42
b 44
c 40
d 4−1
e 4−3
6 a 24
b 28
c 20
d 2−2
e 2−6
7 −4
1 or 2−1
2
8 a
b 21 5
16
F Exercise 1.4 Working with indices
1 a 85
b 74
c 26
d r6
e s6
2 a 43
b 6
c c4
d 24
e e
d 1
e e−1
3 a × a is equal to a . All the rest are equal to a .
0
5
6
4 a 729
b 81
2
5 a a
b 6−2
c 8
1
9
b 1
c
7 a a4
b 55
c f2
8 a 1
b 0
c 4
6 a
2
5
k
Cambridge Checkpoint Mathematics 9
1
100
d
1
2
d 104
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
2 Sequences and functions
F Exercise 2.1 Generating sequences
1
a
b
c
d
e
f
g
h
i
Linear, term-to-term rule is ‘add 4’.
Linear, term-to-term rule is ‘add 1’.
Non-linear, term-to-term rule is ‘add 1, add 2, add 3, ...’ .
Linear, term-to-term rule is ‘subtract 7’.
Non-linear, term-to-term rule is ‘subtract 4, subtract 5, subtract 6, ...’ .
Linear, term-to-term rule is ‘subtract 3’.
Linear, term-to-term rule is ‘add1 1 ’.
2
Linear, term-to-term rule is ‘subtract 1.1’.
Non-linear, term-to-term rule is ‘add 5, add 4, add 3, ...’ .
2 a 9, 5, 1, −3
b 1 1 , 3, 4 1 , 6
c −3, −2, 0, 3
d 10, 9, 6, 1
e 64, 32, 16, 8
f −64, −32, −16, −8
2
2
3 20. Check students’ methods.
4
1 , 1, 3, 9. Check students’ methods.
3
5 a 6, 7, 8, 9
e 4, 7, 12, 19
b −6, −5, −4, −3
f −1, 2, 7, 14
c 3, 5, 7, 9
g 2, 8, 18, 32
d 2, 5, 10, 17
h 4, 10, 20, 34
6 a i 5
c i 5
ii 7
ii 20
iii 23
iii 500
b i 0
d i −99
ii 5
ii −96
iii 45
iii 0
7 Term = 5 × position number + 4
8 Term = position number 2 + 3
F Exercise 2.2 Finding the nth term
1
a 5, 10, 15, 50
d −6, −2, 2, 30
b 5, 6, 7, 14
e 9, 8, 7, 0
c 10, 12, 14, 28
f −8, −18, −28, −98
2 A: i, B: iv, C: ii, D: v, E: iii
3 a 2n + 18
f 10 − 3n
b 2n + 2
g 14 − 7n
c 8n − 5
h −20 + 5n
d 4n − 12
i −n − 1
e 8−n
4 a 58
f −50
b 42
g −126
c 155
h 80
d 68
i −21
e −12
5 The sequence increases by 2 each time, so should include a 2n term, not a 5n term.
6 Yes. The number of squares increases by 4 each time (term-to-term rule is ‘add 4’), so the nth term will
start with 4n. The number of squares in the patterns is: 1, 5, 9, 13 and 4 × 1 − 3 = 1, 4 × 2 − 3 = 5,
4 × 3 − 3 = 9, 4 × 4 − 3 = 13.
7 Mia. Each pattern increases by three dots (term-to-term rule is ‘add 3’), so the nth term will start with 3n. The
numbers of dots in the patterns are: 6, 9, 12, 15 and 3 × 1 + 3 = 6, 3 × 2 + 3 = 9, 3 × 3 + 3 = 12, 3 × 4 + 3 = 15.
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Unit 2 Answers to Practice Book exercises
F Exercise 2.3 Finding the inverse of a function
1 a
y=x+8
b y=x−8
2 a
x→x−7
b x→x+7
3 a
y=x +4
b y= x −3
4 a
3
x
x→ −5
2
5 a i x→5–x
iii x → 100 – x
b i and iii
2
d y = 8x
8
c x→ x
7
d x → 7x
c y = 3(x − 4)
4
x
b x→ +2
c x → 2(x + 5)
5
ii x → x − 3 or 3 − x or 1 − 13 x
−3
3
iv x → x − 4 or 4 − x
−7
7
(
)
d y = 4x − 3
d x → 2x − 5
11 − 1 = 1.2
5
6 a
x → 5(x + 1)
b
7 a
x→x −3
b 4 × 2.25 + 3 = 12
4
c y= x
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
3 Place value, ordering and rounding
F Exercise 3.1 Multiplying and dividing decimals mentally
1 a 1.2
f 0.24
b 2.6
g 0.28
c 3.6
h 0.45
d 8.1
i 1.4
e 3.3
j 5.55
2 a 20
f 250
b 40
g 300
c 30
h 3000
d 40
i 200
e 200
j 400
3 A, C, E, I (0.024); D, G, J, L (0.24); B, F, H, K (2.4)
4 a B
b B
c C
d B
5 a 0.12
f 30
b 1.35
g 9
c 0.072
h 5
d 0.15
i 7
e 0.055
j 40
6 Top: 2.5 × 0.2 = 0.5, not 5. Bottom: 5 × 0.1 = 0.5, not 50. Answer = 1.
7 a 20
b 30
c 500
d 0.2
8 a i 1.1
b Larger
ii 2.2
iii 3.3
iv 4.4
v 5.5
9 a i 80
b Larger
ii 40
iii 20
iv 16
v 10
vi 6.6
F Exercise 3.2 Multiplying and dividing by powers of 10
1 a 2800
e 280 000
i 0.028
b 28 000
f 0.2
j 0.28
c 280
g 28
k 0.028
d 2880
h 0.2
l 28.8
2 a 3.4
e 0.034
i 3400
b 3.4
f 0.034
j 30 400
c 0.034
g 34
k 30
d 0.034
h 3.4
l 340
3 Powers of ten – easy!
4 a
0.04 ÷ 10−2
=4
4 × 100
0.4 × 101
b
400 ÷ 102
0.004 × 103
670 ÷ 103
6.7 ÷ 101
= 0.67
6.7 × 10−1
40 ÷ 101
670 × 10−3
67 ÷ 102
67 × 10−2
5 a i 5000
b Larger
ii 500
iii 50
iv 5
v 0.5
vi 0.05
6 a i 0.099
b Smaller
ii 0.99
iii 9.9
iv 99
v 990
vi 9900
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Unit 3 Answers to Practice Book exercises
F Exercise 3.3 Rounding
1 a 21.7
b 18.55
c 0.847
d 0.99
e 9.5960
f 34.590
2 a 74.0
b 73.95
c 73.953
d 73.9530
e 73.953 02
f 73.953 017
3 a 2000
b 760
c 5.37
d 0.08
e 0.20
f 6.04
4 a D
b A
c C
d D
5 a 300 000
b 250 000
c 254 000
d 254 100
e 254 060
f 254 060
h 254 059.95
i 254 059.952
ii
ii
ii
ii
ii
b i
d i
f i
h i
g 254 060.0
6 2700 km
7 0.0259 g
8 200 000
9 a i
c i
e i
g i
i i
120
12 000
1 000
25
20
119
12 600
962
18.6
17.2
400
80
3
4
ii
ii
ii
ii
401
83.6
2.89
5.19
F Exercise 3.4 Order of operations
1 a 28
f 13
k 14
b 5
g 0
l 41
c 25
h 9
m 19
d 6
i 19
n 17
e 11
j 62
o 9
2 a <
b =
c >
d >
e >
f =
3 a û, 12
b ü
c û, −3
d ü
e û, 6
f û, 4
4 a i Added before multiplying
b i Should have squared the 3 before subtracting the result from 14
c i Should have worked out the numerator and denominator separately before dividing
ii 30
ii 50
ii 2
5 No. Harsha doesn’t understand that 3x means 3 × x. Ahmad doesn’t understand the BIDMAS rules. Answer = 46
6 a 22
2
b 7
c 100
Cambridge Checkpoint Mathematics 9
d 90
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
4 Length, mass, capacity and time
F Exercise 4.1 Solving problems involving mesurements
1 a 53.25 g
b 1.875 g
2 3 days
3 8 hours and 20 minutes
4 1165 miles ≈ 1864 km
5 a 53.3 cm
b 9
6 a 63
b 3
c $340
F Exercise 4.2 Solving problems involving average speed
1 58 km/h
2 12 km
3 20 minutes and 50 seconds
4 13 00 or 1 p.m.
