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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 140 · 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.The mean of 9 numbers is 18. When the number 38 is added to them, what is the new mean? (a) 18 (b) 21 (c) 28 (d) 20
  2. 2.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 8 (b) 72 (c) 27 (d) 24
  3. 3.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
  4. 4.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 95° (c) 86° (d) 265°
  5. 5.What is the product of the roots of x² − 16x + 63 = 0? (a) 16 (b) 64 (c) 62 (d) 63
  6. 6.What is the sum of all the whole numbers from 1 to 50? (a) 1225 (b) 1250 (c) 1275 (d) 2550
  7. 7.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 64 (c) 28 (d) 56
  8. 8.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 10 times (c) 5 times (d) 25 times
  9. 9.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 10° (b) 11° (c) 160° (d) 20°
  10. 10.What are the roots of x² − 16x + 63 = 0? (a) 1 and 63 (b) 1 and 15 (c) 7 and 9 (d) 3 and 21
  11. 11.In a class of 50 children, 26 like mangoes, 24 like bananas and 10 like both. How many like neither? (a) 0 (b) 20 (c) 11 (d) 10
  12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/11 (b) 1/11 (c) 5/36 (d) 1/6
  13. 13.What is the distance between the points (1, 6) and (8, 30)? (a) 26 (b) 625 (c) 25 (d) 31
  14. 14.What is the 32nd term of the AP 15, 20, 25, 30, …? (a) 175 (b) 160 (c) 155 (d) 170
  15. 15.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 7 (d) 6
  16. 16.Which is the correct factorisation of x² + 11x + 30? (a) (x + 5)(x + 6) (b) (x + 1)(x + 10) (c) (x + 1)(x + 30) (d) (x − 5)(x − 6)
  17. 17.A drawer has lots of white, black, blue, 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) 6 (b) 5 (c) 2 (d) 10
  18. 18.How many prime numbers are there between 10 and 40? (a) 7 (b) 9 (c) 10 (d) 8
  19. 19.How many factors does 80 have? (a) 11 (b) 9 (c) 10 (d) 8
  20. 20.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 9 (d) 7
  21. 21.5 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) 10 (b) 20 (c) 15 (d) 7
  22. 22.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 120° (b) 105° (c) 135° (d) 45°
  23. 23.How many factors does 90 have? (a) 11 (b) 10 (c) 12 (d) 13
  24. 24.What is the prime factorisation of 144? (a) 2² × 3⁴ (b) 2³ × 3² (c) 2⁵ × 3² (d) 2⁴ × 3²
  25. 25.A drawer has lots of red, blue, black and yellow 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) 5 (c) 2 (d) 4
  26. 26.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 1/4 (c) 3/5 (d) 5/8
  27. 27.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  28. 28.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) 21 (d) 28
  29. 29.How many factors does 58 have? (a) 2 (b) 4 (c) 5 (d) 3
  30. 30.In a class of 27 children, 14 like tea, 6 like coffee and 2 like both. How many like neither? (a) 9 (b) 2 (c) 11 (d) 7
  31. 31.A bag has 3 white 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) 4 (c) 10 (d) 2
  32. 32.What is the product of the roots of x² − 13x + 42 = 0? (a) 42 (b) 13 (c) 41 (d) 43
  33. 33.What is the distance between the points (8, 4) and (20, 9)? (a) 169 (b) 14 (c) 17 (d) 13
  34. 34.In a class of 45 children, 21 like dance, 23 like music and 6 like neither. How many like both? (a) 4 (b) 5 (c) 6 (d) 39
  35. 35.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 80° (b) 100° (c) 81° (d) 260°
  36. 36.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 6 (b) 18 (c) 9 (d) 12
  37. 37.In a class of 34 children, 10 like tea, 23 like coffee and 7 like both. How many like at least one of the two? (a) 19 (b) 34 (c) 33 (d) 26
  38. 38.What is the 37th term of the AP 5, 9, 13, 17, …? (a) 153 (b) 144 (c) 149 (d) 148
  39. 39.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/9 (b) 4/11 (c) 5/36 (d) 1/11
  40. 40.How many factors does 38 have? (a) 4 (b) 5 (c) 2 (d) 3

Answer key

  1. 20
  2. 24
  3. 9 times
  4. 85°
  5. 63
  6. 1275
  7. 28
  8. 125 times
  9. 10°
  10. 7 and 9
  11. 10
  12. 5/36
  13. 25
  14. 170
  15. 7
  16. (x + 5)(x + 6)
  17. 6
  18. 8
  19. 10
  20. 8
  21. 10
  22. 45°
  23. 12
  24. 2⁴ × 3²
  25. 5
  26. 3/8
  27. 24
  28. 22
  29. 4
  30. 9
  31. 5
  32. 42
  33. 13
  34. 5
  35. 80°
  36. 9
  37. 26
  38. 149
  39. 1/9
  40. 4

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