KS3 complete question bank
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Number, Algebra, Data handling, and Shape, space and measure.
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20769
Page 1 of 1
c)
11.8
11
×
d) 202.44 ÷
129.8
12
16.87 [ 4 ]
1 Calculate the following, showing all working out:
8 Calculate the following, showing all working out:
a)
7642
+
365
8007
b)
7075
-
747
6328
c)
3900
×
7
27300
d)
8412
÷
12
701
[ 4]
1606
×
56
b)
89936
711
×
7000
b)
4977000
12100 ÷
1100
11
[ 4]
0.02
11
[ 4]
9 Calculate the following, showing all working out:
2 Calculate the following, showing all working out:
a)
a)
29655 ÷
45
659
[ 4]
a)
19.95
×
0.8
b)
15.96
0.22
÷
10 Use the information below to work out the following questions:
3 Find the answer to the following problems, showing all working out:
0.643 0.453
a) The total of James and John's age is 104 years.
0.643 × 0.453 = 0.291279
59 45
If James is 59 how old is John?
643
45
b) A crate holds 9 tins.
How many tins in 835 crates?
How many pupils are there in total in Year 7 and Year 8?
993
How many sweets will each receive?
123
3
41
[ 8]
a) Multiplying by 0.02 is the same as dividing by what number?
0.02
50
b) Dividing by 0.5 is the same as muliplying by what number?
0.5
2
12 Answer the following questions about the decimal number 352.25
4 Work out:
×
1000
29.1279 [ 2 ]
11 Answer the following:
549 444
d) A group of 3 friends share 123 sweets equally between themselves.
4273
b) 0.643 × 45.3
291.279
7515
c) There are 549 pupils in Year 7 and 444 pupils in Year 8.
a)
45.3
a) 643 × 0.453
9 835
b)
4273000
11000 ÷
1000
11
[ 2]
[ 2]
352.25
a) How many hundredths does the number have?
5
b) How many tens does the number have?
5
[ 2]
1, 5, 4, 2, 3
[ 2]
2, 4, 5, 1, 3
[ 2]
5, 3, 4, 2, 1
[ 2]
5 Work out:
13 Put these numbers in order, starting with the smallest:
a) 44.147 ×
100
4414.7
b)
×
100
c)
1000
0.012174
d) 83.365 ÷
10
12.174 ÷
84.54
8454
8.3365 [ 4 ]
6 Work out:
3 12 9
5
6
3, 12, 9, 5, 6
14 Put these numbers in order, starting with the smallest:
1.7 4.3 5.7 1.3 4
a)
72.77
×
0.1
7.277
b)
80.09
×
0.001
c)
85.943 ÷
0.1
859.43
d)
61.8
÷
0.01
0.08009
1.7, 4.3, 5.7, 1.3, 4
6180 [ 4 ]
15 Put these numbers in order, starting with the smallest:
7 Calculate the following:
10 -5
6 -10 -12
10, -5, 6, -10, -12
a)
45.2
+
7.69
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b) 14.48
52.89
20769
-
9.14
5.34
Page 3 of 52
© www.teachitmaths.co.uk 2014
20769
Page 4 of 52
16 Put these numbers in order, starting with the smallest:
25 Calculate:
2.7 -9.4 -4.3 -8 -9
2.7, -9.4, -4.3, -8, -9
5, 1, 4, 3, 2
[ 2]
a)
2
×
-7
b)
-14
44 ÷ -11
-4
[ 2]
17 Put these fractions in order, starting with the smallest:
2
4
1
5
1
5
1
9
1 1 1
4 10 6
26 Convert the following between mixed and improper (top heavy) fractions:
3
681.500107
772.7524546
670.3395486
818.2603055
4
8
3
9
687.9088
833.58686
730.188389
10.33060422
5 10 6
1
651.9657176
850.4977904
4 11
741.9368515
2 11 7
2, 4, 1, 5, 3
[ 2]
a)
3
1
1/2
4
=
11
b)
50
4
37/11
2
= 12
2
4
12 1/2 [ 2 ]
18 Put the following in order of size.
Start with the smallest number first.
27 Calculate the following, showing all working out:
⅘ ⅗ ⅖ ⅚ ⅔ ⅜ ⅝ ¾ ⅞ 0.2
0.2
3
0.57
1
0.2
⅖
0.57
100%
4/5
3/5
2/5
5/6
2/3
3/8
5/8
3/4
2/5
0.57
100%
1,2,3,4 [ 2 ]
7/8
a)
1
2
+
1
2
b)
1/1
2
3
-
1
3
4
9
2 12
4
9
-
1
6
1/3
[ 2]
19 Complete the following statements by inserting one of the symbols =, > or <.
⅗ ⅖ ⅚ ⅔
4 11
a)
⅔
0.81
<
3/5
2/5
5/6
2/3
28 Calculate the following, showing all working out:
b)
13%
0.3
[ 2]
<
a)
20 Complete the following statements by inserting one of the symbols =, > or <.
1
8
1
1
8
+
1
5
5
b)
13/40
5 10 4 11
a)
6
5
b)
>
-3
-6
[ 2]
>
c)
4
1
2
×
4
11
9 11
d)
18/11
5/18
4
7
9
÷
11
2
4
7
8
2
3
1
2
4
5
8
÷
2
3
+
7/22 [ 8 ]
21 Work out:
3
6
5
7
2
a) (3 + 6) × (5 + 7)
4
9
29 Calculate the following, showing all working out:
4
b) 2 + 4 × 9 - 4
108
[ 2]
34
22 The temperature in a town at midnight is -5ºC.
5
6
a)
5
6
-5
The temperature rises to 3ºC at midday.
6
+
1
2
1
2
5
×
1
2
b)
8
[ 2]
30 Round these numbers to the degree of accuracy given in the brackets:
7864
1
a) 7864 (nearest 10)
23 Calculate:
a)
-2
+
8
c)
10 +
4
-
-5
6
b)
12
-
8
19
d)
-6
+
-4
-
-4
-6
8
-
6
b)
-8
20769
9
+
5
- -12
26
4124
2
b) 4124 (nearest 100)
7860
4100 [ 2 ]
31 Round these numbers to the degree of accuracy written in the brackets:
4
[ 4]
24 Calculate:
© www.teachitmaths.co.uk 2014
13/12
1
2 119/16 [ 4 ]
3
What has been the overall change in temperature?
a) -10 +
3
[ 2]
Page 5 of 52
a)
23.44 (2 d.p.) 2
23.44
b)
8323 (1 s.f.) 1
c)
61.2317 (3 d.p.) 3
61.232
d)
0.16
(1 s.f.) 1
8000
0
[ 4]
32 A school buys tickets for a theatre trip.
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20769
Page 6 of 52
3
Number of students:
68
Cost per student:
£9.02
3
a)
-11
5
£630
Will the estimate be over or under that actual amount? Explain.
Over [ 3 ]
A
1200
B 12000
C
120
-4
-9
Fraction
12
D
-7
2
-11
-16
7
-5
Percentage
Decimal
⅕
5
⅗ ⅖ ¾
⅘
⅕
¼
3/5
4/5
1/5
1/4
2/5
3/4
5%
A
962
[ 2]
20%, 0.20
1/20, 0.05
0.3
b) Work out the exact answer of 26 × 37.
2
39 Complete the table:
33 a) Write down which of the options below is the best estimate for 26 × 37.
26 37
-2
-16
12
By rounding to 1 significant figure, estimate the total cost of the trip.
b)
3/10, 0.30
[ 6]
[ 2]
40 Complete the table to match up the equivalent fractions, decimals and percentages.
34 By rounding each number in the calculation to one significant figure, estimate:
¾
a)
49.99
×
13.69
44.8
b)
12.5
91.52
×
A
1
89% B
27.3
37.43
67.5 [ 4 ]
35 The length of a room is measured as 9.6 metres, rounded to 1 d.p.
10
9.55
Complete the inequality to show the range of possible lengths.