5 14 km/h
6 a 38 minutes
b 39 km/h
c 6 hours and 20 minutes
7 10.4 m/s
8 32 m/s
9 0.432 km/h
10 17 500 mph
F Exercise 4.3 Using compound measures
1 Aeroplane A. For aeroplane A, speed = 349 km/h; for aeroplane B, speed = 332 km/h.
2 34 – 20 = 14 km/h
3 a Monday = 21.25 km/h, Thursday = 22.5 km/h.
b Thursday
4 a 6 pack = 96.5 cents each, 20 pack = 98.5 cents each.
b The 6 pack
5 a The can = 0.148 cents/ml, the bottle = 0.1345 cents/ml.
b The bottle
6 Neither. 375 g box = 0.44 cents/g, 650 g box = 0.44 cents/g.
7 175 ml tube. 50 ml tube = 1.58 cents/ml, 175 ml tube = 1.31 cents/ml.
8 a 34 clues = 18 seconds/clue, 80 clues = 16.5 seconds/clue.
b The 80-clue crossword.
9 a i 21.6 km/h
ii 13.5 km/h
b To his grandmother’s house
c 16.6 km/h
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
5 Shapes
F Exercise 5.1 Regular polygons
1 The exterior angle is 360° ÷ 8 = 45°. The interior angle is 180° − 45° = 135°.
2 a 150°
3 a
b 156°
Number of sides
Exterior angle
Interior angle
5
72°
108°
10
36°
144°
20
18°
162°
40
9°
171°
b It is halved.
4 a 18
b 20
5 a 36
b 45
c 120
6 a The exterior angle is 24°. 360 ÷ 24 = 15. Yes, it has 15 sides.
b The exterior angle is 48°. 360 ÷ 48 = 7.5 which is not a whole number. It is not possible.
7 9 sides
8 24 sides
F Exercise 5.2 More polygons
1 a 1080°
b 1620°
c 1800°
2 130°
3 If the shape is a polygon with 7 sides, the sum of the angles is 5 × 180° = 900°. If the shape has 6 sides,
the sum is 720°. If the shape has 5 sides, the sum is 540°.
4 a 4, because the sum of the angles of a quadrilateral is 360°.
b (N − 2) × 180 = 720 → N − 2 = 4 → N = 6. Six sides.
c (N − 2) × 180 = 1440 → N − 2 = 8 → N = 10. Ten sides.
5 a 70°
b The sum is (2 × 80°) + (3 × 30°) + 110° = 360°.
6 a (N − 2) × 180 = 1980 → N − 2 = 11 → N = 13. It could be the sum of the interior angles of a 13-sided polygon.
b 2160
7 a 90°
b 30°
8 a 5 sides
b 8 sides
c 60°
F Exercise 5.3 Solving angle problems
1 a 40° + 30° = 70°, the exterior angle of triangle PQR.
b 30°, alternate angles
c 40°, alternate angles
2 a Triangle OXZ is isosceles, so a = (180 − 72) ÷ 2 = 54.
b 72° is the exterior angle of isosceles triangle OZY, so b = 72 ÷ 2 = 36.
c Angle OZY = b° = 36°, as triangle OZY is isosceles. Angle XZY = a° + OZY = 54° + 36° = 90°.
3 The angle opposite 104° is also 104° because the shape is a kite. d° = 360° − (104° + 104° + 57°) = 95°
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Unit 5 Answers to Practice Book exercises
4 Extend the line segment DC.
a = 72, alternate angles; b = 180 − 72 = 108.
c = 57, alternate angles; d = 180 − 57 = 123.
A
B
57°
5 T
he angles of the squares and triangles at the point add
up to 2 × 60° + 2 × 90° = 300°. The remaining angle is
360° − 300° = 60°, which is the angle of an equilateral triangle,
so it will fit exactly.
72°
c°
d°
D
6 r is the fourth angle of a quadrilateral so
r = 360 − (95 + 110 + 100) = 55. s makes a triangle with
r and 100° so s = 180 − (55 + 100) = 25.
t makes a triangle with 95° and r so t = 180 − (55 + 95) = 30.
b° a°
C
F Exercise 5.4 Isometric drawings
1
Other views are possible.
a
b
c
2 21 cm and 28 cm
3
4
or
2
Cambridge Checkpoint Mathematics 9
and
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises Unit 5
5
Other views are possible.
F Exercise 5.5 Plans and elevations
1 a
b
c
B
B
A
A
P
P
P
P
A
A
P
P
B
B
A
A
2 a
b
3 a 5
b
Copyright Cambridge University Press 2013
B
B
Cambridge Checkpoint Mathematics 9
3
RM.DL.BOOKS GROUPS
Unit 5 Answers to Practice Book exercises
F Exercise 5.6 Symmetry in three-dimensional shapes
1 a
b
2
Two like this
Two like this
4
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises Unit 5
3
4 a
5 a Four
b
Cube
b
Two like this
Two like this
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
5
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
6 Planning and collecting data
F Exercise 6.1 Identifying data
1 a
b
c
d
e
f
More men than women like gardening.
Women think men with spiky hair look silly.
Girls are better than boys at texting quickly.
Boys can throw a ball more accurately than girls can.
Good cooks go to resaurants more often than bad cooks do.
Girls who drink lots of water have clearer skin than those who don’t.
2 a For example:
1. Right-handed students are better at writing their name using their left hand than left-handed students are at
writing their name using their right hand.
2. ‘Are you right or left handed?’, ‘Please write your name, using your left hand and then your right hand.’
3. People’s left- or right-handedness and their own names, written with both their left and right hands.
4. Ask people to write on a piece of lined paper.
5. About 75 students.
6. Only give people one chance to write their name as neatly as possible.
b Age, neatness of normal writing, how many left-handed students there are.
c Lots of right-handers but not many left-handers, how to judge how much worse people’s handwriting is when
writing with the wrong hand, some students may think it is a silly idea and refuse.
3 a For example:
1. There are usually more pictures in my dad’s newspaper than in my magazine.
2. How many pictures are there in the newspaper and in the magazine.
3. Number of pictures in several copies of the newspaper and in the same number of copies of the magazine.
4. Read through both the newspapers and magazines and count all pictures.
5. Five copies of the newspaper and of the magazine
6. Count every picture
b Does the newspaper have different number of pictures depending on the day?
c Might not be able to get copies of her dad’s newspapers?
4 aNeed equal numbers of boys and girls in the sample. Need to have a wide range of students, not just those on
her bus.
b Need to have a range of ages, not just in his year group. Need to ask a range of students, not just those that
obviously like hockey.
F Exercise 6.2 Types of data
1 a
b
c
d
Primary. Easy to do a survey on your family.
Secondary. Only the airport would be able to get such a large amount of information.
Secondary. No one could collect that information by themselves.
Either: Secondary. Can’t collect this information for the whole country/world.
Or: Primary. Could survey women in my area.
e Either: Secondary. Can’t collect this information for the whole country/world.
Or: Primary. Could do a survey of the motorcycles passing my house or ask at local garages
or motorcycle sale-rooms.
f Either: Secondary. Can’t collect this information for the whole country/world.
Or: Primary. Could survey the people going to my local supermarket.
2 a Madrid is the capital of Spain, what is sold in this area of Spain might be the same as is sold in other areas.
b Tourists probably read different magazines when they are on holiday compared to when they are at work.
Many tourists will not be Spanish, but most people living in Madrid are, so they might read different
magazines.
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Unit 6 Answers to Practice Book exercises
3 a Mexico is a neighbour of USA, and so they might buy the same types of laptop.
b USA is the richest country in the world, so possibly the people who buy laptops there will spend more money
than people in Mexico.
