Higher booklet answers_(3)_(1)_(1)

GCSE Mathematics

ESSENTIAL REVISION
QUESTIONS

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CONTENTS
Grades
C/D......................................... 3 to 40

B............................................. 41 to 54

A/A* ...................................... 55 to 71

85 Essential Questions at C to D
(1 to 72 are non-calculator)

1T) a) 4t + 7t Grade C a) 11t
b) 4t × 7t b) 28t2
c) 6y + 2w – 5y Clip 102 c) y + 2w
d) 6y × 3t d) 18yt or 18ty
e) 4e2 × 3e3 e) 12e5
f) m7 ÷ m5 f) m2
y5 g) y3
g) y2 h) 3y3

6y 4
h) 2y

1S) a) 3t + 8t a) 11t
b) 2t × 9t b) 18t2
c) 12y + 3w – 5y c) 7y + 3w
d) 4y × 2t d) 8yt or 8ty
e) 3e5 × 2e7 e) 6e12
f) x4 ÷ x3 f) x
r7 g) r4
g) h) 3r2
r3
6r 5
h)
2r 3

2T) a) Expand 5(3y – 1) a) 15y – 5
b) Expand 3x(2x + 4) b) 6x2 + 12x
c) Expand and simplify 2(3x + 5) – 3(4x – 2) c) –6x + 16
d) Expand and simplify 5(2y – 3) + 2(y – 1) d) 12y – 17
e) (2x + 3)(x – 4) e) 2x2 – 5x – 12
Grade C
2S) a) Expand 3(2y – 4) Clip 103 a) 6y – 12
b) Expand 5x(3x + 2) b) 15x2 + 10x
c) Expand and simplify 5(2x + 1) – 2(3x – 4) c) 4x + 13
d) Expand and simplify 4(3y – 2) + 2(3y – 2) d) 18y – 12
e) (3x – 4)(2x – 1) e) 6x2 – 11x + 4

Page 3 ©MathsWatch www.mathswatch.com mathswatch@aol.co.uk Page 3

3T) Find the nth term of the following patterns
a) 3, 5, 7, 9, 11 . . . . . a) 2n + 1
Grade C
b) 8, 13, 18, 23, 28, . . . . . Clip 112 b) 5n + 3

c) 9, 6, 3, 0, –3, . . . . . c) –3n + 12

3S) Find the nth term of the following patterns
a) 2, 6, 10, 14, 18 . . . . . a) 4n – 2

b) 7, 16, 25, 34, 43, . . . . . b) 9n – 2

c) 5, 2, –1, –4, –7, . . . . . c) –3n + 8

4T)
Number of
Frequency
smarties

29 2
30 5
31 2
32 1

a) From the table above, find the mean number of a) 30.2
smarties in a tube.
b) 30
b) Find the median number of smarties in a tube.

Grade C Clip 133
4S)
Number of
Frequency
smarties

29 2
30 1
31 5
32 2

a) From the table above, find the mean number of a) 30.7
smarties in a tube. b) 31
b) Find the median number of smarties in a tube.

5T) Factorise the following:
a) 2x + 6 a) 2(x + 3)
b) 2x + 8 b) 2(x + 4)
c) 2x + 12
Grade C c) 2(x + 6)
d) 3x + 6 Clip 104 d) 3(x + 2)
e) x2 + x e) x(x + 1)
f) 2x2 – 6x
f) 2x(x – 3)
g) 3h(3h + 2)
g) 9h2 + 6h
h) 2x(4x – 5)
h) 8x2 – 10x

5S) Factorise the following:
a) 2t + 10 a) 2(t + 5)
b) 3m – 12 b) 3(m – 4)
c) 4y + 8 c) 4(y + 2)
d) 2x2 + 6 d) 2(x2 + 3)
e) t2 + t e) t(t + 1)
f) 5t2 + 10t
f) 5t(t + 2)
g) 7t2 – 14t
g) 7t(t – 2)
h) 9h2 – 30h
h) 3h(3h – 10)

6T) a) If a piece of wood is measured as 8cm to the a) Greatest is 8.5cm
nearest cm, what is the greatest possible Least is 7.5cm
length and the least possible length?

b) Greatest is 19.85cm
b) If a piece of wood is measured as 19.8cm to the
nearest tenth of a cm, what is the greatest possible Least is 19.75cm

Grade C
Clip 125
6S) a) If a piece of wood is measured as 5cm to the a) Greatest is 5.5cm
nearest cm, what is the greatest possible
Least is 4.5cm

b) If a piece of wood is measured as 6.7cm to the b) Greatest is 6.75cm
nearest tenth of a cm, what is the greatest possible Least is 6.65cm


7T) a) If a = 3 and t = –2 find the value of
(i) 3a a) (i) 9
(ii) a2 Grade D (ii) 9
(iii) 5a2 (iii) 45
(iv) 4a – 2t Clip 66 (iv) 16
(v) 2(3a + t) (v) 14
(vi) 2
(vi) 4a − t
7
b) Colin said “when x = 3, then the value of 4x2 is 144” b) Sue because
4x2 is 4 × x2
Sue said “when x = 3, then the value of 4x2 is 36”
Who was right? Explain why.

