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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 229 · 40 questions
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How to solve it (Name the topic, then solve): Name the topic first: angles, counting, worst case, probability, digits, mensuration, data, coordinates, AP, algebra, primes or Venn diagrams. Use that lesson’s method; draw a quick sketch, list or Venn diagram on rough paper. Rule out options of the wrong kind — a probability above 1, or a triangle angle of 180° or more. Check by working backwards or with a second method when you can.

NameDateTime takenScore ___ / 40
  1. 1.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 49 (c) 14 (d) 42
  2. 2.A drawer has lots of yellow, green, white and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 2 (c) 4 (d) 5
  3. 3.4 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 10 (b) 28 (c) 24 (d) 48
  4. 4.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 135° (b) 100° (c) 45° (d) 125°
  5. 5.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 96 cu cm (c) 64 cu cm (d) 12 cu cm
  6. 6.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 9 cu cm (c) 27 cu cm (d) 54 cu cm
  7. 7.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 21 (c) 66 (d) 189
  8. 8.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 90 (b) 45 (c) 13 (d) 50
  9. 9.What is the 39th term of the AP 12, 17, 22, 27, …? (a) 190 (b) 207 (c) 195 (d) 202
  10. 10.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 70° (d) 60°
  11. 11.What is the sum of the roots of x² − 15x + 56 = 0? (a) 14 (b) 15 (c) 56 (d) 16
  12. 12.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  13. 13.In a class of 52 children, 29 like dance, 24 like music and 10 like both. How many like at least one of the two? (a) 33 (b) 52 (c) 53 (d) 43
  14. 14.Using (a + b)² = a² + 2ab + b², what is 62²? (a) 3604 (b) 3854 (c) 3844 (d) 3364
  15. 15.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 35° (b) 145° (c) 105° (d) 110°
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 54? (a) 3 (b) 4 (c) 5 (d) 6
  17. 17.The mean of 7 numbers is 10. When the number 18 is added to them, what is the new mean? (a) 12 (b) 11 (c) 10 (d) 14
  18. 18.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
  19. 19.In a class of 27 children, 19 like dance, 11 like music and 4 like both. How many like at least one of the two? (a) 30 (b) 22 (c) 27 (d) 26
  20. 20.6 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 9 (b) 18 (c) 24 (d) 36
  21. 21.What is the 14th term of the AP 11, 18, 25, 32, …? (a) 91 (b) 109 (c) 102 (d) 98
  22. 22.A cube has edges of 10 cm. What is its total surface area? (a) 100 sq cm (b) 400 sq cm (c) 600 sq cm (d) 1000 sq cm
  23. 23.Which is the correct factorisation of x² + 11x + 18? (a) (x − 2)(x − 9) (b) (x + 2)(x + 9) (c) (x + 1)(x + 18) (d) (x + 1)(x + 10)
  24. 24.What is the prime factorisation of 112? (a) 2 × 7⁴ (b) 2⁴ × 7 (c) 2³ × 7 (d) 2⁵ × 7
  25. 25.What is the prime factorisation of 180? (a) 2 × 3² × 5² (b) 2² × 3² × 5 (c) 2³ × 3² × 5 (d) 2 × 3² × 5
  26. 26.What is the smallest prime factor of 21? (a) 3 (b) 1 (c) 7 (d) 2
  27. 27.A drawer has lots of red, white, black, blue and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 5 (c) 2 (d) 6
  28. 28.What is the sum of all the whole numbers from 1 to 96? (a) 4656 (b) 4608 (c) 4560 (d) 9312
  29. 29.In a class of 21 children, 8 like maths, 7 like science and 8 like neither. How many like both? (a) 8 (b) 13 (c) 2 (d) 3
  30. 30.Which is the correct factorisation of x² + 12x + 32? (a) (x + 4)(x + 8) (b) (x − 4)(x − 8) (c) (x + 1)(x + 32) (d) (x + 1)(x + 11)
  31. 31.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/8 (b) 1/4 (c) 3/8 (d) 7/8
  32. 32.What is the mean of 12, 18, 12 and 14? (a) 13 (b) 16 (c) 14 (d) 15
  33. 33.What is the mode of 3, 14, 17, 3, 17, 3 and 6? (a) 3 (b) 17 (c) 14 (d) 6
  34. 34.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 207 (c) 23 (d) 69
  35. 35.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 135° (b) 45° (c) 105° (d) 120°
  36. 36.What is the mean of 9, 5, 6, 4, 17 and 13? (a) 11 (b) 9 (c) 8 (d) 10
  37. 37.3 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 42 (c) 21 (d) 10
  38. 38.What is the midpoint of the line joining (3, 16) and (5, 6)? (a) (8, 22) (b) (11, 4) (c) (1, 5) (d) (4, 11)
  39. 39.What is the distance between the points (3, 0) and (19, 12)? (a) 20 (b) 400 (c) 28 (d) 21
  40. 40.If a + b = 14 and ab = 48, what is a² + b²? (a) 196 (b) 100 (c) 292 (d) 148

Answer key

  1. 21
  2. 5
  3. 24
  4. 45°
  5. 64 cu cm
  6. 27 cu cm
  7. 63
  8. 45
  9. 202
  10. 60°
  11. 15
  12. 13
  13. 43
  14. 3844
  15. 35°
  16. 5
  17. 11
  18. 1/3
  19. 26
  20. 18
  21. 102
  22. 600 sq cm
  23. (x + 2)(x + 9)
  24. 2⁴ × 7
  25. 2² × 3² × 5
  26. 3
  27. 6
  28. 4656
  29. 2
  30. (x + 4)(x + 8)
  31. 7/8
  32. 14
  33. 3
  34. 69
  35. 45°
  36. 9
  37. 21
  38. (4, 11)
  39. 20
  40. 100

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