1
9.65
0.89
2 30%
0.7
A
5
610.7085409
1
89%
B
1
533.1259929
2
30%
C
2
4
0.625
D
4
3
70%
E
3
0.3
C
3
⅝
D
4 0.625
404.2405249
70% E
5 75%
492.3428099
[ 4]
41 Write each recurring decimal as a fraction in its lowest terms:
≤ length <
[ 2]
a)
36 The lengths on the rectangle have been rounded to 2 d.p.
0.22222222
b)
2/9
0.65656565
65/99 [ 2 ]
2
42 Write what fraction of the shapes below are shaded:
6
80.02
11.38
cm
3
10/18
a)
NOT TO SCALE
5/9
b)
80.21
7.04
cm
[ 2]
Copy and complete the inequality below to show the range of possible areas.
43 Complete the following:
≤ area <
[ 2]
6 10
a)
37 The attendance in a stadium is estimated as 7900, to the nearest 100.
What is the minimum possible number of people attending?
2
7900
3
5
=
6
b)
4
10
=
18
36
2
[ 2]
7850 [ 2 ]
44 Simplify the following fractions into their lowest terms:
38 To find the next number brick in an addition pyramid we add the two bricks below it.
a)
Work out the missing numbers.
© www.teachitmaths.co.uk 2014
20769
Page 7 of 52
40
=
© www.teachitmaths.co.uk 2014
b)
8
20769
18
=
6
Page 8 of 52
=
60
=
24
12
8
[ 2]
54 Write an answer for the following.
20
100 45%
45 Work out the following:
3
60
a) ⅙ of 60
⅓
⅕
⅙
⅛
¼
½
1/3
1/5
1/6
1/3
1/4
1/2
a) Increase 100 by 45%
5
11
[ 2]
3
⅘
⅗
⅖
⅚
⅔
a) ⅖ of 50
6
b) Decrease 40 by 30%
119
36
[ 2]
[ 4]
480
[ 2]
80% 384
a) 30% of
47 Put the following in order of size, starting with the smallest.
= 315
b) 80% of
1050
= 384
7
3
of
7
70
0.1
×
140
50%
57 A computer is on sale in two different shops.
44
of
30, 14, 22
[ 2]
Megabyte Stores
48 Work out the following:
6 33
a)
28
56 Work out the following:
30% 315
3
30%
96
b) ⅜ of 96
20
40
70%
a) Increase 70 by 70%
⅜
4/5 3/5 2/5 5/6 2/3 3/8
50
15.8 [ 4 ]
55 Write an answer for the following.
70
46 Work out the following:
b) Decrease 20 by 21%
145
44
b) ¼ of 44
10
21%
⅘
⅗
⅖
⅚
⅔
⅜
120
⅜ of
= 33
88
b)
⅕
⅙
⅛
¼
1/3
1/5
1/6
1/3
1/4
⅖ of
= 22
55
PC Magic
3
360 15%
£120 less discount of ⅙
3 22
4/5 3/5 2/5 5/6 2/3 3/8
⅓
[ 4]
£360 plus tax of 15%
£100.00
£414.00
Showing all working out, explain which shop is selling the cheaper computer.
49 A shop buys an item for £29 and sells it to the customer for £80.
29 80
Calculate the percentage profit.
176% [ 2 ]
58 Answer the following problems:
a) After a reduction of 30%, an item in a sale now costs £42.00.
50 Work out the following:
0.05 110
Find the original price of the item.
0.65 240
a) 5% of 110
b) 65% of 240
5.5
[ 4]
156
[ 2]
30
42.00
£60.00
b) After a 40% tip has been added, a bill in a bar costs £123.20.
Find the amount of the bill before the tip is added.
40
123.20
£88.00 [ 4 ]
51 Work out the following:
0.24 310
59 Amy wants to buy a television and sees the offer below.
0.05 310
a) 24% of 310
b) 5% of 310
74.4
15.5 [ 2 ]
20
30 46
Payment by Cash
52 Write an answer for the following:
0.401993435
0.133842698
72 8
discount
b) Decrease 72 by ⅛
49
63
88 3
8
a) Increase 88 by ⅜
© www.teachitmaths.co.uk 2014
£640.00
the sale price plus 12
0.835252053
50 4
5
b) Decrease 50 by ⅘
121
20769
10
A deposit of 30% of
[ 4]
53 Write an answer for the following:
0.624727318
Payment by credit
Sale price less 20%
42 6
a) Increase 42 by ⅙
Sale Price
[ 4]
Page 9 of 52
installments of £46
a) How much is the deposit for the television when paying by credit?
£192
b) What is the total cost of the television when paying by cash?
£512
c) How much more does it cost Amy when paying by credit?
£232 [ 4 ]
© www.teachitmaths.co.uk 2014
20769
Page 10 of 52
60 Assume the exchange rate to be £1 = €1.04.
Copy and complete the following.
68 It takes 5 teachers 30 days to mark a set of exam papers.
1.04
5 30 2
How long would it take 2 teachers?
a)
£38
=
b)
€39.52
= €85.28
75 days [ 2 ]
£82.00 [ 4 ]
69 Look at the set of numbers below.
61 A class contains 7 girls and 2 boys. Give all answers in their simpliest form.
2 19 22 38 42 58 66 75 81 99
2
700% 200%
a) What is the ratio of girls to boys?
7:2
b) What is the ratio of boys to the total number of pupils in the class?
2:9
c) What fraction of the class are girls?
7/9
d) What fraction of the class are boys?
2/9
38
[ 4]
6 150 50 300
a) What is the ratio of orange to cranberry?
3:1
Orange juice 150ml
b) What fraction of the drink is cranberry?
1/10
Cranberry juice 50ml
c) How much sugar syrup would be needed if
Sugar syrup 300ml
900ml of orange juice is available?
42
75
62 Below is a recipe for a fruit cocktail drink.
Fruit Cocktail
19
1
22
58
81
66
99
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
Write down which of the numbers above satisfy the following categories:
2
a) Even numbers.
2,22,38,42,58,66
c) Less than 30.
2,19,22 30
b) Multiples of 7.
7
42
d) Multiples of 11. 11
70 The 1st square number is 1.
1
2
3
4
5
6
22,66,99 [ 4 ]
3
1st 2nd 3rd 4th 5th 6th
Write down the 3rd square number.
9
[ 1]
21
[ 1]
7×3×7
[ 2]
44, 22, 11, 4, 2, 1
[ 2]
1800 ml
d) What's the ratio of sugar to orange?
2:1
[ 4]
71 The 1st triangular is 1.
1
2
3
4
5
6
6
1st 2nd 3rd 4th 5th 6th
Write down the 6th triangular number.
63 Simplify the following ratios:
72 Give each of the following as a product of prime numbers:
a)
c)
6
:
8 cm
18
:
4m
1:3
b) 56
1:50
d) 12 min :
:
35
3
8:5
6 hrs
1:30 [ 4 ]
64 Give the following ratios in the form 1 : n.
a)
11
:
9
3
:
8
1:2.7 [ 2 ]
65 The length of one side of square A is 2cm.
66 Two people, Jo and Bill, share an amount of money in the ratio of 5 : 6.
1:64 [ 2 ]
5
How much Jo will receive if they share £110?
1
1
1
3
b)
7×5×7
7
3
7
1
1
147
1
a) 92
b) 44
92, 46, 23, 4, 2, 1
6
11.7
a) What is the lowest common multiple (LCM) of 6 and 8?
6
8
24
b) What is the highest common factor (HCF) of 43 and 59?
43 59
1
[ 4]
110
£50
9
How much will 7 pens cost?
7
8
Write the ratio of the areas of square A : square B in the form 1 : n.
© www.teachitmaths.co.uk 2014
5
245
74 Find an answer to the following:
2
The length of one side of square B is 8 times the length of square A.
