Download 7. Answers to worksheets - Extended content

Answers to Extended revision
exercises: Number
Worksheet 1: Reviewing number concepts
1 a 9, 18, 27, 36, 45
b 17, 34, 51, 68, 85
2 a 36
b 4
3 a 60
b 36
4 a 23, 29, 31, 37, 41, 43, 47
5 a 2³ × 5²
b 3³ × 7
6 a F
b T
c T
d F
e F
f
T
g T
b 18.25
c 3.716
d 5.68
e 17.74
f
3.92
d 0.5
e 0.2
f
g 15.54
h 0.28
b −12°C, −4°C, 0°C, 7°C, 19°C, 29°C
9 4°C
b 1112.6m
c L
ion’s Head would effectively be at a lower altitude
because altitude here is measured as ‘height above sea
level’; it would now measure 667.15 m above sea level.
−26.94
−115
12 a 1442
b 14.5
c 2.452
d 6.543
e 76.983
f
g 13.608
h −1999
i
1728.694
−8.057
13 a 33 and 61
b 45 and 26
14 6 metres
15 22 members
16 a 772.695
8 a −2°C, 0°C, 2°C, 4°C, 8°C,
10 a −28m
b 1
c 42.75
i
b 59, 61, 67, 71, 73, 79, 83, 89, 97
7 a 16.047
11 a 5.84
b 772.695
c 3.85
d 20.07
e 2 007 000
f
1.925
17 a prime (e.g. 2 → 47, 5 → 71, 10 → 151)
b still prime; 40 → 1681, which is not prime.
18 a 8
b 16
c
2n
© Cambridge University Press 2018
1
Answers to Core revision exercises:
Algebra
Worksheet 2: Making sense of algebra
1 a x −6
b
c x + 2. 5
e 2x
2 a 2a + 6b
2x 2
9
e 9yz
c
g
k 2x8
1
x
2
b 32xy
o 64x12
p
2
a
q x4
r
1
4x2
t
1
x y 4z2
d 2x2y - 4xy
6x
5
5x - 9y
h
x
2 y2
3 a 21
b 20
c -1
d 50
e 56
f
g 3
h 70
i
j
2
64x9
4
n
3xy
m 24x
1
d x
3
f
l
s
2
x2 y
8 a 2.08
2
b 4.42
c 10.1
d 6
e 16
6
13
9 a x
b x 15
5
−7
3
c x 2
k 0.45
l
m 2
n 160
d
x3
5
y2
4
10 a 4(x + 3) = 4x + 12
o 2
b 4(x - 2) + 2(x + 4) = 4x - 8 + 2x + 8 = 6x + 0 = 6x
4 a 4x + 12
c 3(x - 2) + 5(x + 1) = 3x - 6 + 5x + 5 = 8x - 1
b 5x - 10
d 2(x + 3) + 3(x + 4) = 2x + 6 + 3x + 12 = 5x + 18
c 2x2 + 8x
d 3x2 - 6x
e 7x2 + 7xy
f
g 6x - 8
h 2x - 4y
i
j
4x - 8x + 2y + 3y
l
7x3 - 8x2 + 15x
6x + 2
k 3x - 36
5 a 13 × 22
3x + 8
2
d 24 × 32
g 210
h 2 × 52 × 72
2
2
b 2 × 13
c 2 ×3
e 25
2
11 a Total bottles in a day
f
34
6 The only way that we can write the prime number 41
as a product is 41 × 1. But 1 is not a prime number.
Therefore we can’t write 41 as a product of only primes.
In fact this is true for any prime integer.
7 a x
6
b 1
c x
6
d x15
e 2
f
g x-2
h 2x8
i
j
24x3y2
2
2x3y4
bHow many more water bottles were sold than cool
drink bottles
cHow many more cool drink bottle were sold than
water bottles
d Total number of water bottles in d days
e Total number of bottles in d days
f8 less water bottles than the total number of bottles
in d days
12 a
2
3x
c
4
3
5x 2
2
1
3
c x = 27
13 a
x=
b
−1
5
4x 2
d
2 y2
3x 2
b x = -4
d x=
1
4
© Cambridge University Press 2018
2
Worksheet 2: Making sense of algebra
14 a
b
x=
15 a x = 3y
1
2
x =±
1
1
− ≈ −0.290 or −0.710
4 2 2
4
b x=-y
c 3x = 7 - 2y
d 2 y3 =
e 3x + 1 = 9y
f
x
3
x = ±y
© Cambridge University Press 2018
3
Answers to Extended revision
exercises: Shape, space and measures
Worksheet 3: Lines, angles and shapes
1
Name of
polygon
Number Sum of
of sides angles
Size of one
angle when
the polygon is
regular
Triangle
3
180°
60°
Quadrilateral
4
360°
90°
Pentagon
5
540°
108°
Hexagon
6
720°
120°
Octagon
8
1080°
135°
Decagon
10
1440°
144°
2 160°
b NOT TO SCALE
c NOT TO SCALE
3 NOT TO SCALE
Z
70
X
mm
40 mm
50 mm
Y
d NOT TO SCALE
4 a NOT TO SCALE
© Cambridge University Press 2018
4
Worksheet 3: Lines, angles and shapes
5 a 15°
b 150°
c 51°
d 64°
e x = 45° and y = 100°
f
g 30°
h 70°
100°
6 Let angle MQN = x
Then angle PMQ = x (isosceles triangle)
So angle MPQ = 180 - 2x (angles in a triangle add
up to 180 degrees)
Therefore angle MPN = 180 - (180 - 2x) = 2x (angles
on a straight line)
So angle PMN = 2x (isosceles triangle)
And angle NMQ = x + 2x) = 3x
7 a 77°
c 282°
b 143°
d 262°
8 1440°
© Cambridge University Press 2018
5
Answers to Extended revision
exercises: Data handling
Worksheet 4: Collecting, organising and displaying data
1 a Discrete
b
Number of fizzy
drinks consumed
0–4
5–9
10–14
15–19
20–24
25–29
30–34
c
Frequency of
students
16
8
5
6
6
5
4
Number of cans of fizzy drink consumed by students in one week
2 a Black
b White
c 28.9% (3sf)
d 25 (to the nearest whole number)
© Cambridge University Press 2018
6
Worksheet 4: Collecting, organising and displaying data
3 a
Stem
5
6
7
8
9
Leaf
0
0
0
0
0
1
1
1
9
3
1 1 1 2 2 3 3 3 5 5 6 8
2 2 3 3 4 5 5 5 7 7
2 5 5 5 9
Key
5 | 0 = 50 years
9 9 9
b Age of oldest grandparent of 40 sixteen-year-old girls
4 a
Pulse rate before exercise
Stem
Pulse rate after exercise
5 5 0
5
9 9 7 4
6
4 3
7
0
8
4
Key
9
5 7 8
10
3
11
3 5 5
12
0 1
Before exercise
After exercise
0 | 5 = 50 beats per minute
8 | 4 = 84 beats per minute
bIn every person, the pulse rate increased after exercise.
© Cambridge University Press 2018
7
Worksheet 4: Collecting, organising and displaying data
5 a Favourite subject of a group of students in Dhaka
b34
c 48
d English
e Biology
6 a Pictogram
b Each stick man represents 1 billion people
1
c
billion = 500 million
2
d 200 years
e 2012
f
g
9 full stick men and
1
of a stick man.