7S) a) If a = 4 and t = –5 find the value of
a) (i) 12
(i) 3a
(ii) 16
(ii) a2
(iii) 80
(iii) 5a2
(iv) 26
(iv) 4a – 2t
(v) 14
(v) 2(3a + t)
(vi) 3
(vi) 4a − t
7
b) Colin said “when x = 5, then the value of 4x2 is 400” b) Sue because
Sue said “when x = 5, then the value of 4x2 is 100” 4x2 is 4 × x2
Who was right? Explain why

8T) a) Write 2340000 in standard form. a) 2.34 × 106
b) Write 0.00042 in standard form. b) 4.2 × 10–4
c) Write 7.8 × 106 as a normal number. c) 7800000
d) Write 4.71 × 10–5 as a normal number. d) 0.0000471

Grade C Clip 97
8S) a) Write 630000000 in standard form. a) 6.3 × 108
b) Write 0.00000715 in standard form. b) 7.15 × 10–6
c) Write 9.17 × 105 as a normal number. c) 917000
d) Write 8.23 × 10–6 as a normal number. d) 0.00000823


9T) Write the following numbers as the product of their
prime factors
a) 48
Grade C a) 2 × 2 × 2 × 2 × 3
b) 60 Clips 95 & 96 b) 2 × 2 × 3 × 5
c) Find the Highest Common Factor of 48 and 60 c) 12
d) Find the Lowest Common Multiple of 48 and 60 d) 240
9S) Write the following numbers as the product of their
prime factors
a) 90 a) 2 × 3 × 3 × 5
b) 120 b) 2 × 2 × 2 × 3 × 5
c) Find the Highest Common Factor of 90 and 120 c) 30
d) Find the Lowest Common Multiple of 90 and 120 d) 360

10T) a) Draw an angle of 70 degrees and then use ruler Grade C Clip 127
and compasses to bisect it.
b) Draw a line of length 9cm and then bisect it Grade C Clip 129
using compasses.
c) Use compasses to draw a triangle ABC with AB Grade D Clip 80
equal to 9cm, AC 7cm and BC 4cm

10S) a) Draw an angle of 60 degrees and then use ruler
and compasses to bisect it.
b) Draw a line of length 11cm and then bisect it
using compasses.
c) Use compasses to draw an isosceles triangle with
the base equal to 8cm and the other two sides of
length 12cm

11T) What is 2 × 5 + 7 × 3? Grade D 31

Clip 59
11S) Work out the answer to 38 – 3 × 4 26

12T) What is 2.3 × 0.15? 0.345
Grade D
12S) What is 2.7 × 0.13? 0.351
Clip 60
13T) –3 x < 4 Grade C Clip 108
x is an integer. Write down all the possible values. –3, –2, –1, 0, 1, 2, 3
13S) –2 x 3
x is an integer. Write down all the possible values. –2, –1, 0, 1, 2, 3


14T) Here are the front elevation, side elevation and the
plan of a 3-D shape.
Draw a sketch of the 3-D shape. Grade D
Front elevation Side elevation
Clip 81

Plan

14S) Here are the front elevation, side elevation and the
plan of a 3-D shape.
Draw a sketch of the 3-D shape.

Front elevation Side elevation

Plan

3 of 600
15T) a) Work out
10 Grade D a) 180

b) Work out 5 of 800
8
Clip 55 b) 500

c) Work out 5 × 42
c) 30
7

15S) a) Work out 7 of 400
10 a) 280

b) Work out 2 of 900
9 b) 200

c) Work out 3 × 56
8 c) 21


16T) If you share out £240 between Alice and Bill in the £60
ratio 5 : 3, how much more does Alice get compared
with Bill?
Grade C Clip 94
16S) If you share out £60 between Alice and Bill in the £24 for Alice and
ratio 2 : 3, how much does each of them get? £36 for Bill

17T) Sara and Fred share tips from their job in the ratio £14
2 : 5. If Fred receives £35 how much does Sara get?

Grade C Clip 94
17S) Sara and Fred share tips from their job in the ratio £24
3 : 4. If Sara receives £18 how much does Fred get?

18T) Some plant heights are measured as shown in the
table, below.
Height in cm Frequency
0 < h 20 4
20 < h 40 3
40 < h 60 2
60 < h 80 1

a) Find an estimate for the mean height of a plant. a) 30
b) In which interval does the median height lie? b) 20 < h 40

18S) Some plant heights are measured as shown in the
table, below.
Height in cm Frequency
0 < h 20 1
20 < h 40 2
40 < h 60 4
60 < h 80 3

a) Find an estimate for the mean height of a plant. a) 48
b) In which interval does the median height lie? b) 40 < h 60

Grade C
Clip 133


mathswatch@aol.co.uk www.mathswatch.com ©MathsWatch Page 10
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U
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move U back on to the shaded shape.
Decribe fully the single transformation that will c)
centre of rotation and label the new shape U
Rotate T 90º clockwise using (0, 0) as the b)
Reflect the shaded shape in the x axis and label it T 19S) a)
Grade D Clips 74, 75, 77
Reflection in y = –x c)
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Decribe fully the single transformation that will c)
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centre of rotation and label the new shape U
Rotate T 90º anticlockwise using (0, 0) as the b)
Reflect the shaded shape in the y axis and label it T 19T) a)

20T) a) Enlarge triangle A scale factor 3 using (2, 4) as
centre of enlargement
b) Enlarge triangle A scale factor ½ using (4, 0) as

Grade D Clip 76
20S) a) Enlarge triangle A scale factor 2 using (4, 5) as
b) Enlarge triangle A scale factor ½ using (-2, 2) as


21T) Find the exterior angle of this regular octagon
45 degrees

Grade D
Clip 70

21S) Find the exterior angle of this regular hexagon
60 degrees

22T) a) In the triangle below, find an expression, in terms a) 4x + 8
of x, for the perimeter of the triangle.
Simplify your expression. b) x = 9 cm

b) If the perimeter of the triangle 2x 2x
is 44 cm, find the value of x.