67 The cost of 9 pens is £11.70.
7
73 List all the factors of the following numbers:
b)
1:0.8
a)
[ 2]
7
75 Give the first 3 multiples of the numbers below.
1
2
a)
6
3
4
5
6 12 18
3
1
2
a)
5
3
4
5
5 10 15 [ 2 ]
£9.10 [ 2 ]
20769
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20769
Page 12 of 52
76 The 1st prime number is 2.
1
Write down the 2nd prime number.
2
3
4
5
6
2
1st 2nd 3rd 4th 5th 6th
[ 1]
3
84 Simplify the following, giving your answers in index form:
3^16
77 Write down the value of the following:
a)
7
3
a)
b)
343
4
5
3
9
6
3
×
3
4
5
6
6
9
=
5
2
5
11
=
6^3
×
78 Write the following in index form:
2
7
1024 [ 2 ]
c)
1
3
5^-9
b)
6
10^9
d) 10
=
9
9
×
10
10
9
=
9
[ 4]
7
a)
4 ×4
4
3
4^2
b)
2 ×2
2
3
2^2 [ 2 ]
85 Write down the value of the following:
a)
2
-3
b)
1/8
5
-6
1/15625 [ 2 ]
79 Write down the exact value of the following:
86 Give the following numbers in standard form:
a)
144
b)
±12
3
216
[ 2]
6
a)
80 Use a calculator to give the value of the following to 2 d.p.
2700
2.7×10^+3
b)
0.0000075
100000
b)
61
7.5×10^-6
[ 2]
2
87 Calculate the following:
a)
3
b)
1.73
3
23
2.84 [ 2 ]
a)
10
×
10
4
÷
10
3
0.061 [ 2 ]
81 A maths student wants to work out the answer to the calculation below.
4
2
-
88 The following numbers are in standard form. Give them as normal numbers.
11
2
a)
Explain why the following, entered into a calculator, may not give a correct answer.
4
x
2
-
11
÷
2
9.39
×
10
-4
b)
0.000939
6.47
×
10
3820
2.5
82 Using a calculator work out the following to 3 d.p.
3.3
3
16.81
[ 2]
3
b)
0.0647 [ 2 ]
89 Complete the following for the numbers in standard form.
=
What is the correct answer rounded to 1 decimal place?
a)
-2
90.64
+
1.285 [ 4 ]
83 Using a calculator work out the following to 3 d.p.
3
3.82
×
10
3
6.86, -3
=
b)
6.86
× 10
-3
= 0.00686
[ 2]
90 Work out the following and write your answers in standard form.
a)
77.7
10.1
2.138
a)
a)
( 5.8 × 10
1
( 4.6 × 10
2
)
)
×
÷
( 3.5 × 10
-4
)
0.0×10^+0
( 6.8 × 10
2
)
7.0×10^-1
91 A star is 3.9 × 10²² km away from the earth.
[ 2]
3.9
The speed of light is 300,000 km/s.
a)
36.1
×
16.812 +
67
65.3
© www.teachitmaths.co.uk 2014
b)
29.456
20769
17.9
+
43.1
6.9 +
3
×
2
How many years will take the light from the star to reach the earth?
4.12×10^+9
[ 2]
0.605 [ 4 ]
Page 13 of 52
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1 Write down the next two terms in each number sequence:
12 5
1st
7 13 19 25 31
-2 -9 -16
a) 12, 5, -2, -9, -16
5 -20 80
-6 18 -54 162
a) 2, -6, 18, -54, 162
7 A number sequence is generated by multiplying the previous term by 7.
7
If the first term in the sequence is 3, write down the next two terms.
3
-320 1280
b) 5, -20, 80, -320, 1280
-486
15, 23 [ 2 ]
37, 43 [ 2 ]
2 Write down the next term in each number sequence:
2
3rd
7
b) 7, 13, 19, 25, 31
-23, -30
2nd
-5120 [ 2 ]
1st
2nd
3rd
21, 147 [ 2 ]
3
3 Look at this sequence of drawings made up of black and grey squares:
8 This sequence of pictures shows paving slabs surrounding a flower bed:
1
2
3
a) Complete the table below.
a) Draw the next pattern in the sequence.
black
grey
total number
squares
squares
of squares
1
6
7
2
10
12
answer
b) Complete the table below.
Flower bed
Number of
3
14, 17
squares
paving slabs
4
18, 22
1
8
11
2
10
3
12
4
14
b) How many grey squares will there be if there are 11 black squares?
22
28
c) How many black squares will there be if there are 28 grey squares?
[ 8]
9
c) Complete the sequence rule below.
4 Work out the missing numbers in these sequences:
2
1 5.7 1.4 5.7 7.1 8.5 9.9
a) 5.7, ?, 8.5, 9.9, 11.3
2
11.3
1
2 4.3 2 6.3
10.6 14.9 19.2
b) 2, ?, 10.6, 14.9, 19.2
7.1
6.3
[ 2]
5 Work out the missing numbers in these sequences:
2
1 2.6 5.9 2.6 8.5
a) 2.6, ?, 14.4, 20.3, 26.2
1
-4.8
1.1
6 A number sequence is generated by adding 8 to the previous term.
If the first term of the sequence is 7, write down the next two terms.
© www.teachitmaths.co.uk 2013
20769
squares
paving slabs
1
-4.8 -3.7 -2.6 -1.5 -0.4
b) -4.8, ?, -2.6, -1.5, -0.399 -3.7
8.5
Number of
x2, +6 [ 6 ]
9 The sequence below shows a series of tile patterns.
2
14.4 20.3 26.2
Flower bed
2
3
[ 2]
8
7
Page 1 of 11
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Page 2 of 11
-2
-3
a) Draw the next pattern in the sequence.
answer
-4
-5
b) How many tiles will there be in pattern 12?
12
169
c) Which pattern has 4 tiles?
4
1
C -2 -1
#N/A #N/A
D
#N/A #N/A
5
-5
[ 4]
[ 6]
15 Look at the straight lines on the graph below and match each one to the equation.
10 Look at the matchstick sequence below.
y
6
5
4
1 y = -2x + 2 A
D3
1
2
D
2 A
3
2 y = 3x + 2 B
1
a) Draw the next pattern in the sequence.
-4
answer
b) How many sticks are in pattern 12?
12
25
c) Which pattern has 17 sticks?
17
8
C
-3
-2
x
0
-1 0
B-1
1
2
3
4
3
x = -2
C
-2
-3
[ 6]
4
A
-4
y=3
D
a)
1st 2nd 3rd
2
b)
5th
8 14 20 26
12 Find the n
a)
4th
th
13
1st 2nd 3rd
10 4
74
4th
4th
b)
5th
5 14 23 32 41
1st 2nd 3rd
5
9n + -4
2
4th
[ 2]
5th
-1 -4 -7
-4
-3n + 8 [ 4 ]
13 Find the general rule, or n th term, for the number sequences below:
2
4
a)
3
2
1st 2nd 3rd
4th
b)
5th
9 19 33 51 73
3
6
1st 2nd 3rd
4th
5th
11 20 33 50 71
2n²+4n+3
894.6601884
2
1
4
3
3
-4 y = 3x + 2
2
0
2
3
2
8 y = -2x + 2
2
-1 -1
-2
3
-2
0
-2
0
4
3
-1
3
2n²+3n+6
[ 4]
14 Plot these four points on a pair of axes:
D
x = -2
C
[ 4]
-3
-2
7
6
5
4
3
2
1
0
-1 -1 0
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-4 -2
1
2
3
0
2
4
2
-10 -6 -2
2
6
-2
-4 -2
0
2
4
-1
2
-2 -4 -6
-2
4
0
17 a) Copy and complete the function
plot the graph of y = x + 2
y 10
1
0
-1 0
-1
[ 3]
b) Use your answers from a) to
machine below.
2
-2
(0/1, -2/1)
y
3
-3
(0, -2)
c) Write down the point of intersection, if any, between the two lines.