F Exercise 6.3 Designing data-collection sheets
1
Number
Tally
Frequency
1
2
3
4
5
6
Total
2
Make of motorcycle
Tally
Frequency
BMW
Ducati
Harley Davidson
Honda
Moto Guzzi
Other
Total
3
Number of brothers
Tally
Frequency
0
1
2
3
4
Total
4 a No option for 1, 2, 3 or 4 pairs of shoes; overlapping values.
b
Number of pairs of
shoes
Tally
Frequency
0
1–5
6–10
more than 10
Total
2
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises Unit 6
F Exercise 6.4 Collecting data
1 a
Number
Tally
Frequency
1
//// /
6
2
////
5
3
////
4
4
////
5
Total
20
b 1 is the most common number rolled. 3 is the least common number rolled.
2 a
Mass (grams)
Tally
Frequency
70–79
//
2
80–89
////
5
90–99
//// /
6
100–109
////
5
110–119
//
2
Total
20
b The most common mass for new-born kittens is 90–99 g.
3 a
Number of texts sent
Tally
Frequency
0–9
////
4
10–19
////
5
20–29
////
4
30–39
////
4
40–49
/
1
Total
18
b The most common number of texts sent was 10–19.
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
3
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
7 Fractions
F Exercise 7.1 Writing a fraction in its simplest form
1 a 53
5
b 2
9
b 2
3
2 a 1
3 a
c 57
b 4
2
2
5
d 4
e 2
5
d 3
7
d 7
12
c 5
6
c 4
7
3
e 5
12
e 4
5
F Exercise 7.2 Adding and subtracting fractions
1
a 3
9
10
h 15
14
b
8
g 13
20
c 1
d 2
i 11
27
j
2
3 a  1 + 6 = 7 + 18 = 25 , 25 = 1 4
3
7
21
21
21 21
21
10
20
4 a 4 16
b 8 43
1
g 7 14
h 48
20
9
11
f 6
11
f
f 1
l
3
11
48
 9 +1 4 = 10 4
21
21
 87 = 4 7
b  33 − 39 = 165 − 78 = 87
4
2
21
k 1
12
e
9
5
26
f 53
20
20
c 81
8
20
d 3 13
30
57
9
i 1
j
2
21
5 For example: 1 1 + 1 1 = 3, 1 1 + 1 3 = 3 1
2
2
3
4
12
3
1
6 a 8 m
b 2 m
c Check students’ methods.
10
20
7 a 58 m
b Check students’ methods.
e 8 11
24
k 4 11
40
7
f 7 20
7
l 9 36
F Exercise 7.3 Multiplying fractions
1 a 9
b 12
c 15
d 33
e 30
f 33
2 a 6 43
b 9 13
c 3 13
d 13 51
e 11 51
f 21 13
3 a 18
7
15
h 51
b 5 14
f 22 12
c 35
d 19
e 21
f
b
35
1
g 9
3
4 a 3 20
e 2 16
25
48
7
i 11
9
c 4 14
g 10
24
1
j 9
d 11 23
2
h 2 21
40
6
k 11
9
13
6
l 25
5 For example: 1 × 1 = 1 , 2 × 5 = 10
2
1
6 a 16
2
4 3
7
21
1
b 15
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Unit 7 Answers to Practice Book exercises
F Exercise 7.4 Dividing fractions
1
a 35
b 24
c 22
d 27
e 45
f 28
g 25
h 15 43
i 88
j
35 51
k 16 12
l 20 14
2 a 15
16
b 4 16
c 1 19
26
1
d 114
e 2 49
f 4 51
g 10
11
11
h 116
i 1 13
j
k 1
l 4 12
3 a 25
26
b 3 18
c 53
5
d 1 21
3 19
g 6 73
h 16
63
e 4
f
1
4 For example: 1 ÷ 1 = 2 , 2 ÷ 3 = 10
2
5
5 a 12
4
b 4 54
3
5
9
c 13
21
d 1 51
F Exercise 7.5 Working with fractions mentally
1 a 14
b 56
c 23
7
d 10
7
e 1 20
3
f 50
g 56
7
h 12
j
1
110
1
k 1 20
l 1 11
24
1
2 a 10
1
b 15
d 13
e 59
2
f 15
3
g 10
1
h 20
l 11
24
b 92
e 20
63
81
f 200
g 51
7
h 20
k 12
l 15
22
4 a 12
b 14
e 6
f 1 18
1
h 2 10
3
28
d 12
35
j 16
d 16
j 1 12
7
k 12
3 a 16
9
20
4
c 25
1
i 18
9
c 28
i 15
22
1
c 3
11
i 12
k 78
11
l 114
3
7 a 28
5
b 28
c 57
8 a 73
b 72
g 89
i
j
7
5 15
6
2
11
40
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
8 Constructions, shapes and Pythagoras’ theorem
F Exercise 8.1 Constructing perpendicular lines
1 Check students’ drawings, all measurements ± 2 mm and ± 2°.
2 Check students’ drawings, all measurements ± 2 mm and ± 2°.
3 Check students’ drawings, all measurements ± 2 mm and ± 2°.
4 a Check students’ drawings, all measurements ± 2 mm and ± 2°.
b i 30° ± 2°
ii 180° − 90° − 60° = 30°
5 Check students’ drawings, all measurements ± 2 mm and ± 2°.
6 Check students’ drawings, all measurements ± 2 mm and ± 2°.
7 a Check students’ drawings, all measurements ± 2 mm and ± 2°.
b i 180° ± 2°
ii 360° − 90° − 90° = 180°
F Exercise 8.2 Inscribing shapes in circles
1 a Check students’ constructions of an inscribed equilateral triangle, including construction lines.
b Check students’ constructions of an inscribed regular octagon, including construction lines.
2 a Check students’ constructions, including construction lines.
b 7.1 cm ± 2 mm
c Shaded area = 78.5 – [students’ x2] = 25.2 to 30.9 cm2
3Check students’ constructions of the inscribed regular octagon and the inscribed circle, including construction
lines.
Inner circle: radius of 6.2 cm to 6.7 cm, area of 120.70 cm2 to 140.95 cm2
Area of octagon = 137.28 cm2 to 147.41 cm2
4 aCheck students’ constructions of inscribed square, including construction lines. Measurement of side length
of 11.1 cm to 11.5 cm. Area of square = 123.21 cm2 to 132.25 cm2.
Praise, but do not allow alternative method, not involving construction.
b Check students’ explanations involving knowledge that one area must be a quarter (or four times) the area
of the other when dimensions are doubled.
c Check students’ constructions of inscribed square, including construction lines. Measurement of side length
of 5.5 cm to 5.9 cm. Area of square = 30.25 cm2 to 34.81 cm2.
Praise, but do not allow alternative method not involving construction.
F Exercise 8.3 Using Pythagoras’ theorem
1 a a2 = 676, a = 26 cm
b a2 = 62 + 2.52 = 42.5, a = 6.5 cm
2 a c 2 = 2500 – 1600 = 900, c = 30 cm
b c 2 = 2.52 – 22 = 2.25, c = 1.5 m
3 13 cm
4 14.14 cm
5 9.43 km
6 2.24 m or 224 cm
7 33 cm
8 502 cm2
9 78.5 cm2
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
9 Expressions and formulae
F Exercise 9.1 Simplifying algebraic expressions
1
a a7
g g4
b b10
h h4
c c15
i i5
d d10
j j6
e e6
k k
f f4
l l7
2 a 4a4
g 8g 8
b 16b8
h 3h6
c 36c12
i 2x 3
d 64d 6
j 5x 8
e 10e11
k 5x 4
f 12f 10
l 11x
3 a B
b A
c A
d D
4 a One group has x6 terms and one group has x9 terms.
b 9x12 ÷ x9 = 9x3: this is the only one with power of 3; all others are to the power of 9 or 6.