5
World population (in billions) over time
© Cambridge University Press 2018
8
Worksheet 4: Collecting, organising and displaying data
7 a
Africa (60°)
b Students’ own answers. Example:
Asia (215°)
A bar chart with ‘Continent’ on the
horizontal axis, and ‘Percentage’ on the
vertical axis.
Europe (36°)
North America (17°)
South America (31°)
Oceania (2°)
© Cambridge University Press 2018
9
Answers to Extended revision
exercises: Number
Worksheet 5: Fractions and standard form
1 a 15.6 (1dp)
b 383 000 000 (3sf)
c 0.000 035 (2sf)
3
4
0.75
75
17
25
0.68
68%
33
100
0.33
33%
d 1.000 (3dp)
e 32 450 (nearest 10)
f
0.123 (nearest thousandth) g
2 a 5 300 000
130 (nearest 10)
b 9 560 000 000 000
c 108 000 000
d 8 750 000 000
e 0.0053
f
g 0.000 000 91
h 0.000 000 021 45
0.000 002 08
3 a 6.5 × 107
b 3.48 × 1010
c 1.9 × 10-4
d 1.27 × 10-7
e 1.2 × 104
f
g 2.75 × 107
h 3.45 × 10-13
24
35
3
c 8
40
9
e
40
b 2.8 × 10-3
g 9
4 a 8 × 107
5
5.6 × 10-3
c 1.035 × 103
d 3.312 × 104
e 4.465 × 1028
f
Fraction
Decimal
3.04 × 10-9
Percentage
1
3
0.333…
77
100
0.77
7
20
0.35
35
7
5
1.4
140
1
8
0.125
12.5
3
8
0.375
37.5
19
20
0.95
95
Decimal
Percentage
Fraction
0.583…
4
1
5
1.8
9
20
0.45
0.6
77
58.3…
180
45
60
37
70
11
8
28
d 5
45
1
f
12
b
h 3
2
35
5
12
43
5
7
j
k 10
5
9
l 105
i
m
7
12
3
5
33.3…
6 a
7
10
28
45
q 16
5
n 2
3
16
2
9
34
243
r 315
o
p 3
s 32
t
u 23.5
v 7.68
w 150
x 2
7 a 25%
2040
b 66.7% (3sf)
c 400%
d 100%
e 40.4% (3sf)
f
8 a 170
233% (3sf)
b 28
c 11.385
d 88.22
e $36
f
9 a 37.5
3.03 kg
b 776
c 71.04
d 33.88
e $45
f
10 a 3
60.03 seconds
b 45
c 2
d 400
e 40000
f
2
g 35
h
10 5
=
12 6
© Cambridge University Press 2018
10
Worksheet 5: Fractions and standard form
11 $500
12 a 600
b 90
13 a $4400 (2sf)
b $5000 (2sf)
c
x 

V 1 −
 100 
14 On January 1st 2034 the painting is due to be worth
$2520. So the value of the painting will first be worth
more than $2500 during 2033.
n
© Cambridge University Press 2018
11
Answers to Extended revision
exercises: Algebra
Worksheet 6: Equations and transforming formulae
1 a 6 (x − y )
c 3x (2a + b − 3c )
e 3x ( x + 5 y )
g
(2a − 3b) ( x + 2 y )
i
1
(a + 3b)
4
k 8 (x − 4)
2 a -3x + 6y
b 3 (4 x − 3 y + c )
d xy ( x + y )
f
(
x 2 y x 2 y 2 + 7 − 3xy 2
(
)
h 2x 6x 2 − 4 x + 1
j
l
1 2
x (7 x + 6 )
8
3 ( x − 1) (7 − 6 x )
2
b -6x + 4x
2
c -4x + 12x
d -10x2 + 10xy
e -6x2 + 14xy
f
g -2x + 10xy
h -7.2x + 12
i
j
-x2 - 7x
l
-26x + 20y
2
3
2x - 3
k -3x + xy - 2y - 4
3 a 27
c 14
e -2
4
15
-7
-8y + 56
b 0.04
8
d
3
2
f −
3
g −
h 4.5
i
j
4
k 2
l
7
m 24
n 40
1
5
q 21
o 5
s 168
4 a -1
c −
e 0
4
5
10.5
g 1
i
1
6
p -45
r 12
t
16
b
8
9
)
5 x = 2, Area = 275 cm2
v −u
6 a t=
a
g
c f =
h
e x = yz
b y =s−x−z
d −c
b
x = y+3
d a=
f
nx
y
g D = ST
h m=
i b = c (a − x )
j
x = y2
l
 a
y= 
 x
k y=
z2
x
m x = (m − y )
2
 m
o x= 
 y
n y = x −b
2
1
z−x
p y=
qx
p
b b=
1
(c − a)2
d
y=
1
(x + 1)2
y=
z
z +1− x
7 a
y=
c
x=
e
x=
z
y +1
f
g
q=
p +1
p −1
h z=
i
 yz + z 
x=
 y − 1 
1
y
2
−1
y x− x
y +1
2
5
9
f 13
1
h 1
6
d −
© Cambridge University Press 2018
12
Answers to Extended revision
exercises: Shape, space and measures
Worksheet 7: Perimeter, area and volume
b 286 mm
c 3.51 m2
d 450 m2
c 10.7 cm
d 12.8 cm
e 738 cm2
f
e 5.65 m
f
g 0.137 m2
h 2513 mm2
g 44.7 m
h 276 cm
i
31.4 m
j
k πx cm
l
1 a 66.0 m
7.85 cm
51.8 cm
π x + 3π cm
12 a 96 cm3
1357.1 cm
b 14 235.3 m3
c 38 880 cm3
d 1200 mm3
e 374.052 mm3
f
4926.02 cm3
2 a 2.23 mm
b 12.9 cm
g 3.6 cm3
h 19.683 cm3
c 32.8 mm
d 5.01 cm
x
f r=
2π
i
j
95.4 m2
l
1767.1 cm2
e 35.0 cm
3 a 2.62 cm (2dp)
b 17.17 cm (2dp)
4 a 1.54 cm2
b 1.54m2
c 6.61 m2
1697.4 m2
k 1206.4 cm2
13 a
NOT TO SCALE
d 452 cm2
e π(x + 4)2 mm2
5 a 0.349 m2
6 a i
b 0.131 m2
20π mm
b 100π mm
ii 24π mm
2
1
7 Triangle = bh
2
2
Square = a
b
Rectangle = ab
Parallelogram = ah
(a + b ) h
1
Trapezium = (a + b ) h or
2
2
Rhombus = ah
1
Kite = a (b + c ) If you split the kite into two
2
triangles, one with height b and
one with height c:
1
1
ab + ac
2
2
ab ac
= +
2 2
a
= (b + c )
2
1
= a (b + c )
2
8 a 158.76 cm2
b 103.7 m2
c 121.8 cm2
9 24.4 m
10 a 23 cm
b 92 cm
11 a 178.75 cm2
b 32 956.5 mm2
NOT TO SCALE
14 a 136 cm2
b 3259.4 m2
c 8280 cm2
d 1120 mm2
e 468.8 cm2
f
g 15.6 cm2
h 43.74 cm2
i
j
160 cm2
l
706.9 cm2
688.1 m2
k 696.1 cm2
1715.3 cm2
15 153 000 cm2 (3sf)
© Cambridge University Press 2018
13
Worksheet 7: Perimeter, area and volume
16 2940 cuboids
17 a x =
c
180°
π
1
2π
18 a Surface area of B =
1 2
b Area = r
2
4 π(kr )2 = 4 πk 2r 2 = k 2 (4 πr 2 )
4
4
4

b Volume of B = π(kr )3 = πk 3r 3 = k 3  πr 3 
3

3
3
= k3 × volume of A
c
1
16
d
1
( p)
3
2
= k 2 × surface area for A
© Cambridge University Press 2018
14
Answers to Extended revision
exercises: Data handling
Worksheet 8: Introduction to probability
3
10
1
c
10
e 0
1
2 a
2
2
5
1
d
5
1 a
b
b
1
c
4
1
2
3
d
4
1
13
5
g
13
8
i
13
d
g 0
h
35
142
65
c
71
8 a
7 a
12
13
5
h
26
e
1
2
1
c
2
1
e
2
6 a
f
b
f
b
d
1
2
1
6
5
6
5
6
29
142
12
71
3 a
Diagrams will vary but must show six segments
of the same size, and an indication that five
segments are red and one is blue.