4
-4
(1, 0)
b) Where does the line y = -x - 2 cross the y-axis?
A(0, -3), B(-4, -2), C(-2, -1) and D(5, -5).
-5
A
y=3
a) Where does the line y = 2x - 2 cross the x-axis?
5
B
16 The straight lines on the graph below have equations y = 2x - 2 and y = -x - 2.
-62
term for each number sequence:
1st 2nd 3rd
712.6373197
-6
5th
-2 -8 -14
991.3550043
-2
-5
11 Find the 13th term for each number sequence:
986.2451054
1
2
3
4
A
5
x
0
-3
#N/A #N/A
B -4 -2
#N/A #N/A
+
x
9
2
8
y
7
2
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7
0
2
6
Draw a pair of axes with x from 0 to 4 and y from 0 to 20.
1
3
5
Use your table above to complete the graph.
2
4
4
3
5
3
4
6
5
7
[ 6]
22 State whether each of the following is an expression, formula or equation:
2
1
a)
0
0
1
2
3
4
5
2x + 6 = 8
b)
equation
formula [ 2 ]
A=L×W
[ 4]
x
23 Write an algebraic expression for each of the questions below:
18 a) Complete the table below for the graph of y = 2x + 1.
2
a) John's age is x years. His sister is 11 years younger.
1
x
-3 -2 -1
y
-5
0
1
2
-1
11
How old is John's sister?
3
7
x - 11
b) Beth scored n marks on a test. Her friend's score was 7 times better.
-3, 1, 3, 5
What was her friend's score?
7
7n
[ 2]
b) Draw a pair of axes and use the table above to plot the graph.
24 Look at the following algebraic expressions:
c) What is the gradient of the line?
2
d) What is the y-intercept?
1
5
[ 6]
8
n+5
5
4
n
8n
4n²
5
19 Complete the table below:
equation of line
gradient
y-intercept
y = 4x - 6
4
-6
m = 4, c = -6
y=9+x
1
9
m = 1, c = 9
-3
-2
y = -3x - 2
a) When n = 10 which expression gives the largest value?
10
15, 80, 2, 400
b) When n = 10 which expression gives the smallest value?
10
15, 80, 2, 400
25 Look at the following algebraic expressions:
[ 6]
20 Complete the table below for the graph of y = 2x² + 5x - 3.
2
5
-3
x
-4 -3 -2 -1
0
1
2
y
9
?
?
? 30 49
?
-5 -6
3
4
0, -3, 4, 15
Draw a pair of axes with x from -4 to 4 and y from -6 to 49.
5
12
n+5
12n
7
-11
n
-11n²
7
a) When n = 3 which expression gives the largest value?
3
8, 36, 0.4, -99
b) When n = 11 which expression gives the smallest value?
11
16, 132, 1.6, -1331
[ 4]
26 Simplify the following expressions:
Use the table above to complete the graph.
[ 6]
8
a)
21 Complete the table below for the graph of y = 10/x
[ 4]
-8 -9
1
8z - 8y - 9z + y
1
b)
-1z - 7y
-1
3
-2
z + -y + 3z - 2y
4z - 3y [ 2 ]
10
27 Simplify the following expressions:
-9
x 0.5 1 1.5 2 2.5 3 3.5 4
y 20
6.7
© www.teachitmaths.co.uk 2013
2.5
10, 5, 4, 2.9
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Page 5 of 11
a)
6
-7 -5
-9e + 6e - 7e - 5e
© www.teachitmaths.co.uk 2013
7
b)
-15e
20769
8
7
8
7y + 8y + 7y + 8y
30y
[ 2]
Page 6 of 11
28 Expand and simplify each of the following expressions:
1
a)
3
1
-5
a)
1
(a + 3)(a - 5)
b)
a² - 2a - 15
-6
1
2
10 7
(b - 6)(b + 2)
b² - 4b - 12
[ 4]
+5
40
5
b)
-7
×9
27
10
5
5
-5(-5d - 6) - 3(5d + 5)
10d + 15
[ 2]
● I think of a number x .
9
● I multiply my number by -5 then take away 3.
30 Expand and simplify:
6
-48
-16f - 8 [ 2 ]
4
5
11 5
b)
12y + 15
-5x + 3 = x + 39
● I multiply my number by -5 then add 3.
3
11(5c + 3)
55c + 33 [ 2 ]
32 Multiply out:
11 3
39 Use the following statements to form an equation, then find the value of x .
● I think of a number x .
3(4y + 5)
-6
4
-3
2
-4 -6
b) 4h(-3h + 2)
33g² - 66g
-12h² + 8h
[ 2]
4
a) a - 4 = -6
33 Factorise:
-3
c) 3c = 18
3
1
3
a) -96s + 36
3
-6
b) 9t - 18
12(-8s + 3)
9(1t - 2) [ 2 ]
-9
3
6
a) 48s² - 72s
4
-9
6t(4t - 9) [ 2 ]
a)
1
-7
1
y² - 13y + 42
b)
(y - 6)(y - 7)
-3
1
z² + 5z - 24
2
+12
(z - 3)(z + 8)
[ 4]
19
a)
7
4
2
b) b - 2 = 2
a=6
3
b=4
8
d) d ÷ 3 = 8
c = 10
8
2
[ 2]
d = 24 [ 4 ]
3
3
-7
y = -8
b) y/3 - 7 = 2
y=8
b) y/4 + 5 = 10
2
y=3 [ 4 ]
7
8 64
a) 7y + 8 = 64
20 4
5 10
y = 20 [ 4 ]
44 Solve the following:
5
© www.teachitmaths.co.uk 2013
8 40
a) -4y + 8 = 40
8
×4
37 Complete these function machines:
7
d = -24 [ 4 ]
43 Solve the following:
7 12
5
2
c) 2c = 12
-8 -4
8
36 Complete these function machines:
a)
8
42 Solve the following:
35 Factorise:
-6
b = 12
41 Solve the following equations:
2 12
1
b) 24t² - 54t
8s(2s - 3)
8
d) d ÷ -3 = 8
c = 15
a) a + 7 = 13
34 Factorise:
1
x = -6 [ 2 ]
3
7 13
6
3
-6
b) b - 4 = 8
a = -2
3 18
12 -8
-5
● The answer is 39 more than the number I started with.
40 Solve the following equations:
a) 11g(3g - 6)
8
x=9 [ 2]
-2 11 4
31 Multiply out:
3
-5x - 3 = -48
-5 -3
● The answer I get is -48.
6f - 2(11f + 4)
a)
[ 2]
38 Use the following statements to form an equation, then find the value of x .
29 Expand and simplify:
-5 -5 -6 -3
×7
9
7
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3 42
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-7
20769
6 -63
Page 8 of 11
a) 7(z + 3) = 42
b) -7(z + 6) = -63
z=3
z=3 [ 4]
a) a + b - c
b) 4a + 2c
-1
16
5
45 Solve the following:
1
-2
5
c) c / a
-2
-8
a) g - 2 = 5g + 6
2
2
b) -8h + 2 = 2h + 52
g = -2
h = -5 [ 4 ]
5
1
[ 4]
5
52 The formula to find the volume of a square based pyramid is given by V = ⅓ x2 h
Find the value of V when:
46 Solve the following:
7
d) 5b²
2/1
-5
8
6
a) 7j + 5 = j + 53
9
6
6
1
b) 6k + 9 = 6k + 9
j=8
k=1 [ 4]
4
6
a) x = 6cm, h = 4cm
4
b) x = 6cm, h = 4cm
48 cm²
48 cm² [ 4 ]
53 Simplify the following expressions:
47 The sides of this rectangle are given as algebraic expressions:
2
a)
9
3
(
2
2 y
y
(9y - 7) cm
-3
3
-2 -4
)
-3
2
b)
(
4
-2 y
y
4y^9
2
-4
)
4
2
16y^-18 [ 4 ]
-7
2
(2y + 4) cm
54 The formula to find the area of a trapezium is given by A = ½ h (a + b)
4
a) Write an expression, in terms of y, for the perimeter of the rectangle.
b) If the perimeter of the rectangle is 60cm find the value of y.
