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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 36 · 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.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 45° (c) 90° (d) 55°
  2. 2.What is the product of the roots of x² − 10x + 24 = 0? (a) 10 (b) 24 (c) 25 (d) 23
  3. 3.What is the missing term in the AP 17, 22, ?, 32, 37? (a) 32 (b) 26 (c) 28 (d) 27
  4. 4.What is the distance between the points (4, 1) and (20, 13)? (a) 21 (b) 400 (c) 20 (d) 28
  5. 5.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/11 (c) 1/12 (d) 1/18
  7. 7.What is the mode of 20, 20, 18, 15, 20, 5 and 5? (a) 5 (b) 15 (c) 20 (d) 18
  8. 8.In a class of 23 children, 13 like tea, 15 like coffee and 7 like both. How many like only tea? (a) 6 (b) 7 (c) 8 (d) 13
  9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/11 (b) 6/11 (c) 1/6 (d) 7/36
  10. 10.Two angles of a triangle are 20° and 20°. What is the third angle? (a) 160° (b) 140° (c) 320° (d) 40°
  11. 11.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  12. 12.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 300 (c) 576 (d) 600
  13. 13.What is the midpoint of the line joining (4, 3) and (8, 15)? (a) (12, 18) (b) (9, 6) (c) (6, 9) (d) (2, 6)
  14. 14.In which quadrant does the point (−3, −6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  15. 15.A bag has 9 white, 5 yellow and 8 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 7/11 (b) 1/3 (c) 4/11 (d) 15/22
  16. 16.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 3850 cm (d) 220 cm
  17. 17.How many prime numbers are there between 70 and 90? (a) 4 (b) 7 (c) 6 (d) 5
  18. 18.In a class of 50 children, 26 like tea, 23 like coffee and 6 like both. How many like only tea? (a) 26 (b) 27 (c) 17 (d) 20
  19. 19.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 20 (c) 25 (d) 11
  20. 20.Which is the correct factorisation of x² + 6x + 8? (a) (x + 2)(x + 4) (b) (x + 1)(x + 8) (c) (x − 2)(x − 4) (d) (x + 1)(x + 5)
  21. 21.In a class of 40 children, 18 like maths, 22 like science and 9 like neither. How many like both? (a) 31 (b) 10 (c) 8 (d) 9
  22. 22.What is the distance between the points (9, 6) and (21, 22)? (a) 28 (b) 400 (c) 20 (d) 21
  23. 23.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 91 (b) 16 (c) 92 (d) 182
  24. 24.What is the 16th term of the AP 6, 12, 18, 24, …? (a) 102 (b) 90 (c) 96 (d) 97
  25. 25.What is the smallest prime factor of 95? (a) 1 (b) 5 (c) 19 (d) 2
  26. 26.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/11 (b) 3/11 (c) 1/12 (d) 1/9
  27. 27.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  28. 28.In a league, 11 teams each play every other team once. How many matches are played? (a) 55 (b) 66 (c) 110 (d) 121
  29. 29.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 65° (c) 40° (d) 130°
  30. 30.What is the 13th term of the AP 11, 13, 15, 17, …? (a) 24 (b) 37 (c) 35 (d) 26
  31. 31.What is the prime factorisation of 336? (a) 2⁴ × 3 × 7 (b) 2 × 3 × 7⁴ (c) 2⁵ × 3 × 7 (d) 2³ × 3 × 7
  32. 32.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 35° (c) 110° (d) 55°
  33. 33.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
  34. 34.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 279 (c) 270 (d) 258
  35. 35.What is the mode of 18, 11, 16, 16, 5, 5 and 16? (a) 5 (b) 18 (c) 11 (d) 16
  36. 36.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
  37. 37.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 15 (b) 8 (c) 7 (d) 14
  38. 38.In a class of 32 children, 19 like tea, 14 like coffee and 2 like neither. How many like both? (a) 2 (b) 1 (c) 3 (d) 30
  39. 39.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) 29 (b) 21 (c) 22 (d) 28
  40. 40.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 784 (c) 406 (d) 55

Answer key

  1. 45°
  2. 24
  3. 27
  4. 20
  5. 24
  6. 1/18
  7. 20
  8. 6
  9. 1/6
  10. 140°
  11. 6
  12. 576
  13. (6, 9)
  14. Third quadrant
  15. 7/11
  16. 220 cm
  17. 5
  18. 20
  19. 10
  20. (x + 2)(x + 4)
  21. 9
  22. 20
  23. 91
  24. 96
  25. 5
  26. 1/12
  27. 10
  28. 55
  29. 65°
  30. 35
  31. 2⁴ × 3 × 7
  32. 110°
  33. 88 cm
  34. 279
  35. 16
  36. 1/2
  37. 8
  38. 3
  39. 22
  40. 784

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