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IGCSE Maths Core Paper 3: printable

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IGCSE Maths Core 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/igcse-maths/core-paper-3/

  1. 1(a) Question 1(a)

    Write 3.14159 correct to 3 significant figures.

    [1 mark]

    Answer: ____________________

  2. 1(b) Question 1(b)

    Write 0.006284 correct to 2 significant figures.

    [1 mark]

    Answer: ____________________

  3. 2 Question 2

    Work out (5.6 + 2.8) ÷ 1.2.

    [1 mark]

    Answer: ____________________

  4. 3 Question 3

    Work out 35% of 240.

    [1 mark]

    Answer: ____________________

  5. 4 Question 4

    Priya invests $1500 at 3% per year simple interest. Work out the interest she earns in 4 years.

    [2 marks]

    Answer: ____________________

  6. 5 Question 5

    Omar invests $2000 at 4% per year compound interest. Work out the amount in his account after 3 years.

    [3 marks]

    Answer: ____________________

  7. 6 Question 6

    $1 = €0.92. Change $350 into euros.

    [2 marks]

    Answer: ____________________

  8. 7 Question 7

    75% of a number is 18. Find the number.

    [2 marks]

    Answer: ____________________

  9. 8 Question 8

    A metal block has mass 156 g and volume 12 cm³. Work out its density.

    [2 marks]

    Answer: ____________________

  10. 9 Question 9

    A cyclist rides at 18 km/h. How many hours does it take to ride 63 km?

    [2 marks]

    Answer: ____________________

  11. 10(a) Question 10(a)

    A circle has radius 6.5 cm. Work out its area.

    [2 marks]

    Answer: ____________________

  12. 10(b) Question 10(b)

    A circle has diameter 12 cm. Work out its circumference.

    [2 marks]

    Answer: ____________________

  13. 11 Question 11

    A sector has radius 8 cm and angle 45°. Work out the arc length.

    [2 marks]

    Answer: ____________________

  14. 12 Question 12

    A cylinder has radius 4 cm and height 10 cm. Work out its volume.

    [2 marks]

    Answer: ____________________

  15. 13(a) Question 13(a)

    A right-angled triangle has shorter sides 5 cm and 9 cm. Work out the length of the hypotenuse.

    [2 marks]

    Answer: ____________________

  16. 13(b) Question 13(b)

    A right-angled triangle has hypotenuse 13 cm and one shorter side 5 cm. Work out the length of the other side.

    [2 marks]

    Answer: ____________________

  17. 14(a) Question 14(a)

    In a right-angled triangle the hypotenuse is 12 cm and one angle is 35°. Work out the side opposite the 35° angle.

    [2 marks]

    Answer: ____________________

  18. 14(b) Question 14(b)

    In a right-angled triangle the side opposite angle x is 7 cm and the side next to it (adjacent) is 10 cm. Work out x.

    [2 marks]

    Answer: ____________________

  19. 15 Question 15

    From a point 25 m from the foot of a tree, the angle of elevation of the top of the tree is 32°. Work out the height of the tree.

    [2 marks]

    Answer: ____________________

  20. 16 Question 16

    The table shows the times, t minutes, of 20 runs: 0 < t ≤ 10: 4, 10 < t ≤ 20: 9, 20 < t ≤ 30: 5, 30 < t ≤ 40: 2. Calculate an estimate of the mean time.

    [3 marks]

    Answer: ____________________

  21. 17(a) Question 17(a)

    A fair coin is thrown and a fair dice is rolled. Find the probability of a tail and an even number.

    [2 marks]

    Answer: ____________________

  22. 17(b) Question 17(b)

    In a school, 3 out of every 10 students cycle to school. Estimate how many of 500 students cycle to school.

    [1 mark]

    Answer: ____________________

  23. 18(a) Question 18(a)

    Solve 7x − 3 = 2x + 22.

    [3 marks]

    Answer: ____________________

  24. 18(b) Question 18(b)

    v = u + at. Find v when u = 5, a = 3 and t = 4.

    [2 marks]

    Answer: ____________________

  25. 19 Question 19

    Factorise completely 8x² − 12x.

    [2 marks]

    Answer: ____________________

  26. 20 Question 20

    The sequence 5, 9, 13, 17, ... continues in the same way. Find the 30th term.

