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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 112 · 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 cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 864 cu cm (c) 576 cu cm (d) 36 cu cm
  2. 2.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 50° (c) 140° (d) 40°
  3. 3.What is the sum of the roots of x² − 16x + 63 = 0? (a) 17 (b) 15 (c) 63 (d) 16
  4. 4.How many factors does 45 have? (a) 7 (b) 6 (c) 5 (d) 4
  5. 5.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 88 sq cm (d) 2464 sq cm
  6. 6.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 12 (c) 3 (d) 9
  7. 7.What is the smallest prime factor of 87? (a) 29 (b) 2 (c) 3 (d) 1
  8. 8.In a class of 41 children, 20 like maths, 24 like science and 12 like both. How many like neither? (a) 21 (b) 12 (c) 10 (d) 9
  9. 9.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 4 times (c) 6 times (d) 8 times
  10. 10.What is the smallest prime factor of 133? (a) 19 (b) 1 (c) 7 (d) 2
  11. 11.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  12. 12.A drawer has lots of black, yellow and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 6 (c) 3 (d) 4
  13. 13.How many factors does 52 have? (a) 7 (b) 6 (c) 4 (d) 5
  14. 14.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 14 (d) 7
  15. 15.What is the mean of 6, 17, 3, 4 and 20? (a) 11 (b) 10 (c) 9 (d) 12
  16. 16.In a class of 38 children, 21 like cricket, 10 like football and 10 like neither. How many like both? (a) 10 (b) 4 (c) 28 (d) 3
  17. 17.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 105° (c) 30° (d) 75°
  18. 18.Which is the correct factorisation of x² + 15x + 56? (a) (x + 7)(x + 8) (b) (x + 1)(x + 56) (c) (x + 1)(x + 14) (d) (x − 7)(x − 8)
  19. 19.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 72 (b) 14 (c) 138 (d) 69
  20. 20.A drawer has lots of yellow and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 5 (c) 3 (d) 2
  21. 21.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 3 (c) 9 (d) 6
  22. 22.What is the distance between the points (6, 1) and (18, 10)? (a) 225 (b) 16 (c) 15 (d) 21
  23. 23.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
  24. 24.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 22 (b) 29 (c) 28 (d) 21
  25. 25.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 20 (c) 21 (d) 25
  26. 26.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
  27. 27.A bag has 4 blue balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 5 (b) 11 (c) 2 (d) 6
  28. 28.A drawer has lots of white, yellow, black and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 2 (c) 8 (d) 5
  29. 29.How many factors does 74 have? (a) 4 (b) 5 (c) 2 (d) 3
  30. 30.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/3 (c) 1/2 (d) 1/4
  31. 31.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 16) (b) (x − 8)(x − 9) (c) (x + 1)(x + 72) (d) (x + 8)(x + 9)
  32. 32.If a + b = 15 and ab = 44, what is a² + b²? (a) 137 (b) 225 (c) 181 (d) 313
  33. 33.Two angles of a triangle are 30° and 80°. What is the third angle? (a) 100° (b) 150° (c) 70° (d) 110°
  34. 34.If a + b = 11 and ab = 10, what is a² + b²? (a) 111 (b) 101 (c) 121 (d) 141
  35. 35.What is the distance between the points (6, 8) and (30, 1)? (a) 25 (b) 625 (c) 31 (d) 26
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 20° (b) 140° (c) 320° (d) 160°
  37. 37.What is the median of 36, 5, 31, 27 and 2? (a) 27 (b) 31 (c) 5 (d) 28
  38. 38.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 31° (b) 30° (c) 150° (d) 210°
  39. 39.In a class of 33 children, 19 like mangoes, 14 like bananas and 2 like both. How many like neither? (a) 3 (b) 4 (c) 2 (d) 0
  40. 40.A cuboid is 12 cm long, 6 cm wide and 2 cm high. What is its total surface area? (a) 108 sq cm (b) 216 sq cm (c) 144 sq cm (d) 432 sq cm

Answer key

  1. 1728 cu cm
  2. 70°
  3. 16
  4. 6
  5. 616 sq cm
  6. 6
  7. 3
  8. 9
  9. 8 times
  10. 7
  11. 120
  12. 4
  13. 6
  14. 6
  15. 10
  16. 3
  17. 30°
  18. (x + 7)(x + 8)
  19. 69
  20. 3
  21. 6
  22. 15
  23. 1/3
  24. 22
  25. 20
  26. 44 cm
  27. 6
  28. 5
  29. 4
  30. 1/4
  31. (x + 8)(x + 9)
  32. 137
  33. 70°
  34. 101
  35. 25
  36. 160°
  37. 27
  38. 30°
  39. 2
  40. 216 sq cm

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