Grade C 8

Clip 106
22S) a) In the rectangle below, find an expression, in terms a) 8x + 6
of x, for the perimeter of the rectangle.
Simplify your expression. b) x = 5 cm

3x + 5

x–2

b) If the perimeter of the rectangle
is 46 cm, find the value of x.


23T) Find the size of angle n, giving reasons
A
ABC = 60°(angles on st. line
= 180)
n = 78° (angles in add
B C Grade D up to 180)

Clips 68, 69
23S) Find the size of angles x and y, giving reasons
A
x = 56° (angles in =180,
base angles are equal)
ABC = 56°(base angles of
isos. are equal)
y = 124° (angles on st. line
= 180°)
B C

24T) Find the size of angle x, giving reasons
Grade D
°
Clip 67 BRS = 30°(angles on straight
line add up to 180°)
° x = 30° (alternate angles)

24S) Find the size of angles x and y, giving reasons

x = 86° (angles in
quadrilateral
add up to 360°)
y = 74° (alternate angles)


25T) Solve the following equations
a) 2x = 7 a) 3.5
b) x – 8 = 4
c) 2x + 3 = 11
Grade C b)
c)
12
4

d) x +5=7 Clip 105 d) 6
3 e) 3
e) 2(5x – 2) = 26 f) 5
2 x – 3 = –1 g) 3.5
f)
5
g) 3x + 4 = 5x – 3

25S) Solve the following equations
a) 3x = 12 a) 4
b) x – 9 = 3 b) 12
c) 3x + 2 = 14 c) 4
x +6=4 d) –6
d)
3 e) 7
e) 2(3x + 2) = 46 f) 7.5
2 x – 6 = –3 g) –3
f)
5
g) 4x + 3 = 2x – 3

26T) Draw a stem and leaf diagram to show the following 3 4 6
information. 4 1 7 7 9
The heights of 12 plants in cm are: 5 1 2 2 8
3.6, 5.2, 4.1, 3.4, 5.8, 6.2, 4.7, 5.2, 6 2 4
4.7, 6.4, 5.1, 4.9
Key 4 | 1 means 4.1
Grade D Clip 89
26S) Draw a stem and leaf diagram to show the following 5 0 2 9
information. 6 2 4 7 8
The weights of 10 people in kg are: 7 1 5
59, 52, 81, 67, 75, 62, 50, 64, 68, 71 8 1
Key 6 | 2 means 62

27T) For each of the following, state whether it is a length,
area, volume or none of them (a, b, m, q, r, x are lengths)
mq p2 r r3 V A L V A A
a 2b 2ab r ab(m + q) q x
Grade C Clip 124
27S) For each of the following, state whether it is a length,
area, volume or none of them (a, b, m, q, r, x are lengths)
pqr r2 A V A V V L
ab 2ab2 r2 + rx ab(m + q) 2 x


28T) a) Anne buys 46 litres of diesel at £1.32 per litre. a) £60.72
How much does she spend altogether on diesel?

b) James spends £65.72 on 53 litres of petrol. b) £1.24
How much was each litre of petrol?
Grade D Clip 60
28S) a) Sara buys 34 litres of diesel at £1.43 per litre. a) £48.62
How much does she spend altogether on diesel?

b) Sid spends £57.12 on 42 litres of petrol. b) £1.36
How much was each litre of petrol?
2 3 1 1
29T) a) 3 + 8 a) 24

b)
3 1
5 – 4
Grade D b) 7
20

3 8
Clips 56 c) 2
c) × 9 3
4
and 57
d) 2 1 d) 4
3 ÷ 6

3 2 1 5
29S) a) 4 + 3 a) 12
5 2 11
b) 7 – 5 b) 35

c) 3 6 9
c)
10 × 8 40

d) 4 3 d) 22
5 ÷ 10 3
P
30T) Draw a pie chart to show the following information B C

Plain
Crisp flavour Frequency
Cheese Cheese 80°
8
Plain 19
Grade D Plain 190°
Beef Beef
Prawn
6
3
Clip 86 Prawn
60°
30°

30S) Draw a pie chart to show the following information B
P
C
Plain
Crisp flavour Frequency
Cheese 8 Cheese 160°
Plain 6 Plain 120°
Beef 1 Beef 20°
Prawn 3 Prawn 60°

31T) Find the areas of the following shapes

a) 7m b)
a) 21m2

3m 4cm b) 10cm2

c) 160cm2
5cm

c) 18cm

4cm
12cm

11cm

Grade D
Clip 73
31S) Find the areas of the following shapes

a) b) a) 54m2
9m

6m 7cm b) 42cm2

c) 222cm2
12cm

c) 24cm

4cm
13cm

14cm


32T) Find the surface area of this cuboid.
92cm2

Grade C
3cm
Clip 121
2cm
8cm

32S) Find the surface area of this cuboid. 190cm2

5cm

3cm
10cm

33T) Make the letter in the bracket the subject of the
formula.
v-u
a) v = u + at (a) Grade C a) a=
t
b) x – t = bc
a
(x) Clip 107 b) x = a(bc + t)
33S) Make the letter in the bracket the subject of the
formula.
v2 - u2
a) v2 = u2 + 2as (a) a) a=
2s

b) x +y=c (x)
a b) x = a(c – y)

