RM.DL.BOOKS GROUPS
Answers to Practice
Practice Book exercises
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
3 a 3.7
b 12.3
b −20.5
c −1.9
c 20.5
d 1.9
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
1 a
2
Exercise 1.2
Square roots and cube roots
b 12
7
c 19
a 92 = 81 < 95 and 10 2 = 100 > 95 so 9 <
b 43 = 64 < 95 and 5 3 = 125 > 95 so 4 <
3 a 19 <
385
4 a 12 <
N
< 20
< 15
5 a 26
6
3
200
3
95
95
< 10
<5
b 7 < 3 500 < 8
c 8<
b 10 <
c 0<
M
< 20
b 25.5
< 6 because 63 = 216.
200 >
d 7
698
.
3
R
<9
d 3 < 3 555
. <4
<5
c 26.5
14 because 142 = 196. 6 is less than half of 14.
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
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Cambridge Checkpoint Mathematics 9
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RM.DL.BOOKS GROUPS
Unit 1
Answers to Practice Book exercises
F Exercise 1.3
Indices
1
36
d
1
8
1 a 625
b 243
c
e 1
2 a 0.125
b 0.25
c 0.25
d 0.333…
e 0.001
3 112, 121, 62, 26 and 43 (the same), 34
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
8 a
1
2
or 2−1
F Exercise 1.4
b 21 5
16
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
3 a0 × a5 is equal to a5. All the rest are equal to a6.
4 a 729
b 81
2
−1
5 a a
6 a 1
b 6
b 1
c 8
1
c
d 1
d 1
7 a a4
b 55
c f2
d 104
8 a 1
b 0
c 4
9
2
−2
k
100
Cambridge Checkpoint Mathematics 9
e e
2
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RM.DL.BOOKS GROUPS
Answers to Practice
Practice Book exercises
exercises
2 Sequences and functions
F Exercise 2.1
1
Generating sequences
a Linear, term-to
term-to-term
-term rule is ‘add 4’
4’..
b
c
d
e
f
g
h
i
Linear,
term-to-term
term-to
-term rule is
‘add
1’.. 1, add 2, add 3, ...’ .
1’
Non-linear,
term-to-term
rule
is ‘add
Linear, term-to
term-to-term
-term rule is ‘subtr
‘subtract
act 7’.
Non-linear,, term-to-term rule is ‘subtract 4, subtract 5, subtract 6, ...’
Non-linear
...’ .
Linear, term-to
term-to-term
-term rule is ‘subtr
‘subtract
act 3’.
Linear, term-to-term rule is ‘add 1 1 ’.
2
Linear, term-to
term-to-term
-term rule is ‘subtr
‘subtract
act 1.1’
1.1’..
Non-linear, term-to
term-to-term
-term rule is ‘add 5, add 4, add 3, ...’ .
2 a 9, 5, 1, −3
d 10, 9, 6, 1
b
1
1
2
, 3,
4
1
2
,6
e 64, 32, 16, 8
c −3, −2, 0, 3
f −64, −32, −16, −8
3 20. Check students’ methods.
4
1
,
3
1, 3, 9. Check students’ methods.
5 a 6, 7, 8, 9
b −6, −5, −4, −3
c 3, 5, 7, 9
d 2, 5, 10, 17
e 4, 7, 12, 19
6 a i 5
c i 5
f −1, 2, 7, 14
ii 7
ii 20
g 2, 8, 18, 32
iii 23
iii 500
h 4, 10, 20, 34
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
b 5, 6, 7, 14
e 9, 8, 7, 0
a 5, 10, 15, 50
d −6, −2, 2, 30
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 5 n 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:
i s: 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 3 n. The
numbers of dots in the
t he 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
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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
b
y=x
2 a
x
−7
b
x
3 a
y=
4
b
y=
b
ii
x
→
x
→
iv
x
→
→
+8
x
x +
3
x − 5
4 a x→ 2
5 a i x→5–x
iii
x
→
100 – x
→
−8
x+
x
7
−3
4
x +
x
c
y
=
c
x
→
c
y
= 3(x − 4)
c
x
→
8
x
7
d
y=
d
x
d
y=
d
x
8x
→
7x
4x − 3
2
5
− 3 or 3 − x
−3
3
x − 4
4
or − x
−7
7
x
(
or1
−
2(x + 5)
1
x
3
)
→
2x − 5
b i and iii
2
6 a
x
→
7 a
x
→
5(x + 1)
x
−3
4
b
11
5
− 1 = 1.2
b 4 × 2.25
2.25 + 3 = 12
12
Cambridge Checkpoint Mathematics 9
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RM.DL.BOOKS GROUPS
Answers to Practice
Practice Book exercises
exercises
3 Place value, ordering and rounding
F Exercise 3.1
Multiplying and dividing decimals mentally
1 a 1.2
b 2.6
c 3.6
d 8.1
e 3.3
f 0.24
2 a 20
f 250
g 0.28
b 40
g 300
h 0.45
c 30
h 3000
i 1.4
d 40
i 200
j 5.55
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
ii 40
iii 20
iv 16
v 10
vi 6.6
b Larger
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
b
0.004 × 10
4 × 10
3
0
400
÷
10
=4
0.4 × 10
1
2
0.04
40
÷
67
÷
2
−
10
1
670
÷
÷
10
2
3
= 0.67
10
1
6.7 × 10−
10
3
670 × 10−
6.7
1
10
2
67 × 10−
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
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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
d
f
h
g 254 060.0
6 2700 km
7 0.0259 g
8 200 000
9 a
c
e
g
i
i
i
i
i
i
120
12 000
1 000
25
20
F Exercise 3.4
119
12 600
962
18.6
17.2
i
i
i
i
400
80
3
4
ii
ii
ii
ii
401
83.6
2.89
5.19
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 >
3 a
û,
12
b
ü
c
û,
−3
d
ü
e
û,
f =
6
4 a i Added before multiplying
b i Should have
have squared the
the 3 before
before subtracting the
the result from 14
14
c i Should hav
havee worked
worked out the
the numerator
numerator and denominator
denominator separately
separately before dividing
f
û,
4
ii 30
ii 50
ii 2
5 No. Harsha doesn’t understand that 3 x 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
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RM.DL.BOOKS GROUPS
Answers to Practice
Practice Book exercises
4 Length, mass, capacity and time
F Exercise 4.1
1 a 53.25 g
Solving problems involving mesuremen
mesurements
ts
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
F Exercise 4.2
Solving problems involving average speed
c $340
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.
