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IGCSE Maths Core Paper 1: printable

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IGCSE Maths Core Paper 1 (non-calculator)

Name: ______________________   Date: __________   Marks: ____ / 80

Time: 90 minutes. You must not use a calculator. Answer all questions. Show your working. The marks for each part are shown in brackets. steplyclass.com/igcse-maths/core-paper-1/

  1. 1 Question 1

    Write 4827 correct to 2 significant figures.

    [1 mark]

    Answer: ____________________

  2. 2 Question 2

    Work out 34 + 2/5. Give your answer as a fraction.

    [2 marks]

    Answer: ____________________

  3. 3(a) Question 3(a)

    Write 0.375 as a fraction in its simplest form.

    [1 mark]

    Answer: ____________________

  4. 3(b) Question 3(b)

    Write 720 as a percentage.

    [1 mark]

    Answer: ____________________

  5. 4 Question 4

    Work out 15% of 60.

    [2 marks]

    Answer: ____________________

  6. 5 Question 5

    Share $72 in the ratio 4 : 5.

    [2 marks]

    Answer: ____________________

  7. 6(a) Question 6(a)

    Simplify 5x + 3y − 2x + y.

    [2 marks]

    Answer: ____________________

  8. 6(b) Question 6(b)

    Expand 3(2x − 5).

    [1 mark]

    Answer: ____________________

  9. 6(c) Question 6(c)

    Factorise completely 6x + 15.

    [1 mark]

    Answer: ____________________

  10. 7 Question 7

    Solve 4x + 7 = 31.

    [2 marks]

    Answer: ____________________

  11. 8 Question 8

    Solve 5(x − 2) = 3x + 6.

    [3 marks]

    Answer: ____________________

  12. 9 Question 9

    Find the value of 5a − 2b when a = 3 and b = −4.

    [2 marks]

    Answer: ____________________

  13. 10 Question 10

    Find the nth term of the sequence 7, 11, 15, 19, ...

    [2 marks]

    Answer: ____________________

  14. Two angles lie on a straight line.

    11(a) Question 11(a)

    One angle is 118°. Find the other angle, x.

    [1 mark]

    Answer: ____________________

  15. 11(b) Question 11(b)

    Two angles of a triangle are 52° and 71°. Find the third angle.

    [2 marks]

    Answer: ____________________

  16. 12(a) Question 12(a)

    Find the sum of the interior angles of a hexagon.

    [1 mark]

    Answer: ____________________

  17. 12(b) Question 12(b)

    Find the size of one exterior angle of a regular octagon.

    [2 marks]

    Answer: ____________________

  18. 13 Question 13

    A triangle has base 12 cm and height 7 cm. Find its area.

    [2 marks]

    Answer: ____________________

  19. 14 Question 14

    A trapezium has parallel sides 6 cm and 10 cm. The height is 4 cm. Find its area.

    [2 marks]

    Answer: ____________________

  20. 15 Question 15

    A cuboid measures 5 cm by 4 cm by 3 cm. Find its volume.

    [2 marks]

    Answer: ____________________

  21. 16 Question 16

    A fair dice is rolled. Find the probability that it shows a number more than 4.

    [1 mark]

    Answer: ____________________

  22. Here are the marks of 6 students: 4, 7, 9, 3, 7, 6.

    17(a) Question 17(a)

    Find the mean.

    [2 marks]

    Answer: ____________________

  23. 17(b) Question 17(b)

    Find the median.

    [1 mark]

    Answer: ____________________

  24. 17(c) Question 17(c)

    Find the range.

    [1 mark]

    Answer: ____________________

  25. 18 Question 18

    Write 45 000 in standard form.

    [1 mark]

    Answer: ____________________

  26. 19 Question 19

    Find the gradient of the line through (1, 2) and (3, 8).

    [2 marks]

    Answer: ____________________

  27. 20 Question 20

    The point (3, 2) is reflected in the x-axis. Write down the coordinates of its image.

    [1 mark]

    Answer: ____________________

  28. ξ = {1, 2, 3, ..., 12}, A = {2, 4, 6, 8, 10, 12}, B = {3, 6, 9, 12}.

    21 Question 21

    List the elements of A ∩ B.

    [1 mark]

    Answer: ____________________

  29. 22 Question 22

    Solve the inequality 3x − 4 < 11.

    [2 marks]

    Answer: ____________________

  30. 23(a) Question 23(a)

    Simplify x³ × x⁴.

    [1 mark]

    Answer: ____________________

  31. 23(b) Question 23(b)

    Simplify x⁸ ÷ x².