22y - 6
3
y=3 [ 4 ]
a)
1 -11
6
-4 -34
5
5a + b = -11
-3
a = -3
6a - 4b = -34
4
b=4
3
b) Find the value of a if A = 12cm², b = 3cm and h = 6cm.
12 3
5 10
40 cm²
6
1 cm [ 4 ]
55 Make x the subject of the following formulae:
48 Solve the following pairs of simultaneous equations:
5
a) Find the value of A if a = 3cm, b = 5cm and h = 10cm.
b)
-5 -10
c
-3 -5 14
1
x
x
a) c = 1x
5c - 5d = -10
-3
c = -3
-3c - 5d = 14
-1
d = -1 [ 4 ]
v
-6
x
-5
y
b) x - 5 = y
x=c/1
4
A -1 -3
c) v = -6x + 4
x=y+5
x
-5
d) A + 1 = -3x - 5
x = (v - 4) / -6
x = (A + 6) / -3
[ 6]
49 Solve the following pairs of simultaneous equations:
-2
a)
5 10
-2
6 14
-2e + 5f = 10
5
e=5
-2e + 6f = 14
4
f=4
56 Use trial and improvement to find x to 2 d.p. when x² + 2x = 65.
-5
2 12
-2
2
b)
-5g + 2h = 12
-4
g = -4
-2g + 2h = 0
-4
h = -4 [ 4 ]
50 If a = -1, b = -4 and c = 5 find the value of the following:
-1 -4
2
0
x value
working out
result
7
7² + 2(7) = 63
too low
5
2
2 65
7.12, -9.12
[ 4]
-2
a) a + b - c
-10
b) 2a - 2c
c) c / a
-5/1
d) -4b²
57 Use trial and improvement to find x to 1 d.p. when x³ = 27.
-12
Show all your workings.
-4
-64
27
3
[ 4]
[ 4]
58 Write down two possible values of x that satisfy each inequality.
51 If a = 2, b = 1 and c = 4 find the value of the following:
2
4
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1
4
a) x ≤ -8
2
Page 9 of 11
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b) -12 < x < 6
answer
20769
answer [ 2 ]
Page 10 of 11
59 Solve the following inequalities:
6
8
-3
a) x + 6 > 8
-5 -3
2
x>2
b) x - -3 < 2
x < -5
d) x/-7 + 8 > 11
-21 -7
3 18
c) -3x + 3 < 18
x < -1
8 11
x > -21 [ 6 ]
60 Solve the following inequalities:
9 12
8
a) x + 9 > 12
3
8
3
b) x - 8 < 3
x>3
3 27
27 9
c) 8x + 3 < 27
x < 11
5
8
d) x/9 + 5 > 8
x<3
x > 27 [ 6 ]
61 Write an algebraic inequality for each number line below.
a)
b)
x ≥ -6
-7
-6
-5
x < 10
-4
8
9
10
[ 4]
11
62 Write down the two inequalities that define the shaded area of the graphs below.
-1
2
outside
a)
3
y
x ≥2
-2
x ≤ -1
b)
2
3
2
2
1
1
0
-3
-2
y>2
outside
-1
y < -2
y
0
0
1
2
-1
3
-3
x
-2
-1
0
-1
-2
-2
-3
-3
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1
2
3
x
[ 4]
Page 11 of 11
1 For the rectangle below, calculate:
5 The perimeter of a rectangle is 40cm.
2 cm
NOT TO
a) the perimeter
24 cm
SCALE
b) the area.
20 cm²
The rectangle has a width of 8cm.
1
Work out the length of the rectangle.
12 cm [ 2 ]
8
6 Using 1cm square paper, a pencil and a ruler draw accurately the following shapes:
[ 2]
10 cm
12 40
2 For the shape below, calculate:
a) a rectangle with an area of 22cm²
22
b) a rectangle with a perimeter of 10cm.
10 [ 2 ]
7 Work out the area of these shapes:
11 cm
a)
b)
10 cm
6 cm
NOT TO
10 cm
12 cm
NOT TO
SCALE
7 cm
a) the perimeter
70 cm
b) the area.
194 cm²
9 cm
SCALE
5 cm
120 cm²
4 cm
3 cm
12 cm² [ 4 ]
[ 4]
2 cm
8 Work out the area of these triangles:
3 For the shape below, calculate:
a)
10 cm
5 cm
2 cm
8 cm
44 cm
b) the area.
52 cm²
2 cm
[ 4]
4 For the shapes below, find the missing values.
a)
4 cm
5 cm²
5 cm
9 The area of a triangle is 45cm².
10 cm² [ 4 ]
10 45
The height of the triangle is 9cm.
1
9
Work out the length of the base of the triangle.
10 cm [ 2 ]
10 Work out the area of the shape below.
b)
Area =
Area
?
cm
NOT TO SCALE
? cm2
7 cm
11
4 cm
NOT TO
SCALE
a) the perimeter
4 cm
© www.teachitmaths.co.uk 2014
5.4 cm
NOT TO
SCALE
44cm²
b)
11
Perimeter = 44cm
20769
8 cm
121
12 cm
NOT TO SCALE
[ 4]
Page 1 of 18
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20769
Page 2 of 18
86 cm² [ 4 ]
5 cm
5 cm
NOT TO
SCALE
11 The circle below has a diameter of 8cm.
21.5 cm²
[ 4]
Find:
NOT TO
a) the circumference
25.14 cm
SCALE
b) the area.
50.27 cm²
15 The diagram below shows a sector of a circle AOB with radius 6cm.
A
[ 4]
8 cm
12 The diagram below shows a bicycle wheel with a diameter of 0.5m.
75
º
NOT TO
Find:
SCALE
a) the arc length AB
b) the area of sector AOB. 23.6 cm²
B
6
7.9 cm
cm
[ 4]
O
0.5 m
16 Work out the volume of the following shapes:
NOT TO
SCALE
a)
a) What is the circumference of the bicycle wheel?
b) How many revolutions of the wheel would be needed to cover 1km?
b)
1.6 cm
159
12 cm
NOT TO
[ 4]
8.1 cm
SCALE
11 cm
4 cm
13 The diagram shows a badge made from an isoceles triangle and a semi-circle.
7 cm
Work out the area of the badge.
98 cm³
7 cm
4976.9 cm³
[ 4]
17 Work out the volume of this gold bar:
3 cm
NOT TO
NOT TO
SCALE
9 cm
SCALE
2 cm
11 cm
144.5 cm²
[ 4]
9 cm
72 cm³ [ 4 ]
5 cm
14 The diagram shows a circle of radius 5cm enclosed within a square.
18 Work out the volume of the cuboid below.
Calculate the area of the shaded section.
5
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cm
NOT TO
20769
Page 4 of 18
23 Use a protractor to measure these angles:
SCALE
4
200 cm³ [ 2 ]
10 cm
15 345
110º
250 110
cm
a)
345º
b)
19 The total volume of the cuboid below is 45 cm³.
Work out the length of the missing side.