F Exercise 9.2 Constructing algebraic expressions
1
a n+1
b n − 10
c 100n
d
n −5
4
g 6n − 7
h n +9
8
i
k 3(n + 20)
l 20(n − 3)
f
n
1000
1
n −1
2 a 6x
b 3x + 10
c 12x − 2
d 13x − 4
3 a xy
b y2
c 4xy
d 16x2
b i 2b + 2
d i 12d − 2
ii 5b − 20
ii 5d2 − 5d
4 a i 2a + 16 ii 5a + 15
c i 4c − 16 ii c2 − 8c
e 2n + 3
j
10
2n
5 a i 2(a + 3) + 2(3a + 1) = 8a + 8, 4(2a + 2) = 8a + 8
ii 3(a + 3) + 3(3a + 1) = 12a + 12, 6(2a + 2) = 12a + 12
iii 5(a + 3) + 5(3a + 1) = 20a + 20, 10(2a + 2) = 20a + 20
b n black rods + n striped rods = 2n white rods (or similar explanation given in words)
c i 4(a + 3) + 2(2a + 2) = 8a + 16 , 8(a + 2) = 8a + 16
ii 6(a + 3) + 3(2a + 2) = 12a + 24, 12(a + 2) = 12a + 24
iii 8(a + 3) + 4(2a + 2) = 16a + 32, 16(a + 2) = 16a + 32
d 2n black rods + n white rods = 4n grey rods (or similar explanation given in words)
F Exercise 9.3 Substituting into expressions
1
a −8
e −8
i −4 1
2
2 a 15
e 8
i 8
b −4
f 3
j 12
c −7
g 5
k −26
d −2
h 94
l −11
b 20
f −64
j 2
c −20
g 2
k −25
d 11
h −7
l 10
3 a For example: Let a = 2, 10a2 = 10 × 22 = 40 and (10a)2 = (10 × 2)2 = 400, so 10x2 ≠ (10x)2
b For example: Let b = 2, (2b)3 = (2 × 2)3 = 64 and 2b3 = 2 × 23 = 16, so (2b)3 ≠ 2b3
c For example: Let c = 2 and d = 3, 3c − 3d = 3 × 2 − 3 × 3 = −3 and 3(d − c) = 3(3 − 2) = 3, so 3c − 3d ≠ 3(d − c)
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Unit 9 Answers to Practice Book exercises
F Exercise 9.4 Deriving and using formulae
1 a H = 24D
b H = 240
c D=H
d D = 20
2 a D = 150
b D = 180
c S = 20
d T = 5.5
3 a F = 25
e e=5
b F = 54
f a=7
c I = 40
d I = 21
4 a d+3
b T = 2d + 3
c T = 19
d d = T −3
5 a 50%
b 8%
c 110%
6 a 450 m
b 1303 m
c 1078 m
24
e 12
2
d 1615 m
7 Anders is correct. 20 °C = 68 °F and 68 °F > 65 °F.
F Exercise 9.5 Factorising
1
a 6(a + 4)
d g(7g + 1)
b 3(3c – 5)
e 4(2 – 3j)
c 4f(e + 4)
f m(7m – 4)
2 a 5(z + 3)
e 2(3v + 4)
i 3(4 − 5w)
b 2(y – 7)
f 7(2u − 3)
j 8(2 + 3x)
c 4(5x + 1)
g 6(2 − u)
k 2(4 + 7y)
d 3(3w − 1)
h 7(2 + 3v)
l 7(2 − 5z)
3 a m(7m + 1)
e 3s(1 + 4s)
i 7e(2i − 1)
b 5a(a – 3)
f 4y(3 − 4y)
j 4a(3 + 2b)
c t(t + 9)
g 8(2e − i)
k 3g(7 + 5h)
d 4h(2 − h)
h 3(5e + 2i)
l 15w(2 − t)
4 a 2(a + 2h + 4)
d e(3e + 4 + f)
b 5(b – 5 + j)
e k(7 – k – a)
c 4(3tu + 4u – 5)
f 3n(2n – 3 + m)
5 5(3x − 2) − 5(2 + x) = 15x − 10 − 10 − 5x = 10x − 20 = 10(x − 2)
Tanesha’s mistake was expanding −5(2 + x) to give −10 + 5x, which adds to 15x − 10 to give 20x − 20.
F Exercise 9.6 Adding and subtracting algebraic fractions
1 a 23x
y
2
g
2 a
g
x+y
2
4a + 5b
20
b 35x
c x3
d 47x
h 14 y
i 15y
j
9
2x + y
6
21
a
+ 4b
h
28
b
18
c
i
9x + y
12
10a + 15b
18
d
j
2y
9
15x − y
18
5a − 7b
35
e 34x
f
17 y
24
l
k
7x − 8 y
12
15
a
− 2b
k
24
e
f
l
2x
5
5y
16
7 x − 15 y
18
12a − 35b
42
3 a A, D, F each equal 1 x and B, C each equal 1 x.
b E, which equals 1 .
4
2
3
c You can ignore the letter, work out the fractions, then put the letter back in at the end.
2
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises Unit 9
F Exercise 9.7 Expanding the product of two linear expressions
1 a x2 + 7x + 10
d x2 − 3x − 18
g x2 + 15x + 50
b x2 + 7x + 6
e x2 − 6x + 9
h x2 + 5x − 50
c x2 + 2x − 8
f x2 − 13x + 40
i x2 − 15x + 50
2 a B
b A
c C
3 a a + 4a + 4
d d2 − 6d + 9
b b + 8b + 16
e e2 − 10e + 25
c c + 2c + 1
f f 2 − 2f + 1
2
4 a
b
c
d
2
d C
2
ii a2 − 16
iii a2 − 81
i a2 − 1
There is no term in x, and the number term is a square number.
a2 − 64
a2 − b2
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
3
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
10 Processing and presenting data
F Exercise 10.1 Calculating statistics
1 a 0
b 1
c 1.7 or 1.71
2 a 1
b 2
c 2.55
3 a 50–55 minutes
d i 1
ii 2
iii 2.67
b The median is in the class 55–60.
4 a The mode is 5 and the median is 4.
b The mean is 156 ÷ 40 = 3.9 which is less than the median of 4.
5 10.125 kg
6 a 31–35 seconds
b 21–25 seconds
c
26–30 seconds
F Exercise 10.2 Using statistics
1 aThe median is 41 and the mean is 40.3. Both show that the average is above 40. The mode is not a good
choice here.
b There is no reason to complain if the average is above 40.
2 The median is 19 (< 20) and the mean is 21.1 (> 20).
3 aYou can use the modal class or the median. The modal class for the boys is 36–40 and for the girls it is 41–45.
The median for the boys is in the class 36–40 and for the girls it is in the class 41–45, so the girls have done
better than the boys.
b The range for the boys is greater because there are no girls in the lowest class.
4 a The mean.
b They had all played 14 games.
c 1 045 980
5 a The Book Club. The medians are 35 and 47.
b The Music Club. The ranges are 24 years and 15 years.
6 The men. The median for the men is in the class 40–44; for women it is in the class 35–39.
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
11 Percentages
F Exercise 11.1 Using mental methods
1 a $468
b $702
c $117
d
$23.40
2 a For example: Find 25% (a quarter) and 10% (divide by 10) and add them.
b i 15.4 kg
ii 98 m
iii $30.80
3 a 219.3
b 2646
c 57.6
d
320
4 a 204.12 kg
b $136.08
c 816.48 m
d
40.824 litres
5
Amount
164
328
82
16.4
32.8
65% of the amount
106.6
213.2
53.3
10.66
21.32
6 a C, 69% of 272
b The rest are all equal. This one should be 69% of 282 to be the same as the others.
7 a 1024
b 1536
c 2112
d
3712
8 D C A B
F Exercise 11.2 Comparing different quantities
1 No. 76% for English and 82% for science.
2 9% of the young people and 27% of the older people wear glasses. The percentage of the older people is greater.
3 a Rovers 45%, United 62%
4 a 56% (or 55.6%)
5 a
b
c
d
b United, because the percentage is higher.
b 44% (or 44.1%)
i 36%
ii 64%
68% were boys and 32% were girls.
Yes. 23/75 = 31%.
Yes. 62% of the girls chose tennis but only 31% of the boys.