34T) Find the following:
a) 10% of £700 a) £70
b) 15% of £80 Grade D b) £12
c) 35% of £600 c) £210
d) 17.5% of £48 Clip 52 d) £8.40

34S) Find the following:
a) 40% of £260 a) £104
b) 15% of £900 b) £135
c) 85% of £800 c) £680
d) 17.5% of £240 d) £42


35T) Sally’s mother lives 80km from Sally. This is the
journey to her mother’s house.
a) 100km/h
100 b) 30 mins
Distance in km from home
c) 30km/h
80

60

40

20

0800 0900 1000 1100 1200
Time

a) Sally has a rest at 8.30. What speed had she
been travelling at until 8.30?
b) How long did she rest for?
c) What speed did she travel at for the last part of
the journey to her mother’s house?
d) For the return journey, Sally travelled at 60km/h
without a break. Complete the travel graph to
show this.
Grade C Clip 117
35S) Sally’s mother lives 90km from Sally. This is the
journey to her mother’s house.
a) 120km/h
b) 30km/h
100
Distance in km from home

80

60

40

20

0800 0900 1000 1100 1200
Time

a) What speed did Sally travel at until her first
rest?
b) What speed did she travel at for the last part of
the journey to her mother’s house?
c) For the return journey, Sally travelled at 80km/h
without a break. Complete the travel graph to
show this.


36T) a) Complete the table for the equation
y = 2x2 – 3x

x –2 –1 0 1 2 3 Grade C –2 –1 0 1 2 3
y 14 Clip 116 14 5 0 –1 2 9

b) Draw the graph of y = 2x2 – 3x on the
axes at the bottom of the page
c) Use your graph to find the value of y c) 3.6
when x = 2.3
d) Use your graph to find the value of y d) 9
when x = –1.5
e) Use your graph to solve 2x2 – 3x = 5 e) x = –1 and x = 2.5
f) Use your graph to solve 2x2 – 3x = 8 f) x = –1.3 and x = 2.9

y
14

13

12

11

10

9

8

7

6

5

4

3

2

1

O
x
-2 -1 1 2 3

-1

-2


36S) a) Complete the table for the equation
y = 3x2 – x

x –2 –1 0 1 2 Grade C –2 –1 0 1 2
y 14 Clip 116 14 4 0 2 10

b) Draw the graph of y = 3x2 – x on the
axes at the bottom of the page
c) Use your graph to find the value of y c) 5.3
when x = 1.5
d) Use your graph to find the value of y d) 8.25
when x = –1.5
e) Use your graph to solve 3x2 – x = 10 e) x = –1.7 and x = 2

y
14

13

12

11

10

9

8

7

6

5

4

3

2

1

O
x
-2 -1 1 2 3

-1

-2


5

37T) Draw a set of axes going from –5 to +5 y = 3x + 1
4

3
a) Draw the graph of y = 2x – 3
b) What is the gradient? Grade C b) 2
2

1

37S) Draw a set of axes going from –5 to +5 Clip 113 -5 -4 -3 -2 -1 O
-1
1 2 3 4 5

-2
a) Draw the graph of y = 3x + 1 y = 2x – 3
-3

b) What is the gradient? b) 3 -4

-5

38T) The table below shows the probability of an oddly
shaped 4-sided dice landing on 1, 2, 3, or 4.
a) Work out the value of x a) 0.24
b) If the dice is rolled 1000 times how many 2s b) 370
would you expect to get?
1 2 3 4
Grade C
0.15 0.37 0.24 x Clip 132
38S) The table below shows the probability of an oddly
shaped 4-sided dice landing on 1, 2, 3, or 4.
a) Work out the value of x a) 0.23
b) If the dice is rolled 1000 times how many 3s b) 140
would you expect to get?
1 2 3 4
0.29 0.34 0.14 x

other answers
39T) Draw a plane of symmetry on this shape
are possible

Grade D
Clip 83

39S) Draw a plane of symmetry on this shape other answers
are possible


40T) Frequency Frequency
Height Frequency
0 to 10 1 7 7
10 to 20 4 6 6
20 to 30 3
5 5
30 to 40 2
4 4

a) On the first set of axes, 3 3
draw a frequency diagram
2 2
b) On the second set of axes,
draw a frequency polygon 1 1

0 0
0 10 20 30 40 50 0 10 20 30 40 50
Grade D Height Height
Frequency Frequency

Clip 88 7 7

6 6

5 5
ANSWERS for 40T 4 4 ×
3 3 ×
2 2 ×
1 1 ×
0 0
0 10 20 30 40 50 0 10 20 30 40 50
Height Height

40S) Frequency Frequency
Height Frequency
0 to 10 3 7 7
10 to 20 7 6 6
20 to 30 2
5 5
30 to 40 1
4 4

a) On the first set of axes, 3 3
draw a frequency diagram
2 2
b) On the second set of axes,
draw a frequency polygon 1 1

0 0
0 10 20 30 40 50 0 10 20 30 40 50
Height Height
Frequency Frequency

7 7 ×
6 6

5 5
ANSWERS for 40S 4 4

3 3 ×
2 2 ×
1 1 ×
0 0
0 10 20 30 40 50 0 10 20 30 40 50
Height Height


41T) a) In a room there are 7 boys and 3 girls. a) 70%
What percentage of the people are boys?

b) 35%
b) In a room there are 13 boys and 7 girls.
What percentage of the people are girls?

c) 60%
c) Sally scores 24 marks out of 40 in a Science test.
What was her percentage score?

