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IGCSE Maths Extended Paper 2: printable

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IGCSE Maths Extended Paper 2 (non-calculator)

Name: ______________________   Date: __________   Marks: ____ / 100

Time: 120 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/extended-paper-2/

  1. 1 Question 1

    Write the recurring decimal 0.363636... as a fraction in its simplest form.

    [2 marks]

    Answer: ____________________

  2. 2(a) Question 2(a)

    Work out 2 13 + 1 3/4. Give your answer as a mixed number.

    [3 marks]

    Answer: ____________________

  3. 2(b) Question 2(b)

    Work out 2 23 ÷ 1 1/9. Give your answer as a fraction in its simplest form.

    [3 marks]

    Answer: ____________________

  4. 3(a) Question 3(a)

    Simplify √50 + √18.

    [2 marks]

    Answer: ____________________

  5. 3(b) Question 3(b)

    Rationalise the denominator of 4/(√5 + 1). Give your answer in its simplest form.

    [3 marks]

    Answer: ____________________

  6. 4(a) Question 4(a)

    Find the value of 272/3.

    [1 mark]

    Answer: ____________________

  7. 4(b) Question 4(b)

    Find the value of 16−12.

    [1 mark]

    Answer: ____________________

  8. 4(c) Question 4(c)

    Simplify (2x³)⁴.

    [2 marks]

    Answer: ____________________

  9. 5 Question 5

    Work out (6 × 10⁵) ÷ (3 × 10⁻²). Give your answer in standard form.

    [2 marks]

    Answer: ____________________

  10. 6 Question 6

    x = 7.2 and y = 3.5, both correct to 1 decimal place. Find the upper bound of x − y.

    [2 marks]

    Answer: ____________________

  11. 7(a) Question 7(a)

    Factorise x² + 2x − 15.

    [2 marks]

    Answer: ____________________

  12. 7(b) Question 7(b)

    Solve 2x² + 5x − 3 = 0 by factorising.

    [3 marks]

    Answer: ____________________

  13. 8 Question 8

    Simplify x² − 9x² + 3x.

    [3 marks]

    Answer: ____________________

  14. 9 Question 9

    Write 2/(x + 1) + 3/(x − 2) as a single fraction in its simplest form.

    [3 marks]

    Answer: ____________________

  15. 10 Question 10

    Solve the simultaneous equations 3x + 2y = 12 and 5x − 2y = 4.

    [3 marks]

    Answer: ____________________

  16. 11 Question 11

    Solve the inequality −3 ≤ 2x + 1 < 7.

    [3 marks]

    Answer: ____________________

  17. f(x) = 2x + 1 and g(x) = x² − 3.

    12(a) Question 12(a)

    Find f(g(2)).

    [2 marks]

    Answer: ____________________

  18. 12(b) Question 12(b)

    h(x) = 3x − 4. Find the inverse function h⁻¹(x).

    [2 marks]

    Answer: ____________________

  19. 13(a) Question 13(a)

    y = 2x³ − 5x² + 4x. Find dy/dx.

    [2 marks]

    Answer: ____________________

  20. 13(b) Question 13(b)

    Find the coordinates of the turning point of y = x² − 6x + 1 and decide whether it is a maximum or a minimum.

    [4 marks]

    Answer: ____________________

  21. 14 Question 14

    Find the nth term of the sequence 3, 8, 15, 24, 35, ...

    [3 marks]

    Answer: ____________________

  22. 15(a) Question 15(a)

    u = (3, −2) and v = (−1, 4) as column vectors. Find 2u − v.

    [2 marks]

    Answer: ____________________

  23. 15(b) Question 15(b)

    OA = a and OB = b. Write the vector AB in terms of a and b.

    [1 mark]

    Answer: ____________________

  24. 16(a) Question 16(a)

    A, B and C are points on a circle, centre O. Angle ACB = 35°. Find angle AOB.

    [2 marks]

    Answer: ____________________

  25. 16(b) Question 16(b)

    ABCD is a cyclic quadrilateral. Angle A = 110°. Find angle C.

    [1 mark]

    Answer: ____________________

  26. 16(c) Question 16(c)

    The line TA is a tangent to a circle at A. B and C are on the circle. The angle between the tangent and AB is 65°. Find angle ACB.

    [2 marks]

    Answer: ____________________

  27. 17 Question 17

    y is inversely proportional to x. y = 6 when x = 4. Find y when x = 3.

    [3 marks]

    Answer: ____________________

  28. 18 Question 18

    A bag has 5 red and 3 blue counters. Two counters are taken at random without replacement. Find the probability that both are red.