F Exercise 11.3 Percentage changes
1 Carpet 14% (or 13.8%), table 22% (21.7%), chair 42% (41.7%)
2 7% (6.5%)
3 3% (3.125%)
4 a 6.6% increase
b 10.4% decrease
c 7.2% decrease
5 a 10%
b 9.1%
c 8.3%
6 a 130% (129.7%)
b About 67.5 million
7 a 12.5%
b 11.1%
8 a A: 50%, B: 33.3%, C: 25%
b A is the best.
Copyright Cambridge University Press 2013
d 7.1%
c 75 km/h (74.9)
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Unit 11 Answers to Practice Book exercises
F Exercise 11.4 Practical examples
1 Radio 30% profit; Television 11.1% profit; Computer 11.5% loss; Jewellery 25.5% profit.
2 $225
3 a $53 300
b $270
c 4%
4 12.4% profit
5 Hockey stick $81.75; football boots $100.28; track suit $140.61.
6 $1287.50
7 18%
8 a $0
2
b $1350
c $5250
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
12 Tessellations, transformations and loci
F Exercise 12.1 Tessellating shapes
1 Check students’ tessellations; each should show at least five of the shape being tessellated.
2 Check students’ explainations, involving corners of square = 90° and 360 ÷ 90 = 4 (i.e. no remainder),
with a suitable diagram.
3 Exterior angle = 36°, so interior angle = 144° and 360 ÷ 144 = 2.5 (i.e. not a whole number).
F Exercise 12.2 Solving transformation problems
1
y
3
2
1
c
a
0
–4 –3 –2 –1 0 A 1
–1
d
–2
b
–3
2
2
3
x
4
y
6
5
4
c
3
B
2
a
b
1
0
0
3
1
2
3
4
y
6
5
6
7
6
7
x
d
5
a
4
b
C
3
2
1
c
0
0
4 a
1
2
3
4
5
x
y
6
y
6
yb
6
y
6
5
5
5
5
4
4
4
4
3
3
3
3
2
2
2
2
1
1
1
1
0
0
a
a
0
x
1 02 13 24 35 46 57 6
Copyright Cambridge University Press 2013
7
0
x
0
b
b
0
x
1 02 13 24 35 46 57 6
7
x
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Unit 12 Answers to Practice Book exercises
5
y
4
3
2
1
0
–4 –3 –2 –1 0
–1
–2
Q –3
P
1
R
2
3
4
x
–4
6 a A(2, 6), B(7, 6), C(6, 3) and D(0, 2).
c A´(6, 2), B´(6, 7), C´(3, 6) and D´(2, 0).
d The x- and y-coordinates have changed places.
b
y
7
B′ y = x
6
A
5
C′
B
4
C
3
2
D
1
A′
D′
0
0
1
2
3
4
5
6
7
x
7 The shape is symmetrical about the line y = 3, so when it is reflected in the line y = 3 the shape stays in the same
position. The shape has rotational symmetry of order 4 about the centre (3, 3), so when the shape is rotated 90°
about (3, 3) it again stays in the same position. So the starting shape and finishing shape are exactly the same, in
exactly the same position.
F Exercise 12.3 Transforming shapes
1
y
6
5
c
b
0
–6 –5 –4 –3 –2 b–1–1 0
A
2 a
b
c
d
e
f
g
h
2
d
4
c
3
2
1
–2
–3
–4
–5
–6
1
2
3
d
4
5
6
x
a
a
Reflection in the y-axis.
Reflection in the line y = 1.
Reflection in the line y = 2.
Reflection in the line y = −2.
Reflection in the line x = −2.
Rotation 90° anticlockwise about (0, 0).
Rotation 180° about (0, 1).
Rotation 180° about (–2, –1).
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises Unit 12
3 a i
Rotation 90° anticlockwise about (−1, 3).
4
ii
Translation  
–4
iii Reflection in the line x = −1.
iv Reflection in the line x = −3.5.
b i Check students’ combinations of at least two transformations.
ii Check students’ combinations of at least two transformations.
F Exercise 12.4 Enlarging shapes
1
y
4
3
2
1
0
–4 –3 –2 –1–1 0
1
2
3
4
x
–2
2 a Enlargement scale factor 3, centre (6, 2).
b Enlargement scale factor 2, centre (3, 5).
3 Enlargement scale factor 3, centre (6, 1).
4 a
y
4
3
2
1
0
–6 –5 –4 –3 –2 –1–1 0
1
2
3
4
x
–2
–3
b Grid showing a square and its enlargement with centre of enlargement anywhere except (0, 0) and words to
the effect that in this case multiplying the coordinates by 2 does not make the equal to the coordinates of the
enlarged square
F Exercise 12.5 Drawing a locus
1
A
4.5 cm
2
3
3 cm
3 cm
3 cm
3 cm
4 cm
P
4 cm
6 cm
4 cm
Q
4 cm
4 Check students’ circles; they must have a radius of 3 cm.
G
6 cm
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
3
RM.DL.BOOKS GROUPS
Unit 12 Answers to Practice Book exercises
5
C
6 cm
1.5 cm
8 cm
6 a
b
c
7 W
X
Z
Y
8
W
X
160 km
Check students’ circles; they must have radii of 5 cm and 4 cm.
4
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
13 Equations and inequalities
F Exercise 13.1 Solving linear equations
1 a g = 12
b g = −5
c g = −10
d g=7
2 a p = 5.25
b p=0
c p=7
d p = 0.5
3 a y = 2 74
b y =11 16
c y = 3 18
d y = 5 79
4 a x = −8
b x = −3
5 a 5x + 15 = 10x − 20 → x = 7
c x = −12 13
d x = −2
b x + 3 = 2x − 4 → x = 7
6 a 8x − 32 + 20 − 4x = 0 → 4x − 12 = 0 → x = 3
b 2(x − 4) + 5 − x = 0 → 2x − 8 + 5 − x = 0 → x − 3 = 0 → x = 3
7 a x=4
b x = −3
8 a 5x + 30 = 60 − 2x
c x = 11
b x = 4 72
9 Multiplying out the brackets: 4x − 8 = 40 − 2x → 6x = 48 → x = 8.
Dividing by 2: 2(x − 2) = 20 − x → 2x − 4 = 20 − x → 3x = 24 → x = 8.
Both give x = 8.
F Exercise 13.2 Solving problems
1 a n + 2(n + 3) = 90 → 3n + 6 = 90
b n = 28
c 28 and 62
2 a x + 50 and 2x + 80
b 2x + 80 = 144
c x = 32
3 a s + 2s + 2s + 5 = 100 → 5s + 5 = 100
b s = 19
c 43 cm
4 a y + 3y + y − 2 + 4(y − 2) = 116
b y = 14
c 48
5 a 5(x − 8) = 2(x + 10)
b 20
6 a 2a + 6(a − 2) = 44 or a + 3(a − 2) = 22 → 4a − 6 = 22
b 7 cm and 15 cm
F Exercise 13.3 Simultaneous equations 1
1 x = 6, y = 18
2 x = 6, y = −3
3 x = 2, y = 5
4 a x = 6, y = 24
b x = 4, y = 6
c x = 1, y = −3
5 (2 × 4) + (3 × 5) = 23 and (5 × 4) + (2 × 5) = 30
6 x = 10, y = 20
7 x = 1.6, y = 18.4
8 x = 14, y = −9
9 x = −2, y = 4
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Unit 13 Answers to Practice Book exercises
F Exercise 13.4 Simultaneous equations 2
1 a x = 18, y = 2
b a = 9.5, b = 5.5
c p = −4, q = 8
2 a x = 9, y = 3
b x = 9, y = 6
3 a x = 2.5, y = 10
b x = 12, y = 14
4 a x = 7.5, y = 5.5
b Using the values in part a, 2x + y = 20.5 and not 19.