Diagrams will vary but must show five segments
of the same size, each one labelled with a letter
from A, B, C, D, E.
b i
4 a
1
11
1
5
ii 0
iii
4
5
iv
b
2
11
9
c
11
e 0
4
d
11
1
16
1
c
16
7
e
16
15
16
9
d
16
5 a
2
5
v
b
3
5
Diagrams will vary but must show three
segments of the same size, and an indication that
one is blue, one is white and one is black.
b
© Cambridge University Press 2018
15
Worksheet 8: Introduction to probability
9 a
c
Black dice
White dice
1
2
3
4
5
6
Diagrams will vary but must show eight
segments of the same size, and an indication that
only one segment is not coloured blue.
d
b i
iii
2
3
4
5
6
1, 1
2, 1
3, 1
4, 1
5, 1
6, 1
1, 2
2, 2
3, 2
4, 2
5, 2
6, 2
1, 3
2, 3
3, 3
4, 3
5, 3
6, 3
1, 4
2, 4
3, 4
4, 4
5, 4
6, 4
1, 5
2, 5
3, 5
4, 5
5, 5
6, 5
1, 6
2, 6
3, 6
4, 6
5, 6
6, 6
1
18
ii
11
36
1
36
2
5
b
4
25
c
9
25
d
6
25
e
12
25
f
16
25
11 a
1
21
b
1
21
12 a 30
b
5
10 a
Diagrams will vary but must show five segments
of the same size, and an indication that only
one segment is coloured blue, the other four are
coloured black.
1
13
4
45
© Cambridge University Press 2018
16
Answers to Core revision exercises:
Number
Worksheet 9: Sequences and sets
1 a 17
b 28
c 80
d 11
e 1, 4, 9, 16, 25
f
5 a 5, 8, 11, 14, 17
b i
b 0, -3, -6
c 25, 36, 49
1 1 1
e
, ,
32 64 128
3 a 2n + 4
d 24, 30, 36
f
6 a r ational because can be expressed as a fraction in its
simplest terms
b irrational because it’s a decimal that does not
terminate and does not recur
b 5n - 3
d -2n + 21
e 0.75n - 0.5
f
i
iii 15 002
3, 3.5, 4
c 2n .
4 a i
ii 602
9, 18, 27, 36, 45
2 a -10, -12, -14
-1.2n + 10.2
n
1
2
3
4
5
6
d
1
4
7
10
13
16
d = 3n - 2
c rational because it’s an integer (and because it can
3
be expressed as a fraction )
1
d irrational because 3 is irrational and you get an
irrational number when you subtract (or add) an
irrational number from another number
e rational because the answer is zero
iii 748
b i
f
n
1
2
3
4
5
6
d
5
10
15
20
25
30
rational because it is a recurring decimal
g rational because it is a recurring decimal
ii d = 5n
h rational because the answer is the integer 2 (when
you divide an irrational number by an irrational
number, the answer can be rational or irrational)
iii 1250
i
irrational because it is not a terminating or
recurring decimal (when you multiply an irrational
number by an irrational number, the answer can be
rational or irrational)
j
rational because when you square the square root of
a number, you get the number and 17 is a rational
number (it’s an integer)
c i
n
1
2
3
4
5
6
d
3
5
7
9
11
13
ii d = 2n + 1
iii 501
d i
n
1
2
3
4
5
6
d
5
9
13
17
21
25
n
1
2
3
4
5
6
d
1
6
11
16
21
26
n
1
2
3
4
5
6
d
4
8
12
16
20
24
ii d = 4n + 1
iii 1001
e i
ii d = 5n - 4
iii 1246
f
77
i
ii d = 4n
iii 1000
k irrational because this would mean multiplying a
rational number (17) by an irrational number ( 17)
l
irrational because when you divide a rational
number (1) by an irrational number (π) you get an
irrational number
m rational because it can be expressed as a fraction in
 1
its simplest terms  
 3
n irrational because it cannot be expressed as a
fraction in its simplest terms (and the decimal does
not terminate or recur)
o rational because the answer has a terminating
decimal and can be expressed as a fraction in its
 5
simplest terms  
 2
© Cambridge University Press 2018
17
Worksheet 9: Sequences and sets
7 a Integers from 9 to 16 inclusive
b
b 8
c {9, 11, 13, 15}
d {9, 12, 15}
e {9, 15}
8 a {x: x is an integer, 0  x  6}
b {x: x is a letter in the word ‘Mathematics’}
c {x: x is a prime, 2  x  19}
d {x: x is a square, 1  x  64}
c
9 a {1, 3, 6, 7, 9}
b {1, 4, 7, 8, 12, 16, 20}
c {1, 7}
d {1, 3, 4, 6, 7, 8, 9, 12, 16, 20}
10 a 1, 1, 2, 3, 5, 8, 13, 21
b Fibonacci numbers
c
u13
11 a 1, 3, 6, 10, 15
b triangular numbers
c n = 20
1
d un−1 = (n − 1)n
2
8
9
b
1
2
c
49
99
d
5
90
e
172
333
f
34
333
g
1
1
12 a
13 a F
d T
d
e
b T
c
T
e
f
F
F
14 a {2, 4, 5, 8, 11, 12, 16, 20}
b {2, 3, 5, 6, 9, 11}
c {2, 3, 4, 5, 6, 8, 9, 11, 12, 16, 20}
d {2, 5, 11}
e {2, 5, 11}
f
{2, 3, 4, 5, 6, 8, 9, 11, 12, 16, 20}
15 a 108
d 61
b 47
c
51
e
f
26
57
f
g 16
16 a
© Cambridge University Press 2018
18
Worksheet 9: Sequences and sets
g
j
h
k
i
l
© Cambridge University Press 2018
19
Answers to Core revision exercises:
Algebra
Worksheet 10: Straight lines and quadratic equations
1 a
b
c
x
y
−1
0
1
2
3
2
3
4
5
6
x
y
−1
0
1
2
3
3
3
3
x
−1
0
1
2
3
1
2
−1
0
1
2
y
d
e
f
g
h
i
j
2
−1
−
1
2
x
y
−1
0
1
2
3
−6
−4
−2
0
2
x
−1
0
1
2
3
y
1
2
0
−1
−1
x
y
−1
0
1
2
3
3
1
−1
−3
−5
x
y
−1
0
1
2
3
2
−1
0
1
2
x
y
−1
0
1
2
3
−6
−4
−2
0
2
7
7
7
7
7
−1
0
1
2
3
−1
0
1
2
3
0
−1
−2
−3
−4
x
y
x
y
−
1
2
1
2
3 a gradient = 1, equation: y = x + 1
b gradient = -1, equation: y = -x + 5
4
4x
c gradient = , equation: y =
+4
3
3
d gradient = 0, equation: y = 2
1
x
e gradient = − , equation: y = − − 2
5
5
4 a y = 4x + 4
b y = -3x + 13
c y = 0.5x + 0.9
3
d y = 0.5 − x ( or 4 y + 3x = 2)
4
e y = 2.5x + 3.5 (or 5x - 2y = -7)
5 a x2 + 12x + 11
b x2 + 5x - 84
c y2 - y - 12
d x2 - 16
e p2 - 17p + 72
f
g h2 - 10h - 75
h p2 - 13p + 30
i
x2 - 6x + 9
4x2 - 2x - 12
6 ( a) and (h), (c) and (g), (d) and (e), (i) and (j) are all
pairs of perpendicular lines.
