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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 641 · 40 questions
TalentJR

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.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 49 (b) 48 (c) 37 (d) 36
  2. 2.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 90° (c) 91° (d) 135°
  3. 3.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 6 (c) 3 (d) 12
  4. 4.What is the mode of 2, 2, 5, 7, 20, 20 and 20? (a) 2 (b) 5 (c) 7 (d) 20
  5. 5.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
  6. 6.What is the 13th term of the AP 2, 6, 10, 14, …? (a) 48 (b) 50 (c) 54 (d) 52
  7. 7.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 6 (c) 5 (d) 9
  8. 8.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
  9. 9.A drawer has lots of black, white, red, green and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 10 (c) 6 (d) 2
  10. 10.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 91 (c) 78 (d) 156
  11. 11.A cuboid is 9 cm long, 8 cm wide and 2 cm high. What is its total surface area? (a) 212 sq cm (b) 144 sq cm (c) 424 sq cm (d) 106 sq cm
  12. 12.In a class of 25 children, 10 like maths, 10 like science and 5 like both. How many like neither? (a) 11 (b) 15 (c) 5 (d) 10
  13. 13.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 12 (c) 6 (d) 5
  14. 14.In a class of 33 children, 12 like cricket, 25 like football and 4 like neither. How many like both? (a) 8 (b) 4 (c) 29 (d) 9
  15. 15.How many factors does 50 have? (a) 4 (b) 6 (c) 5 (d) 7
  16. 16.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 28 (c) 56 (d) 64
  17. 17.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 230° (b) 50° (c) 51° (d) 130°
  18. 18.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
  19. 19.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
  20. 20.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 120° (c) 30° (d) 60°
  21. 21.What is the median of 5, 24, 25, 33 and 8? (a) 8 (b) 19 (c) 24 (d) 25
  22. 22.Which is the correct factorisation of x² + 12x + 32? (a) (x + 1)(x + 11) (b) (x − 4)(x − 8) (c) (x + 4)(x + 8) (d) (x + 1)(x + 32)
  23. 23.Two angles of a triangle are 25° and 95°. What is the third angle? (a) 85° (b) 155° (c) 120° (d) 60°
  24. 24.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 100° (b) 30° (c) 150° (d) 110°
  25. 25.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 1/3 (c) 2/3 (d) 5/6
  26. 26.What is the smallest prime factor of 319? (a) 2 (b) 11 (c) 1 (d) 29
  27. 27.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
  28. 28.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
  29. 29.A bag has 6 blue balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 16 (b) 11 (c) 2 (d) 7
  30. 30.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 140° (b) 60° (c) 100° (d) 120°
  31. 31.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/36 (c) 1/12 (d) 1/18
  32. 32.Two angles of a triangle are 25° and 110°. What is the third angle? (a) 135° (b) 70° (c) 45° (d) 155°
  33. 33.What is the 29th term of the AP 1, 8, 15, 22, …? (a) 196 (b) 203 (c) 204 (d) 197
  34. 34.What is the missing term in the AP 15, 17, 19, ?, 23? (a) 22 (b) 20 (c) 23 (d) 21
  35. 35.How many factors does 20 have? (a) 5 (b) 4 (c) 7 (d) 6
  36. 36.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 162 (c) 18 (d) 54
  37. 37.8 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 16 (b) 32 (c) 10 (d) 24
  38. 38.What is the median of 38, 31, 25, 36 and 7? (a) 36 (b) 31 (c) 25 (d) 32
  39. 39.In a class of 36 children, 20 like maths, 23 like science and 11 like both. How many like only maths? (a) 13 (b) 20 (c) 12 (d) 9
  40. 40.If a + b = 19 and ab = 88, what is a² + b²? (a) 273 (b) 185 (c) 537 (d) 361

Answer key

  1. 37
  2. 90°
  3. 6
  4. 20
  5. 4 times
  6. 50
  7. 6
  8. 1/2
  9. 6
  10. 78
  11. 212 sq cm
  12. 10
  13. 6
  14. 8
  15. 6
  16. 28
  17. 50°
  18. 1/2
  19. 1386 sq cm
  20. 30°
  21. 24
  22. (x + 4)(x + 8)
  23. 60°
  24. 150°
  25. 2/3
  26. 11
  27. 88 cm
  28. 8
  29. 11
  30. 60°
  31. 1/36
  32. 45°
  33. 197
  34. 21
  35. 6
  36. 54
  37. 16
  38. 31
  39. 9
  40. 185

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