5 a x = 6, y = 10
b x = 3.5, y = 3
c a = 3, b = −1
F Exercise 13.5 Trial and improvement
1 a x=9
b x = 10
c x=3
2 8.7
3 3.2
4 a 0.9
b 12.5
5 If x = 4.8, x² − 4x = 3.84. If x = 4.9, x² − 4x = 4.41.
6 x = 2.3. Here are some possible values.
x
2
3
2.5
2.2
2.3
x² + 3x
10
18
13.75
11.44
12.19
7 x = 2.7
8 x = 1.6 and x = 4.4
F Exercise 13.6 Inequalities
b x ≥ −6
1 a x>2
c x<0
d x ≤ 10
2 a
–3 –2 –1 0 1
b
0
c
d
–3
–10
3.5
0
0
10
20
3 a Could be true.
b Could be true.
c Must be true.
d Cannot be true.
4 a x ≥ 0.5
b x<3
c x ≤ 13
d x < 6.5
5 a x ≤ 10
b x>4
c x≥2
6 a A + A + 5 + 2(A + 5) < 100 → 4A + 15 < 100
b A < 21.25
c Because if A < 21.25 then 2(A + 5) < 52.5.
7 a x + 2x + 3(x − 10) < 360 → 6x − 30 < 360
b x < 65
c Yes. 2x = 3(x − 10) → x = 30 and this is in the solution set.
2
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
14 Ratio and proportion
F Exercise 14.1 Comparing and using ratios
1 a Banana yellow 1 : 0.6, Mellow yellow 1 : 0.71
b Mellow yellow
2 a Gavin 1 : 3.5, Matt 1 : 3.3
b Gavin
3 a 1 : 13.12
b 1 : 15.67
c Raine’s
4 a 1 : 1.41
b 1 : 1.34
c The Bounders
5 300 g
6 a 2.5 kg cement and 5 kg lime
7
b 27.5 kg
Activity
Child : staff
ratios
Number of
children
Number of
staff
Horse-riding
4:1
22
6
Sailing
5:1
17
4
Rock-climbing
8:1
30
4
Canoeing
10 : 1
26
3
Total:
17
c $312
d €258.50
8 a $744
b $525
9 a $154
b Check students’ methods for checking.
F Exercise 14.2 Solving problems
1 a
b
c
d
e
f
Yes, as the number of bottles bought increases, so does the total cost (the ratio stays the same).
No, the ratio does not stay the same.
Yes, as the number of stamps bought increases, so does the total cost (the ratio stays the same).
Yes, as the distance increases, so does the time taken (the ratio, on average, stays the same).
No, the ratio does not stay the same.
No, the ratio does not stay the same.
2 a $50
b $75
c $187.50
3 a $33.30
b $20.35
4 a $1.18
b $1.15
c 120 tea bags
5 a The box of 50 pens
b The 750 g pack of cereal
c The 450 ml pot of yoghurt
6 £208
7 a S$517.50
b A$104
8 €187 = $239.74, $254 = €198.12. He should buy the phone in Paris.
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
15 Area, perimeter and volume
F Exercise 15.1 Converting units of area and volume
1
a
d
g
j
2 a
d
g
j
70 000 cm2
500 mm2
9 m2
3 cm2
b 8000 cm2
e 40 mm2
h 3.4 m2
k 2.8 cm2
c
f
i
l
32 500 cm2
920 mm2
0.5 m2
0.8 cm2
2 000 000 cm3
8000 mm3
9 m3
7 cm3
b 240 000 cm3
e 500 mm3
h 0.48 m3
k 0.23 cm3
c
f
i
l
5 600 000 cm3
7200 mm3
82.2 m3
77.6 cm3
b 348 ml
e 8.4 litres
h 3900 cm3
c 2500 ml
f 0.92 litres
i 880 cm3
3 a 70 ml
d 7 litres
g 8000 cm3
4 a 12.2425 m2. Check that students check correctly, using estimation.
b $312. Check that students check correctly, using inverse operations.
Wall 2: 8.28 m2
5 Wall 1: 10.08 m2
2
Wall 3: 9.72 m
Wall 4: 10.44 m2
2
Total = 38.52 m
Check students’ own choice of method for checking the answer.
F Exercise 15.2 Using hectares
1
a 40 000 m2
e 8200 m2
b 52 000 m2
f 340 m2
c 9000 m2
d 452 000 m2
2 a 7 ha
e 0.07 ha
b 3.2 ha
f 237.5 ha
c 67 ha
d 0.88 ha
3 a 151200 m2
b 15.12 ha
4 a 39861 m2
b 3.9861 ha
5 a 28275 m
b 2.8275 ha
c $6220.50
d Check students’ own methods for checking their answers by estimation.
2
6 Area = 98 701 m2
Cost = $38 493.39
$38 493.39 < $40 000 so he can afford it.
Check students’ own methods for checking their answers by estimation.
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Unit 15 Answers to Practice Book exercises
F Exercise 15.3 Solving circle problems
1 a A = 12.6 cm2, C = 12.6 cm
c A = 254.5 cm2, C = 56.5 cm
b A = 66.5 m2, C = 28.9 m
d A = 21.2 m2, C = 16.3 m
2 a A = 113.5 cm2, P = 43.7 cm
c A = 402.1 cm2, P = 82.3 cm
b A = 904.8 mm2, P = 123.4 mm
d A = 88.4 m2, P = 38.6 m
3 a d = 8.37 cm
b d = 28.49 mm
c d = 1.51 m
d d = 11.30 cm
4 a r = 7.07 cm
b r = 3.82 m
c r = 0.53 m
d r = 10.78 mm
5 1.4 cm (14 mm)
6 7.59 m (759 cm)
7 27 cm2
8 a 168.18 cm2
b 120.82 cm2
F Exercise 15.4 Calculating with prisms and cylinders
1 a 150 cm3
2
c 427.5 cm3
Area of cross-section
Length of prism
Volume of prism
a
8.4 cm2
20 cm
168 cm3
b
24 cm
2
6.5 cm
156 cm3
c
58 m2
5.7 m
330.6 m3
d
56.85 mm2
62 mm
3524.7 mm3
3 a V = 480 cm3, SA = 416 cm2
c V = 675 cm3, SA = 558 cm2
b V = 576 cm3, SA = 544 cm2
4 a V = 754.0 cm3, SA = 477.5 cm2
c V = 42 411.5 mm3, SA = 8482.3 mm2
b V = 492.6 cm3, SA = 401.1 cm2
5
Radius of circle
Area of circle
Height of cylinder
Volume of cylinder
a
7 cm
153.94 cm
12 cm
1847.26 cm3
b
1.5 m
7.07 m2
2.4 m
16.96 m3
c
9 cm
254.47 cm2
7.51 cm
1910 cm3
d
2.19 m
15 m
3.8 m
57 m3
e
4.55 mm
65 mm2
22 mm
1430 mm3
6 a x = 4.3
2
b 129.6 cm3
2
2
b x = 3.3
Cambridge Checkpoint Mathematics 9
c x = 2.1
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
16 Probability
F Exercise 16.1 Calculating probabilities
1 a 0.9
b 0.7
c 0.45
2 a 0.95
b 0.9
c 0.15
3 a 5%
b 80%
c 15%
4 a 0.15
b 0.85
c 0.2
5 a 1
16
b 7
16
6 a 0.17
b 0.31
c 0.11
F Exercise 16.2 Sample space diagrams
1 a
T
+
+
H
+
+
H
T
+
+
+
+
+
+
+
+
+
+
+
+
2 a 6
5
4
3
2
1
+
+
+
+
+
+
b The probabilities are 1 and 1 . One is twice the other.
2
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
4
b i
11
36
ii 1
iii 2
b i
1
6
ii 5
iii 1
b i
1
3
ii 2
b i
1
4
ii 3
6
9
1 2 3 4 5 6
3 a 4
+
+
+
+
3
+
+
+
+
2
+
+
+
+
0
2
4
6
4 a C
+
+
+
B
+
+
+
A
+
+
+
A
B
C
5 a D
+
+
+
+
C
+
+
+
+
B
+
+
+
+
A
+
+
+
+
A
B
C
D
Copyright Cambridge University Press 2013
6
6
3
4
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Unit 16 Answers to Practice Book exercises
6 1 and 4
5
7 a
5
3
16
8 a 0.1
b 13
16
b 0.18
c 0.16
F Exercise 16.3 Using relative frequency
1 a 0.46
b 0.67
c 0.21
2 a i A: 0.72, B: 0.77
ii A: 0.18, B: 0.16
iii A: 0.10, B: 0.08
b School B. The probability of a student being normal weight is higher, and the probabilities of a student being
underweight or overweight are lower than in school A.