    [1 mark]

    Answer: ____________________

  32. 24 Question 24

    Make t the subject of the formula v = u + at.

    [2 marks]

    Answer: ____________________

  33. 25(a) Question 25(a)

    Write 360 as a product of its prime factors.

    [2 marks]

    Answer: ____________________

  34. 25(b) Question 25(b)

    Find the highest common factor (HCF) of 24 and 36.

    [2 marks]

    Answer: ____________________

  35. 25(c) Question 25(c)

    Find the lowest common multiple (LCM) of 6 and 8.

    [1 mark]

    Answer: ____________________

  36. 26 Question 26

    A right-angled triangle has shorter sides 6 cm and 8 cm. Find the length of the hypotenuse.

    [2 marks]

    Answer: ____________________

  37. 27 Question 27

    Solve the simultaneous equations x + y = 10 and x − y = 2.

    [3 marks]

    Answer: ____________________

  38. 28 Question 28

    A car travels 150 km in 3 hours. Find its average speed in km/h.

    [1 mark]

    Answer: ____________________

  39. 29 Question 29

    $1 = €0.80. Change $250 into euros.

    [2 marks]

    Answer: ____________________

  40. 30 Question 30

    Find the percentage increase when a price goes from $50 to $60.

    [2 marks]

    Answer: ____________________

  41. 31 Question 31

    A coat costs $80. In a sale the price is reduced by 25%. Find the sale price.

    [2 marks]

    Answer: ____________________

  42. 32 Question 32

    Using a ruler and compasses only, construct triangle ABC with AB = 7 cm, BC = 5 cm and AC = 6 cm.

    [2 marks]

  43. 33 Question 33

    Expand and simplify (x + 3)(x + 5).

    [2 marks]

    Answer: ____________________

  44. 34 Question 34

    In a class of 32 students, 20 play football, 14 play tennis and 9 play both. How many students play neither?

    [2 marks]

    Answer: ____________________

  45. 35 Question 35

    The point (3, 1) is rotated 180° about the origin. Write down the coordinates of its image.

    [1 mark]

    Answer: ____________________

  46. 36 Question 36

    Three more than four times a number is 31. Write an equation and solve it to find the number.

    [3 marks]

    Answer: ____________________

  47. 37 Question 37

    At midnight the temperature is −4°C. By noon it has risen by 9 degrees. Find the temperature at noon.

    [1 mark]

    Answer: ____________________

  48. 38 Question 38

    Work out 0.4 × 0.3.

    [1 mark]

    Answer: ____________________

  49. 39 Question 39

    Write 3.476 correct to 1 decimal place.

    [1 mark]

    Answer: ____________________

Answers

  1. 1 4827 ≈ 4800
  2. 2 2320
  3. 3(a) 38
  4. 3(b) 35%
  5. 4 9
  6. 5 32 and 40
  7. 6(a) 3x + 4y
  8. 6(b) 6x − 15
  9. 6(c) 3(2x + 5)
  10. 7 x = 6
  11. 8 x = 8
  12. 9 23
  13. 10 an = 4n + 3
  14. 11(a) x = 62
  15. 11(b) x = 57
  16. 12(a) sum = 720°
  17. 12(b) one angle = 45°
  18. 13 A = 42 cm2
  19. 14 A = 32 cm2
  20. 15 V = 60 cm3
  21. 16 P(more than 4) = 13
  22. 17(a) mean = 6
  23. 17(b) median = 6.5
  24. 17(c) range = 6
  25. 18 4.5 × 104
  26. 19 m = 3
  27. 20 P' = (3, −2)
  28. 21 A ∩ B = {6, 12}
  29. 22 x < 5
  30. 23(a) x7
  31. 23(b) x6
  32. 24 t = v − ua
  33. 25(a) 360 = 23 × 32 × 5
  34. 25(b) GCF(24, 36) = 12
  35. 25(c) LCM(6, 8) = 24
  36. 26 c = 10
  37. 27 (x, y) = (6, 4)
  38. 28 x = 50
  39. 29 $250 = €200
  40. 30 20%
  41. 31 sale price: $60
  42. 32 triangle ABC: AB = 7 cm, BC = 5 cm, AC = 6 cm
  43. 33 x2 + 8x + 15
  44. 34 7 play neither
  45. 35 P' = (−3, −1)
  46. 36 x = 7
  47. 37 5°C
  48. 38 0.12
  49. 39 3.476 ≈ 3.5

Full mark scheme: steplyclass.com/igcse-maths/core-paper-1/mark-scheme/

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