Grade D Clip 54
41S) a) In a room there are 11 boys and 9 girls. a) 55%
What percentage of the people are boys?

b) In a room there are 13 boys and 12 girls. b) 48%
What percentage of the people are girls?

c) 90%
c) Emma scores 54 marks out of 60 in a Science test.
What was her percentage score?

42T) A point, P, moves so that the locus of P is always 2 cm
from the line AB.
Draw the locus of P.
Grade C Clip 130

B

A

42S) A point, P, moves so that the locus of P is always
equidistant from lines AB and AC.
Draw the locus of P.

B

A

C

43T) a) Sketch a scatter diagram with positive a)
correlation ×
×
×
× ×
×× ××
‘hair length’, ‘hair colour’, ‘intelligence,’ ×× ×
‘circumference of wrist’, ‘height’, ‘ice cream ××
sales’, ‘weight’, ‘outside temperature’
‘sale of extra-warm jackets’, ‘eye colour’
b) (i) height and weight
b) From the list above select two sets of data which
would have or Ice cream sales and
temp.
(i) a positive correlation
(ii) hair length and hair colour
(ii) no correlation or hair colour and intelligence
Grade D Clip 87 etc

43S) a) Sketch a scatter diagram with negative a)
××
correlation
××
× ×
×
‘hair length’, ‘hair colour’, ‘intelligence,’ ×× ×
××
‘circumference of wrist’, ‘height’, ‘ice cream × ×
sales’, ‘weight’, ‘outside temperature’
‘sale of extra-warm jackets’, ‘eye colour’
b) From the list above select two sets of data which b) (i) temp. and sale of jackets
would have (ii) eye colour and intelligence
(i) a negative correlation or hair length and weight
(ii) no correlation etc

44T) a) What are the first four multiples of 7? a) 7 14 21 28
b) Write down all the factors of 30. b) 1 2 3 5 6 10 15 30
c) What are the first six prime numbers? c) 2 3 5 7 11 13

44S) a) What are the first four multiples of 5? a) 5 10 15 20
b) Write down all the factors of 40. b) 1 2 4 5 8 10 20 40
c) Which two prime numbers come next, after 13? c) 17 19
Grade D Clip 44
45T) Solve the inequality 2x + 3 < 11 x<4
45S) Solve the inequality 5x – 7 > 43 x > 10

Grade C Clip 109
46T) Evaluate 53 125
Grade D Clip 45 16
46S) Evaluate 24


47T) Find the volume of this triangular prism.

Volume = 84cm3
6cm
7cm Grade C
4cm
Clip 122
47S) Find the volume of this triangular prism.

Volume = 160cm3
4cm
m
10c
8cm

48T) a) Write as a power of 7
73 × 75
Grade C a) 78

b) Write as a power of 2 Clip 111 b) 26
28 ÷ 22

48S) a) Write as a power of 5 a) 57
52 × 54 × 5
b) Write as a power of 3 b) 35
39 ÷ 34

49T) Complete the two-way table which shows the favourite
soup of 100 people.
Oxtail Tomato Chicken Total
Oxtail Tomato Chicken Total
Male 25 42 Male 25 12 5 42
Female 18 11 Female 29 18 11 58
Total 54 30 16 100
Total 16 100

Grade D Clip 85
49S) 110 students studied History and Geography as shown
in the two-way table.
History Geography Both Total
History Geography Both Total
Female Female 11 12 35 58
Male 8 Male 4 8 40 52
Total 15 20 110 Total 15 20 75 110

40 males studied both subjects.
52 of the students were male.
Complete the two-way table.


50T) Measure this angle.

48°

50S) Measure this angle.
Grade D
Clip 79
114°

51T) The price of a pair of shoes is £75. £82.50
How much are they after a price increase of 10%?

51S) A new car costs £8000. Grade C Clip 93
£6800
If the price is reduced by 15% what is the new price?

52T) 73.5 ÷ 0.21 350
Grade C Clip 100
52S) 18.02 ÷ 0.34 53

53T) What are the first 5 terms of the number sequence 5 8 11 14 17
with the nth term of 3n + 2?
Grade D Clip 65
53S) What are the first 5 terms of the number sequence 1 5 9 13 17
with the nth term of 4n – 3?


54T) Translate triangle A by vector -5
-3

87654321
87654321
87654321
87654321
87654321
87654321
87654321
87654321

Grade D Clip 77
54S) Describe fully the transformation which maps triangle
A onto triangle B.