4 a 6 pack = 96.5 cents
cents each, 20 pack = 98.5 cents
cents each.
b Thursday
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.
seconds/clue,
e, 80 clues = 16.5 seconds/clue.
8 a 34 clues = 18 seconds/clu
b The 80-clue crossword.
9 a i 21.6 km/h
ii 13.5 km/h
b To his grandmo
grandmother’s
ther’s house
c 16.6 km/h
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Answers to Practice
Practice Book exercises
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°
Num
umb
ber of sid
ides
es
Ext
xte
eri
rio
or an
angl
gle
e
Int
nter
eriior an
angl
gle
e
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
6
c 120
a The exterior angle is 24°. 360 ÷ 24 = 15. Yes, it has 15 sides.
b The exterior angle is 48°. 360
360 ÷ 48 = 7.5
7.5 which is not a whole number.
number. It is not possible.
7 9 sides
8 24 sides
F Exercise 5.2
1 a 1080°
More polygons
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
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°)
80°) + (3 × 30°) + 110°
110° = 360°.
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
F Exercise 5.3
c 60°
Solving angle problems
1 a 40° + 30° = 70°, the exterior
exterior angle of triangle PQR.
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
the exterior angle of isosceles triangle OZY,
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
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RM.DL.BOOKS GROUPS
Unit 5
4
Answers to Practice Book exercises
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 The 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.
6
72°
c°
d°
D
b°
a°
C
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
Exercise
se 5.4
F Exerci
1
so t = 180 − (55 + 95) = 30.
Isometric drawings
Other views are possible.
a
b
c
2 21 cm and 28 cm
3
4
or
2
Cambridge Checkpoint Mathematics 9
and
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RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
5
Unit 5
Other views are possible.
F Exercise 5.5
Plans and elevations
1 a
A
B
P
b
P
c
A
B
P
A
2 a
b
3 a 5
b
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B
Cambridge Checkpoint Mathematics 9
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RM.DL.BOOKS GROUPS
Unit 5
Answers to Practice Book exercises
Exercise
se 5.6
F Exerci
Symmetry in three-dimens
three-dimensional
ional shapes
1 a
b
2
Two like this
Two like this
4
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
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Answers to Practice Book exercises
Unit 5
3
4 a
5 a Four
b
Cube
b
Two like this
Two like this
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Cambridge Checkpoint Mathematics 9
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Answers to Practice
Practice Book exercises
6 Planning and collecting data
Exercise
se 6.1
F Exerci
Identifying data
1 a More men than women like gardening
gardening..
b
c
d
e
f
W
omen
hair look
silly.
Girls
arethink
bettermen
thanwith
boysspiky
boys
at texting
quickly.
quickly
.
Boys can
can throw
throw a ball more accurately than
than girls can.
can.
Good cooks go to resaura
resaurants
nts more often than bad cooks do.
Girls who drink lots of water have clearer skin
skin than those who
who don’t.
don’t.
2 a For example:
1. Right-handed students
students are better at writing their name using their left hand than left-handed
left-handed students are at
writing their name using their right hand.
2. ‘Are
Are you right or left handed?’
handed? ’, ‘Please write
wri te your name, using your left hand and then your right hand.’
hand.’
3. People
People’’s left- or right-handedness and their own names,
names, written with both their left and right hands.
4. Ask people to
to write on a piece
piece of lined paper.
paper.
5. About 75 students.
6. Only give people one
one chance to write their name as neatly as possible.
normal writing, how
how many left-handed students
students there
there are.
b Age, neatness of normal
right-handers
handers but not many left-handers, how to judge how much worse people’s handwriting is when
c Lots of rightwriting 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
dad’s newspaper than
t han in my magazine.
2. How many
many pictures are there
there in the newspaper and
and in the magazine.
3. Number of pictures in several copies of
of the newspaper and in the same number of copies
copies of the magazine.
4. Read through both the newspapers and magazines
magazines and count
count all pictures.
5. Five copies of the newspaper
newspaper and of the magazine
6. Count every picture
b Does the newspaper have
have different
different number of pictures depending
depending on the
the day?
c Might not be able to get copies
copies of
of her dad’s newspapers?
4 a Need equal numbers of boys and
and girls in the sample. Need to have a wide range of students, not just those on
on
her bus.
have a range of ages, not just in his year group. Need to ask a range of
of students, not just those
those that
b Need to have
obviously like hockey.
F Exercise 6.2
Types of data
1 a
b
c
d
Primar y. Easy to do a survey on your family.
Primary.
Secondary.. Only the
Secondary
the airport would be able to
to get such a large amount of
of information.
Secondary.
Secondar
y. No one could collect that informati
information
on by themselves.
Either: Secondary. Can’t collect this informati
information
on for the whole country/world.
Or: Primary. Could survey women in my area.
Either:
Secondary. Can’t collect this informati
information
on for the whole country/world.
e
Or: Primary. Could do a survey of the motorcycles
motorcycles passing my house or ask at local garages
or motorcycle sale-rooms.
f Either: Secondary. Can’t collect this informati
information
on for the whole country
country/world.
/world.
Or: Primary. Could survey the people going to my local supermarket.
2 a Madrid is the capital of
of Spain, what is sold in this area of Spain might
might be the same as is sold in other areas.
b Tourists probabl
probablyy 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.
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Cambridge Checkpoint Mathematics 9
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Unit 6
Answers to Practice Book exercises
3 a Mexico is a neighbour of USA, and
and so they might buy the same types of
of laptop.
b USA is the richest country in the world,
world, so possibly
possibly the people who buy laptops there
there will spend more money
than people in Mexico.
F Exercise 6.3
1
Number
Designing data-collectio
data-collection
n sheets
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
values .
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
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Answers to Practice Book exercises
F Exercise 6.4
1 a
Unit 6
Collecting data
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
of texts sent was 10–19.
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Answers to Practice
Practice Book exercises
exercises
7 Fractions
F Exercise 7.1
Writing a fractio
fraction
n in its simplest form
1 a
3
5
b
2 a
1
2
b
2
b
3 a
5
c
5
2
9
c
5
6
d
2
c
4
d
4
5
3
Exercise
se 7.2
F Exerci
1
3
4
3
g
1
a

6
7
18
25 25
1
,
+
=
+
=
3
7
21
21
21 21
b

33
a
4
1
6
b
8
g
7
1
14
h
4
b
3
h
20
4
39
−
10
5 For example:
6
a
8
7
a
5
8
3
20
m
m
1
20
b
6
3
4
b
3
a
18
b
g
1
9
a
3
e
2
6 a
5
14
78
−
20
8
21
2
1
10
f
9
11
4
f
e
7
e
12
5
6
11
1
i
1
=
d
2
1
1
27
4
21
1
c
8
i
1
8
2
k
26
9 +1 4

20
e
5
j

2
9
21
87
=
20
4
=
10
2
21
1
12
f
1
l
11
f
7
7
20
l
9
7
36
3
48
4
21
7
20
d
3
13
30
e
8
j
5
7
9
k
4
11
24
11
40
m
c Check students’ methods.