( b) and (f) are not perpendicular to any other lines, or
to each other.
1
7 gradient of AB = -3, gradient of DE =
3
x 13
8 equation: y = − +
3 3
© Cambridge University Press 2018
20
Worksheet 10: Straight lines and quadratic equations
9 gradient AB = −
gradient AC =
2
4
, gradient BC = ,
3
7
7.
4
4 7
gradient AB × gradient AC = − × = −1 , therefore
7 4
triangle ABC is right-angled.
10 a 12x2 - 19x - 21
c 6p - 13pq - 28q
2
b 2 + 13x - 45x2
2
e x -1
3
g p + 2pq + q
2
2 2
h (x + 7)2
i
j
(x - 5)2
k 2(x + 3)2
l
2(x2 - 8)
m (x + 1)(x + 2)
n (x - 2)(x - 4)
o (x + 8)(x - 3)
q (x + 1)(x - 3)
p (x + 5)(x - 4)
r 3(x + 5)(x - 5)
s (xy + 5)(xy - 5)
t
(x - 6)2
h p + 3p q + 3pq + q
e x = 3 or x = -2
f
g x = -1 or x = -6
h x = -11
i
j
x = 7 or x = -6
l
x = -2 or x = -5
2
3
x + y - z + 2xy
2
2
2
11 a x3 + 3x2 - 6x - 8
x = 3 or x = 1
k x = 6 or x = -8
b x - 19x + 30
17 a i
3
2
2x4 - 6x3 + 6x2 - 2x
c t = 64 or t = 4
d d = ± 3 or ±
b 343 cm3
-1
c i
1
2
1
d i
0
e i
4
f
1
b i
i
18
b x=8
 1 1
 −1 2 , 1 2 
ii 4.24
iii
ii 4.47
iii (6, 3)
ii
2 2 = 2.83 iii (3, -2)
ii 10
iii (0, 0)
1
ii 4.12
iii  − , 6
 2 
ii 5.66
iii (2, -1)
1
iii  , 0
2 
g i
ii 13.9
h i
3
4
ii 10
iii (5, 5)
i
−
ii 6.71
iii
1
2
15 a (x + 4)(x - 4)
c (x - 3)(x - 1)
( x ) +1= 2 x
⇒
( x) −2
⇒
( x − 1)
1

 1, −5 2 
b 5(x + 2)(x - 2)
d (x + 4)(x - 7)
2
2
2
12
−
7
i
x +1= 0
b p = 36 or p = 25
x 3 3x 2 3x
+
+ +1
8
4
2
12 a V = 8x3 + 36x2 + 54x + 27
g
14 a i
2
⇒
y 2 − 7 x + 12 = 0
ii x = 9 or x = 16
e x3 + 6x2 + 12x + 8
3x 2
13 a V = x3 - 9x - 4
2
( x) −2
⇒
d -x4 + 8x2 - 16
x = 1 or x = -6
x − 7 x + 12 = 0
c 2x - 10x - 44x - 32
f
b x=2
d x = 7 or x = -5
2
k m4 - 4m3n + 6m2n2 - 4mn3 + n4
3
2(1 + xy)(1 - xy)
c x = -1 or x = -2
j
4
g (4x + 3)(4x - 3)
(7 + x)(7 - x)
f 6p q + 8pq - 9p - 12q
2
3
x - 2x y + y
4
f
16 a x = -7
2
2
2
i
d x - 2x - 8
4
e (x + 8)(x - 8)
x +1= 0
2
⇒ x = 1 or 1(repeated solution)
⇒ x = 1is the only solution
(Alternative answer:
Let y =
y+
x
1
=2
y
y2 + 1 = 2 y
(× y )
(−2 y )
y2 − 2 y + 1 = 0
( y − 1)( y − 1) = 0 factorise
y = 1, so as 1 = 1, x = 1)
© Cambridge University Press 2018
21
Worksheet 10: Straight lines and quadratic equations
19 a a = 2, b = -7
20 x = 4 or x = 8
b min value = -7, when x = -2
c
x = 0.65 and x = - 4.65
© Cambridge University Press 2018
22
Answers to Extended revision
­exercises: Shape, space and measures
Worksheet 11: Pythagoras’ theorem and similar shapes
d If (a, b, c) is a Pythagorean Triple then a2 + b2 = c2
1 A and K
If (ka, kb, kc) is a Pythagorean Triple then
(ka)2 + (kb)2 = (kc)2
B, F and I
C and G
⇒ k 2a2 + k 2b2 = k 2c 2
H and J
2 a 12 cm
b 14.1 cm (3sf)
c 25 mm
d 44 cm
e 50 mm
f
g 1m
h 1.7 m
e Any two of:
3 149 m
7, 24, 25
4 3.7 km
10, 24, 26
5 a y = 18 mm
18, 24, 30
b y = 4.29 cm
24, 32, 40
c x = 1.2 cm, y = 1.3 cm
24, 70, 74
d x = 27.5 mm, y = 30 mm
24, 143, 145
b yes
c no
0 no
7 a 8.25 (3sf)
b 4.24 (3sf)
c 18.0 (3sf)
d 5.10 (3sf)
e 17.7 (3sf)
f
g 6.40 (3sf)
h
8 a ABD = ACD, SSS or RHS or ASA or SAS
b MNO = QPO, SSS or SAS
c no
a2
g CAB = DEF, ASA
h RQP = RTS, RHS
no (sides are not marked as the same length)
9 64 : 27
10 a 6 m
blarger tank volume = 402 m (3sf), smaller tank
volume = 170 m3 (3sf)
12 a 2.87 m
2
c2
 u2 − v 2   u2 + v 2 
(uv ) +  2  =  2 

 

2
u2v 2 +
⇒
2
u 4 − 2u2v 2 + v 4 u2 + 2u2v 2 + v 2
=
4
4
4u2v 2 + u 4 − 2u2v 2 + v 4 = u 4 + 2u2v 2 + v 4
⇒
u 4 + 2u2v 2 + v 4 = u 4 + 2u2v 2 + v 4
c Let a = prime (p), then a = p × 1 (so u = p, v = 1)
If b and c differ by 1 then:
⇒
b +1= c
⇒
p2 − 12
p2 + 12
+1=
2
2
⇒
p2 1
p2 1
− +1=
+
2 2
2 2
⇒
p2 1 p2 1
+ =
+
2 2 2 2
3
b 1:4
2
=
b2
(If a = 17 then uv = 1 × 17 because 17 is a prime
number and its only factors are 1 and itself. If you
substitute the values of 1 and 17 into the formulae
for b and c then you get b = 144 and c = 145.)