?
cm
NOT TO
[ 2]
SCALE
3
5
cm
3 cm [ 2 ]
cm
24 For triangle ABC, measure the following, giving answers to the nearest whole number:
A
20 Work out the surface area of the cube below.
9 cm
Measure
a) angle ABC
answer
b) side AC
answer
NOT TO
C
SCALE
[ 2]
B
9 cm
486 cm² [ 2 ]
9 cm
25 Calculate the missing angles.
a)
21 Work out the surface area of the cuboid below.
b)
157º
a=
118º
NOT TO
4
cm
NOT TO
141 º
SCALE
SCALE
4
101 º
a
23
o
b
[ 2]
b =
cm
192 cm² [ 2 ]
10 cm
26 Calculate the missing angles.
22 The total surface area of the cuboid below is 268 cm².
Work out the length of the missing side.
a)
b)
a
32 º
NOT TO
?
cm
NOT TO
119 º
SCALE
SCALE
4
29º
cm
b
74º
[ 2]
6 cm [ 2 ]
11 cm
27 Calculate the missing angles.
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20769
Page 5 of 18
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20769
Page 6 of 18
a)
b)
35 º
a)
a
a=
b)
b=
c=
b
64 º
NOT TO
a
b
c
SCALE
NOT TO
d
SCALE
183º
84 º
d=
74º
106 º
[ 2]
23
º
167 º
157º, 23º
167º, 13º
[ 4]
32 The diagrams below show part of a regular polygon.
28 Calculate the missing angles.
Work out how many sides each polygon has.
60 º
a)
NOT TO
b)
6
60º
SCALE
60
NOT TO
SCALE
70 º
1
a
6
2
3
4
6
8
174º
9 10 12 15 20 30 40 60 90 120
[ 4]
60º, 50º [ 4 ]
b
33 Complete the following sentences.
29 Calculate the missing angles below.
a) A triangle where all sides are equal is called ...............
b) A ............... is a quadrilateral with one line of symmetry and no parallel sides.
66 º
a=
125º
NOT TO
equilateral
kite
c) An irregular quadrilateral with all its angles the same is called a ...............
rectangle
d) A triangle where only two sides are equal is called ...............
issosceles
[ 4]
SCALE
b=
55 º
a
34 Complete the following sentences.
59º
[ 4]
b
a) A regular polygon has 6 sides.
6
Each exterior angle is ............... degrees.
b) A regular polygon has 3 sides.
30 Calculate the missing angles, giving a reason for your answers.
3
Each interior angle is ............... degrees.
a)
60º
60º
[ 4]
b)
35 Complete the following sentences.
b
a
NOT TO
SCALE
147 º
6º
147º [ 4 ]
174º
a) A cube has ............... vertices.
8
b) A cuboid has ............... edges.
12
c) A triangular prism has ............... faces.
5
d) A square based pyramid has ............... vertices.
5
[ 4]
31 Calculate the missing angles below.
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36 For each scale below, give the value represented by the question mark.
a) A length of wood measuring 4m has a length of 15cm cut off.
4 15
What length remains?
a)
3
b)
13
2
b) A container holds 90 litres of water.
94
90 170
How many cups of 170ml can be filled from the container?
?
4
385 cm
16
80
?
529
[ 2]
115
43 A map has a scale of 1:60. Two points are shown 10.3cm apart.
37 Put these numbers in order, starting with the smallest:
1000
cm 5 km
1000
mm
10.3
How far apart, in km, are the two points in real life?
90 m
1000cm, 5km, 1000mm, 90m
1000
500000
100
9000
3
1
4
2
[ 4]
3, 1, 4, 2 [ 2 ]
60
0.00618 km
44 A film starts at 22:20 and lasts for 2 hours 5 minutes.
22:20
What time will the film will end?
2
[ 2]
5
00:25 [ 2 ]
38 Choose an appropriate unit of measure below to measure each item.
45 Complete the following conversions:
cm
l
g
ml
m
kg
a) Write 14:10 using the 12 hour clock.
a) mass of a person
b) length of a pen
kg
l
c) water in a bath
d) height of a classroom.
m
14 10
b) Write 10:10 am using the 24 hour clock.
cm or mm
2:10 PM
am 10 10
10:10 [ 2 ]
[ 4]
46 Give the times shown on these analogue clocks in digital form:
39 Choose an appropriate unit of measure below to measure each item.
a)
inch
litre
a) Room temperature
gallon
mile
tonne
C
b) Length of a pen
ºC
l
c) Water in a bath
o
cm or mm
d) The mass of a car
tonne [ 4 ]
9
9 ft
00
0
0
b)
13:28
PM
=
in
b) 10 stone =
108
lbs
140
km
80
a)
gal
d) 50 miles =
4
[ 4]
0
0
0
0
0
0
0
0
0
Min arm length
0
0
1.25
0.259889614
-1.222684501
1.25
-1.011271243
0.734731565
Hrs arm length
0
0
Hrs arm length
0
0
0.75
0.520993778
0.53950485
0.75
0.058844322
-0.747688
13 28 00
4 m2
=
2
cm
b)
40000
05:51
AM
[ 2]
05 51 00
5 cm3 =
mm3
5000 [ 2 ]
48 Complete the transformations described below:
3
a)
41 Complete the following unit conversions:
3
c)
0
0
50
32 pts =
3 cm
0
Sec arm length
Min arm length
3
a)
Origin
10
32
c)
00
Sec arm length
47 Complete the following conversions:
40 Complete the following unit conversions:
a)
Origin
b)
425
=
mm
l
= 5000 ml
30
b)
5
d)
425 g
=
kg 0.425
cm = 7.97 m
797
42 Show all workings to solve the problems below:
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three quarters
[ 4]
Page 9 of 18
Reflect the shape in the dotted
Rotate the shape three quarters
line of symmetry.
of a turn clockwise.
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[ 4]
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49 Look at the shape below.
3
3
54
a) How many lines of mirror symmetry does the shape have?
1
b) What is the order of rotational symmetry of the shape?
1
a=
-4
4
and
b=
[ 2]
2
4
2
Using the vectors above, work out:
[ 2]
3
-5
4
a) 3a - 5b
4
b) 4a + 4b
-32, 2
0, 24 [ 4 ]
50 Copy the shape below onto 1cm square paper.
Translate the shape 5 squares to the left and 5 squares up.
5
5
55 Triangle XYZ has co-ordinates (2, 3), (0, 1), (1, 2).
759.3921027
8
y
7
62.48414162
533.0920624
836.7115034
3
1
2
4
586.0445553
248.2570121
412.7265101
205.6954211
4
2
3
1
6
5
[ 2]
51 Copy the shape below onto 1cm square paper.
Enlarge the shape by scale factor 3.
-6
-5
-4
-3
-2
0
1
2
1
3
1
2
3
1
4
#N/A #N/A #N/A #N/A
3
#N/A #N/A #N/A #N/A
2
#N/A #N/A #N/A #N/A
1
3
2
0
-1 0
-1
#N/A #N/A #N/A #N/A
x
1
2
3
4
5
#N/A #N/A #N/A #N/A
6
#N/A
-2
#N/A #N/A #N/A #N/A
-3
#N/A #N/A #N/A #N/A
-4
[ 4]
centre of enlargement
a) Reflect triangle XYZ in the x axis and label it A.
b) Rotate triangle XYZ 90o anti-clockwise about the point (0, 0) and label it B.
c) Translate triangle XYZ with the vector (
52 Look at the letters in the word below:
2
1
) and label it C.
2
d) Enlarge triangle XYZ, scale factor 2, centre of enlargement (0, 0) and label it D.
1
[ 8]
MATHEMATICS
56 Triangle XYZ has co-ordinates (3, 3), (2, 2), (4, 1).
a) Write down ONE letter which has only 1 line of mirror symmetry.
b) Write down ONE letter which has order of rotational symmetry order 2.
MATCE
HIS [ 2]
Enlarge triangle XYZ using the centre of enlargement (0, 0) and scale factor 2.
y
8
345.8973653
278.9773547
453.2943381
162.4623337
6
3
2
4
1
5
3
2
4
3
4
3
2
1
3
3
2
1
4
7
53 How many planes of symmetry do each of these 3D shapes have?
a)
b)
3
2
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2
643.3385553
606.5658505
521.8186232
61 Draw an accurate net of this cuboid using a pencil and ruler.
688.0108392
1
0
0
1
2
3
4
5
6
7
8
[ 4]
x
6 cm
57 Use a ruler, compass, pencil and protractor to construct the shapes below.
2 cm
In each question measure and write down the length AC .
