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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 713 · 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.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 66 (c) 132 (d) 24
  2. 2.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/4 (c) 2/3 (d) 1/3
  3. 3.In a class of 26 children, 7 like tea, 17 like coffee and 4 like both. How many like at least one of the two? (a) 20 (b) 26 (c) 24 (d) 16
  4. 4.What is the midpoint of the line joining (1, 15) and (13, 7)? (a) (6, 4) (b) (14, 22) (c) (11, 7) (d) (7, 11)
  5. 5.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 110° (b) 70° (c) 150° (d) 100°
  6. 6.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  7. 7.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 54 (c) 6 (d) 21
  8. 8.In a class of 43 children, 28 like mangoes, 23 like bananas and 12 like both. How many like only mangoes? (a) 20 (b) 28 (c) 16 (d) 11
  9. 9.What are the roots of x² − 17x + 72 = 0? (a) 2 and 36 (b) 8 and 9 (c) 1 and 16 (d) 1 and 72
  10. 10.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 115° (b) 85° (c) 95° (d) 150°
  11. 11.A drawer has lots of blue, black, green and white 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
  12. 12.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 75 (c) 72 (d) 24
  13. 13.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 135° (d) 150°
  14. 14.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 120 (c) 105 (d) 225
  15. 15.What is the smallest prime factor of 143? (a) 1 (b) 11 (c) 13 (d) 2
  16. 16.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
  17. 17.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) 5 (b) 6 (c) 9 (d) 12
  18. 18.What is the sum of the roots of x² − 15x + 56 = 0? (a) 16 (b) 56 (c) 14 (d) 15
  19. 19.How many prime numbers are there between 50 and 60? (a) 3 (b) 2 (c) 1 (d) 4
  20. 20.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
  21. 21.Two angles of a triangle are 20° and 110°. What is the third angle? (a) 130° (b) 50° (c) 160° (d) 70°
  22. 22.What is the missing term in the AP 4, 6, 8, ?, 12? (a) 9 (b) 10 (c) 11 (d) 12
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 13 (b) 15 (c) 4 (d) 14
  24. 24.What is the mean of 9, 8, 11, 3 and 14? (a) 9 (b) 8 (c) 11 (d) 10
  25. 25.What is the midpoint of the line joining (10, 12) and (14, 4)? (a) (12, 8) (b) (8, 12) (c) (2, 4) (d) (24, 16)
  26. 26.Which is the correct factorisation of x² + 6x + 8? (a) (x + 2)(x + 4) (b) (x + 1)(x + 8) (c) (x − 2)(x − 4) (d) (x + 1)(x + 5)
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 20 (b) 8 (c) 18 (d) 19
  28. 28.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 6 (d) 10
  29. 29.What is the sum of the first 8 terms of the AP 1, 6, 11, …? (a) 168 (b) 36 (c) 296 (d) 148
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 21 (b) 19 (c) 9 (d) 20
  31. 31.Two angles of a triangle are 50° and 65°. What is the exterior angle at the third corner? (a) 245° (b) 65° (c) 130° (d) 115°
  32. 32.Which is the correct factorisation of x² + 8x + 15? (a) (x + 1)(x + 15) (b) (x − 3)(x − 5) (c) (x + 1)(x + 7) (d) (x + 3)(x + 5)
  33. 33.What is the mode of 20, 18, 2, 15, 18, 2 and 2? (a) 20 (b) 15 (c) 18 (d) 2
  34. 34.4 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) 11 (b) 32 (c) 56 (d) 28
  35. 35.How many factors does 43 have? (a) 1 (b) 4 (c) 3 (d) 2
  36. 36.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 9 (d) 12
  37. 37.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  38. 38.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 25 (c) 37 (d) 24
  39. 39.What is the mode of 2, 16, 15, 12, 16, 12 and 16? (a) 15 (b) 12 (c) 2 (d) 16
  40. 40.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 22 (c) 55 (d) 110

Answer key

  1. 66
  2. 1/2
  3. 20
  4. (7, 11)
  5. 70°
  6. 8
  7. 18
  8. 16
  9. 8 and 9
  10. 85°
  11. 5
  12. 72
  13. 75°
  14. 105
  15. 11
  16. 1/3
  17. 6
  18. 15
  19. 2
  20. 88 cm
  21. 50°
  22. 10
  23. 14
  24. 9
  25. (12, 8)
  26. (x + 2)(x + 4)
  27. 19
  28. 5
  29. 148
  30. 20
  31. 115°
  32. (x + 3)(x + 5)
  33. 2
  34. 28
  35. 2
  36. 8
  37. 9
  38. 25
  39. 16
  40. 110

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