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GCSE Maths Higher Paper 3: printable

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GCSE Maths Higher Paper 3 (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-3/

  1. 1 Question 1

    Write 58 as a percentage.

    [1 mark]

    Answer: ____________________

  2. 2 Question 2

    A £200 bag goes down in price by 10%. Later the new price goes up by 10%. Work out the final price.

    [3 marks]

    Answer: ____________________

  3. 3 Question 3

    A metal has density 8.9 g/cm³. A block of it has volume 25 cm³. Work out its mass.

    [2 marks]

    Answer: ____________________

  4. 4 Question 4

    Solve 4(2x − 3) = 5(x + 6).

    [3 marks]

    Answer: ____________________

  5. 5 Question 5

    Simplify (3a²b)³.

    [2 marks]

    Answer: ____________________

  6. 6 Question 6

    Factorise x³ + 4x² + 3x + 12 by grouping.

    [2 marks]

    Answer: ____________________

  7. 7 Question 7

    The sequence 50, 46, 42, 38, ... continues in the same way. Work out the 20th term.

    [2 marks]

    Answer: ____________________

  8. 8 Question 8

    Work out the equation of the line through (1, 4) and (4, 13).

    [3 marks]

    Answer: ____________________

  9. 9 Question 9

    Work out the distance between (−2, 1) and (4, 9).

    [2 marks]

    Answer: ____________________

  10. 10 Question 10

    Each exterior angle of a regular polygon is 24°. How many sides does it have?

    [2 marks]

    Answer: ____________________

  11. 11 Question 11

    In a right-angled triangle, the sides next to the right angle are 7 cm and 11 cm. Work out the smaller angle of the triangle.

    [3 marks]

    Answer: ____________________

  12. 12 Question 12

    A frustum is cut from a cone of radius 6 cm and height 12 cm by removing a cone of radius 2 cm and height 4 cm from the top. Work out the volume of the frustum.

    [4 marks]

    Answer: ____________________

  13. 13 Question 13

    A sector has radius 8 cm and arc length 4π cm. Work out the angle of the sector.

    [3 marks]

    Answer: ____________________

  14. 14 Question 14

    Here are 9 marks: 3, 7, 8, 5, 12, 14, 21, 13, 18. Work out the median and the quartiles, and draw a box plot.

    [3 marks]

  15. 15 Question 15

    Masses, m kg, of 30 parcels: 0 < m ≤ 4: 5, 4 < m ≤ 8: 12, 8 < m ≤ 12: 9, 12 < m ≤ 16: 4. Work out an estimate of the mean mass.

    [4 marks]

    Answer: ____________________

  16. 16 Question 16

    In a class of 32 students, 20 study French, 15 study Spanish and 6 study both. A student is chosen at random. Work out the probability that they study French only.

    [3 marks]

    Answer: ____________________

  17. 17 Question 17

    A box has 6 red and 4 blue counters. Two are taken at random without replacement. Work out the probability that both are blue.

    [3 marks]

    Answer: ____________________

  18. 18 Question 18

    Solve x² − 4x = 12 by completing the square.

    [3 marks]

    Answer: ____________________

  19. 19 Question 19

    Work out the equation of the tangent to y = x² at the point (2, 4).

    [3 marks]

    Answer: ____________________

  20. 20 Question 20

    A colony of 500 bacteria grows by 8% every hour. How many bacteria are there after 6 hours?

    [3 marks]

    Answer: ____________________

  21. 21 Question 21

    Triangle XYZ has XY = 7 cm, XZ = 10 cm and angle YXZ = 125°. Work out its area.

    [3 marks]

    Answer: ____________________

  22. 22 Question 22

    A triangle has sides 7 cm, 8 cm and 9 cm. Work out the largest angle.

    [3 marks]

    Answer: ____________________

  23. 23 Question 23

    £1 = €1.16. Change €290 into pounds.

    [2 marks]

    Answer: ____________________

  24. 24 Question 24

    Work out the centre and radius of the circle x² + y² − 6x = 7.

    [3 marks]

    Answer: ____________________

  25. 25 Question 25

    Ana can paint a fence in 6 hours. Ben can paint the same fence in 12 hours. How long does it take them working together?

    [3 marks]

    Answer: ____________________

  26. 26 Question 26

    The point (5, 2) is rotated 180° about the point (2, 1). Write down the coordinates of its image.

    [2 marks]

    Answer: ____________________

  27. 27 Question 27

    A length is 6.4 cm, correct to 1 decimal place. Write down the error interval.

    [2 marks]

    Answer: ____________________

  28. 28 Question 28

    Here are some data: 2, 15, 17, 18, 20, 21, 23, 45. Use the rule "more than 1.5 × IQR beyond a quartile" to find any outliers.

    [2 marks]

    Answer: ____________________

  29. 29 Question 29

    Solve 15x − 2 = 3.

    [3 marks]

    Answer: ____________________

  30. 30 Question 30

    A square has sides of 6 cm. A quarter circle of radius 6 cm, centred on one corner, is cut out. Work out the area that is left.

    [3 marks]

    Answer: ____________________

Answers

  1. 1 62.5%
  2. 2 £198
  3. 3 m = 222.5
  4. 4 x = 14
  5. 5 27a6b3
  6. 6 (x + 4)(x2 + 3)
  7. 7 a20 = −26
  8. 8 y = 3x + 1
  9. 9 d = 10
  10. 10 sides = 15
  11. 11 θ ≈ 32.5°
  12. 12 V = 416π/3 ≈ 435.41
  13. 13 angle = 90°
  14. 14 min 3, Q1 6, median 12, Q3 16, max 21
  15. 15 mean ≈ 7.6
  16. 16 P(french only) = 716
  17. 17 P(all blue) = 215
  18. 18 x = 6 or x = −2
  19. 19 y = 4x − 4
  20. 20 ≈ 793
  21. 21 A ≈ 28.7
  22. 22 C ≈ 73.4°
  23. 23 €290 = £250
  24. 24 center (3, 0) and r = 4
  25. 25 x = 4
  26. 26 P' = (−1, 0)
  27. 27 6.35 ≤ length < 6.45
  28. 28 outliers: 2 and 45
  29. 29 x = 3
  30. 30 A ≈ 7.74

Full mark scheme: steplyclass.com/gcse-maths/higher-paper-3/mark-scheme/

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