Steply

GCSE Maths Higher Paper 2: printable

Take it online with a timer Mark scheme

GCSE Maths Higher Paper 2 (calculator)

Name: ______________________   Date: __________   Marks: ____ / 80

Time: 90 minutes. You may use a calculator. Answer all questions. Show your working. The marks for each part are shown in brackets. steplyclass.com/gcse-maths/higher-paper-2/

  1. 1 Question 1

    Write 0.03846 correct to 3 significant figures.

    [1 mark]

    Answer: ____________________

  2. 2 Question 2

    £4500 is invested at 3.2% compound interest per year. Work out its value after 5 years.

    [3 marks]

    Answer: ____________________

  3. 3 Question 3

    A van is bought for £24 000. Its value falls by 18% each year. Work out its value after 3 years.

    [3 marks]

    Answer: ____________________

  4. 4 Question 4

    Tom gets a 15% pay rise. He now earns £575 a week. Work out how much he earned each week before the rise.

    [3 marks]

    Answer: ____________________

  5. 5 Question 5

    x = 36 and y = 8, both correct to the nearest whole number. Work out the upper bound of x ÷ y. Give your answer to 3 significant figures.

    [3 marks]

    Answer: ____________________

  6. In triangle PQR, PQ = 9 cm, PR = 12 cm and angle QPR = 38°.

    6(a) Question 6(a)

    Work out QR.

    [3 marks]

    Answer: ____________________

  7. 6(b) Question 6(b)

    Work out the area of triangle PQR.

    [2 marks]

    Answer: ____________________

  8. 7 Question 7

    In triangle ABC, angle A = 48°, angle B = 63° and BC = 14 cm. Work out AC.

    [3 marks]

    Answer: ____________________

  9. 8 Question 8

    A cuboid measures 4 cm by 7 cm by 9 cm. Work out the length of the longest straight rod that fits inside it.

    [3 marks]

    Answer: ____________________

  10. 9 Question 9

    A cone has base radius 5 cm and slant height 13 cm. Work out its volume.

    [3 marks]

    Answer: ____________________

  11. 10 Question 10

    A hemisphere has radius 4 cm. Work out its total surface area (curved surface and flat face).

    [2 marks]

    Answer: ____________________

  12. 11 Question 11

    A sector has radius 12 cm and angle 150°. Work out its area.

    [2 marks]

    Answer: ____________________

  13. 12 Question 12

    Solve 3x² + 4x − 2 = 0. Give your answers to 2 decimal places.

    [4 marks]

    Answer: ____________________

  14. 13 Question 13

    Solve the simultaneous equations x² + y² = 10 and y = 3x.

    [5 marks]

    Answer: ____________________

  15. 14 Question 14

    Ages of people at a club: 0 < age ≤ 10: 8, 10 < age ≤ 20: 6, 20 < age ≤ 40: 10. Work out the frequency densities for a histogram.

    [3 marks]

  16. 15 Question 15

    Times, t minutes: 0 < t ≤ 10: 4, 10 < t ≤ 20: 9, 20 < t ≤ 30: 15, 30 < t ≤ 40: 8, 40 < t ≤ 50: 4. Use cumulative frequency to estimate the median time.

    [3 marks]

    Answer: ____________________

  17. 16 Question 16

    Two similar solids have lengths 3 cm and 7.5 cm. The small one has volume 16 cm³. Work out the volume of the large one.

    [2 marks]

    Answer: ____________________

  18. 17 Question 17

    A cuboid has a base 6 cm by 8 cm and height 10 cm. Work out the angle between a long diagonal and the base.

    [3 marks]

    Answer: ____________________

  19. 18 Question 18

    Solve 2 cos x − 1 = 0 for 0° ≤ x ≤ 360°.

    [3 marks]

    Answer: ____________________

  20. 19 Question 19

    Solve 2x − 1 = 64.

    [2 marks]

    Answer: ____________________

  21. 20 Question 20

    y is directly proportional to the square of x. When x = 2, y = 20. Work out y when x = 5.

    [3 marks]

    Answer: ____________________

  22. 21 Question 21

    A cyclist speeds up from rest to 10 ms in 2 s, keeps that speed for 6 s, then slows to rest in 2 s. Work out the total distance travelled.

    [3 marks]

    Answer: ____________________

  23. 22 Question 22

    A fair coin is thrown 4 times. Work out the probability of exactly 2 heads.

    [3 marks]

    Answer: ____________________

  24. 23 Question 23

    Work out (5.4 × 10⁸) ÷ (1.8 × 10⁻³). Give your answer in standard form.

    [2 marks]

    Answer: ____________________

  25. 24 Question 24

    A boat sails 10 km on a bearing of 030°. How far north and how far east of its start is it?

    [3 marks]

    Answer: ____________________

  26. 25 Question 25

    A kite string is 50 m long and makes an angle of 20° with the ground. Work out the height of the kite.

    [3 marks]

    Answer: ____________________

  27. 26 Question 26

    Work out the average rate of change of f(x) = x² from x = 1 to x = 4.

    [2 marks]

    Answer: ____________________

  28. 27 Question 27

    x = 15.2 and y = 9.7, both correct to 1 decimal place. Work out the upper bound of x − y.

    [2 marks]

    Answer: ____________________

  29. 28 Question 28

    A cone has base radius 8 m and perpendicular height 6 m. Work out its total surface area.

    [3 marks]

    Answer: ____________________

Answers

  1. 1 0.03846 ≈ 0.0385
  2. 2 A ≈ £5267.58
  3. 3 ≈ £13232.83
  4. 4 x = 500
  5. 5 upper bound ≈ 4.87
  6. 6(a) c ≈ 7.4
  7. 6(b) A ≈ 33.2
  8. 7 b ≈ 16.8
  9. 8 D ≈ 12.1
  10. 9 V ≈ 314 cm3
  11. 10 S ≈ 150.72 cm2
  12. 11 area = 60π ≈ 188.50 cm²
  13. 12 x ≈ 0.39 or x ≈ −1.72
  14. 13 (−1, −3) and (1, 3)
  15. 14 heights 0.8, 0.6, 0.5
  16. 15 median ≈ 24.7
  17. 16 large volume = 250
  18. 17 θ ≈ 45.0°
  19. 18 x = 60°, 300°
  20. 19 x = 7
  21. 20 y = 125
  22. 21 distance = 80 m
  23. 22 P(2 heads) = 38
  24. 23 3 × 1011
  25. 24 8.7 km north, 5.0 km east
  26. 25 x ≈ 17.1 m
  27. 26 5
  28. 27 upper bound = 5.6
  29. 28 S ≈ 452.16 m2

Full mark scheme: steplyclass.com/gcse-maths/higher-paper-2/mark-scheme/

Steply practice papers are our own questions in the style of GCSE Mathematics papers in England (layout and timing as AQA 8300); they are not official and not endorsed by AQA or any exam board. Official past papers: your exam board's website.