3 a 0.64
b 0.8
4 a City 0.12, Mountain View 0.17
b City 0.57, Mountain View 0.33
c City. It has a higher probability of a good grade, and a lower probability of a poor grade.
5 a i 0.27
ii 0.16
b Afternoon trains are more likely to be on time and are less likely to be early or late.
6 a i 0.58
ii 0.17
b It is not a good way. One reason is that it makes a difference whether a team is playing at home or away.
2
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
17 Bearings and scale drawing
F Exercise 17.1 Using bearings
1 a 065°
b 145°
2 a 057°
b 237°
3 a 110°
b 045°
c 200°
d 315°
c 155°
d 275°
e 330°
4 a Ai 036°
Aii 216°
b Answer to ii = answer to i + 180°
c Ai 083°
Aii 263°
Bi 124°
Bii 304°
Ci 073°
Cii 253°
Bi 137°
Bii 317°
Ci 022°
Cii 202°
5 a Ai 238°
Aii 058°
b Answer to ii = answer to i – 180°
c Ai 232°
Aii 052°
Bi 288°
Bii 108°
Ci 261°
Cii 081°
Bi 336°
Bii 156°
Ci 198°
Cii 018°
F Exercise 17.2 Making scale drawings
1 a Check students’ scale drawings.
b 178 km
c 286°
2 a Check students’ scale drawings.
b 229 km
c 090°
3 a Check students’ scale drawings.
b 26 km
c 247°
4 7.4 km, 218°
5 Their paths cross, so they could collide. It depends on when they start moving and how fast they travel.
Students’ scale drawings should show that the paths cross.
6 a 24 km
b 14 cm
7 a 256 km
b 5.75 cm
8 She ran 12.5 km, so she raised $450.
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
18 Graphs
F Exercise 18.1 Gradient of a graph
1 a 1
b 2
c 1
2 a −1
b −5
c − 13
3
y
4
4
b
3
2
1
a
–4 –3 –2 –1 0
–1
1
2
3
4
5
6
x
7
8
9 10
7
8
9 10 x
c
–2
–3
–4
4
y
8
7
6
5
d
4
b
3
c
2
1
–4 –3 –2 –1 0
–1
1
2
3
4
5
6
–2
–3
–4
–5
–6
–7
–8
5 a 2.5
b −1.5
c 0.5
6 a 0.1
b 0.05 or 1
c −0.1
7 a 25
b 0.1
c −1
20
Copyright Cambridge University Press 2013
d −5
d 2
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Unit 18 Answers to Practice Book exercises
F Exercise 18.2 The graph of y = mx + c
1 a
b All have gradient 4.
y
8
7
6
5
ii
iii
i
4
3
2
1
–2 –1 0
–1
1
2
3
4
x
–2
–3
–4
–5
–6
–7
–8
2 a A and B
b −4 (C)
c A and D
3 a y = −2x
b y = −4 − 2x
c y = 4 − 2x
b −10
4 a If x = 0, y = 50 − 10 × 0 = 50; if x = 5, y = 50 − 10 × 5 = 0
5 a −25
b 25
c 50
c y = −10x
d 75
6 A, C and D are parallel; B and E are parallel.
F Exercise 18.3 Drawing graphs
1
a i y = −x + 12
ii y = −2x + 12
iii y = − 12 x + 6
b i −1
ii −2
iii − 12
2 a y = 1.5x − 3
b
c 1.5
y
8
6
4
2
–4 –2 0
–2
2
4
6
8
x
–4
–6
–8
3 a y = 0.1x + 1.4 is the equation of a straight line.
4 a 1.5
b −0.4
c −1
b
0.1
d 5
5 a The top line. It passes through (0, 5).
b 5x + 8y = 0 (through the origin) and 5x + 8y = 20 (through (0, 2.5))
2
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises Unit 18
6 a y = 0.05x + 5 or y = 1 x + 5
b 0.05 or 1
20
c
20
y
10
8
6
4
2
–140
–120
–100
–80
–60
–40
0
–20
20
40
80
60
100
120
140
x
–2
7 a −10
b −0.1
8 a – 23
c 50
b c = 2 and d = 3
d 0.02
F Exercise 18.4 Simultaneous equations
1 a x = −4 and y = −7
b x = −1 and y = 2
c x = 2 and y = −1
2 a x = 3.2 and y = 4.6
b x = −0.8 and y = 2.6
c x = 1.4 and y = −1.9
3 a i
ii y = x − 3
b
y = −x + 5
y
6
4
2
–2 0
–2
2
4
6
8
x
–4
–6
d −x + 5 = x − 3 → 8 = 2x → x = 4 and then y = x − 3 = 4 − 3 = 1
c x = 4 and y = 1
4 a, b
c x = −3 and y = 6
y
8
6
4
2
–6 –4 –2 0
–2
2
4
6
8 10
x
–4
–6
–8
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
3
RM.DL.BOOKS GROUPS
Unit 18 Answers to Practice Book exercises
5 a and b
c i x = 2 and y = 60
y
100
ii x = 4 and y = 20
80
60
40
20
–6 –4 –2 0
–20
2
4
6
8 10
x
–40
6 The graph should look like this. x = 3.4 and y = −0.9
y
2
1
–4 –3 –2 –1 0
–1
1
2
3
4
5
6
x
–2
–3
–4
–5
–6
F Exercise 18.5 Direct proportion
Other scales are possible for the graphs.
1 a
Dollars ($)
y
150
b 1.64
c D = 1.64E
b y = 7.35g
c i $24.99
d i $484
ii €179.88
(100, 164)
100
50
0
50
100
Euros (€)
y
40
2 a
x
ii 2.72 grams
(5, 36.75)
Dollars
30
20
10
0
4
1
2
3 4
Grams
5
x
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises Unit 18
b
y
15000
Litres of fuel
3 a 15 000 litres
(60, 15000)
10000
5000
0
4 a
Length of hair (cm)
c f = 250m
d i 41 250 litres
y
4
Distance (cm)
x
ii 400 minutes or 6 hours and 40 minutes
b 0.3
c l = 0.3w
d 333 weeks or about 6.4 years
b 16.5
c Just over 6 minutes or about 6 minutes and 4 seconds
(12, 3.6)
3
2
1
0
5 a
10 20 30 40 50 60
Minutes
5
y
40
15
10
Weeks
x
(2, 33)
30
20
10
0
1
2
Minutes
x
F Exercise 18.6 Practical graphs
Other scales are possible on the graphs.
