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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 628 · 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.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 9 (d) 7
  2. 2.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 65° (b) 245° (c) 115° (d) 66°
  3. 3.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  4. 4.What is the prime factorisation of 90? (a) 2² × 3² × 5 (b) 2 × 3² × 5² (c) 2³ × 3² × 5 (d) 2 × 3² × 5
  5. 5.What is the smallest prime factor of 55? (a) 1 (b) 2 (c) 11 (d) 5
  6. 6.In a class of 27 children, 20 like tea, 15 like coffee and 4 like neither. How many like both? (a) 23 (b) 8 (c) 12 (d) 4
  7. 7.If a + b = 16 and ab = 63, what is a² + b²? (a) 382 (b) 193 (c) 130 (d) 256
  8. 8.In a class of 40 children, 26 like maths, 18 like science and 11 like both. How many like at least one of the two? (a) 40 (b) 22 (c) 44 (d) 33
  9. 9.What is the mean of 20, 15, 5, 6 and 14? (a) 12 (b) 10 (c) 13 (d) 15
  10. 10.A bag has 7 green balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 14 (c) 9 (d) 8
  11. 11.In a class of 43 children, 32 like tea, 18 like coffee and 5 like neither. How many like both? (a) 5 (b) 38 (c) 12 (d) 7
  12. 12.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 240 (c) 20 (d) 25
  13. 13.What is the mean of 7, 16, 10, 20, 14 and 5? (a) 12 (b) 14 (c) 13 (d) 11
  14. 14.A canteen sells 3 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 21 (c) 36 (d) 18
  15. 15.The mean of 9 numbers is 31. When the number 41 is added to them, what is the new mean? (a) 36 (b) 31 (c) 32 (d) 33
  16. 16.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  17. 17.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 65° (b) 35° (c) 150° (d) 145°
  18. 18.Two angles of a triangle are 60° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 70° (c) 110° (d) 120°
  19. 19.Using (a − b)² = a² − 2ab + b², what is 35²? (a) 2025 (b) 1575 (c) 1225 (d) 1235
  20. 20.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 5/8 (c) 1/4 (d) 3/5
  21. 21.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) 9 (c) 12 (d) 6
  22. 22.In a class of 25 children, 18 like tea, 16 like coffee and 12 like both. How many like at least one of the two? (a) 34 (b) 25 (c) 10 (d) 22
  23. 23.Which is the correct factorisation of x² + 12x + 27? (a) (x − 3)(x − 9) (b) (x + 1)(x + 27) (c) (x + 1)(x + 11) (d) (x + 3)(x + 9)
  24. 24.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 108 (b) 60 (c) 14 (d) 54
  25. 25.What is the mean of 14, 13, 20, 6, 4 and 9? (a) 13 (b) 10 (c) 12 (d) 11
  26. 26.What is the prime factorisation of 30? (a) 2² × 3 × 5 (b) 2 × 3 × 5² (c) 2³ × 3 × 5 (d) 2 × 3 × 5
  27. 27.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
  28. 28.A bag has 4 white balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 6 (c) 13 (d) 5
  29. 29.What is the 11th term of the AP 3, 8, 13, 18, …? (a) 50 (b) 55 (c) 53 (d) 58
  30. 30.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) 36 (b) 48 (c) 49 (d) 37
  31. 31.A bag has 10 white balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 8 (c) 17 (d) 2
  32. 32.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/9 (b) 1/11 (c) 5/36 (d) 4/11
  33. 33.How many factors does 76 have? (a) 4 (b) 7 (c) 5 (d) 6
  34. 34.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 10 (c) 20 (d) 11
  35. 35.In a class of 46 children, 23 like dance, 25 like music and 6 like both. How many like neither? (a) 10 (b) 6 (c) 5 (d) 4
  36. 36.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
  37. 37.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 9 (c) 27 (d) 30
  38. 38.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°
  39. 39.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 65° (c) 25° (d) 130°
  40. 40.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 6 (c) 9 (d) 3

Answer key

  1. 8
  2. 65°
  3. 6
  4. 2 × 3² × 5
  5. 5
  6. 12
  7. 130
  8. 33
  9. 12
  10. 9
  11. 12
  12. 120
  13. 12
  14. 18
  15. 32
  16. 20
  17. 35°
  18. 110°
  19. 1225
  20. 3/8
  21. 6
  22. 22
  23. (x + 3)(x + 9)
  24. 54
  25. 11
  26. 2 × 3 × 5
  27. 1/2
  28. 6
  29. 53
  30. 37
  31. 11
  32. 1/9
  33. 6
  34. 10
  35. 4
  36. 15
  37. 27
  38. 160°
  39. 130°
  40. 6

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