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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 39 · 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 distance between the points (0, 2) and (6, 10)? (a) 100 (b) 10 (c) 14 (d) 11
  2. 2.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 15 (b) 5 (c) 18 (d) 45
  3. 3.What is the mean of 18, 5, 12, 11, 12 and 8? (a) 13 (b) 11 (c) 10 (d) 12
  4. 4.What is the product of the roots of x² − 12x + 32 = 0? (a) 31 (b) 33 (c) 12 (d) 32
  5. 5.How many factors does 14 have? (a) 3 (b) 2 (c) 4 (d) 5
  6. 6.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 25 (b) 13 (c) 12 (d) 24
  7. 7.What is the smallest prime factor of 49? (a) 3 (b) 2 (c) 7 (d) 1
  8. 8.How many prime numbers are there between 60 and 90? (a) 9 (b) 7 (c) 6 (d) 8
  9. 9.Two angles of a triangle are 60° and 25°. What is the exterior angle at the third corner? (a) 95° (b) 155° (c) 85° (d) 120°
  10. 10.Using (a − b)² = a² − 2ab + b², what is 59²? (a) 3481 (b) 3599 (c) 3491 (d) 3721
  11. 11.What is the mean of 16, 12, 20, 17, 16 and 3? (a) 13 (b) 12 (c) 15 (d) 14
  12. 12.What is the midpoint of the line joining (6, 6) and (8, 16)? (a) (14, 22) (b) (1, 5) (c) (7, 11) (d) (11, 7)
  13. 13.A canteen sells 6 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 48 (c) 10 (d) 24
  14. 14.What is the mean of 13, 8, 7 and 12? (a) 8 (b) 10 (c) 9 (d) 11
  15. 15.Which is the correct factorisation of x² + 13x + 36? (a) (x + 1)(x + 12) (b) (x + 1)(x + 36) (c) (x − 4)(x − 9) (d) (x + 4)(x + 9)
  16. 16.What is the distance between the points (6, 17) and (14, 2)? (a) 23 (b) 17 (c) 289 (d) 18
  17. 17.Using (a − b)² = a² − 2ab + b², what is 39²? (a) 1681 (b) 1521 (c) 1599 (d) 1531
  18. 18.7 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) 28 (b) 21 (c) 42 (d) 10
  19. 19.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) 12 (c) 9 (d) 6
  20. 20.What is the distance between the points (1, 12) and (6, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  21. 21.In a class of 34 children, 25 like tea, 18 like coffee and 11 like both. How many like at least one of the two? (a) 34 (b) 43 (c) 21 (d) 32
  22. 22.What is the median of 32, 11, 21, 27, 19, 12 and 4? (a) 19 (b) 27 (c) 18 (d) 21
  23. 23.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 18 (b) 270 (c) 140 (d) 135
  24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/9 (b) 1/12 (c) 1/11 (d) 3/11
  25. 25.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 105 (c) 225 (d) 120
  26. 26.What is the sum of all the whole numbers from 1 to 51? (a) 2652 (b) 1327 (c) 1326 (d) 1275
  27. 27.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 36 (c) 12 (d) 15
  28. 28.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  29. 29.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  30. 30.How many factors does 98 have? (a) 7 (b) 6 (c) 5 (d) 4
  31. 31.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 81 (c) 36 (d) 45
  32. 32.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 70° (c) 50° (d) 140°
  33. 33.Two angles of a triangle are 40° and 105°. What is the exterior angle at the third corner? (a) 35° (b) 140° (c) 145° (d) 75°
  34. 34.What is the 10th term of the AP 1, 5, 9, 13, …? (a) 40 (b) 37 (c) 41 (d) 36
  35. 35.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 28 (c) 21 (d) 49
  36. 36.What is the missing term in the AP 19, 26, ?, 40, 47? (a) 33 (b) 40 (c) 34 (d) 32
  37. 37.A drawer has lots of green, black, red 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) 2 (c) 8 (d) 4
  38. 38.In a class of 27 children, 14 like maths, 9 like science and 4 like both. How many like only maths? (a) 14 (b) 18 (c) 5 (d) 10
  39. 39.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 60 (c) 20 (d) 63
  40. 40.In a class of 51 children, 29 like cricket, 25 like football and 9 like both. How many like at least one of the two? (a) 54 (b) 36 (c) 45 (d) 51

Answer key

  1. 10
  2. 15
  3. 11
  4. 32
  5. 4
  6. 13
  7. 7
  8. 7
  9. 85°
  10. 3481
  11. 14
  12. (7, 11)
  13. 24
  14. 10
  15. (x + 4)(x + 9)
  16. 17
  17. 1521
  18. 21
  19. 6
  20. 13
  21. 32
  22. 19
  23. 135
  24. 1/12
  25. 105
  26. 1326
  27. 30
  28. 120
  29. 5
  30. 6
  31. 36
  32. 70°
  33. 145°
  34. 37
  35. 21
  36. 33
  37. 5
  38. 10
  39. 60
  40. 45

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