Multiplying fractio
fractions
ns
9
c 15
1
3
7
15
1
5
3
20
b
5
16
25
f
22
1
16
c
87
=
3
4
h
5 For example:
5
12
3
7
3
b Check students’ methods.
2 a
4
1
b 12
35
3
5
2
1
1
1
3
1
+1
= 3, 1
+1
= 3
2
2
3
4
12
F Exercise 7.3
1 a 9
9
10
165
=
7
f
e
4
5
Adding and subtracting fractions
a
8
d
7
1
4
1
2
d 33
e 30
c
3
1
3
d
13
c
35
d
19
i
7
11
j
1
9
c
4
d
11
h
2
48
9
14
g 10
1
5
24
e
e
k
11
1
5
21
40
6
11
f 33
f
f
l
1
3
21
9
13
6
25
2
3
2
21
5
10
1
1
1, 2
×
=
×
=
2
2
4 3
7
21
b
1
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
1
a 35
b 24
g 25
h
15
2 a
15
16
b
4
g
10
11
h
3 a
25
26
b
f
e 4
4 For example:
5
12
5 a
1
2
÷
b
F Exercise 7.5
3
4
1
6
c 22
d 27
i 88
j
35
d
1
19
26
e 45
1
5
k
16
1
14
e
2
c
1
11
116
i
13
j
1
3
1
8
c
3
5
d
1
3
1
9
g
6
3
7
h
16
63
13
21
d
1
1
4
=
2,
4
5
4
f 28
1
2
4
9
2
3
÷
3
5
=
k 1
1
4
l
20
f
4
l
42
1
1
5
1
5
21
10
9
c
1
5
Working with fractio
fractions
ns mentally
1 a
1
4
b
5
6
c
2
3
d
7
10
g
5
6
h
7
12
i
9
20
j
1
1
2
Dividing fractio
fractions
ns
1
4
1
10
e
1
7
20
f
3
50
k
1
1
20
l
1
5
1
11
24
2
2 a
g
10
b
h
15
1
18
d
j
3
28
e
k
7
12
f
l
15
1
20
c
i
3
3
10
3 a
1
6
b
2
9
c
9
28
d
12
35
e
20
63
f
81
200
g
1
5
h
7
20
i
15
22
j
1
6
k
1
2
l
15
22
4 a
1
2
b
1
4
c
1
3
d
1
6
e 6
f
1
1
8
g
8
9
h
2
i
11
12
j
1
7
8
l
1
11
14
7 a
3
28
b
5
28
c
5
7
8 a
3
7
b
2
7
5
7
15
6
11
40
1
10
25
Cambridge Checkpoint Mathematics 9
1
2
k
9
11
24
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice
Practice Book exercises
8 Constructions, shapes and Pythagoras’ theorem
Exercise
se 8.1
F Exerci
Constructing
Con
structing 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’
students’ drawings, all measurements ± 2 mm and ± 2°.
b i 30° ± 2°
ii 180° − 90°
90° − 60° = 30°
30°
5 Check students’ drawings, all measurements ± 2 mm and ± 2°.
6 Check students’ drawings, all measurements ± 2 mm and ± 2°.
students’ drawings,
drawings, all measurements
measurements ± 2 mm and ± 2°.
7 a Check students’
90° − 90° = 180°
180°
b i 180° ± 2°
ii 360° − 90°
F Exercise 8.2
Inscribing shapes in circles
1 a Check students’
students’ constructions of an inscribed equilateral
equilateral triangle, including
including construction
construction lines.
b Check studen
students’
ts’ constructions of an inscribed regular octagon,
octagon, including
including construction
construction lines.
2 a Check students’ constructi
constructions,
ons, includin
includingg constructi
construction
on lines.
b 7.1 cm ± 2 mm
c Shaded area = 78.5 – [students’ x2] = 25.2 to 30.9 cm 2
students’ constructions of the inscribed regular octagon
octagon and the inscribed circle, including
including construction
construction
3 Check students’
lines.
Inner circle: radius of 6.2 cm to 6.7 cm, area of 120.70 cm2 to 140.95
140 .95 cm2
Area of octagon = 137.28 cm2 to 147.41
147. 41 cm2
students’ constructions of inscribed square, including
including construction
construction lines. Measurement
Measurement of
of side length
4 a Check students’
of 11.1 cm to 11.5 cm. Area of square = 123.21 cm2 to 132.25 cm2.
Praise, but do not allow alternat
alternative
ive method, not involving constructi
construction.
on.
b Check students’
students’ explanations
explanations involving
involving knowledge that one
one area must be a quarter (or four times)
times) the area
of the other when dimensions are doubled.
c Check students’
students’ constructions of inscribed square, including
including construction
construction lines. Measurement
Measurement of
of side length
of 5.5 cm to 5.9 cm.
cm. Area of square = 30.25 cm2 to 34.81 cm2.
Praise, but do not allow alternati
alternative
ve method not involving constructi
construction.
on.
F Exercise 8.3
Using Pythagoras
Pythagoras’’ theorem
2
= 676,
2
= 2500 – 1600 = 900, c = 30 cm
1 a
a
2 a
c
a
= 26 cm
cm
2
= 62 + 2.52 = 42.5, a = 6.5 cm
cm
2
= 2.52 – 22 = 2.25, c = 1.5 m
b
a
b
c
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
Practice Book exercises
exercises
9 Expressions and formulae
F Exercise 9.1
1
a a7
b b10
4
2
Simplifying
Simplif
ying algebraic expressions
c c15
4
g g
a 4a4
g 8g 8
3 a B
d d10
e e6
5
6
h h
b 16
16bb8
h 3h6
i i
c 36
36cc12
i 2x 3
j j
d 64
64d
d6
j 5x 8
b A
c A
d D
f f4
7
k k
e 10
10ee11
k 5x 4
l l
f 12f 10
l 11
11xx
4 a One group has x6 terms and one group has x9 terms.
b 9x12 ÷ x9 = 9x
9x3: this is the only one with power of 3; all others are to the power of 9 or 6.
