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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 207 · 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.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 32 (c) 16 (d) 20
  2. 2.What is the distance between the points (9, 1) and (25, 13)? (a) 20 (b) 28 (c) 400 (d) 21
  3. 3.If a + b = 12 and ab = 27, what is a² + b²? (a) 198 (b) 144 (c) 117 (d) 90
  4. 4.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  5. 5.5 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) 10 (b) 20 (c) 15 (d) 7
  6. 6.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
  7. 7.The mean of 7 numbers is 14. When the number 30 is added to them, what is the new mean? (a) 14 (b) 17 (c) 22 (d) 16
  8. 8.8 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 11 (c) 32 (d) 48
  9. 9.What is the mean of 3, 15, 4, 11, 15 and 6? (a) 8 (b) 9 (c) 10 (d) 11
  10. 10.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
  11. 11.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 75° (b) 15° (c) 105° (d) 285°
  12. 12.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  13. 13.What is the mean of 14, 5, 3 and 6? (a) 7 (b) 8 (c) 9 (d) 6
  14. 14.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 130° (b) 120° (c) 70° (d) 110°
  15. 15.A bag has 5 blue balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 10 (b) 6 (c) 2 (d) 7
  16. 16.A drawer has lots of green, red, blue, black and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 2 (c) 10 (d) 5
  17. 17.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 64 (d) 72
  18. 18.A drawer has lots of red and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 5 (c) 4 (d) 2
  19. 19.In a class of 51 children, 23 like mangoes, 30 like bananas and 12 like both. How many like at least one of the two? (a) 41 (b) 29 (c) 51 (d) 53
  20. 20.How many prime numbers are there between 50 and 80? (a) 6 (b) 8 (c) 9 (d) 7
  21. 21.In a class of 32 children, 18 like maths, 18 like science and 9 like both. How many like only maths? (a) 9 (b) 14 (c) 10 (d) 18
  22. 22.In a class of 44 children, 22 like cricket, 29 like football and 2 like neither. How many like both? (a) 7 (b) 9 (c) 42 (d) 2
  23. 23.What is the prime factorisation of 20? (a) 2³ × 5 (b) 2 × 5 (c) 2² × 5 (d) 2 × 5²
  24. 24.If a + b = 12 and ab = 11, what is a² + b²? (a) 166 (b) 144 (c) 122 (d) 133
  25. 25.A bag has 8 green, 3 yellow and 4 red balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 4/5 (b) 1/5 (c) 1/3 (d) 13/15
  26. 26.What is the mode of 2, 12, 2, 19, 1, 2 and 12? (a) 1 (b) 19 (c) 12 (d) 2
  27. 27.A bag has 8 white balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 9 (b) 13 (c) 2 (d) 10
  28. 28.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 10 (b) 5 (c) 9 (d) 7
  30. 30.What is the prime factorisation of 45? (a) 3 × 5 (b) 3 × 5² (c) 3² × 5 (d) 3³ × 5
  31. 31.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 240 (c) 120 (d) 25
  32. 32.What is the 21st term of the AP 6, 10, 14, 18, …? (a) 84 (b) 86 (c) 80 (d) 90
  33. 33.In which quadrant does the point (−3, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  34. 34.What is the 28th term of the AP 12, 15, 18, 21, …? (a) 81 (b) 93 (c) 84 (d) 96
  35. 35.A bag has 6 red balls and 7 green 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) 7 (c) 8 (d) 13
  36. 36.What is the sum of the roots of x² − 11x + 30 = 0? (a) 12 (b) 11 (c) 30 (d) 10
  37. 37.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 25 (b) 37 (c) 36 (d) 24
  38. 38.Which is the correct factorisation of x² + 10x + 24? (a) (x − 4)(x − 6) (b) (x + 4)(x + 6) (c) (x + 1)(x + 9) (d) (x + 1)(x + 24)
  39. 39.What is the distance between the points (0, 25) and (12, 9)? (a) 21 (b) 28 (c) 400 (d) 20
  40. 40.What is the sum of all the whole numbers from 1 to 20? (a) 210 (b) 200 (c) 190 (d) 420

Answer key

  1. 16
  2. 20
  3. 90
  4. 120
  5. 10
  6. 2464 sq cm
  7. 16
  8. 24
  9. 9
  10. 1/3
  11. 105°
  12. 5
  13. 7
  14. 110°
  15. 7
  16. 6
  17. 64
  18. 3
  19. 41
  20. 7
  21. 9
  22. 9
  23. 2² × 5
  24. 122
  25. 4/5
  26. 2
  27. 10
  28. 20
  29. 9
  30. 3² × 5
  31. 120
  32. 86
  33. Third quadrant
  34. 93
  35. 8
  36. 11
  37. 25
  38. (x + 4)(x + 6)
  39. 20
  40. 210

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