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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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

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

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

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

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

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 3827.25 Answer grams

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 75 25 = 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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