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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 148 · 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 10th term of the AP 20, 23, 26, 29, …? (a) 50 (b) 47 (c) 30 (d) 27
  2. 2.In a class of 44 children, 19 like tea, 24 like coffee and 7 like both. How many like only tea? (a) 19 (b) 12 (c) 17 (d) 20
  3. 3.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 33 (c) 10 (d) 90
  4. 4.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  5. 5.How many factors does 120 have? (a) 15 (b) 14 (c) 17 (d) 16
  6. 6.A drawer has lots of yellow 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) 5 (b) 2 (c) 3 (d) 4
  7. 7.Using (a − b)² = a² − 2ab + b², what is 49²? (a) 2411 (b) 2601 (c) 2401 (d) 2499
  8. 8.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 16 (b) 18 (c) 7 (d) 17
  10. 10.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 36 (c) 72 (d) 18
  11. 11.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  12. 12.In a class of 29 children, 12 like dance, 24 like music and 1 like neither. How many like both? (a) 7 (b) 1 (c) 8 (d) 28
  13. 13.What is the sum of all the whole numbers from 1 to 97? (a) 9506 (b) 4754 (c) 4753 (d) 4656
  14. 14.8 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 56 (b) 14 (c) 96 (d) 48
  15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/11 (b) 1/9 (c) 1/12 (d) 3/11
  16. 16.What is the mean of 12, 17, 6, 19, 17 and 13? (a) 14 (b) 13 (c) 15 (d) 12
  17. 17.Which is the correct factorisation of x² + 7x + 10? (a) (x + 1)(x + 10) (b) (x + 2)(x + 5) (c) (x + 1)(x + 6) (d) (x − 2)(x − 5)
  18. 18.In a class of 49 children, 26 like maths, 31 like science and 11 like both. How many like at least one of the two? (a) 49 (b) 46 (c) 35 (d) 57
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 4 (b) 7 (c) 5 (d) 6
  20. 20.How many factors does 85 have? (a) 3 (b) 5 (c) 2 (d) 4
  21. 21.A cuboid is 7 cm long, 3 cm wide and 5 cm high. What is its total surface area? (a) 71 sq cm (b) 284 sq cm (c) 105 sq cm (d) 142 sq cm
  22. 22.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
  23. 23.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 14 (c) 126 (d) 42
  24. 24.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 1/3 (c) 3/4 (d) 1/4
  25. 25.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 55 (c) 812 (d) 406
  26. 26.How many prime numbers are there between 70 and 100? (a) 7 (b) 8 (c) 6 (d) 5
  27. 27.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 68? (a) 17 (b) 6 (c) 16 (d) 18
  29. 29.In a class of 40 children, 16 like mangoes, 21 like bananas and 3 like both. How many like neither? (a) 6 (b) 9 (c) 3 (d) 7
  30. 30.What is the missing term in the AP 14, ?, 24, 29, 34? (a) 18 (b) 19 (c) 20 (d) 24
  31. 31.A bag has 12 white balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 13 (c) 2 (d) 15
  32. 32.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 15) (b) (x + 1)(x + 63) (c) (x + 7)(x + 9) (d) (x − 7)(x − 9)
  33. 33.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 6 (b) 18 (c) 12 (d) 9
  34. 34.A drawer has lots of black, white 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) 3 (b) 6 (c) 4 (d) 2
  35. 35.What is the midpoint of the line joining (5, 11) and (17, 5)? (a) (8, 11) (b) (11, 8) (c) (6, 3) (d) (22, 16)
  36. 36.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) 7 (b) 8 (c) 14 (d) 15
  37. 37.What is the midpoint of the line joining (6, 1) and (12, 3)? (a) (2, 9) (b) (9, 2) (c) (3, 1) (d) (18, 4)
  38. 38.What is the product of the roots of x² − 11x + 18 = 0? (a) 19 (b) 11 (c) 17 (d) 18
  39. 39.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 145° (c) 120° (d) 35°
  40. 40.In a class of 39 children, 11 like cricket, 22 like football and 4 like both. How many like neither? (a) 6 (b) 4 (c) 10 (d) 14

Answer key

  1. 47
  2. 12
  3. 30
  4. 6
  5. 16
  6. 3
  7. 2401
  8. 1/3
  9. 17
  10. 72
  11. 120
  12. 8
  13. 4753
  14. 48
  15. 1/12
  16. 14
  17. (x + 2)(x + 5)
  18. 46
  19. 6
  20. 4
  21. 142 sq cm
  22. 220 cm
  23. 42
  24. 3/4
  25. 784
  26. 6
  27. 44 cm
  28. 17
  29. 6
  30. 19
  31. 13
  32. (x + 7)(x + 9)
  33. 9
  34. 4
  35. (11, 8)
  36. 8
  37. (9, 2)
  38. 18
  39. 145°
  40. 10

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