F Exercise 9.2
1
Constructing algebraic expressions
a n+1
b n − 10
c 100
100n
n
n
g 6n − 7
h
f
4
−5
k 3(
3(n
n + 20)
n
8
+
9
d
i
n
1000
1
n
−1
e 2n + 3
j
10
2n
l 20(
20(n
n − 3)
2 a 6x
b 3x + 10
c 12
12xx − 2
d 13
13xx − 4
3 a xy
b y2
c 4xy
d 16
16xx2
b i 2b + 2
d i 12d
12d − 2
ii 5b − 20
ii 5d2 − 5d
5d
4
a i 2a + 16 ii 5a + 15
c i 4c − 16 ii c2 − 8c
8c
5
a i 2(
2(aa + 3) + 2(3a
2(3a + 1) = 8a
8a + 8, 4(2a
4(2 a + 2) = 8a
8a + 8
ii 3(
3(aa + 3) + 3(3a
3(3a + 1) = 12a
12a + 12, 6(2a
6(2a + 2) = 12a
12a + 12
iii 5(
5(aa + 3) + 5(3a
5(3a + 1) = 20a
20a + 20, 10(2a
10(2a + 2) = 20a
20a + 20
b n black rods + n striped rods = 2n
2n white rods (or similar explanation given in words)
c i 4(
4(aa + 3) + 2(2a
2(2a + 2) = 8a
8a + 16 , 8(a
8(a + 2) = 8a
8a + 16
ii 6(
6(aa + 3) + 3(2a
3(2a + 2) = 12a
12a + 24, 12(a
12(a + 2) = 12a
12a + 24
iii 8(
8(aa + 3) + 4(2a
4(2a + 2) = 16a
16a + 32, 16(a
16(a + 2) = 16a
16a + 32
d 2n black rods + n white rods = 4n
4n grey rods (or similar explanation given in words)
F Exercise 9.3
1
2
a −8
e −8
i −4
a 15
e 8
i 8
1
2
Substituting
Substitu
ting into expressions
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, 10a
10a2 = 10 × 22 = 40 and (10a
(10 a)2 = (10 × 2)2 = 400, so 10x
10x2 ≠ (10
(10xx)2
b For example: Let b = 2, (2b
(2b)3 = (2 × 2)3 = 64 and 2b
2 b3 = 2 × 23 = 16, so (2b
(2b)3 ≠ 2
2bb3
c For example: Let c = 2 and d = 3, 3c
3c − 3d
3d = 3 × 2 − 3 × 3 = −3 and 3(
3(d
d − c) = 3(3 − 2) = 3, so 3c
3c − 3d
3d ≠ 3(
3(d
d − c)
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Unit 9
Answers to Practice Book exercises
Exercise
se 9.4
F Exerci
Deriving and using formulae
H
1 a H = 24D
24D
b H = 240
c
2 a D = 150
b D = 180
c S = 20
d T = 5.5
3
b F = 54
f a=7
c I = 40
d I = 21
4 a d+3
2d + 3
b T = 2d
c T = 19
d
5 a 50%
b 8%
c 110%
6 a 450 m
b 1303 m
c 1078 m
a F = 25
e e=5
D
=
d D = 20
24
d
T
=
−
2
e 12
3
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
6(a + 4)
d g(7
(7gg + 1)
b 3(3c
3(3c – 5)
e 4(2 – 3j)
c 4f(e + 4)
f m(7m
(7m – 4)
2
a 5(z
5(z + 3)
e 2(3
2(3vv + 4)
i 3(4 − 5w)
b 2(y – 7)
f 7(2
7(2u
u − 3)
j 8(2 + 3x)
c 4(5x
4(5x + 1)
g 6(2 − u)
k 2(4 + 7y)
d 3(3w
3(3w − 1)
h 7(2 + 3v)
l 7(2 − 5z)
3
a m(7
(7m
m + 1)
4s)
e 3s(1 + 4s
i 7e(2
(2ii − 1)
b 5a(a – 3)
f 4y(3 − 4y)
j 4a(3 + 2b
2b)
c t(t + 9)
8(2ee − i)
g 8(2
k 3g(7 + 5h
5h)
d 4h(2 − h)
3(5ee + 2i
2i)
h 3(5
l 15
15w
w(2 − t)
4
a 2(a
2(a + 2h
2h + 4)
d e(3
(3ee + 4 + f)
b 5(b
5(b – 5 + j)
e k(7 – k – a)
c 4(3tu
4(3tu + 4u
4u – 5)
f 3n(2
(2n
n – 3 + m)
5
5(3x − 2) − 5(2 + x) = 15x
5(3x
15x − 10 − 10 − 5x
5 x = 10x
10x − 20 = 10(x
10(x − 2)
Tanesha’s mistake was expanding −5(2 + x) to give −10 + 5x
5x, which adds to 15x
15 x − 10 to give 20x
20x − 20.
Exercise
se 9.6
F Exerci
1 a
g
2
Adding and subtracting algebraic fractions
2x
3
b
y
h 14 y
2
3x
5
+
a
x
y
g
4a + 5b
b
20
3
d
i 15y
j
2x + y
c
6
h
28
1
4
9x + y
d
4x
7
i
k
9
15x
−y
e
18
10a + 15b
j
18
x and B, C each equal
e
2y
12
21a + 4b
a A, D, F each equal
x
18
9
2
3
c
1
2
x.
5a
− 7b
35
3x
4
f
17 y
l
24
7x
− 8y
f
2x
5
5y
16
7x
12
k
15a
18
− 2b
24
− 15 y
l
12a
− 35b
42
b E, which equals 1 .
3
c You can ignore the letter, work out the fracti
fractions,
ons, 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
F Exercise 9.7
Expanding the product of two linear expressions
1 a x2 + 7x
7x + 10
d x2 − 3x
3x − 18
2
g x + 15
15xx + 50
b x2 + 7x
7x + 6
e x2 − 6x
6x + 9
2
h x +5
5xx − 50
c x2 + 2x
2x − 8
f x2 − 13x
13x + 40
2
i x − 15
15xx + 50
2 a B
b A
c C
2
2
2
46d
3 a
d ad2 +
− 4a
6ad +
+ 49
4 a
b
c
d
Unit 9
+ 10e
8be++16
8b
b
e be2 −
10
25
d C
22cf +
+ 11
cf cf 2 +
− 2c
i a2 − 1
ii a2 − 16
iii a2 − 81
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
Practice Book exercises
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
4
d i 1
ii 2
iii 2.67
b The median is in the
the class 55–60.
a The mode is 5 and the
the median is 4.
b The mean is 156 ÷ 40 = 3.9
3.9 which is less than the median of 4.