    [3 marks]

    Answer: ____________________

  29. 20(a) Question 20(a)

    The point (2, 4) is rotated 90° anticlockwise about the origin. Write down the coordinates of its image.

    [1 mark]

    Answer: ____________________

  30. 20(b) Question 20(b)

    The point (3, 2) is reflected in the line y = x. Write down the coordinates of its image.

    [1 mark]

    Answer: ____________________

  31. 22 Question 22

    Write x² − 6x + 5 in the form (x + a)² + b.

    [2 marks]

    Answer: ____________________

  32. 23 Question 23

    Draw the lines y = 2x − 1 and y = −x + 3 on a grid. Shade the region where y > 2x − 1 and y ≤ −x + 3.

    [3 marks]

  33. 25 Question 25

    Find the equation of the line through (2, 3) that is perpendicular to y = 2x + 1.

    [3 marks]

    Answer: ____________________

  34. 26 Question 26

    Find the distance between the points (−1, 2) and (5, 10).

    [2 marks]

    Answer: ____________________

  35. 27 Question 27

    Two solids are similar. Their lengths are 3 cm and 6 cm. The small solid has volume 20 cm³. Find the volume of the large solid.

    [2 marks]

    Answer: ____________________

  36. 28 Question 28

    Make x the subject of 3x + p = qx − 2.

    [3 marks]

    Answer: ____________________

  37. 29 Question 29

    Expand and simplify (x + 1)(x + 2)(x − 3).

    [3 marks]

    Answer: ____________________

  38. 30 Question 30

    The masses, m kg, of some parcels are grouped: 0 < m ≤ 10: 5, 10 < m ≤ 30: 12, 30 < m ≤ 60: 9. Find the frequency density of each group, for a histogram.

    [2 marks]

  39. 31 Question 31

    A car speeds up from rest to 12 ms in 4 seconds, keeps that speed for 6 seconds, then slows down to rest in 4 seconds. Find the total distance it travels.

    [3 marks]

    Answer: ____________________

  40. 32 Question 32

    Using a ruler and compasses only, construct the locus of points 3 cm from a point A.

    [2 marks]

  41. 34 Question 34

    Solve 12x + 1 = 4.

    [3 marks]

    Answer: ____________________

  42. 35 Question 35

    Solve x² + 6x = 7 by completing the square.

    [3 marks]

    Answer: ____________________

  43. 37 Question 37

    A survey: boys, 12 like cats and 8 like dogs; girls, 10 like cats and 20 like dogs. A girl is chosen at random. Find the probability she likes dogs.

    [2 marks]

    Answer: ____________________

Answers

  1. 1 x = 411
  2. 2(a) 4 112
  3. 2(b) 125
  4. 3(a) 8√2
  5. 3(b) √5 − 1
  6. 4(a) 9
  7. 4(b) 14
  8. 4(c) 16x12
  9. 5 2 × 107
  10. 6 upper bound = 3.8
  11. 7(a) (x − 3)(x + 5)
  12. 7(b) x = 12 or x = −3
  13. 8 x − 3x
  14. 9 5x − 1(x + 1)(x − 2)
  15. 10 (x, y) = (2, 3)
  16. 11 −2 ≤ x < 3
  17. 12(a) f(g(2)) = 3
  18. 12(b) f −1(x) = x + 43
  19. 13(a) f′(x) = 6x2 − 10x + 4
  20. 13(b) min (3, −8)
  21. 14 an = n2 + 2n
  22. 15(a) 2u − v = ⟨7, −8⟩
  23. 15(b) AB = b − a
  24. 16(a) x = 70
  25. 16(b) x = 70
  26. 16(c) angle ACB = 65°
  27. 17 y = 8
  28. 18 P(all red) = 514
  29. 20(a) P' = (−4, 2)
  30. 20(b) P' = (2, 3)
  31. 22 (x − 3)2 − 4
  32. 23 the part shaded twice
  33. 25 y = −12x + 4
  34. 26 d = 10
  35. 27 large volume = 160
  36. 28 x = −2 − p3 − q
  37. 29 x³ − 7x − 6
  38. 30 heights 0.5, 0.6, 0.3
  39. 31 distance = 120 m
  40. 32 points 3 cm from A
  41. 34 x = 4
  42. 35 x = 1 or x = −7
  43. 37 P(dog | girl) = 23

Full mark scheme: steplyclass.com/igcse-maths/extended-paper-2/mark-scheme/

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