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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 674 · 40 questions
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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. 1.7 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) 42 (b) 49 (c) 13 (d) 84
  2. 2.Two angles of a triangle are 25° and 115°. What is the third angle? (a) 140° (b) 155° (c) 65° (d) 40°
  3. 3.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/4 (c) 1/2 (d) 1/3
  4. 4.What is the mode of 13, 6, 17, 17, 12, 6 and 17? (a) 12 (b) 17 (c) 6 (d) 13
  5. 5.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 294 cu cm (c) 343 cu cm (d) 21 cu cm
  6. 6.There are 7 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 42 (b) 28 (c) 21 (d) 10
  7. 7.The mean of 8 numbers is 19. When the number 28 is added to them, what is the new mean? (a) 21 (b) 19 (c) 22 (d) 20
  8. 8.What is the distance between the points (6, 7) and (21, 15)? (a) 18 (b) 23 (c) 17 (d) 289
  9. 9.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
  10. 10.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  11. 11.What is the median of 34, 11, 10, 25 and 1? (a) 25 (b) 11 (c) 12 (d) 10
  12. 12.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 574 (b) 564 (c) 573 (d) 454
  13. 13.What is the distance between the points (9, 6) and (25, 18)? (a) 20 (b) 21 (c) 28 (d) 400
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 17 (b) 7 (c) 18 (d) 19
  15. 15.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 61° (c) 30° (d) 60°
  16. 16.What is the mean of 7, 14, 4, 5, 18 and 12? (a) 10 (b) 9 (c) 11 (d) 12
  17. 17.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 51 (c) 16 (d) 144
  18. 18.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
  19. 19.What is the mean of 16, 5, 7, 13, 2 and 11? (a) 9 (b) 10 (c) 11 (d) 8
  20. 20.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 12 (c) 30 (d) 36
  21. 21.In a class of 46 children, 23 like dance, 20 like music and 3 like both. How many like at least one of the two? (a) 46 (b) 40 (c) 37 (d) 43
  22. 22.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
  23. 23.What is the prime factorisation of 280? (a) 2³ × 5 × 7 (b) 2⁴ × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7³
  24. 24.What is the median of 1, 31, 9, 36, 39, 15 and 24? (a) 36 (b) 24 (c) 31 (d) 15
  25. 25.In a class of 39 children, 22 like tea, 11 like coffee and 2 like both. How many like at least one of the two? (a) 29 (b) 33 (c) 39 (d) 31
  26. 26.A bag has 8 white, 9 yellow and 3 green balls. One ball is taken out without looking. What is the probability that it is white? (a) 2/5 (b) 2/3 (c) 1/3 (d) 3/5
  27. 27.A bag has 9 blue balls and 7 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) 16 (c) 8 (d) 10
  28. 28.What is the midpoint of the line joining (4, 6) and (6, 10)? (a) (1, 2) (b) (8, 5) (c) (10, 16) (d) (5, 8)
  29. 29.The mean of 3 numbers is 11. When the number 23 is added to them, what is the new mean? (a) 11 (b) 15 (c) 17 (d) 14
  30. 30.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 12 (c) 6 (d) 9
  31. 31.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 15 (c) 72 (d) 36
  32. 32.A bag has 2 blue, 3 yellow and 3 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/3 (b) 5/8 (c) 3/8 (d) 3/5
  33. 33.Which term of the AP 2, 6, 10, 14, … is 158? (a) 41st (b) 40th (c) 39th (d) 42nd
  34. 34.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
  35. 35.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 63 (c) 66 (d) 189
  36. 36.What is the mean of 6, 8, 9 and 13? (a) 10 (b) 12 (c) 9 (d) 8
  37. 37.How many prime numbers are there between 30 and 50? (a) 4 (b) 5 (c) 6 (d) 7
  38. 38.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 6 (b) 9 (c) 12 (d) 5
  39. 39.How many prime numbers are there between 10 and 20? (a) 6 (b) 5 (c) 3 (d) 4
  40. 40.What is the 26th term of the AP 12, 19, 26, 33, …? (a) 182 (b) 175 (c) 187 (d) 194

Answer key

  1. 42
  2. 40°
  3. 1/4
  4. 17
  5. 343 cu cm
  6. 21
  7. 20
  8. 17
  9. 1/2
  10. 7
  11. 11
  12. 573
  13. 20
  14. 18
  15. 60°
  16. 10
  17. 48
  18. 42
  19. 9
  20. 30
  21. 40
  22. 88 cm
  23. 2³ × 5 × 7
  24. 24
  25. 31
  26. 2/5
  27. 10
  28. (5, 8)
  29. 14
  30. 6
  31. 64
  32. 3/8
  33. 40th
  34. 2464 sq cm
  35. 63
  36. 9
  37. 5
  38. 6
  39. 4
  40. 187

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