5 10.125 kg
6
a 31–35 seconds
F Exercise 10.2
b 21–25 seconds
c
26–30 seconds
Using statistics
1 a The median is 41 and the mean is 40.3. Both show that
that the average is above
above 40. The mode is not a good
good
choice here.
b There is no reason to complain if the average
average is above
above 40.
2 The median is 19 (< 20) and the mean is 21.1 (> 20).
3 a You can use the modal class or the median.
median. The modal class for the
the boys is 36–40 and for the
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
the boys is greater
greater because there
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
Book Club.
Club. The medians are 35 and 47.
47.
b The M
Music
usic Club. The ranges are
are 24 years
years and 15 years.
6 The men. The median for the
the men is in the
the class 40–44; for women
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
Practice Book exercises
exercises
11 Percentages
F Exercise 11.1
1 a $468
Using mental methods
b $702
c $117
d
$23.40
example: Find 25% (a quarter) and 10% (divide by
by 10) and add them.
2 a For example:
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
one should be 69% of 282 to be the same as the others.
7 a 1024
8
b 1536
c 2112
d
3712
D C A B
Exercise 11.2
Comparing different quantit
quantities
ies
F
1 No. 76% for English and 82% for science.
p eople is greater.
2 9% of the young people and 27% of the older people wear glasses. The percentage of the older people
3 a Rovers 45%, United 62%
4 a 56% (or 55.6%)
5 a
b
c
d
b United, becaus
becausee 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 Hock
Hockey
ey 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
Practice Book exercises
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.
explainations, involving
involving corners of square = 90° and 360 ÷ 90 = 4 (i.e. no remainder),
2 Check students’ explainations,
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
1
Solving transformation problems
y
3
2
c
1
a
0
–4 –3 –2 –1 0 A 1
–1
d
–2
b
–3
2
2
3
4
x
y
6
5
4
c
3
B
2
a
b
1
0
0
3
1
2
3
4
y
5
6
7
x
6
7
x
d
6
5
a
4
b
C
3
2
1
c
0
0
4
a
1
2
3
4
5
b
y
y
6
6
5
5
4
4
a
3
3
2
2
1
1
0
b
0
0
1
2
3
4
5
6
7 x
Copyright Cambridge University Press 2013
0
1
2
3
4
5
6
7 x
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Unit 12
Answers to Practice Book exercises
5
y
4
3
P
2
1
0
–4 –3 –2 –1 0
–1
1
R
2
3
4
x
–2
Q –3
–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).
-coordinates
es have changed places.
d The x- and y-coordinat
b
y
B′ y = x
7
6
C′
A
B
5
4
C
3
2
A′
D
1
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
d
4
c
3
c
d
2
1
b
0
–6 –5 –4 –3 –2 b–1 0
–1
1
2
3
–2
4
5
6
x
a
–3
A
–4
a
–5
–6
2 a
b
c
d
e
f
g
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).
h Rotation 180° about (–2, –1).
2
Cambridge Checkpoint Mathematics 9
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Answers to Practice Book exercises
3
a i
Rotation 90° anticlockwise about (−1, 3).
ii
Translation
Unit 12
4 

–4
iii Reflection in the line x = −1.
iv Reflection in the line x = −3.5.
b i Check students’ combinations
combinations of at least two transformations.
two transformations.
ii Check students’ combinations of at least two
F Exercise 12.4
1
Enlarging shapes
y
4
3
2
1
0
–4 –3 –2 –1 0
–1
1
2
3
4
x
–2
2 a Enlargement scale factor 3, centre (6, 2).
b Enlargement scale factor
factor 2, centre (3, 5).
3 Enlargement scale factor 3, centre (6, 1).
4 a
4
y
3
2
1
0
0
–6 –5 –4 –3 –2 –1
–1
1
2
3
4
x
–2
–3
enlargement with centre
centre of enlargement anywhere
anywhere except
except (0, 0) and words
words to
b Grid showing a square and its enlargement
the effect that in this case multiplying the coordinates by 2 does not make the equal to the coordinates of the
enlarged square
F
1
Exercise 12.5
Drawing a locus
A
4.5 cm
2
3
3 cm
3 cm
3 cm
3 cm
4 cm
P
4 cm
6 cm
4 cm
4
Q
4 cm
Check students’ circles; they must have a radius of 3 cm.
G
6 cm
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
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Unit 12
Answers to Practice Book exercises
5
C
6 cm
1.5 cm
8 cm
6 a
7
b
c
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
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Answers to Practice
Practice Book exercises
exercises
13 Equations and inequalities
F Exercise 13.1
Solving linear equatio
equations
ns
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 47
b y = 1116
c y = 3 18
d y = 5 79
4 a x = −8
b x = −3
c x = −1213
d x = −2
10 x − 20 → x = 7
5 a 5x + 15 = 10x
2x − 4 → x = 7
b x + 3 = 2x
4x = 0 → 4
4xx − 12 = 0 → x = 3
6 a 8x − 32 + 20 − 4x
2(x
2(
x
−
4)
+
5
−
x
=
0
→
2x
2
x
−8+5−x=0→x−3=0→x=3
b
7 a x=4
b x = −3
c x = 11
b x = 4 72
8 a 5x + 30 = 60 − 2x
2x
4 x − 8 = 40 − 2x
2x → 6
6xx = 48 → x = 8.
9 Multiplying out the brackets: 4x
Dividing by 2: 2(x
2(x − 2) = 20 − x → 2
2xx − 4 = 20 − x → 3
3xx = 24 → x = 8.
Both give x = 8.
F Exercise 13.2
Solving problems
1 a n + 2(n
2(n + 3) = 90 → 3
3n
n + 6 = 90
b n = 28
c 28 and 62
2 x + 80
2 a x + 50 and 2x
b 2x + 80 = 144
c x = 32
2s + 2s
2s + 5 = 100 → 5
5ss + 5 = 100
3 a s + 2s
b s = 19
c 43 cm
4 a y + 3y + y − 2 + 4(y − 2) = 116
b y = 14
c 48
5(xx − 8) = 2(x
2(x + 10)
5 a 5(
b 20
6 a 2a + 6(a
6(a − 2) = 44 or a + 3(a
3(a − 2) = 22 → 4
4aa − 6 = 22
F Exercise 13.3
b 7 cm and 15 cm
Simultaneous
Simultaneo
us equati
equations
ons 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
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RM.DL.BOOKS GROUPS
Unit 13
Answers to Practice Book exercises
F Exercise 13.4
Simultaneous
Simultaneo
us equatio
equations
ns 2
1 a x = 18, y = 2
b a = 9.5, b = 5.5
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
2x + y = 20.5 and not 19.
b Using the values in part a, 2x
5 a x = 6, y = 10
b x = 3.5, y = 3
F Exercise 13.5
c p = −4, q = 8
c a = 3, b = −1
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
4x = 3.84. If x = 4.9, x² − 4x
4x = 4.41.