Translation by vector -6
1

B

.. 3
55T) Change the recurring decimal 0.27 into a fraction in
its simplest form. 11
.. 7
55S) Change the recurring decimal 0.63 into a fraction in
its simplest form. 11

Grade C Clip 98


56T) What is the equation of the line? y = 2x + 1
y
5

4

3

2

1

x
-3 -2 -1 O 1 2 3
-1

-2

-3
Grade D Clip 114
56S) What is the equation of the line? y = 3x – 2
y
5

4

3

2

1

-3 -2 -1 O 1 2 3
-1

-2

-3
57T) List all of the outcomes if you roll a dice and 1H 2H 3H 4H 5H 6H
flip a coin. 1T 2T 3T 4T 5T 6T
57S) List all of the outcomes if you flip three coins. HHH HHT HTH THH
TTT TTH THT HTT
Grade D Clip 90

58T) Use a protractor to work out the bearing of A from B.
Bearing of A from B is 293°

Grade C Clip 131

A

A

N

B
B

58S) Use a protractor to work out the bearing of B from A.
Bearing of B from A is 046°
B
N B

A A

59T) In the list of fractions, below, which two are
equivalent to 4 ?
5
5 8 8 10 16 18 8 16
6 9 10 11 20 24 10 20
59S) In the list of fractions, below, which two are
equivalent to 2 ?
3
8 7 6 8 10 14 8 14
12 8 12 14 16 21 12 21
Grade C Clip 47
60T) A map has a scale of 1:100 000.
If town A is 5cm away from town B on the map, what is 5km
the actual distance between them in kilometres?
60S) A map has a scale of 1:500 000.
If town A is 3cm away from town B on the map, what is 15km
the actual distance between them in kilometres?
Grade C Clip 61


61T) a) -3 × -4 61S) a) 6 × -3 a) 12 a) -18
b) 7 × -5 b) -10 × -2 b) -35 b) 20
c) -12 ÷ 4 c) 15 ÷ -3 c) -3 c) -5
d) -8 – 6 d) 12 – 18 d) -14 d) -6
e) 9 – -5 e) 2 – -13 e) 14 e) 15
f) 10 + -6 f) 15 + -17 f) 4 f) -2
g) -4 + -5 g) -6 + -8 g) -9 g) -14
Grade C Clip 99
62T) Use the graph to solve the simultaneous equations
y = 7 – x and y = 2x – 2
y
8
y = 2x – 2 x = 3 and y = 4
y=7–x
7

6

5

4

3

2

1

0 x
0 1 2 3 4 5 6 7 8

Grade C Clip 115
62S) Use the graph to solve the simultaneous equations
y = 8 – 2x and y = ½x + 3
y
8
y = 8 – 2x x = 2 and y = 4
7 y = ½x + 3

6

5

4

3

2

1

0 x
0 1 2 3 4 5 6 7 8


40 400
37.9 × 417 37.9 × 417
63T) Estimate the answer to 1000 1.94 × 8.03
1.94 × 8.03 2 8

873 × 18 900 20
63S) Estimate the answer to 180
104 873 × 18
104
Grade C Clip 101 100

64T) Point P has coordinates (7, 4, 3)
Point T is the intersection of PR and SQ.
Work out the coordinates of T. (3.5, 2, 3)
y

Grade C
Clip 120

S
. .
P

.
T x

R . . Q
z

64S) Point P has coordinates (8, 3, 4)
a) Work out the coordinates of T. a) (8, 3, 0)
b) Work out the coordinates of S. b) (0, 0, 4)
y

. T

.
P

x

S .
z

65T) If the probability of passing a driving test is 0.42 what is 0.58
the probability of failing the test?

65S) The probability of a school football team winning a 0.45
football match is 0.34 and the probability of
losing is 0.21.
What is the probability of the team drawing the match?
Grade D Clip 91

66T) Draw the net of this right-angled triangular prism.

5 squares
Grade D
4 squares Clip 82
ares
3 squares 5 squ

66S) Draw the net of this cuboid

3 squares
2 squares
5 squares


67T) Write the following fractions in their simplest forms.

a) 16 a) 4
20 5
9 Grade D 3
b) 15 b)
Clip 48 5
c) 24 c) 2
60 5
67S) Write the following fractions in their simplest forms.

a) 12 a) 2
30 5
b) 7 b) 1
21 3
c) 40 c) 5
64 8

68T) Here are the ingredients needed to make salmon
fishcakes for four people.
450g potatoes
900g of salmon
25g butter Grade D
15g dill Clip 62
50g flour
2 eggs
150g breadcrumbs
a) What weight of salmon would be needed to use a) 1350g
the recipe for six people?

b) For seven people, what weight of flour is needed? b) 87.5g

68S) Here are the ingredients needed to make shepherd's pie
for five people.
500g potatoes
50g of cheese
150g butter
1 onion
2 carrots
300ml stock
1kg of lamb
a) What weight of cheese would be needed to use a) 80g
the recipe for eight people?

b) For six people, how much stock is needed? b) 360ml
c) For nine people, what weight of lamb c) 1.8kg
should be used?


69T) Put these fractions in order of size, smallest to largest.
5 7 2 3 7 5 2 3
8 12 3 4 12 8 3 4

69S) Put these fractions in order of size, smallest to largest.
4 9 7 1 9 1 7 4
5 20 10 2 20 2 10 5

Grade D Clip 49

70T) a) What is the square of 6? a) 36
Grade D
b) Find the cube of 4. b) 64
c) What is the square root of 49?
Clip 46 c) 7
d) What is the cube root of 27? d) 3
e) Evaluate 144 e) 12

70S) a) What is the square of 8? a) 64
b) Find the cube of 2. b) 8
c) What is the square root of 100? c) 10
d) What is the cube root of 125? d) 5
e) Evaluate 169 e) 13

71T) Sara wishes to find out how much pocket money people How much pocket money do you
in her class received. receive each week?
Design a suitable question she could use Less than £2
on a questionnaire. Between £2.01 and £4
More than £4
You should include some tickboxes.

