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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 52 · 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.What is the smallest prime factor of 65? (a) 2 (b) 5 (c) 1 (d) 13
  2. 2.What is the distance between the points (2, 0) and (17, 8)? (a) 23 (b) 289 (c) 18 (d) 17
  3. 3.What is the sum of the first 7 terms of the AP 5, 8, 11, …? (a) 101 (b) 23 (c) 98 (d) 196
  4. 4.Which is the correct factorisation of x² + 13x + 42? (a) (x + 6)(x + 7) (b) (x + 1)(x + 42) (c) (x − 6)(x − 7) (d) (x + 1)(x + 12)
  5. 5.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 9 times (d) 6 times
  6. 6.What is the distance between the points (8, 2) and (12, 5)? (a) 25 (b) 6 (c) 7 (d) 5
  7. 7.A bag has 9 black balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 20 (b) 10 (c) 11 (d) 2
  8. 8.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
  9. 9.A bag has 3 green, 3 red and 4 blue balls. One ball is taken out without looking. What is the probability that it is green? (a) 7/10 (b) 3/7 (c) 3/10 (d) 1/3
  10. 10.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 50° (c) 100° (d) 40°
  11. 11.How many prime numbers are there between 70 and 100? (a) 7 (b) 5 (c) 8 (d) 6
  12. 12.What is the sum of the first 7 terms of the AP 9, 11, 13, …? (a) 105 (b) 112 (c) 21 (d) 210
  13. 13.How many factors does 73 have? (a) 3 (b) 2 (c) 4 (d) 1
  14. 14.Two angles of a triangle are 80° and 50°. What is the third angle? (a) 230° (b) 50° (c) 100° (d) 130°
  15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 1/11 (c) 1/9 (d) 3/11
  16. 16.What is the mode of 18, 1, 8, 8, 8, 5 and 5? (a) 5 (b) 1 (c) 8 (d) 18
  17. 17.A drawer has lots of black, yellow, blue, red and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 5 (c) 6 (d) 10
  18. 18.What is the missing term in the AP 15, 18, 21, ?, 27? (a) 23 (b) 25 (c) 24 (d) 27
  19. 19.A bag has 8 yellow balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 13 (c) 20 (d) 9
  20. 20.Which is the correct factorisation of x² + 8x + 12? (a) (x + 1)(x + 7) (b) (x − 2)(x − 6) (c) (x + 1)(x + 12) (d) (x + 2)(x + 6)
  21. 21.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 1/4 (c) 1/3 (d) 3/4
  22. 22.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
  23. 23.What is the mean of 7, 3, 16, 7 and 7? (a) 7 (b) 8 (c) 10 (d) 9
  24. 24.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 94? (a) 15 (b) 12 (c) 9 (d) 14
  26. 26.What is the sum of the first 7 terms of the AP 5, 6, 7, …? (a) 11 (b) 57 (c) 56 (d) 112
  27. 27.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  28. 28.In a class of 47 children, 23 like maths, 29 like science and 5 like neither. How many like both? (a) 11 (b) 5 (c) 10 (d) 42
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 16 (b) 14 (c) 15 (d) 4
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 1 (b) 2 (c) 3 (d) 4
  31. 31.Two angles of a triangle are 45° and 35°. What is the exterior angle at the third corner? (a) 135° (b) 100° (c) 80° (d) 145°
  32. 32.A bag has 4 yellow balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 6 (c) 5 (d) 2
  33. 33.A bag has 3 blue balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 4 (c) 5 (d) 15
  34. 34.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
  35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 1/6 (c) 1/11 (d) 7/36
  36. 36.What is the mean of 20, 11, 2, 11, 18 and 10? (a) 13 (b) 11 (c) 14 (d) 12
  37. 37.In a class of 24 children, 8 like maths, 11 like science and 7 like neither. How many like both? (a) 3 (b) 2 (c) 7 (d) 17
  38. 38.Which term of the AP 1, 6, 11, 16, … is 146? (a) 32nd (b) 29th (c) 31st (d) 30th
  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) 22 (c) 28 (d) 21
  40. 40.A bag has 12 green balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 14 (b) 21 (c) 2 (d) 13

Answer key

  1. 5
  2. 17
  3. 98
  4. (x + 6)(x + 7)
  5. 9 times
  6. 5
  7. 11
  8. 1/2
  9. 3/10
  10. 100°
  11. 6
  12. 105
  13. 2
  14. 50°
  15. 1/12
  16. 8
  17. 6
  18. 24
  19. 13
  20. (x + 2)(x + 6)
  21. 3/4
  22. 27 times
  23. 8
  24. 5
  25. 14
  26. 56
  27. 120
  28. 10
  29. 15
  30. 3
  31. 80°
  32. 6
  33. 5
  34. 2464 sq cm
  35. 1/6
  36. 12
  37. 2
  38. 30th
  39. 22
  40. 14

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