no
11 a 1 : 2
+
b 17, 144, 145
e CAB = CDE, SSS or SAS
i
14 a
⇒
d WXY = YZW, SSS
f
24, 45, 51
3
(a2 + b2 )
2
a 2 + b2 = c 2
15 cm
6 a no
(÷ k )
k 2 (a2 + b2 ) = k 2c 2
b 0.0298 m3
13 a 152 + 202 = 225 + 400 = 625 = 252
b 62 + 82 = 36 + 64 = 100 = 102
c (3k)2 + (4k)2 = 9k2 + 16k2 = 25k2 = (5k)2
© Cambridge University Press 2018
23
Worksheet 11: Pythagoras’ theorem and similar shapes
15 Diagram of the cuboid with sides x cm, y cm and
z cm:
Let x = a, y = b, z = c and the diagonal of the base face
(x × y) = e
The diagonal of the cuboid forms a triangle with the
e = a 2 + b2
diagonal of the base face:
So,
e = a2 + b2 and d = e 2 + c 2
⇒
d2 =
(
a 2 + b2
) +c
2
2
d 2 = a 2 + b2 + c 2
d = a 2 + b2 + c 2
© Cambridge University Press 2018
24
Answers to Extended revision
­exercises: Data handling
Worksheet 12: Averages and measures of spread
1 a mean = 4.58, median = 4.5, mode = 3, range = 7
b mean = 5.27, median = 6, mode = no mode, range = 9
c mean = 7.6, median = 12, mode = 12 , range = 21
d mean = 5.14, median = 5, mode = no mode, range = 7
e mean = 7.45, median = 8, mode = 8, range = 11
4 a 126
b 23
5 a Anna = 40, Zane = 40
b no
c mean, no extreme data
6 a
Shoe size
4
Frequency
7
fx
28
5
6
30
2 mode = 11 mins, median = 23.5 mins, range = 53 mins
6
14
84
3 a
7
8
56
8
6
48
f
mean = 49, median = 48, mode = 48, range = 18
g mean = 11.5, median = 11.5, mode = 11.8, range = 1
h mean = 74.6, median = 76.5, mode = 77, range = 16
Outcome
1
Frequency
2
fx
2
2
4
8
9
6
54
3
6
18
10
3
30
4
3
12
5
2
10
6
2
12
mean = 3.26, median = 3, mode = 3, range = 5
b
c 6.6
d 6
e m
ean, there is no extreme data and will be an
understandable average, OR mode, owners of shoe
shops will want to know the most common shoe
size so they can stock enough shoes of that size
Outcome
123
Frequency
8
fx
984
124
4
496
125
5
625
126
6
756
127
7
889
8 a 74
128
8
1024
129
9
1161
9 mean = $33.67, modal class = $40 – $49.99, median
class = $30 – $39.99
mean = 126, median = 127, mode = 129, range = 6
c
b 6
Outcome
7
Frequency
12
fx
84
8
9
72
9
16
144
10
13
130
11
20
220
12
20
240
mean = 9.89, median = 10, mode = no mode, range = 5
7 a I t is the age where there are the same number of
people below and above it.
b Th
e median is quite low so there are a lot of children
and young people. This may mean the birth rate is
high or that life expectancy is low. The median is
getting larger so life expectancy may be increasing.
b 56
c 98
10 a median = 3
upper quartile = 4.25
lower quartile = 2
interquartile range = 2.25
0
1
2
3
4
5
6
7
b median = 30
upper quartile = 42.5
lower quartile = 20
© Cambridge University Press 2018
25
Worksheet 12: Averages and measures of spread
interquartile range = 22.5
mean =
=
0
10
20
30
40
50
60
70
n + (n + 1) + (n + 2) + (n + 3) + (n + 4) + (n + 5)
6
6n + 15
6
=n+2
c median = 3
1
2
mean of 3rd and 4th largest integers = mean of c + d:
upper quartile = 5.25
lower quartile = 2
mean of c + d =
interquartile range = 3.25
=
0
2
4
6
8
10
13 a
Mixture 1
Leaf
a=n
c = (n + 2)
e = (n + 4)
=
n + (n + 1) + (n + 2) + (n + 3) + (n + 4)
5
5n + 10
5
b
=n+2
This is the third integer: c = n + 2
12 Let a, b, c, d, e and f be represented as follows:
b = (n + 1)
Mixture 1
e = (n + 4)
f = (n + 5)
11
15789
01146789
268
123567
c
Mixture 2
d = (n + 3)
Mixture 2
Leaf
Range Q1
Median Q3
IQR
26.35 30.25
32.45 6.1
Mixture 1 8
27.83 28.65
30.03 2.2
Mixture 2 4.6
a=n
c = (n + 2)
25
26
27
28
29
30
31
32
33
320
85
7
9540
9753
210
d = (n + 3)
1
2
Stem
9532
532
b = (n + 1)
mean =
2n + 5
2
=n+2
12
11 Let a, b, c, d and e be represented as follows:
(n + 2) + (n + 3)
2
0
25
26
27
28
29
30
31
32
33
34
The data for Mixture 2 is more symmetrical than the
data for Mixture 1 and the variation in Mixture 1 is
higher. The data suggests that Mixture 2 has a lower
viscosity than Mixture 1.
© Cambridge University Press 2018
26
Answers to Extended revision
­exercises: Measurement
Worksheet 13: Understanding measurement
1 a 4500
b 970
7 12.25 kg, 12.75 kg
c 970
d 2.324 65
8 a i
e 80
f
g 5800
h 26 670
i
900
j
0.077
b 3851.35
k 0.0125
l
3
c 1502.79
2 a 9 km, 100 m
0.059
b 69 015 cm, 15 cm
4462
ii 3493.5
iii 10 466.1
iv 38 544
v 5440.5
vi 14 977.6
9 a 0.2 m
c 285 mm, 2 mm
d 4.99 m, 98 cm
c 10 feet
e 0.7 km, 15 m
f
e 1.8 m
3 a 700
5.5 km, 50 m
b 1200
c 6420
d 70 000
e 0.009 543
f
4 a 56 000
Upper bound = 1.35 kg
Could also be written as:
b 11 000
d 485 000
e 0.149
f
1.05 kg  combined mass < 1.35 kg
11 Lower bound = 5.88 m
0.000 019 6
Upper bound = 5.92 m
5 a
Day
Time in
Time out Lunch
Monday
8.15 a.m. 5.25 p.m.
