1. Direct Proportion – Higher – GCSE Questions – AQA
These questions are the same format as previous GCSE exams.
COPY means they use the exact same numbers as the original GCSE question.
Otherwise, they are clone questions using different numbers.
The worksheets are provided in 2 sizes.

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3. AQA Higher: June 2018 Paper 3, Q21 AQA Higher: June 2018 Paper 3, Q21
The mass of an ornament is m grams.
The height of the ornament is h centimetres.
m is directly proportional to the cube of h .
m = 1134 when h = 6 1
The mass of an ornament is m grams.
The height of the ornament is h centimetres.
m is directly proportional to the cube of h .
m = 1134 when h = 6
1 (a)
Work out an equation connecting m and h
1 (a)
Work out an equation connecting m and h
[3 marks]
[3 marks]
Answer
Answer
1 (b)
Work out the mass of an ornament of height 9 centimetres.
1 (b)
Work out the mass of an ornament of height 9 centimetres.
[2 marks]
[2 marks]
Answer
grams
Answer
grams

5. AQA Higher: November 2017 Paper 2, Q20
A ball is thrown upwards with a speed of 𝑣 metres per second.
The ball reaches a maximum height of ℎ metres.
ℎ is directly proportional to 𝑣2
When 𝑣 = 5, ℎ = 4
Work out the maximum height reached when 𝑣 = 14 1
A ball is thrown upwards with a speed of 𝑣 metres per second.
The ball reaches a maximum height of ℎ metres.
ℎ is directly proportional to 𝑣2
When 𝑣 = 5, ℎ = 4
Work out the maximum height reached when 𝑣 = 14
[4 marks]
[4 marks]
Answer m
Answer m
AQA Higher: November 2017 Paper 2, Q20
AQA Higher: November 2017 Paper 2, Q20 1
A ball is thrown upwards with a speed of 𝑣 metres per second.
The ball reaches a maximum height of ℎ metres.
ℎ is directly proportional to 𝑣2
When 𝑣 = 5, ℎ = 4
Work out the maximum height reached when 𝑣 = 14 1
A ball is thrown upwards with a speed of 𝑣 metres per second.
The ball reaches a maximum height of ℎ metres.
ℎ is directly proportional to 𝑣2
When 𝑣 = 5, ℎ = 4
Work out the maximum height reached when 𝑣 = 14
[4 marks]
[4 marks]
Answer m
Answer m

7. AQA Higher: June 2017 Paper 2, Q22 AQA Higher: June 2017 Paper 2, Q22
A ball, dropped vertically, falls d metres in t seconds.
d is directly proportional to the square of t .
The ball drops 75 metres in the first 5 seconds.
How far does the ball drop in the next 5 seconds? 1
A ball, dropped vertically, falls d metres in t seconds.
d is directly proportional to the square of t .
The ball drops 75 metres in the first 5 seconds.
How far does the ball drop in the next 5 seconds?
[4 marks]
[4 marks]
Answer
metres
Answer
metres

9. AQA Higher: June 2018 Paper 3, Q21
The mass of an ornament is m grams.
The height of the ornament is h centimetres.
m is directly proportional to the cube of h .
m = 1134 when h = 6
1 (a)
Work out an equation connecting m and h
[3 marks]
Answer
1 (b)
Work out the mass of an ornament of height 9 centimetres.
[2 marks]
Answer
grams

11. AQA Higher: June 2017 Paper 2, Q22
A ball, dropped vertically, falls d metres in t seconds.
d is directly proportional to the square of t .
The ball drops 75 metres in the first 5 seconds.
How far does the ball drop in the next 5 seconds?
[4 marks]
Answer
metres

12. AQA Higher: June 2018 Paper 3, Q21
The mass of an ornament is m grams.
The height of the ornament is h centimetres.
m is directly proportional to the cube of h .
m = 1134 when h = 6
m = kh3
1 (a)
Work out an equation connecting m and h
1134 = k63
[3 marks]
1134 = 216k
1134 ÷ 216 = k = 5.25
m = 5.25h3
Answer
1 (b)
Work out the mass of an ornament of height 9 centimetres.
[2 marks]
m = 5.25(9)3
= 5400
Answer
grams

14. Distance for full 10 seconds = 𝑑 = 3 × 102 𝑑 = 300
AQA Higher: June 2017 Paper 2, Q22 1
A ball, dropped vertically, falls d metres in t seconds.
d is directly proportional to the square of t .
The ball drops 75 metres in the first 5 seconds.
How far does the ball drop in the next 5 seconds?
[4 marks]
𝑑 ∝ 𝑡2
75 = 𝑘 × 52=𝑘25
= 𝑘=3
𝑑 ∝ 3𝑡2
Distance for full 10 seconds =
𝑑 = 3 × 102
𝑑 = 300
Distance for second 5 seconds
= 300−75=225
225
Answer
metres

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