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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 448 · 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 25th term of the AP 3, 5, 7, 9, …? (a) 48 (b) 51 (c) 50 (d) 53
  2. 2.A bag has 6 yellow, 5 green and 7 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/3 (b) 11/18 (c) 7/11 (d) 7/18
  3. 3.What is the prime factorisation of 21? (a) 3 × 7 (b) 3² × 7 (c) 3 × 7² (d) 3³ × 7
  4. 4.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm
  5. 5.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 310 (b) 358 (c) 357 (d) 348
  6. 6.What is the 26th term of the AP 19, 28, 37, 46, …? (a) 244 (b) 234 (c) 225 (d) 253
  7. 7.What is the smallest prime factor of 93? (a) 2 (b) 1 (c) 31 (d) 3
  8. 8.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 80° (b) 100° (c) 160° (d) 120°
  9. 9.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 110° (b) 145° (c) 105° (d) 75°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 130° (b) 51° (c) 50° (d) 100°
  11. 11.A drawer has lots of white, yellow and blue 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) 4 (c) 3 (d) 2
  12. 12.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 12 (c) 6 (d) 8
  13. 13.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 81 (c) 45 (d) 72
  14. 14.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
  15. 15.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
  16. 16.What is the median of 2, 12, 28, 40 and 7? (a) 7 (b) 28 (c) 13 (d) 12
  17. 17.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
  18. 18.In a class of 37 children, 20 like cricket, 12 like football and 5 like both. How many like neither? (a) 11 (b) 10 (c) 15 (d) 5
  19. 19.4 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) 32 (b) 16 (c) 20 (d) 8
  20. 20.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 130° (c) 40° (d) 50°
  21. 21.What is the prime factorisation of 84? (a) 2 × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7² (d) 2² × 3 × 7
  22. 22.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
  23. 23.What is the sum of the roots of x² − 9x + 14 = 0? (a) 9 (b) 14 (c) 8 (d) 10
  24. 24.What is the midpoint of the line joining (8, 18) and (20, 10)? (a) (6, 4) (b) (28, 28) (c) (14, 14) (d) (15, 14)
  25. 25.A drawer has lots of black, blue, green and red 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) 8 (c) 4 (d) 2
  26. 26.What is the prime factorisation of 504? (a) 2⁴ × 3² × 7 (b) 2² × 3² × 7 (c) 2³ × 3² × 7 (d) 2 × 3² × 7³
  27. 27.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 6 (b) 21 (c) 42 (d) 24
  28. 28.A cuboid is 12 cm long, 11 cm wide and 5 cm high. What is its volume? (a) 28 cu cm (b) 132 cu cm (c) 494 cu cm (d) 660 cu cm
  29. 29.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 16 (d) 4
  30. 30.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 182 (c) 169 (d) 91
  31. 31.Two angles of a triangle are 20° and 30°. What is the third angle? (a) 130° (b) 50° (c) 160° (d) 150°
  32. 32.What is the prime factorisation of 80? (a) 2 × 5⁴ (b) 2³ × 5 (c) 2⁴ × 5 (d) 2⁵ × 5
  33. 33.What is the mean of 17, 5, 15, 20 and 8? (a) 14 (b) 15 (c) 13 (d) 12
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 19 (b) 18 (c) 20 (d) 8
  35. 35.A drawer has lots of blue, black, yellow 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) 5 (c) 4 (d) 8
  36. 36.If a + b = 11 and ab = 18, what is a² + b²? (a) 121 (b) 157 (c) 85 (d) 103
  37. 37.The mean of 7 numbers is 38. When the number 14 is added to them, what is the new mean? (a) 26 (b) 35 (c) 36 (d) 38
  38. 38.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 184 (b) 183 (c) 192 (d) 174
  39. 39.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 28 (c) 64 (d) 16
  40. 40.What is the sum of the roots of x² − 7x + 12 = 0? (a) 6 (b) 8 (c) 7 (d) 12

Answer key

  1. 51
  2. 7/18
  3. 3 × 7
  4. 88 cm
  5. 357
  6. 244
  7. 3
  8. 100°
  9. 75°
  10. 50°
  11. 4
  12. 8
  13. 36
  14. 1/2
  15. 4 times
  16. 12
  17. 1/2
  18. 10
  19. 16
  20. 65°
  21. 2² × 3 × 7
  22. 176 cm
  23. 9
  24. (14, 14)
  25. 5
  26. 2³ × 3² × 7
  27. 21
  28. 660 cu cm
  29. 4
  30. 169
  31. 130°
  32. 2⁴ × 5
  33. 13
  34. 19
  35. 5
  36. 85
  37. 35
  38. 183
  39. 28
  40. 7

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