6 x = 2.3. Here are some possible values.
x
2
3
2.5
2.2
2.3
x² + 3x
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
Inequalit
ies
1 a x>2
b x ≥ −6
c x<0
d x ≤ 10
2 a
–3 –2 –1
0
1
b
0
3.5
c
–3
0
d
–10
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
2(A + 5) < 100 → 4
4A
A + 15 < 100
b A < 21.25
c Because if A < 21.25 then 2(A
2( A + 5) < 52.5.
7 a x + 2x
2x + 3(x
3(x − 10) < 360 → 6
6xx − 30 < 360
b x < 65
c Yes.
es . 2x = 3(x
3(x − 10) → x = 30 and this is in
i n the solution set.
2
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
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Answers to Practice
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
cement and 5 kg lime
6 a 2.5 kg cement
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
17
Total:
8 a $744
b $525
9 a $154
b Check students’ methods for checking.
F Exercise 14.2
1 a
b
c
d
e
f
c $312
d
€258.50
Solving problems
Yes, as the number
number of bottles bought increases, so does the total
total cost (the ratio stays the same).
No, the ratio does not stay the same.
Yes, as the number of stamps bought increases, so
so does the total
total cost (the
(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
750 g pack
pack of
of cereal
c The 450
450 ml pot
pot of
of yoghurt
yoghurt
6 £208
7 a
8
S$517.50
€187 = $239.74, $254
b A$104
= €198.12. He should buy the phone in Paris.
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
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Answers to Practice
Practice Book exercises
15 Area, perimeter and volume
F Exercise 15.1
1
a 70 000 cm2
Converting units of area and volume
b 8000 cm2
2
d 5002mm
g 9m
j 3 cm2
2 a
d
g
j
2 000 000 cm3
8000 mm3
9 m3
7 cm3
3 a 70 ml
d 7 litres
g 8000 cm3
c 32 500 cm2
2
e 40 mm
h 3.4 m2
k 2.8 cm2
b
e
h
k
240 000 cm3
500 mm3
0.48 m3
0.23 cm3
b 348 ml
e 8.4 litres
h 3900 cm3
2
f 920 mm
i 0.5 m2
l 0.8 cm2
c
f
i
l
5 600 000 cm3
7200 mm3
82.2 m3
77.6 cm3
c 2500 ml
f 0.92 litres
i 880 cm3
4 a 12.2425 m2. Check that students check correctly, using estimation.
correctly, using inverse operati
operations.
ons.
b $312. Check that students check correctly,
Wall 2: 8.28 m2
5 Wall 1: 10.08 m2
Wall 3: 9.72 m2
Wall 4: 10.44 m2
Total = 38.52
38. 52 m2
Check students’ own choice of method for checking the answer.
F Exercise 15.2
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
1
a 40 000 m2
e 8200 m2
Using hectares
5 a 28275 m2
b 2.8275 ha
c $6220.50
students’
ts’ own methods for checking
checking their answers
answers by estimation.
d Check studen
6 Area = 98 701 m2
Cost = $38 493.39
$38 493.39 < $40 000 so he can afford it.
Check students’ own
own methods for checking their answers by estimation.
Copyright Cambridge University Press 2013
Cambridge Checkpoint Mathematics 9
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RM.DL.BOOKS GROUPS
Unit 15
Answers to Practice Book exercises
F Exercise 15.3
Solving circle problems
1 a
c
A=
12.6 cm2, C = 12.6 cm
cm
2
A = 254.5 cm
cm , C = 56.5 cm
b
d
A=
2 a
c
A=
113.5 cm
cm2, P = 43.7 cm
A = 402.1 cm
cm2, P = 82.3 cm
b
d
A=
3 a
4 a
d=
r=
8.37 cm
7.07 cm
b
b
d=
r=
66.5 m2, C = 28.9 m
A = 21.2 m2, C = 16.3 m
904.8 mm2, P = 123.4 mm
A = 88.4 m2, P = 38.6 m
28.49 mm
3.82 m
c
c
d=
r=
1.51 m
0.53 m
d
d
d = 11.30 cm
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
Exercise
se 15.4
F Exerci
Calculating
Calculatin
g with prisms and cylinders
1 a 150 cm3
b 129.6 cm3
2
Area of cross-section
Length of prism
Volume of prism
a
2
8.4 cm
20 c m
168 cm3
b
c
24 cm2
58 m2
6.5 cm
5.7 m
156 cm3
330.6 m3
d
56.85 mm2
62 m m
3524.7 mm3
3 a V = 480 cm3, SA = 416 cm2
c V = 675 cm
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 mm 2
b V = 492.6 cm3, SA = 401.1 cm2
5
6 a
2
c 427.5 cm3
Radius of
of ci
circle
Area of
of ci
circle
Height of
of cy
cylinder
Volume of
of cy
cylinder
a
7 cm
153.94 cm
12 c m
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 m2
3. 8 m
57 m 3
e
4.55 mm
65 mm2
22 mm
1430 mm3
x = 4.3
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
Practice Book exercises
16 Probability
F Exercise 16.1
Calculating probabiliti
probabilities
es
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
7
16
b
6 a 0.17
b 0.31
Exercise
se 16.2
F Exerci
1 a
2 a
3 a
4 a
5 a
T
+
+
H
+
+
H
T
c 0.11
Sample space diagrams
b The probabilities are
6
+
+
+
+
+
+
5
+
+
+
+
+
+
4
+
+
+
+
+
+
3
+
+
+
+
+
+
2
+
+
+
+
+
+
1
+
+
+
+
+
+
1
2
3
4
5
6
4
+
+
+
+
3
+
+
+
+
2
+
+
+
+
0
2
4
6
C
+
+
+
B
+
+
+
A
+
+
+
A
B
C
D
+
+
+
+
C
+
+
+
+
B
+
+
+
+
A
+
+
+
+
A
B
C
D
Copyright Cambridge University Press 2013
1
2
and
1
4
. One is twice the other.
b i
11
36
ii
1
6
iii
2
9
b i
1
6
ii
5
6
iii
1
6
b i
1
3
ii
2
3
b i
1
4
ii
3
4
Cambridge Checkpoint Mathematics 9
1
RM.DL.BOOKS GROUPS
Unit 16
1
5
and
7 a
3
16
6
Answers to Practice Book exercises
4
5
8 a 0.1
b
13
16
b 0.18
F Exercise 16.3
c 0.16
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
student being normal weight
weight is higher,
higher, and the probabilities of a student
student being
b School B. The probability of a student
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
probability of a good
good grade, and
and a lower
lower probability of
of a poor grade.
c City. It has a higher probability
5 a i 0.27
ii 0.16
b Afternoon trains are more likely to be on time and are
are less likely to
to be early or late.
late.
