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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 7 · 40 questions
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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 mean of 8, 2, 3 and 19? (a) 9 (b) 10 (c) 7 (d) 8
  2. 2.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 5/6 (c) 1/4 (d) 2/3
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 25° (b) 50° (c) 26° (d) 155°
  4. 4.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 15° (c) 30° (d) 105°
  5. 5.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 8 times (d) 4 times
  6. 6.What is the mean of 13, 14, 9, 14 and 10? (a) 12 (b) 10 (c) 13 (d) 15
  7. 7.Two angles of a triangle are 35° and 105°. What is the exterior angle at the third corner? (a) 140° (b) 75° (c) 40° (d) 145°
  8. 8.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  9. 9.A bag has 3 blue balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 4 (c) 5 (d) 12
  10. 10.What is the sum of the first 9 terms of the AP 4, 9, 14, …? (a) 216 (b) 432 (c) 221 (d) 44
  11. 11.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 2 (d) 3
  12. 12.What is the midpoint of the line joining (3, 8) and (9, 6)? (a) (3, 1) (b) (6, 7) (c) (12, 14) (d) (7, 6)
  13. 13.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 5 times (c) 25 times (d) 125 times
  14. 14.The mean of 8 numbers is 10. When the number 28 is added to them, what is the new mean? (a) 19 (b) 10 (c) 13 (d) 12
  15. 15.What is the 21st term of the AP 16, 23, 30, 37, …? (a) 156 (b) 140 (c) 147 (d) 163
  16. 16.In a class of 39 children, 20 like mangoes, 22 like bananas and 5 like neither. How many like both? (a) 5 (b) 34 (c) 3 (d) 8
  17. 17.How many factors does 96 have? (a) 12 (b) 11 (c) 13 (d) 10
  18. 18.What is the prime factorisation of 60? (a) 2 × 3 × 5² (b) 2 × 3 × 5 (c) 2² × 3 × 5 (d) 2³ × 3 × 5
  19. 19.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 75° (b) 76° (c) 105° (d) 255°
  20. 20.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 19 (d) 100
  21. 21.In a class of 22 children, 17 like cricket, 12 like football and 8 like both. How many like neither? (a) 9 (b) 1 (c) 8 (d) 2
  22. 22.What is the prime factorisation of 280? (a) 2³ × 5 × 7 (b) 2² × 5 × 7 (c) 2 × 5 × 7³ (d) 2⁴ × 5 × 7
  23. 23.If a + b = 17 and ab = 60, what is (a − b)²? (a) 169 (b) 289 (c) 7 (d) 49
  24. 24.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 21 (c) 28 (d) 42
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 70° (b) 125° (c) 55° (d) 250°
  26. 26.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 110° (b) 70° (c) 135° (d) 115°
  27. 27.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
  28. 28.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
  29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 5/36 (b) 1/9 (c) 4/11 (d) 1/11
  30. 30.Using (a − b)² = a² − 2ab + b², what is 87²? (a) 7579 (b) 7569 (c) 8649 (d) 8091
  31. 31.What is the 35th term of the AP 18, 20, 22, 24, …? (a) 86 (b) 88 (c) 70 (d) 68
  32. 32.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
  33. 33.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 1/8 (c) 7/8 (d) 1/4
  34. 34.In which quadrant does the point (−2, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  35. 35.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 135° (b) 75° (c) 150° (d) 105°
  36. 36.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 5 times (c) 125 times (d) 25 times
  37. 37.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 171 (c) 342 (d) 324
  38. 38.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 3 (c) 12 (d) 9
  39. 39.A bag has 9 black balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 11 (c) 17 (d) 10
  40. 40.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 40° (b) 140° (c) 220° (d) 41°

Answer key

  1. 8
  2. 2/3
  3. 25°
  4. 30°
  5. 4 times
  6. 12
  7. 140°
  8. 8
  9. 5
  10. 216
  11. 3
  12. (6, 7)
  13. 25 times
  14. 12
  15. 156
  16. 8
  17. 12
  18. 2² × 3 × 5
  19. 75°
  20. 100
  21. 1
  22. 2³ × 5 × 7
  23. 49
  24. 21
  25. 125°
  26. 70°
  27. 1/2
  28. 154 sq cm
  29. 1/9
  30. 7569
  31. 86
  32. 176 cm
  33. 1/8
  34. Second quadrant
  35. 105°
  36. 125 times
  37. 324
  38. 6
  39. 11
  40. 40°

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