NOT TO
SCALE
[ 4]
3 cm
a)
A
b)
4.1 cm
A
4 cm
62 Which two of these diagrams could be the net of a cube?
NOT TO
5.2 cm
SCALE
30
B
º
10
5.3 cm
º
85
C
C
º
B
4.1 cm
[ 4]
58 Use a ruler, compass and pencil to construct and label the triangles below.
A
B
C
[ 2]
D
63 The diagrams below are represented on 1cm isometric paper.
In each question measure and write down the size of angle BAC .
a) Write down the dimensions of
a)
A
b)
148.1º
2.2 cm
5.8 cm
A
the cuboid below.
44.4º
NOT TO
b) Complete the drawing of a
2cm cube below.
2x2x4
answer
7 cm
SCALE
B
C
B
C
4.1 cm
4.9 cm
[ 4]
59 Use a ruler, compass, pencil and protractor to construct the shapes below.
a)
[ 4]
64 A ship sails from a point A and travels on a bearing of 255º for 2km to a point B.
b)
Using a scale of 1cm = 10km make an accurate, labelled scale drawing.
2.7 cm
120
º
NOT TO
255
2 [ 2]
5.9 cm
65 The diagram below shows two points A and B .
SCALE
80
º
100
º
North
3.2 cm
Find:
[ 4]
A
153 º
North
60 In triangle ABC, AB = 4.4 cm, AC = 5.2 cm and angle ABC = 5º.
Show that triangle ABC can be constructed in two different ways.
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153º
b) the bearing of A from B.
333º
[ 3]
B
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a) the bearing of B from A
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66 A car travels a distance of 97.5km in 3 hrs and 15 mins.
97.5
3 15
a)
34 miles
=
km
b)
54.4
2 km =
miles
1
[ 2]
30
[ 6]
30 km/h [ 2 ]
Work out the average speed of the car.
70 A teacher says "10 kilograms (kg) is approximately equal to 22 pounds (lbs)"
67 A car travels at an average speed of 50km/h for 2 hrs and 15 mins.
50 2 15
Work out the distance travelled.
112.5 km
[ 2]
a) Draw a conversion graph for kilograms and pounds using this information.
Kilograms should go on the horizontal axis, with a scale of 0 to 40.
68 Below is a distance-time graph for a person's journey between towns A and B .
Pounds should go on the vertical axis, with a scale of 0 to 80.
Distance (km)
B
11
Use your graph to copy and complete the following:
10
9
8
0
2
7
0
4
6
2
4
4
4
3
4
6
2
4 10
5
4
b)
20 kg =
lbs
kg =
66 lbs
71 Calculate the missing sides in these right-angled triangles :
a)
b)
8.5 cm
2 cm
b
1
a
3 cm
0
A
c)
44
0
1
2
3
4
5
6
7
8 cm
Time (hours)
NOT TO
SCALE
a) What was the furthest distance the person travelled from town A ?
10 km
b) What was the total time of the journey?
6 hrs
c) Calculate the average speed, in km/h, for the first stage of the journey.
2/1
3.6 cm
[ 4]
3 cm
[ 4]
72 Using a calculator, give the answer to these calculations to 1 decimal place.
69 Below is a conversion graph for miles and km.
a)
miles
cos
15 º
b)
1
sin-1
0.32
18.7º [ 2 ]
50
73 Find the missing sides and angles to 1 d.p. in the right-angled triangles below.
40
15 3.2 11.9 12.3 3
2
5.6 7.4 4.8
a)
30
20
km
miles
0
0
2
b)
11.9 cm
49.4º
4.8 cm
3.2 cm
12.3 cm
NOT TO
80 50
5.6 cm
SCALE
b
15º
10
a
0
0
10
20
30
40
50
60
70
80
[ 4]
7.4 cm
km
74 The diagram below shows the journey of a ship that sets sail from A to B .
The ship sails on a bearing of 054º for a distance of 4 km.
Use the graph to complete the following:
54 4
North
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78 Work out the missing length in the enlarged photograph.
B
North
054 º
4
a) How far north of A is B ?
2.4 km
b) How far east of A is B ?
3.2 km
10 cm
4 cm
km
NOT TO
[ 4]
A
SCALE
?
cm
9 cm
75 The diagram shows a vertical mast supported be two cables of equal length.
22.5 cm [ 2 ]
The angle between each cable and the horizontal ground is 65º.
79 Find the pair of similar triangles from the diagrams below:
mast
8m
A
cable
cable
26 º
NOT TO
B
C
85 º
D
64 º
5º
SCALE
24 º
65
º
65
64 º
º
26 º
111 º
NOT TO SCALE
130º, 111º, 69º, 5º
[ 2]
80 The triangles below are similar.
9m
a) Calculate the combined length of the two cables.
21.3 m
b) Calculate the total height of the telephone mast.
17.7 m [ 4 ]
Z
A
11 cm
NOT TO
76 Complete the following, showing all your construction lines.
SCALE
X
B
a) Draw an angle of 10º using a protractor, then bisect it using a compass.
10
b) Draw a 3 cm line, then use a compass to draw its perpendicular bisector.
3 [ 4]
36 cm
C
8 cm
Y
a) Find the length XZ.
77 The diagram below shows a garden ABCD .
49.5 cm
b) How many times bigger is the area of XYZ than ABC?
20.25 [ 4 ]
The owner wants to plant a tree so that it is nearer to the side AB than AD.
81 Which of these triangles are congruent?
The owner also wants the tree to be more than 1 metres from point B.
A and D
A
B
A
11 m
B
C
D
GARDEN
D
[ 2]
C
3m
Using a scale of 1cm = 2m make a scale drawing of the garden.
Shade the area where the tree can be planted (showing all construction lines).
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2
1 The table below shows the total number of visitors to three cinemas in a Multiplex.
Winter
Spring
Summer
Autumn
Cinema 1
7958
3557
3638
5073
20226
Cinema 2
7519
2643
3383
3824
17369
Cinema 3
7129
5243
2141
4084
18597
||
2
3
0
4
|||
3
5
||
2
Total
[ 4]
4 Some students were asked how long it took to travel to school in the morning.
Their times, to the nearest minute, are shown below.
a) How many people visited Cinema 2 during the summer?
b) What is the difference in people visiting Cinema 1 in spring and winter?
4401
c) In total, how many people visited the three cinemas during the spring?
11443
d) Which cinema had the fewest visitors across the year?
1
3383
Cinema 2
2
[ 4]
Blue
K
7
8
9 10 11 12 13 14 15 16 17 18 19 20
0 28 1 35
Tally
0 - 9
††††
5
10 - 19
|
1
20 - 29
|||
3
L
30 - 39
†††† |
6
Green
J
Red
I
Other
H
Green
G
Red
F
Red
E
Blue
D
Green
Red
Green
Other
Colour
C
6
Time (minutes)
40 - 49
|||
3
The results are shown in the data collection sheet below.
B
5
Complete the frequency table:
Students were asked about their height, weight, favourite colour and favourite subject.
A
4
18 1 25 46 33 5 22 13 39 48 32 42 38 35 7
2 A questionnaire aims to find out information about a group of students.
Pupil
3
Frequency
[ 4]
Total
50
47
Art
44
Other
41
PE
48
Other
56
Other
Other
62
Maths
66
PE
41
PE
47
Other
Subject
PE
Weight 50
43
5 Jim asked his friends about their favourite colour.
Maths
Height 159 172 143 173 146 149 136 139 143 135 131 133
The results are shown in the bar chart below.
12
11
Selecting one qualitative data question, represent the data in a tally chart.
10
Write a sentence about what you notice about this data.
9
[ 4]
Frequency
8
3 Some students were asked how many brothers and sisters they had.
The results are shown below.
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
10 4
5
5
2
0
4
2
4
0
7
Frequency
Red
8
6
Blue
5
5
Green
7
Other
6
4
3
1
Colour
2
1
0
Use this data to complete the frequency table below.