71S) Fred wants to know which sports are watched by pupils in Sport Tally Frequency
his class. Football
Design a suitable data collection sheet he can use Cricket
to find out. Tennis
Athletics
Grade D Clip 84
Rugby
Grade C Clip 134 Other

72T) Change the following fractions to decimals.
a) 4 b) 3 a) 0.8 b) 0.375
5 8

72S) Change the following fractions to decimals. a) 0.6 b) 0.625
a) 6 b) 5
10 8

Grade D Clip 58


Questions 73 to 85 are all calculator questions
73T) Find the length of sides A, B and C giving your answers to
one decimal place.
14cm
A 13.9cm

B 18.2cm
A B
12cm 23cm
C 5.6cm

7cm

Grade C
C 3.9cm
Clip 118

6.8cm

73S) Find the length of sides A, B and C giving your answers to
one decimal place.
A 14.4cm
58cm
B 111.9cm
17cm
A 126cm
C 12.7cm

9cm B

9.5cm

8.5cm

C

74T) The equation x3 + 2x = 20 has a solution between 2 and 3. x=2 23 + 2 × 2 = 12 Too low
x=3 33 + 2 × 3 = 33 Too big
Use a trial and improvement method to find this solution.
x = 2.4 2.43 + 2 × 2.4 = 18.624 Too low
Give your answer to 1 decimal place and show all workings. x = 2.5 2.53 + 2 × 2.5 = 20.625 Too big
x = 2.45 2.453 + 2 × 2.45 = 19.60612 Too low
x = 2.5 to 1 decimal place.
x=4 43 – 4 × 4 = 48 Too low
74S) The equation x3 – 4x = 88 has a solution between 4 and 5. x=5 53 – 4 × 5 = 105 Too big
Use a trial and improvement method to find this solution. x = 4.7 4.73 – 4 × 4.7 = 85.023 Too low
Give your answer to 1 decimal place and show all workings. x = 4.8 4.83 – 4 × 4.8 = 91.392 Too big
x = 4.75 4.753 – 4 × 4.75 = 88.17187 Too big
Grade D Clip 110 x = 4.7 to 1 decimal place.


75T) a) 34% of £28.76 = Grade D a) £9.78
b) 76% of 900 = b) 684
Clip 46
c) Reduce £45.50 by 12.5% c) £39.81
75S) a) 29% of £235.60 = a) £68.32
b) 43% of 2400 = b) 1032
c) Reduce £260 by 30% c) £182
76T) If £1 = 1.23 Euros, Grade D
a) Change £38 to Euros. Clip 64 a) 46.74 Euros
b) Change 650 Euros to pounds (£). b) £528.46
76S) If £1 = 1.27 Euros,
a) Change £2000 to Euros. a) 2540 Euros
b) Change 923 Euros to pounds (£). b) £726.77
77T) a) Find the area of the following circles.
Give both answers to 1 decimal place.
(i) (ii) a) (i) 153.9cm2
(ii) 452.4cm2
7cm
24cm

b) Find the area of this quarter circle. b) 78.5cm2

Grade D Clip 71
10cm
77S) a) Find the area of the following circles.
(i) (ii) a) (i) 380.1cm2
(ii) 243.3cm2
11cm
17.6cm

b) Find the area of this semicircle. 19cm b) 141.8cm2


78T) Which is the best value for money 0.55p per gram
500g of sausages for £2.75 or 0.57p per gram
650g of the same type of sausages for £3.70? 500g for £2.75 best value
You must show all your working.
78S) Which is the best value for money 0.106p per ml
800ml of orange juice for £0.85 or Grade D 0.13p per ml
350ml of orange juice for £0.46? Clip 50 800ml for £0.85 best value
You must show all your working.

79T) a) Find the circumference of the following circles.
(i) (ii) a) (i) 44.0cm
(ii) 75.4cm
7cm
24cm

b) Find the perimeter of this b) 35.7cm
quarter circle to 1 decimal place.
Grade D Clip 72
10cm
79S) a) Find the circumference of the following circles.
(i) (ii) a) (i) 69.1cm
(ii) 55.3cm
11cm
17.6cm

b) 48.8cm
b) Find the perimeter of this semicircle 19cm
to 1 decimal place.


80T) a) Change the following to percentages.
Give your answers to 1 decimal place.
(i) 17 out of 67 a) (i) 25.4%
(ii) 134 out of 386 (ii) 34.7%
b) If Sue scores 82 marks out of a possible 120 marks, b) 68.3%
what was her score as a percentage?