45 mins
Tuesday
8.17 a.m. 5.30 p.m.
30 mins
Wednesday 8.23 a.m. 5.50 p.m.
45 mins
Thursday
8.22 a.m. 6.00 p.m.
60 mins
Friday
7.58 a.m. 7.00 p.m.
45 mins
Hours
worked
8 hours
25 mins
8 hours
43 mins
8 hours
42 mins
8 hours
38 mins
10 hours
17 mins
b 44 hours 45 mins
c $221.51
6 a 33.5, 34.5
d 4.5 m
10 Lower bound = 1.05 kg
4 423 000
c 34 400
b 1 foot
d $194.93
b 12 877.5, 12 878.5
c 550, 650 (continuous data) or 649 (discrete data)
Could also be written as:
5.88 m  width < 5.92 m
12 a 4106.363  abc < 5182.427
b - 2.205  (a - b) < - 2.095
c 3452.095  c - (a - b) < 3551.205
 1
d 0.685    < 0.840
 ab 
 a
e 0.169    < 0.208
 b
 c 
< 1694.033
f 1564.626  
 b − a 
 (a + b) 
< 1.212
g 1.166  
 b 
13 4.6 cm  x < 6.4 cm
d 15.335, 15.345
e 12.685, 12.695
f
4.25, 4.75
g 665, 675 (continuous data) or 674 (discrete data)
h 3.1415, 3.1425
© Cambridge University Press 2018
27
Answers to Extended revision
­exercises: Algebra
Worksheet 14: Further solving of equations and inequalities
1 a x = 4, y = 0
b x = 12, y = 4
c x = 1, y = 4
d x = 5.43, y = -3.86
e x = 8.57, y = 3.43
f
g x = 4, y = 3
h x = 2.5, y = 2
2 a x = 2, y = 5
c x = 0, y = 3
c
x = -3, y = 9
b x = 5, y = 2
d x = -2, y = 1
3 a
x = 0.5, y = 1.5
d
x = 2, y = 5
b
x = 1, y = −
4 a x4
1
2
b x6
c x6
x = 4, y = 2
© Cambridge University Press 2018
28
Worksheet 14: Further solving of equations and inequalities
d x<8
c
e x  –6
f
x 18
1
3
d
Also acceptable is:
x
g
55
3
x>−
5
8
e
5
a
f
b
g
© Cambridge University Press 2018
29
Worksheet 14: Further solving of equations and inequalities
Profit = 5c + 4t and this has its maximum value in
the shaded region when t = 13 and c = 27. He should
therefore order 13 T-shirts and 27 caps.
h
8 a x = 2, y = 6
b x = 1.67, y = 2.67
9 a (x − 3) (2x − 3)
b 2(x + 1) (5x − 7)
c (3x + 2) (4x + 5)
d 6(x + 2) (x − 1)
10 a 0.65, −4.65
6
b −0.84, −7.16
c 1.54, − 0.87
d 0.82, −1.82
11 a 1.84, −0.18
b 1.18, − 0.85
c 0.92, −3.25
d x = 1.70, x = − 4.70
e 1.45, −3.45
f
g 1
h −0.62, 1.62
12 a xy
t  10 and c  25
c  2t
d 2x2 + 3x
e x+3
f
g x−1
h 2x – 1
15c + 8t  360
b
x (2 x + 1)
6(x + 1)(4 x − 5)
c
x+2
2
d
7 x − 11
(x + 3)(x − 5)
e
2x − 7
(x + 4)2
f
2(x 2 + 4)
x2 − 4
h
4 x 2 − 3x + 3
x − x3
i
c
t = 10
2
(x − 4)(x − 2)(x + 1)
14 a i
40
x+1
(2 x − 1)
(x + 1)
3
2
g 2 x − 418 x − 213x + 117
x − 13x + 36
t + c  40
32
ii − 3
iii 5
b when x = –7 answer is zero
c − 3  x  −7
30
2
1
15 x = , y =
3
4
c = 25
t + c = 40
20
10
15t + 8c = 360
c = 2t
0
b y
c x − 2xy
13 a
7 Inequalities
4.44, 0.56
10
20
t
16 −b + b2 − 4ac −b − b2 − 4ac
−
2a
2a
2
−b + b − 4ac + b + b2 − 4ac
=
2a
2
2 b − 4ac
=
2a
2
b − 4ac
=
a
© Cambridge University Press 2018
30
Worksheet 14: Further solving of equations and inequalities
17 If x = 1 +
1
denominator is 1 +
1
1+
1+…
then x − 1 = 1 +
so x − 1 =
1
1+
1
1+…
=x
1
1+…
1
so x − 1 =
x
1− 5 1+ 5
x=
,
2
2
−1
1
1+
1
1+…
1
1+
18 2
© Cambridge University Press 2018
31
Answers to Extended revision
exercises: Shape, space and measures
Worksheet 15: Scale drawings, bearings and trigonometry
1 a
5 a 10.1
b 14.3
b
c 8.09
d 11.9
e 8.46
f
6 185 m
c
d
1.74
7 a 64.2°
NOT TO SCALE
b 4.36 m
8 50.3°
9 a x = 30° or x = 150°
b x = 120° or x = 240°
e
c x = 44.4° or x = 135.6°
d x = 60° or x = 240°
f
e x = 210° or x = 330°
NOT TO SCALE
2
f
x = 30° or x = 60° or x = 210° or x = 240°
g x = 30° or x = 210°
h x = 135° or x = 225°
i
x = 45° or x = 225°
j
x = 40° or x = 80° or x = 160° or x = 200° or x = 280°
or x = 320°
10 a x = 190° or x = 310°
b x = 56.3° or x = 236.3°
c x = 72.2° or x = 117.8°, 297.8°, 252.2°
11 AB = 9.90 cm, AC = 5.43 cm
12 E = 22.2°, F = 34.8°, DE = 89.2 mm
13 a 992 mm2
b 585 mm2
14 54 m
15 10.2 cm
3 a 150°
b 160°
4 a 36.9°
b 23.2°
c 45.6°
d 66.0°
e 68.0°
f
9.6°
16 a 4.83 m
c 5.97 m
17 a 9.28 km (3sf)
b 58.3°
d 6.77 m
b 268.0° (1dp)
18 a A = 150° B = 190°
b A = 134.730 km, B = 153.209 km
© Cambridge University Press 2018
32
Answers to Extended revision
exercises: Data handling
Worksheet 16: Scatter diagrams and correlation
1 a iA negative correlation. The more hours of
watching TV, the less the test score.
iv
iiA positive correlation. The longer the length of
arm, the higher the bowling speed.
iiiNo correlation. The month of birth has no effect
on mass.
ivA negative correlation. the more cigarettes
smoked daily, the less the length of life.
vA positive correlation. The taller one is, the
bigger the shoe size
b i
ii
v
2
Mid-year
mark x
coordinate
iii
78
57
30
74
74
88
94
83
70
61
64
49
End-ofyear test
mark y
coordinate
73
51
39
80
74
73
88
69
63
67
68
54
End-ofMid-year
year test
mark x
mark y
coordinate
coordinate
92
86
41
50
75
64
84
77
55
58
90
80
89
87
95
96
67
70
45
50
70
64
29
34
© Cambridge University Press 2018
33
Worksheet 16: Scatter diagrams and correlation
a, c
b Strongly correlated
d 66 or 67
e Quite accurate as there is such a strong correlation.