Red
Blue
Green
Other
Colour
siblings
Tally
0
||
1
|
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Frequency
2
1
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a) What was the favourite colour?
Red
b) How many people chose green?
7
c) What is the difference in the number of people that said red and green?
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1
Page 2 of 9
d) Why do you think a category of "other" has been included?
answer [ 4 ]
Bus
Train
6 This line graph shows the average rainfall each month, in mm, of a city:
Month Rainfall
12
135o
Jan
6
10
Feb
12
9
Mar
3
8
Apr
8
a) How many pupils travel to school by train?
12
7
May
8
b) What angle represents the pupils who walk to school?
45º
6
Jun
3
c) How many pupils travel to school by car?
18
Jul
3
d) How many more pupils travel to school by car than by bus?
6
Aug
5
Sep
2
11
5
4
Walk
Car
[ 4]
3
2
9 Students in Year 9 were asked what their favourite subject was.
Dec
Nov
Jun
Feb
Oct
2
Sep
Dec
Aug
Draw a pie chart to show this information.
Jul
0
May
The results are shown in the frequency table below.
Apr
8
5
Mar
Oct
Nov
Jan
1
3
Subject
Pupils
Feb
Maths
15
0 mm
Science
15
c) Which months had the same rainfall?
answer
English
9
d) What is the range of rainfall?
10 mm [ 4 ]
PE
12
Other
9
a) Which month had the highest rainfall?
b) What was the change in rainfall between June and July?
7 The pictogram below shows the number of merits received by students in a term.
0
2
4
6
8
10
6
60
12
3
Year 7
Year 8
= 6 merits
Year 9
Year 10
4
5
6
8
Year 7
0
Year 8
11
Year 9
6
1
2
Year 10
9
2
0
9
4
Year 11
3
3
1
6
6
2
6
2
3
4
8
3
4
8
Year 11
0
b) Which year received the least merits?
Year 7
30
d) In the previous term Year 8 received 48 merits.
How many symbols would be needed to represent this?
9 10 12 15 18 20 24 30 36 40 45 60 72 90 120 180 360 [ 4 ]
10 This stem and leaf diagram gives the times taken (minutes) when waiting for a bus.
a) How many merits did Year 7 receive?
c) What is the difference in merit totals between Year 8 and Year 9?
Angle
48
3
4
5
6
5
5
8
9
4
2
2
9
7
8
9
Key
1
7
2
= 12
7
a) What was the shortest time waited?
4
b) What was the longest time waited?
39
[ 2]
[ 4]
8
11 Supermarket shoppers were asked how many items they had bought:
8 This pie chart shows how 48 students in Year 7 travel to school each day.
48
4
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1
2
3
4
6
6
1
3
5
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7
8
9 10 11 12
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80 - 99
4
Total
16
Find:
a) the mode
b) the median
6
c) the mean
4
4.5
d) the range
5
[ 6]
11
[ 4]
16 This graph shows the time taken for students to get to school.
Cumulative Frequency
12 A set of 8 numbers has a mean of 6.375, a range of 10 and a median of 5.5.
8
1
2
3
4
5
6
7
60
8
50
7 12 3
4 11 2
2 10
Write down what the numbers are.
7, 12, 3, 4, 11, 2,
[ 4]
Time
(minutes)
Cumulative
Frequency
40
30
13 Some students recorded how many skipping rope jumps they could do in 10 seconds.
Frequency
The results for the boys and the girls are shown below.
0
-
10
4
4
11
-
20
8
12
21
-
30
13
25
31
-
40
12
37
41
-
50
7
44
51
-
60
5
49
20
1
2
3
9
3
7
3
Girls:
2
Boys: 6 10
4
5
6
7
8
9 10
10
0
0
a) Work out the mean for the girls.
10
20
30
40
50
60
6.3
Time (minutes)
b) Work out the range for the girls.
6
c) Work out the mean for the boys.
8
a) What is the median journey length?
d) Work out the range for the boys.
4
b) Find the inter-quartile range.
e) Write a sentence to compare the results for the boys and the girls.
30
40-21 [ 3 ]
answer [ 5 ]
17 A probability scale goes from zero to one:
14 A football team recorded the number of goals scored in 26 matches.
0
1
|
Goals
Frequency
0
1
|
|
|
impossible
1
Find:
1
3
4
a) the mode
2
2
11
15
b) the median
2
3
11
26
c) the mean.
2.2
Total
26
|
certain
Indicate on the scale where you would place the following events:
[ 4]
a) You will throw a 2 on a normal dice.
answer
b) You will have homework today.
answer [ 2 ]
18 A normal unbiased dice is thrown.
15 The test results of 16 students was recorded in a frequency table.
Find the following probabilities:
Percentage
Frequency
0 - 19
5
5
Find:
20 - 39
0
5
a) the modal class
60 - 79
40 - 59
1
6
b) the median class
60 - 79
60 - 79
6
12
c) the mean.
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54.5
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a) P(3)
3
1/6
b) P(not getting a 2)
2
5/6
[ 2]
19 A box contains 7 cards with the numbers below.
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Page 6 of 9
7
1
2
3
4
5
6
3
8
5
7 11 7
6
7
8
9 10
b) How many outcomes are there?
36
c) Find the probability of getting a score less than 15.
a) What is the probability of choosing a card which is less than 4?
4
1/7
b) What is the probability of choosing a multiple of 11?
11
#VALUE!
25 The table below shows the weight and height of 10 students.
[ 2]
7
2
9
23/36 [ 4 ]
10
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
height (cm)
20 A bag contains some coloured balls: 7 red, 2 blue, and 9 green.
15
weight (kg)
A ball is chosen at random.
132 172 134 142 154 166 180 130 152 131
69 81 37 68 75 54 79 67 32 44
FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
Plot the points on the scatter diagram below.
Find the probability of picking the following:
weight (kg)
a) a red ball
b) not a blue ball.
7/18
16/18 [ 2 ]
190
180
21 The probability that it will rain tomorrow is 0.638
0.64
What is the probability that it will not rain tomorrow?
0.362 [ 2 ]
170
160
22 A football team can either win, lose or draw a match.
The probability that they win their next match is 0.4.
0.40
The probability that they will lose their next match is ¼.
150
¼
What is the probability that they will draw their next match?
0.35 [ 2 ]
140
130
23 A contains three balls numbered 3, 1 and 6.
3
1
6
30
40
50
60
70
80
90
height (cm)
Describe any correlation between the results.
The three balls are drawn to generate a three digit number.
positive [ 6 ]
By considering all of the possible outcomes, find the following probabilities:
26 A bag contains a selction of coloured balls: 6 white and 6 black.
a) P(odd 3 digit number)
odd
2/3
b) P(3 digit number greater than 800)
800
1/3
24 Two dice numbered 1 to 6 are thrown and their scores multiplied.
A ball is picked at random, replaced, then a second ball chosen.
[ 4]
0.5462281
Complete the tree diagram below.
6
First ball
Second ball
Outcome
a) Complete the sample space table below to show all possible outcomes.
W
multiplied
×
1
2
3
4
5
6
6
1
1
2
3
4
5
6
12
2
2
4
6
3
3
6
9 12 15 18
4
4
8 12 16 20 24
5
5 10 15 20 25 30
6
6 12 18 24 30 36
WW
1/2
W
6
WB
B
12
8 10 12
1/2
W
BW
B
6
1/2
BB
B
12
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Find:
a) P (WW )
b) P (same colour)
1/4
1/2
[ 8]
27 An experiment is done to find out if a dice is fair or biased.
A dice is thrown and the results are recorded in the frequency table below.
Score
Frequency
1
2
3
4
5
6
0 11 12 7
4
1
Based on these results, find the relative frequencies of the following.
4
a) P(4)
6
2
b) P(6 or 2)
1/5
Write down, with a reason, if you think that the dice is biased or unbiased.
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12/35
answer [ 3 ]
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