6 a i 0.58
ii 0.17
b It is not a good way.
way. One reason is that it makes a difference whether a team is playing at home or away.
away.
2
Cambridge Checkpoint Mathematics 9
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Answers to Practice
Practice Book exercises
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
drawings.
s.
1 a Check students’ scale drawing
b 178 km
c 286°
drawings.
s.
2 a Check students’ scale drawing
b 229 km
c 090°
3 a Check students’ scale drawing
drawings.
s.
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.
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1
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Answers to Practice
Practice Book exercises
exercises
18 Graphs
F Exercise 18.1
Gradient of a graph
1
4
1 a 1
b 2
c
2 a −1
b −5
c − 13
3
y
4
b
3
2
1
a
0
–4 –3 –2 –1
–1
1
2
3
4
5
6
7
8
9
10
x
7
8
9
10
x
c
–2
–3
–4
4
y
8
7
6
5
d
4
b
3
c
2
1
0
–4 –3 –2 –1
–1
1
2
3
4
5
6
–2
–3
–4
–5
–6
–7
–8
5 a 2.5
b −1.5
6 a 0.1
b 0.05 or
7 a 25
b 0.1
c 0.5
1
20
Copyright Cambridge University Press 2013
d −5
c −0.1
c −1
d 2
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Unit 18
Answers to Practice Book exercises
F Exercise 18.2
1 a
The graph of y = mx + c
b All have gradient 4.
y
8
7
6
5
ii
iii
i
4
3
2
1
0
–2 –1
–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
−2x
b y = −4 − 2x
2x
c y = 4 − 2x
2x
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
b −10
d 75
6 A, C and D are parallel; B and E are parallel.
F Exercise 18.3
1
2
Drawing graphs
a i y = −x
−x + 12
ii y = −2x
−2x + 12
iii y = − 12 x + 6
b i −1
ii −2
iii − 12
1.5x − 3
a y = 1.5x
b
y
8
c 1.5
6
4
2
0
–4 –2
–2
2
4
6
8
x
–4
–6
–8
3 a y = 0.1x
0.1x + 1.4 is the equation of a straight
str aight line.
4 a 1.5
b −0.4
c −1
b
0.1
d 5
top line. It passes through (0, 5).
5).
5 a The top
b 5x + 8y = 0 (through the origin) and 5x
5 x + 8y = 20 (through (0, 2.5))
c y = −10x
−10x
1
Cambridge Checkpoint Mathematics 9
2
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
6 a y = 0.05x
0.05x + 5 or y =
1
x
20
1
20
b 0.05 or
+5
Unit 18
c
y
10
8
6
4
2
–140
–120
–100
–80
–60
–40
0
–20
20
40
60
80
1 00
1 20
–2
7 a −10
b −0.1
8 a –2
b c = 2 and d = 3
3
c 50
d 0.02
Exercise
Exerci
se 18.4 Simultaneous equations
F
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
−x + 5
y
6
4
2
0
–2
–2
2
4
6
8
x
–4
–6
c x = 4 and y = 1
4 a, b
d −x + 5 = x − 3
y
8
6
4
2
0
–6 –4 –2
–2
–4
–6
–8
2
4
6
8
10
x
→
→
8 = 2x
2x
x = 4 and then y = x − 3 = 4 − 3 = 1
c x = −3 and y = 6
140
x
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Unit 18
5
Answers to Practice Book exercises
a and b
c i x = 2 and y = 60
y
ii x = 4 and y = 20
100
80
60
40
20
0
–6 –4 –2
–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
0
–4 –3 –2 –1
–1
1
2
3
4
5
6
x
–2
–3
–4
–5
–6
F Exercise 18.5
Direct proporti
proportion
on
Other scales are possible for the graphs.
1 a
y
b 1.64
c D = 1.64E
1.64E
b y = 7.35g
7.35g
c i $24.99
d i $484
ii
(100, 164)
150
)
$
(
s
r
lla100
o
D
50
0
2
a
50
100
Euros (€)
x
y
40
(5, 36.75)
30
s
r
a
ll
o
20
D
10
0
1
2
3 4
Grams
5
x
ii 2.72 grams
€179.88
3
Cambridge Checkpoint Mathematics 9
4
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
3
a 15 000 litres
b
Unit 18
y
(60, 15000)
15000
l
e
u
f
f
o
s
e
r
t
i
L
10000
5000
0
4
c
f = 250m
250m
a
) y
m
(c 4
ir
a
h3
f
o2
h
t
g1
n
e
L
d i 41 250 litres
a
5
15
10
Weeks
ii 400 minutes
minutes or 6 hours and 40 minutes
b 0.3
c l = 0.3w
0.3w
d 333 weeks
weeks or
or about 6.4 years
years
b 16.5
c Just over 6 minutes or about 6 minutes and 4 seconds
x
y
)
m40
(c
e30
c
n
20
ta
is
D10
0
x
(12, 3.6)
0
5
10 20 30 40 50 60
Minutes
(2, 33)
1
2
Minutes
F Exercise 18.6
x
Practical graphs
Other scales are possible on the graphs.