3 a Th
ere is no correlation. As one variable increases
(x), there is no increase or decrease in the other
variable.
b Th
ere is no correlation. As one variable increases
(y), there is no increase or decrease in the other
variable.
© Cambridge University Press 2018
34
Answers to Extended revision
exercises: Number
Worksheet 17: Managing money
1 a $200
b $886.24
b 33.3%
c
2 $1080
3 £1500
4 a $2700
b $3680
c $980
5 $19.25
6 $29 400
7 a $817.60
b $952
c $672
d $1036
8 $830.72
9 a $63.05
b $4656.79
c $1109.16
10 a $2000
11 a
Years
Simple interest
Compound interest
b $9000
7
6300
8280.39
8
7200
9925.63
12 a 2.04x
b 3.1216x
c $200 000
© Cambridge University Press 2018
35
Answers to Extended revision
exercises: Algebra
Worksheet 18: Curved graphs
1 a
b
c
x
-6
-5
-4
-3
-2
y
-33
-22
-13
-6
x
y
−6
50
−5
37
−4
26
x
y
−6
4
−5
1
−4
0
2 a x = 1, x = 3
0
1
2
3
4
5
6
-1
-1
2
3
2
-1
-6
-13
-22
-33
−3
17
−2
10
−1
5
0
2
1
1
2
2
3
5
4
10
5
17
6
26
−3
1
−2
4
−1
9
0
16
1
25
2
36
3
49
4
64
5
81
6
100
b x = 0, x = 4
c x = 4.2, x = -0.2
3 x = 1, y = 0/ or x = 3.5, y = 1.25
© Cambridge University Press 2018
36
Worksheet 18: Curved graphs
4
x −5
−4
−3 −2
y −0.4 −0.5 −0.67 −1
−1
−2
1
2
2
3
4
5
1 0.67 0.5 0.4
x −1 −0.5 0 0.5
1 1.5 2 2.5
3
4
y 3 0.875 0 −0.875 −1 0.375 4 10.625 21 35.875
x −5 −4 −3 −2 −1 1
2
3
4
5
y 0.2 0.25 0.33 0.5 1 −1 −0.5 −0.33 −0.25 −0.2
x
−1
−0.5
0
0.5
1
1.5
2
2.5
y
4
4.25
2
0.25
2
3.58
5.5
7.85
© Cambridge University Press 2018
37
Worksheet 18: Curved graphs
5 a
8 a gradient = - 4
y
b gradient = 12
y
9
f(x) = x2 − 4x + 3
3
y = x2 – 2x – 7
x
0
–1
1
3
–1.8
0
3.8
x
b f(x) = -1 [when x = 2]
c x=2
6
–7
y
y = x + 4x + 3
2
a i
4
4
ii -6
b x = 3.8, x = -1.8 (1dp)
3
10 a and c
y = x+ 2
2
–1.6
1
–2.6
–4
–3
–2
x
–1 –0.4 –0.6 1
–1
(x,y) = (-0.4, 1.6) and (-2.6, -0.6)
7 a
y
2
f
1
x
–4
–3
–2
–1 0
–1
1
2
3
4g
–2
–3
g
b x = 1 or x = -1
c 1.5 units
© Cambridge University Press 2018
38
Worksheet 18: Curved graphs
b x = 1 and x = -1.5 (answers within the range of
-1.5 to - 1.6 are acceptable)
d (1.7, 4.4) and (-1.2, -1.4) (1dp)
e A
t the points of intersection, the two equations are
equal, so:
2x2 + x - 3 = 2x + 1
I f you rearrange this equation, you
get 2x2 - x - 4 = 0.
11 a and b
c x=1
d It is the tangent to the curve at the point (1,1).
e 2
dy
13 a
dx
dy
b
dx
dy
c
dx
dy
d
dx
dy
e
dx
= 3x2
= -2
= 6x2 + 4
= 6x - 10
=
9
4x
14 y = 4x - 5
1
4
+2
15 a x = 1
b x=2
16 a
y
y = x3 – 3x2
4
3
2
1
–3
–2
(3, 0)
(0, 0)
–1 0
–1
1
2
3
4
x
5
–2
–3
–4
c ±1.41
12 a and b
b
(2, –4)
y
4
3
y = x (x – 1)(x + 1)
2
(–0.58, 0.38) 1
(–1, 0)
(0, 0) (1, 0)
–3
–2
–1 0
1
2
3
–1 (0.58, –0.38)
x
4
–2
–3
–4
© Cambridge University Press 2018
39
Answers to Extended revision
exercises: Shape, space and measures
Worksheet 19: Symmetry and loci
1 a C = 1, A = 1, M = 1, B = 1, R = 0, I = 2, D = 1,
G = 0, E = 1
b I = 2, all other letters have roational symmetry of
order 1.
2 Students’ own answers: drawing and naming of a
rectangle or rhombus.
3 Answers will vary: student must copy shape and draw
its mirror image according to the line of symmetry
they have chosen. Student must draw in the line of
symmetry.
4 a 7.75 cm
b 13.9 cm
c 25.4 cm
5 Working and reasoning may vary but size of angle
should be as given below. Students must show their
working and valid reasoning using statements that
demonstrate knowledge of angle properties and
relationships.
a 40°
b 22°
c 45°
d 40°
e 122°
f
g 64°
h 60°
i
j
33°
l
90°
144°
k 37°
64°
6 22 cm
7 75°
8 a angle QSP = 80° (alternate segment theorem)
b angle SQP = 60° (angle sum of triangle)
c angle PBQ = 60° (angle sum of triangle)
d angle QRS = 140° (PQRS is cyclic quadrilateral)
© Cambridge University Press 2018
40
Answers to Extended revision
exercises: Data handling
Worksheet 20: Histograms and frequency distribution diagrams
1 a 1.3-1.4 kg
b 1 kg
c 5
5 a
d 85
2 a 60-80
1  time < 21
b About 23
21  time < 31
c N
o. We are not given the distribution of marks in
each bar.
