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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 73 · 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.Two angles of a triangle are 40° and 30°. What is the exterior angle at the third corner? (a) 140° (b) 110° (c) 150° (d) 70°
  2. 2.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
  3. 3.A drawer has lots of red, blue, green, yellow and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 2 (c) 5 (d) 6
  4. 4.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 15 (c) 30 (d) 12
  5. 5.In a class of 42 children, 16 like maths, 24 like science and 7 like both. How many like neither? (a) 9 (b) 7 (c) 2 (d) 16
  6. 6.What is the mean of 15, 9, 17 and 19? (a) 20 (b) 12 (c) 15 (d) 16
  7. 7.A drawer has lots of red, green and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 2 (c) 6 (d) 3
  8. 8.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
  9. 9.How many factors does 27 have? (a) 3 (b) 4 (c) 2 (d) 5
  10. 10.What is the median of 21, 30, 5, 11, 16, 38 and 25? (a) 21 (b) 25 (c) 16 (d) 11
  11. 11.Which term of the AP 6, 8, 10, 12, … is 46? (a) 23rd (b) 21st (c) 20th (d) 22nd
  12. 12.What is the 23rd term of the AP 8, 11, 14, 17, …? (a) 74 (b) 66 (c) 77 (d) 69
  13. 13.8 T-shirts and 4 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) 40 (c) 32 (d) 64
  14. 14.What is the median of 22, 3, 34, 39, 8, 27 and 31? (a) 22 (b) 39 (c) 27 (d) 31
  15. 15.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/2 (c) 1/4 (d) 1/3
  16. 16.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) 22 (b) 28 (c) 21 (d) 29
  17. 17.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 282 (c) 283 (d) 260
  18. 18.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 91 (c) 78 (d) 169
  19. 19.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 56) (b) (x + 7)(x + 8) (c) (x + 1)(x + 14) (d) (x − 7)(x − 8)
  20. 20.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 2/3 (b) 1/4 (c) 5/6 (d) 1/3
  21. 21.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  22. 22.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  23. 23.In a class of 49 children, 25 like mangoes, 24 like bananas and 8 like both. How many like only mangoes? (a) 16 (b) 25 (c) 8 (d) 17
  24. 24.How many factors does 95 have? (a) 5 (b) 2 (c) 4 (d) 3
  25. 25.A drawer has lots of green and white 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) 3 (c) 5 (d) 4
  26. 26.How many prime numbers are there between 10 and 40? (a) 8 (b) 9 (c) 10 (d) 7
  27. 27.In a class of 28 children, 17 like cricket, 13 like football and 9 like both. How many like only cricket? (a) 17 (b) 15 (c) 8 (d) 4
  28. 28.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
  29. 29.Two angles of a triangle are 35° and 100°. What is the third angle? (a) 45° (b) 80° (c) 145° (d) 135°
  30. 30.What is the sum of the first 9 terms of the AP 5, 7, 9, …? (a) 21 (b) 234 (c) 126 (d) 117
  31. 31.A bag has 3 red balls and 10 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) 13 (c) 11 (d) 4
  32. 32.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/5 (b) 1/3 (c) 5/6 (d) 1/6
  33. 33.In a class of 19 children, 11 like dance, 14 like music and 7 like both. How many like neither? (a) 8 (b) 7 (c) 2 (d) 1
  34. 34.In a class of 35 children, 15 like tea, 19 like coffee and 10 like neither. How many like both? (a) 10 (b) 9 (c) 8 (d) 25
  35. 35.A bag has 10 black balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 11 (b) 12 (c) 16 (d) 2
  36. 36.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 66 (c) 24 (d) 132
  37. 37.How many factors does 41 have? (a) 2 (b) 4 (c) 3 (d) 1
  38. 38.In a class of 29 children, 8 like cricket, 25 like football and 5 like both. How many like at least one of the two? (a) 28 (b) 33 (c) 29 (d) 23
  39. 39.What is the product of the roots of x² − 7x + 12 = 0? (a) 12 (b) 11 (c) 13 (d) 7
  40. 40.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 9 (b) 30 (c) 81 (d) 27

Answer key

  1. 70°
  2. 176 cm
  3. 6
  4. 15
  5. 9
  6. 15
  7. 4
  8. 1/2
  9. 4
  10. 21
  11. 21st
  12. 74
  13. 32
  14. 27
  15. 1/2
  16. 22
  17. 282
  18. 78
  19. (x + 7)(x + 8)
  20. 2/3
  21. 3
  22. 15
  23. 17
  24. 4
  25. 3
  26. 8
  27. 8
  28. 154 sq cm
  29. 45°
  30. 117
  31. 11
  32. 5/6
  33. 1
  34. 9
  35. 12
  36. 132
  37. 2
  38. 28
  39. 12
  40. 27

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