80S) a) Change the following to percentages.
Give your answers to 1 decimal place.
(i) 44 out of 78 a) (i) 56.4%
(ii) 12.6 out of 59 (ii) 21.4%
b) If Sue scores 14 marks out of a possible 75 marks, b) 18.7%
what was her score as a percentage?
Grade D Clip 53
81T) Find the volume of this cylinder.
Give your answer to 1 decimal place.
9cm
Volume = 6107.3cm3
Grade D
24cm
Clip 122

81S) Find the volume of this cylinder.
Give your answer to 1 decimal place.
20cm
Volume = 14765.5cm3

47cm

8.23 + 2.32 23.59360083
82T) Evaluate = 0.907097302
(12.4 – 7.3)2 Grade D 26.01

Clip 63
19.62 + 73 + 25 403.5249167
= 3.433767009
82S) Evaluate 117.5166852
3
5 – 56


83T) Find the length of the line.
y
6
5cm
Grade C
5 6
Clip 119
5
4
4
3
3

2 2

1 1

x O 1 2 3 4 5 6
O 1 2 3 4 5 6

83S) Find the length of the line to 1 decimal place.
y
6
5.4cm
5 6

4 5

4
3
3
2
2
1 1

x
O 1 2 3 4 5 6 O 1 2 3 4 5 6

84T) a) A cyclist travels 12 miles in 2 hours. a) 6mph
What is the cyclist's speed in mph? Grade C
b) Sue walks for 45 minutes at 14mph. b) 10.5 miles
How far does she travel?
Clip 126
c) A piece of lead has a mass of 340g and a c) 11.3 g/cm3
volume of 30cm3.
Work out its density in g/cm3.
84S) a) A cyclist travels at 14.3mph for 4 hours. a) 57.2 miles
What distance does he cover?
b) Sue drives at an average speed of 57mph and covers b) 4 hours 30 minutes
a distance of 256.5 miles.
How long does the journey take in hours
and minutes?
c) A piece of lead has a density of 12g/cm3 and a c) 166.7cm3
mass of 2kg.
Work out its volume in cm3.


85T) The two triangles are similar.

37.8cm
x
y
5cm

8cm 43.2cm

a) Work out the size of x. a) x = 27cm
b) Work out the size of y. b) y = 7cm

85S) BE is parallel to CD
Find the length of BC. Grade C BC = 8cm
Clip 123
A

10cm

B E
12cm
x

C D
21.6cm


22 Essential Questions at grade B
(A calculator can be used on all questions apart from qu. 13)

1T) Solve these two simultaneous equations
2r + 3s = 6
3r – 2s = 22 Grade B Clip 142 r = 6 and s = –2

1S) Solve these two simultaneous equations
h + 3t = –10 h = 2 and t = –4
2h – t = 8

2T) Mary recorded the heights, in centimetres, of the girls in
a) LQ = 152
her class.
Grade B b) UQ = 177
She put the heights in order.
Clip 152
132 144 150 152 160 162 162 167
167 170 172 177 181 182 182

a) Find the lower quartile
b) Find the upper quartile
c) On the grid, draw a boxplot for this data.

2S) Mary recorded the heights, in centimetres, of the girls in
her class. a) LQ = 154
She put the heights in order. b) UQ = 181

131 142 142 150 158 161 165 169
169 169 173 179 183 185 186 188

a) Find the lower quartile
b) Find the upper quartile
c) On the grid, draw a boxplot for this data.


3T) Work out the lengths or angles indicated by the
letters a to d.

a = 23.2cm
25cm b
a 8cm b = 58.4°

c = 61.8cm
13cm
68°
d = 64.6°

Grade B
Clip 153
50cm 42cm

36°

c d

18cm

3S) Work out the lengths or angles indicated by the
letters e to h.
13cm
e e = 56.9°
f
15cm
f = 24.5cm

23cm 32° g = 21.3cm

h = 54.1°

h
14°

22cm 19.6cm
g 24.2cm


4T) TR and TQ are tangents to the circle
a) Explain why angle PQR = 42º a) PQT = 90°(Tangent meets
radius at 90°)
Grade B 90° – 48° = 42°

Clip 150
b) PRQ = 90°(angle in semicircle
is 90°)
TRQ = 48°(tri. TRQ is isosceles
and base angles are
equal)
PRT = 90° + 48° = 138°

b) Find the size of angle PRT giving reasons

4S) TR and TQ are tangents to the circle
a) Explain why angle PQR = 35º
a) PQT = 90°(Tangent meets
radius at 90°)
90° – 55° = 35°

b) PRQ = 90°(angle in semicircle
is 90°)
TRQ = 55°(tri. TRQ is isosceles
and base angles are
equal)
PRT = 90° + 55° = 145°

b) Find the size of angle PRT giving reasons

a
5T) Find angles a and b a = 85° (opp angles of cyclic
105° quad. add up to 180)
b = 75°(opp angles of cyclic
Grade B 95° b
quad. add up to 180)
Clip 150
5S) Find angles a and b b a = 55° (opp angles of cyclic
125° quad. add up to 180°)
a
b = 117°(opp angles of cyclic
63° quad. add up to 180°)


6T) Find the size of angle x. x = 112°

124

o
x

Grade B
6S) Find the size of angle y.
Clip 150 y = 138°

84
o

y

7T) a) John places £13000 in a bank which pays 4.6% a) £1877.79
compound interest per year. How much interest
does he earn if he leaves the money in the bank
for 3 years?
b) Sue buys a new car for £8700. b) £2354.90
Its annual rate of depreciation is 23% per year.
How much is it worth after 5 years?
Grade B Clip 142
7S) a) Sarah buys a 5-year bond which pays compound a) £10605.19
interest of 5.8% per year. She buys the bond for
£8000. How much can she cash the bond in for at
the end of the 5 year period?
b) Tom buys a house for £145000. b) £135223.35
It will depreciate at the rate of 2.3% per year for
the next three years. How much will it then be worth?


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