Histogram to show the distribution of the mass
of 200 students
3
seconds
31  time < 41
41  time < 46
seconds
1  time < 21
21  time < 31
31  time < 41
41  time < 46
Ages
10
9
3
b 21  time < 31
c
4 a
Frequency
8
Frequency
8
Frequency
density
0.4
10
1
9
0.9
3
0.6
Frequency
10  age < 15
6
15  age < 20
24
20  age < 25
3
b H
istogram to show the age of young adults
attending a youth camp
6 14.3 (3sf)
© Cambridge University Press 2018
41
Worksheet 20: Histograms and frequency distribution diagrams
7 a
Mass
Cumulative
frequency
0 < m  3 3 < m  3.5 3.5< m  4 4 < m  4.5 4.5 < m  6
8
57
92
b
c i
8
99
100
c
3.4 kg
ii 3.7kg
iii 0.5kg
iv 43
Swimming time (x minutes) Frequency density
3
0  x < 10
10  x < 15
15  x < 25
25  x < 30
30  x < 40
9
4.1
6.6
2.5
© Cambridge University Press 2018
42
Answers to Extended revision
exercises: Number
Worksheet 21: Ratio, rate and proportion
1 a 188 km/h
b 1.25 runs/min
b c $12.52 $/m
2 a 3:7
b 5:8
c 8:9
d 3:2
e 1:2
f
g 9 : 17
h 10 : 9
3 a 50 m
Graph showing the relationship between the
price of books and the number that can be
bought for $600
9 : 44
b 300 m
c 750 m
4 167 seconds or 2.78 minutes
5 stone = 21 wheelbarrows, cement = 7 wheelbarrows
6 1 cm : 90 km
7 a 12
c 21
b 2.4
d 0.16
8 625 : 1.44
9 a (a) 8 mm (b) 16 mm (c) 21 mm
Example diagram labelling:
NOT TO SCALE
12 a 192
b 300
c 168
d 200
e 137 (3sf)
13 a 53.3 (3sf)
c 60
b (a) 6 m (6000 mm acceptable)
(b) 12 m (12 000 mm acceptable)
(c) 15.75 m (15 750 mm acceptable)
10 a 2 hours 40 mins
c 4 hours 26 mins 40 sec
b 2 hours 30 mins
d 1 hour 40 mins
e 50 000 mins or 34 days 17 hours 17 mins
11 a
Price $1 $2 $5 $7.50 $10 $12 $15 $20 $25 $50
No of 600 300 120 80 60 50 40 30 24 12
books
b 20
d 46.7 (3sf)
e 48
14 a 280 cm2
c 4:1
2
15 a i y ∝ x
c i
1
x2
m ∝T
d i
A∝
b i
16 a 1.5
c 8
17 a 4k
y∝
1
M
b 1120 cm2
ii y = kx 2
k
ii y = 2
x
ii m = kT
ii A =
b 15
k
M
 2. 5 
b  
 k 
2
© Cambridge University Press 2018
43
Worksheet 21: Ratio, rate and proportion
18 a i
c i
200 m/min or 12 km/h
ii 5.09 km/h
b 4.25 km
19 a i
0.75 km
ii 0.833 km
iii 7.58 km
c 5 km
d 3.79 km/h
0 km/h
ii 3 km/h
20 r = 3
iii 8 km/h
iv 2 km/h
21 8192
b 1 0 until 10:20 the speed remains constant at 8
km/h
22 a F = 0.02125v2
b 200 m/s
rom 10:20 to 10:30 the speed drops uniformly to
F
2 km/h
© Cambridge University Press 2018
44
Answers to Extended revision
exercises: Algebra
Worksheet 22: More equations, formulae and functions
2
3
c 27
1 a 4
d
b 36
d 124
2 26.5 cm, 33.5 cm
3 144 km
4 Pauline = 11, Alice = 22
5 4 p.m.
6 80 km
7 0.98 m
8 b2 + 25b = 2000. Using the quadratic formula, b = 339
or –589, but as this is a length, –589 is an impossible
answer, so the width is 339 mm.
ote that the curves are symmetrical about y = x
N
when
9 96 km
10 a x =
y −2
3
11 a 3
T 
b l= g 
 2π 
b 1.5
c -1.5
d 0.75
e 9
f
g 36
h 27
i
j
36
k 0.375
5
12 a
3
c 1
13 a x
9
c
7
14 a 3 x + 1 + 1
c g −1 (x ) = x 2 − 1
24
27
x  0 for y = x2 - 1
2
and x  - 1 for y = x + 1 .
15 a x = - 2 and x = - 6
b x > 1 and x < - 1
c -3x3
d -2<x<3
e - 4  x < 1.5
f
all values can be included
b -5
d -3
x +1
b
x −1
b
1± 5
2
© Cambridge University Press 2018
45
Answers to Extended revision
­exercises: Shape and space
Worksheet 23: Transformations
1 A to B: reflection in the line x = -1
6 ab
A to C: rotation 90°, clockwise, about (5, 1)
 1 
A to D: rotation 180°, about  − , 0
 2 
A to E: rotation 90°, clockwise, about (0, 0)
2
c 1:2
7 a 26.4
c 14.9
d 4:1
b 3.0
d 11.1
8 a
 −6
e  
 −7
9 
3 
 −14
 −3
4 a  
 10 
9 
c  
 12
 −2
b  
 18 
4 
d 
 −15
 −2
e  
 −5
5 a i
AF = -a + b
ii OE = -a + b
b AD = AO + OD = -2a, BC = -a, so AD = 2BC
© Cambridge University Press 2018
46
Worksheet 23: Transformations
b
b
y
D′′
y
12
5
10
A′
6
2
4
C′′
B′
2
1
–6
–4
D′
–2 0 B′′ 2
–2
4
6
8
10
–5
–4
–4
–3
–2
–1 0
–1
1
–2
Z
–6
Centre
(0, 1)
Y
x
–10 –8
C
4
A
3
A′′
8
B
∴ Scale factor (–1)
x
2
3
4
5
X
C′
Centre (0, 1)
–8
Scale factor -1
–10
c Rotation of 180° about centre (0, 1).
11 a Rotation of 90° anti-clockwise about (1, 1).
9 a (-1, 2)
b Scale factor -2
y
c A″(3, -1), B″(3, 1), C″(-1, 1), D″(-1, -1)
5
10 a
4
5
A'
2
1
–3
–2
–1 0
–1
–2
3
C
4
A
3
C'
Z
–5
–4
Y
–3
–1 0
–1
–2
x
2
3
4
1
X
B
B'
1
2
x
1
–2
Z′′ Z′
–3
5
–4
Y′′
–3
Y′
2
3
4
5
X′
X′′
y =–
3
2
x– 3
c A(3, 1) B(3, 3) C(2, 1)
© Cambridge University Press 2018
47
Answers to Extended revision
­exercises: Data handling
Worksheet 24: Probability using tree diagrams and Venn diagrams
1 a
b
7 a
1
16
2 a
1
b i 27
ii
7
27
19
27
iv
1
27
iii
8 a
1
8
3 a 0.49
3
8
b 0.09
b i
ii
c 0.21
d 0.42
e 0.51
4 a
Newspaper Online
10
15
16
9
b 9
c P(newspaper) =
d P(neither) =
5 a 10
1
or 0.2
5
9
or 0.18
50
b P(maths) = 0.84
c P(maths or physics) = 0.96
5
9
6 a
b
14
14
15
c
28
b n=4
9 a
A
12
B
18
17
28
© Cambridge University Press 2018
48
Worksheet 24: Probability using tree diagrams and Venn diagrams
b i
0.47
ii 0.24
iii 0.63
iv 0.63
11 a
14
24
c They are not. P(A) + P(B) ≠ P(A or B)
10 a
Music
12
10
24
Maths
25
78
G
B
13
23
G
10
23
B
14
23
G
9
23
B
b 0.33
25
c 0.51
b P(music) = 0.264
c P(music given maths) = 0.243
© Cambridge University Press 2018
49