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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 104 · 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.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 6 (d) 15
  2. 2.In a class of 37 children, 16 like mangoes, 21 like bananas and 9 like both. How many like at least one of the two? (a) 19 (b) 28 (c) 37 (d) 29
  3. 3.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
  4. 4.What is the mode of 8, 11, 8, 12, 12, 7 and 12? (a) 11 (b) 8 (c) 7 (d) 12
  5. 5.What is the median of 32, 28, 36, 17 and 20? (a) 28 (b) 36 (c) 32 (d) 20
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 140° (b) 70° (c) 110° (d) 71°
  7. 7.In a league, 8 teams each play every other team once. How many matches are played? (a) 36 (b) 56 (c) 28 (d) 64
  8. 8.What is the distance between the points (4, 8) and (10, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  9. 9.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
  10. 10.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 36 (c) 11 (d) 21
  11. 11.What is the sum of the roots of x² − 14x + 48 = 0? (a) 14 (b) 13 (c) 15 (d) 48
  12. 12.If a + b = 12 and ab = 20, what is a² + b²? (a) 144 (b) 184 (c) 124 (d) 104
  13. 13.Which term of the AP 19, 25, 31, 37, … is 109? (a) 16th (b) 18th (c) 17th (d) 15th
  14. 14.How many factors does 27 have? (a) 5 (b) 3 (c) 2 (d) 4
  15. 15.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 130° (c) 155° (d) 25°
  16. 16.What is the 38th term of the AP 4, 11, 18, 25, …? (a) 266 (b) 259 (c) 270 (d) 263
  17. 17.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 156 (c) 169 (d) 78
  18. 18.What is the mode of 10, 12, 17, 12, 10, 12 and 18? (a) 10 (b) 18 (c) 17 (d) 12
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 70° (b) 40° (c) 220° (d) 110°
  20. 20.What is the distance between the points (5, 9) and (8, 13)? (a) 7 (b) 25 (c) 6 (d) 5
  21. 21.What is the prime factorisation of 168? (a) 2² × 3 × 7 (b) 2⁴ × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7³
  22. 22.What is the midpoint of the line joining (7, 6) and (15, 14)? (a) (11, 10) (b) (4, 4) (c) (10, 11) (d) (22, 20)
  23. 23.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 20 (c) 100 (d) 90
  24. 24.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2² × 5 × 7 (c) 2 × 5 × 7³ (d) 2³ × 5 × 7
  25. 25.What is the missing term in the AP 5, 11, 17, ?, 29? (a) 23 (b) 22 (c) 29 (d) 24
  26. 26.In a class of 37 children, 24 like tea, 15 like coffee and 12 like both. How many like only tea? (a) 3 (b) 22 (c) 24 (d) 12
  27. 27.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/6 (b) 5/36 (c) 1/11 (d) 5/11
  28. 28.Using (a + b)² = a² + 2ab + b², what is 61²? (a) 3721 (b) 3601 (c) 3731 (d) 3481
  29. 29.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 27 cu cm (c) 36 cu cm (d) 54 cu cm
  30. 30.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 72 (c) 45 (d) 81
  31. 31.4 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) 12 (b) 6 (c) 16 (d) 8
  32. 32.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/8 (b) 3/8 (c) 3/4 (d) 1/4
  33. 33.What is the mode of 10, 11, 18, 11, 17, 17 and 17? (a) 10 (b) 18 (c) 11 (d) 17
  34. 34.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  35. 35.A bag has 8 green balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 9 (b) 10 (c) 11 (d) 2
  36. 36.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/11 (c) 1/9 (d) 1/12
  37. 37.In a class of 29 children, 13 like cricket, 14 like football and 3 like both. How many like neither? (a) 8 (b) 2 (c) 5 (d) 3
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 8 (b) 4 (c) 6 (d) 9
  39. 39.What is the mean of 20, 11, 20, 3 and 6? (a) 12 (b) 10 (c) 13 (d) 15
  40. 40.If a + b = 18 and ab = 80, what is a² + b²? (a) 244 (b) 484 (c) 324 (d) 164

Answer key

  1. 5
  2. 28
  3. 88 cm
  4. 12
  5. 28
  6. 70°
  7. 28
  8. 10
  9. 1/2
  10. 36
  11. 14
  12. 104
  13. 16th
  14. 4
  15. 130°
  16. 263
  17. 78
  18. 12
  19. 110°
  20. 5
  21. 2³ × 3 × 7
  22. (11, 10)
  23. 90
  24. 2³ × 5 × 7
  25. 23
  26. 12
  27. 5/36
  28. 3721
  29. 27 cu cm
  30. 36
  31. 8
  32. 3/4
  33. 17
  34. 6
  35. 10
  36. 1/12
  37. 5
  38. 8
  39. 12
  40. 164

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