    [2 marks]

    Answer: ____________________

  27. 21(a) Question 21(a)

    Find the equation of the straight line through (0, 1) and (2, 7). Give it in the form y = mx + c.

    [3 marks]

    Answer: ____________________

  28. 21(b) Question 21(b)

    Find the midpoint of the line joining (−2, 3) and (6, 7).

    [2 marks]

    Answer: ____________________

  29. 22 Question 22

    Complete a table of values for y = 2x − 3 for x = −1, 0, 1, 2, 3 and draw the graph.

    [3 marks]

  30. 23 Question 23

    A map has a scale of 1 cm to 4 km. Two towns are 6.5 cm apart on the map. Work out the real distance.

    [2 marks]

    Answer: ____________________

  31. 24(a) Question 24(a)

    The point (5, −1) is translated 3 units left and 4 units up. Write down the coordinates of its image.

    [1 mark]

    Answer: ____________________

  32. 24(b) Question 24(b)

    The point (2, 3) is enlarged with scale factor 3, centre the origin. Write down the coordinates of its image.

    [1 mark]

    Answer: ____________________

  33. 25 Question 25

    Work out (3.2 × 10⁵) × (4 × 10³). Give your answer in standard form.

    [2 marks]

    Answer: ____________________

  34. 26 Question 26

    Write the ratio 40 cm : 2 m in its simplest form.

    [2 marks]

    Answer: ____________________

  35. 27 Question 27

    A length is 24 cm, correct to the nearest centimetre. Write down the lower bound and the upper bound of the length.

    [2 marks]

    Answer: ____________________

  36. 28(a) Question 28(a)

    Four angles of a pentagon are 100°, 120°, 95° and 110°. Find the fifth angle, x.

    [2 marks]

    Answer: ____________________

  37. 28(b) Question 28(b)

    Each interior angle of a regular polygon is 140°. How many sides does it have?

    [2 marks]

    Answer: ____________________

  38. 29 Question 29

    Two triangles are similar. The small one has sides 4 cm, 6 cm and 7 cm. The large one has sides 10 cm, 15 cm and x cm. Find x.

    [2 marks]

    Answer: ____________________

  39. 30 Question 30

    In a group of 40 students, 22 play football, 15 play tennis and 8 play both. A student is picked at random. Find the probability that they play both.

    [2 marks]

    Answer: ____________________

  40. 31 Question 31

    A car was worth $8000. It is now worth $6800. Find the percentage decrease.

    [2 marks]

    Answer: ____________________

  41. 32 Question 32

    Share $360 in the ratio 2 : 3 : 4.

    [2 marks]

    Answer: ____________________

Answers

  1. 1(a) 3.14159 ≈ 3.14
  2. 1(b) 0.006284 ≈ 0.0063
  3. 2 7
  4. 3 84
  5. 4 x = 180
  6. 5 A ≈ $2249.73
  7. 6 $350 = €322
  8. 7 24
  9. 8 density = 13 g/cm³
  10. 9 3.5 hours
  11. 10(a) A ≈ 132.67 cm2
  12. 10(b) C ≈ 37.68 cm
  13. 11 arc = 2π ≈ 6.28 cm
  14. 12 V ≈ 502.4 cm3
  15. 13(a) c ≈ 10.3
  16. 13(b) b = 12
  17. 14(a) x ≈ 6.9
  18. 14(b) θ ≈ 35.0°
  19. 15 x ≈ 15.6 m
  20. 16 mean ≈ 17.5
  21. 17(a) P(tails and even) = 14
  22. 17(b) ≈ 150
  23. 18(a) x = 5
  24. 18(b) 17
  25. 19 4x(2x − 3)
  26. 20 a30 = 121
  27. 21(a) y = 3x + 1
  28. 21(b) M = (2, 5)
  29. 22 (−1, −5), (0, −3), (1, −1)
  30. 23 26 km
  31. 24(a) P' = (2, 3)
  32. 24(b) P' = (6, 9)
  33. 25 1.28 × 109
  34. 26 1 : 5
  35. 27 23.5 ≤ length < 24.5
  36. 28(a) x = 115
  37. 28(b) sides = 9
  38. 29 x = 17.5
  39. 30 P(both) = 15
  40. 31 15%
  41. 32 80, 120 and 160

Full mark scheme: steplyclass.com/igcse-maths/core-paper-3/mark-scheme/

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