h
1
0.5d
a h = 2 + 0.5d
b
c i 4 metres
7
s 6
e
tr
e 5
m
in 4
t
h
ig 3
e
H2
1
0
0
1
2
3
4
5 6
Days
7
8
9 10 d
ii 9 days
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Unit 18
2
Answers to Practice Book exercises
a D = 3w
3w + 20
b
c i $32
D
ii 10 weeks
60
50
s
r40
a
ll
o
30
D
20
10
0
0
1
2
3
4
5
6
7
8
9
10
w
Weeks
3
a n = 14 000 − 500m
500m
b
c 8 minutes
n
14000
12000
le
p
o
e
P
10000
8000
6000
4000
2000
0
0
1
2
3
4
5
6
7
8
9
10
m
Minutes
4
a t = 30 − 4d
4d
b
c On the 8th day ( 7 1 days)
t
2
32
28
24
s
t 20
le
b
a
T16
12
8
4
0
0
5 a L = 20 000 − 1500d
1500d
1
2
b
3
4 5
Days
6
7
8 d
L
20000
18000
16000
)s 14000
e
tr
l(i 12000
r
tea10000
W8000
6000
4000
2000
0
0
1
2
3
4
5
6
7
8
Days
c
12 500 litres
d
13 days (13 1 )
3
9 10 11
11 12 13
13 14 d
5
Cambridge Checkpoint Mathematics 9
6
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
6
a P = 25 + 0.1 y
b
c 30 years
P
)s 30
n
o
lli 25
i
(m20
n
ito15
la
u10
p
o
P 5
0
0
10
20
30
Years
40
50
y
Unit 18
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice
Practice Book exercises
19 Interpreting and discussing results
F Exercise 19.1
1
Interpreting and drawing frequenc
frequency
y diagrams
a 32
b
Time, t (minutes)
Frequency
10 ≤ t < 12
4
11
12 ≤ t < 14
16
13
14 ≤ t < 16
7
15
16 ≤ t < 18
5
17
c
Mid-point
Time taken by 9C to complete
cross-country run
18
16
14
12
y
c
n
e
u
q
e
r
F
10
8
6
4
2
0
10
d
12
14
16
Time (minutes)
18
5
8
2 a 50
b
Wednesday
Height,
h
((ccm)
Saturday
Frequency
Midpoint
Height,
h
((ccm)
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
180 ≤ h < 200
22
18
170
190
160 ≤ h < 180
180 ≤ h < 200
7
2
170
190
c
Heights of people on roller coaster
Wednesday
Saturday
35
30
25
y
c
n
e
u
q
e
r
F
20
15
10
5
0
120
140
160
180
Height (cm)
200
d For example: On Saturday
Saturday there were
were fewer taller people and more
more shorter people. There
There were only two
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.
7
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
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
30
y
c
n
e
u
q
e
r
F
20
10
0
0
5
10
15
20
Number of hours
25
b For example: The most popular training time for the Falcons
Falcons Club was between 5 and 10 hours,
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
surveyed at each club was nearly
nearly the same.
d Yes, because the number of athletes surveyed
F Exercise 19.2
1
Interpreting and drawing line graphs
a
Average
Ave
rage monthly rainfall in Faro, Portugal
100
90
80
70
)
m60
(m
ll 50
fa
in 40
a
R
30
20
10
0
J
F
M
A
M
J
J
A
S
O
N
D
Month
b For example: The year
year starts with just under 80 mm of rain in January, then there is less rain every month until
until
c
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.
February and March
2 a
Company profit
7
)s
n
o
lli6.5
i
m
$
(
t
fi 6
o
r
P
5.5
2002
2004
2006 2008
Year
2010
2012
b For example:
example: The profit
profit is increasing
increasing by a roughly similar
similar amount each year.
year.
c $6 million
d Answer from $6.8 million
million to
to $6.9 million (inclusive)
(inclusive)
1
Cambridge Checkpoint Mathematics 9
2
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RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
3 a
Unit 19
Daily temperatures in Marrakech in July
Maximum temperature (ºC)
Minimum temperature (ºC)
) 40
C
(º
30
e
r
u
t 20
a
r
e
p10
m0
e
T
Mon
Tues
Wed
Thur
Day
Fri
Sat
Sun
temperatu res increased from Monday to
to Thursday, then decreased for the next
b For example: The maximum temperatures
two days, finally increasing again on Sunday.
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
1
a
25
e
r
o
c
s
t
s
e
t
g
n
i
ll
e
p
S
Interpreting and drawing scatter graphs
Time spent reading and spelling test score
20
15
10
5
0
0
5
10
15
Hours reading
20
25
Positive
ve correlation.
correlation. The more
more hours reading
reading a student does,
does, the better
better their spelling test
test score.
b Positi
2 a
Art and Science exam results
90
80
)
70
%
( 60
tl
u
s 50
e
r
e
c 40
n
ie 30
c
S
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.
Cambridge Checkpoint Mathematics 9
Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Unit 19
3 a
Answers to Practice Book exercises
Numberr of packets of biscuits and crisps sold
Numbe
ts
e
k
c
a
p
f
o
r
e
b
m
u
N
30
25
ld
o
s 20
s
p15
isr
c
f 10
o
5
0
0
5
10
15
20
25
Number of packets of biscuits sold
30
correlation. The number of packets
packets of biscuits sold has no relationship to the number
number of packets
b No correlation.
of crisps sold.
station, the less it is worth.
4 a Negative correlation. The further the house is from the railway station,
The
house
that
doesn
doesn’t
’t
fit
the
tren
trend
d
is
worth
$146
000
and
is
6
km
from the train station.
station.
b
For example:
example: It might not be in a very good state
state of repair,
repair, which
which is why
why it isn’t
isn’t worth
worth as much
much as it should be.
F Exercise 19.4
1
a
Interpreting and drawing stem-and-l
stem-and-leaf
eaf diagrams
June
6
6
6
5
3
August
3
9
1
2
8
0
2
7
0
3
4
6
0
7
3
8
7
5
0
2
4
6
2
0
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
boys, showing
showing that their times
times are more varied. The girls have
have a lower
lower
b For example: The range is larger for the boys,
median and mean which shows that using these averages they were quicker at solving the puzzle.
girls’,, which makes them appear faster.
c The mode, as the boys’ mode is lower than the girls’
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
12
0
7
9
0
13
1
3
14
0
2
2
4
6
5
8
7
Key: For the top shelf, 4 | 10 means 104 boxes of cereal
For the middle shelf, 11 | 5 means 115 boxes
b oxes of cereal
9
9
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Cambridge Checkpoint Mathematics 9
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Copyright Cambridge University Press 2013
RM.DL.BOOKS GROUPS
Answers to Practice Book exercises
b
Mode
Median
Range
Mean
Top shelf
112
123
26
120.5
Middle shelf
139
137
32
134.5
Unit 19
For example:
example: The sales of cereal were
were better on the middle shelf as on average more
more boxes
boxes were
were sold (the
(the mean,
median and mode were all greater on the top shelf than the middle shelf).
shelf ). The sales on the middle shelf were
more varied, but included the largest number of boxes sold on one day.
day. The smallest number of box
boxes
es sold on
one day were on the top shelf.
F Exercise 19.5
Comparing distribut
distributions
ions 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
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
Team A
Team B
Mode
Median
Range
Mean
18
28
19
27.5
16
7
21.25
27.25
For example: Steph
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.