a h = 2 + 0.5d
b
c i 4 metres
h
7
Height in metres
1
ii 9 days
6
5
4
3
2
1
0
0
Copyright Cambridge University Press 2013
1
2
3
4
5 6
Days
7
8
9 10 d
Cambridge Checkpoint Mathematics 9
5
RM.DL.BOOKS GROUPS
Unit 18 Answers to Practice Book exercises
2 a D = 3w + 20
b
c i $32
D
60
ii 10 weeks
Dollars
50
40
30
20
10
0
0
3 a n = 14 000 − 500m
1
b
2
3
4
5 6
Weeks
7
8
9 10 w
c 8 minutes
n
14000
People
12000
10000
8000
6000
4000
2000
0
0
4 a t = 30 − 4d
b
1
2
3
4
5 6 7
Minutes
8
9 10 m
c On the 8th day ( 7 1 days)
t
32
2
28
Tablets
24
20
16
12
8
4
0
0
5 a L = 20 000 − 1500d
1
b
2
3
4 5
Days
6
7
8 d
1
3
4
5
L
20000
18000
Water (litres)
16000
14000
12000
10000
8000
6000
4000
2000
0
0
c 12 500 litres
6
d
2
6
7 8
Days
9 10 11 12 13 14 d
13 days (13 13 )
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises Unit 18
b
Population (millions)
6 a P = 25 + 0.1y
c 30 years
P
30
25
20
15
10
5
0
0
Copyright Cambridge University Press 2013
10
20
30
Years
40
50
y
Cambridge Checkpoint Mathematics 9
7
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
19 Interpreting and discussing results
F Exercise 19.1 Interpreting and drawing frequency diagrams
1
a 32
b
Time, t (minutes)
c
Frequency
Mid-point
10 ≤ t < 12
4
11
12 ≤ t < 14
16
13
14 ≤ t < 16
7
15
16 ≤ t < 18
5
17
Time taken by 9C to complete
cross-country run
18
16
Frequency
14
12
10
8
6
4
2
0
10
d
12
14
16
Time (minutes)
18
5
8
2 a 50
b
Wednesday
Saturday
Height, h (cm)
Frequency
Midpoint
Height, h (cm)
Frequency
Midpoint
120 ≤ h < 140
4
130
120 ≤ h < 140
25
130
140 ≤ h < 160
6
150
140 ≤ h < 160
16
150
160 ≤ h < 180
22
170
160 ≤ h < 180
7
170
180 ≤ h < 200
18
190
180 ≤ h < 200
2
190
c
Heights of people on roller coaster
Wednesday
Saturday
35
Frequency
30
25
20
15
10
5
0
120
140
160
180
Height (cm)
200
d For example: On Saturday there were fewer taller people and more shorter people. There were only two people
with a height between 180 cm and 200 cm on Saturday compared with 18 on Wednesday. There were 25 people
between 120 cm and 140 cm on Saturday compared with four on Wednesday.
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Unit 19 Answers to Practice Book exercises
3 a
Hours of training each week by
athletes at two clubs
Falcons Club
Harriers Club
Frequency
30
20
10
0
0
5
10
15
20
Number of hours
25
b For example: The most popular training time for the Falcons Club was between 5 and 10 hours, whereas for
the Harriers Club it was between 15 and 20 hours. In the Falcons Club only 22 athletes trained for more than
15 hours a week compared with 42 athletes from the Harriers Club.
c Falcons Club 68, Harriers Club 70
d Yes, because the number of athletes surveyed at each club was nearly the same.
F Exercise 19.2 Interpreting and drawing line graphs
1
a
Average monthly rainfall in Faro, Portugal
100
90
80
Rainfall (mm)
70
60
50
40
30
20
10
0
J
F
M
A
J
M
J
A
S
O
N
D
Month
b For example: The year starts with just under 80 mm of rain in January, then there is less rain every month until
July. July is the driest month. After July it starts getting wetter each month for the rest of the year, with a large
increase in rain in October.
c February and March
2 a
Company profit
Profit ($ millions)
7
6.5
6
5.5
2002
2004
2006 2008
Year
2010
2012
b For example: The profit is increasing by a roughly similar amount each year.
c $6 million
d Answer from $6.8 million to $6.9 million (inclusive)
2
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises Unit 19
3 a
Daily temperatures in Marrakech in July
Temperature (ºC)
Maximum temperature (ºC)
Minimum temperature (ºC)
40
30
20
10
0
Mon
Tues
Wed
Thur
Day
Sat
Fri
Sun
b For example: The maximum temperatures increased from Monday to Thursday, then decreased for the next
two days, finally increasing again on Sunday. The minimum temperatures stayed the same for the first two days
then increased until Thursday, then decreased each day for the rest of the week.
c Wednesday
4 a 42 million
b 2002 to 2004
c 2008 to 2010
d Yes, the figures are increasing each year, but by a smaller amount each time. The increases between the years
shown are 5 million, 4 million, 3 million and 2 million, so an estimate for the number of visitors in 2012 could
be an extra 1 million added on to the 2010 figure, i.e. 50 million.
F Exercise 19.3 Interpreting and drawing scatter graphs
a
Spelling test score
1
25
Time spent reading and spelling test score
20
15
10
5
0
0
5
10
15
Hours reading
20
25
b Positive correlation. The more hours reading a student does, the better their spelling test score.
2 a
Art and Science exam results
90
Science result (%)
80
70
60
50
40
30
20
10
0
30
40
50
60
70
Art result (%)
80
90
b Negative correlation. The better the students’ result in art, the worse their science result.
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
3
RM.DL.BOOKS GROUPS
Unit 19 Answers to Practice Book exercises
3 a
Number of packets of biscuits and crisps sold
Number of packets
of crisps sold
30
25
20
15
10
5
0
0
5
10
15
20
25
Number of packets of biscuits sold
30
b No correlation. The number of packets of biscuits sold has no relationship to the number of packets
of crisps sold.
4 a Negative correlation. The further the house is from the railway station, the less it is worth.
b The house that doesn’t fit the trend is worth $146 000 and is 6 km from the train station.
For example: It might not be in a very good state of repair, which is why it isn’t worth as much as it should be.
F Exercise 19.4 Interpreting and drawing stem-and-leaf diagrams
1
a
June
6
6
6
5
3
August
3
2
0
2
9
7
3
6
7
8
1
0
4
0
3
7
5
0
2
4
8
0
6
2
5
6
8
8
Key: For June, 0 | 2 means 20 customers
For August, 3 | 6 means 36 customers
b
i Mode
ii Median
iii Range
iv Mean
June
46
43
48
44
August
58
51
26
49
c In August the mode, median and mean are all greater than in June, showing that on average there are more
customers. The range, however, is smaller in August than in June, showing that there is more variation in the
numbers of customers riding in June.
d Yes, because the mode, median and mean are all greater in August than in June.
2 a
i Mode
ii Median
iii Range
iv Mean
Girls’ times
27.3
26.05
2.6
26.1
Boys’ times
26.5
27.4
3.6
27.3
b For example: The range is larger for the boys, showing that their times are more varied. The girls have a lower
median and mean which shows that using these averages they were quicker at solving the puzzle.
c The mode, as the boys’ mode is lower than the girls’, which makes them appear faster.
d The median or the mean, as the girls’ median and mean are lower than the boys’, so the girls were faster.
e The girls, as their median and mean are lower, therefore they were faster than the boys.
3 a
Top shelf
9
8
7
6
5
Middle shelf
9
4
10
9
2
2
11
5
4
2
0
12
0
7
9
0
13
0
2
6
8
14
2
4
5
7
9
9
Key: For the top shelf, 4 | 10 means 104 boxes of cereal
For the middle shelf, 11 | 5 means 115 boxes of cereal
4
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises Unit 19
b
Mode
Median
Range
Mean
Top shelf
112
123
26
120.5
Middle shelf
139
137
32
134.5
For example: The sales of cereal were better on the middle shelf as on average more boxes were sold (the mean,
median and mode were all greater on the top shelf than the middle shelf). The sales on the middle shelf were
more varied, but included the largest number of boxes sold on one day. The smallest number of boxes sold on
one day were on the top shelf.
F Exercise 19.5 Comparing distributions and drawing conclusions
1 For example: On Saturday 20 more cars were parked for less than 2 hours than on Wednesday. On Saturday the
most popular length of time in the car park was between 2 and 4 hours, whereas on Wednesday it was between 6
and 8 hours. On Wednesday there were 38 cars parked for between 4 and 6 hours, compared with 16 on Saturday.
2 For example: The most popular mass of suitcase going to Spain was between 18 and 20 kg compared with 22 to
24 kg going to Sweden. There were 10 cases over 24 kg going to Sweden compared with 4 going to Spain. There
were 16 cases less than 18 kg going to Spain compared with 6 going to Sweden.
3 a Yes, as the graph has a positive correlation.
b No, she should get a mark between about 52% and 60%.
4
Mode
Median
Range
Mean
Team A
18
19
16
21.25
Team B
28
27.5
7
27.25
For example: Steph is correct in saying that on average team A are younger as their mode, median and mean are
all less than team B. However, team A have a larger range which means that team B are more similar in age, so this
part of her statement is incorrect.
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
5