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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 473 · 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 mean of 7, 3, 6, 9, 19 and 4? (a) 9 (b) 8 (c) 10 (d) 7
  2. 2.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 549 (b) 444 (c) 558 (d) 559
  3. 3.What is the distance between the points (8, 8) and (20, 13)? (a) 169 (b) 14 (c) 13 (d) 17
  4. 4.What is the 29th term of the AP 1, 3, 5, 7, …? (a) 58 (b) 59 (c) 57 (d) 56
  5. 5.A bag has 5 black balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 2 (c) 6 (d) 8
  6. 6.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
  7. 7.How many prime numbers are there between 10 and 40? (a) 10 (b) 7 (c) 9 (d) 8
  8. 8.What is the midpoint of the line joining (8, 14) and (20, 10)? (a) (12, 14) (b) (14, 12) (c) (28, 24) (d) (6, 2)
  9. 9.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 145° (b) 150° (c) 35° (d) 65°
  10. 10.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/8 (b) 1/4 (c) 3/4 (d) 3/8
  11. 11.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 21 (c) 15 (d) 30
  12. 12.What is the mean of 5, 9, 11, 10, 15 and 10? (a) 11 (b) 10 (c) 9 (d) 12
  13. 13.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
  14. 14.How many prime numbers are there between 30 and 60? (a) 6 (b) 8 (c) 7 (d) 9
  15. 15.If a + b = 13 and ab = 30, what is a² + b²? (a) 109 (b) 169 (c) 229 (d) 139
  16. 16.A drawer has lots of white, 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) 6 (b) 3 (c) 4 (d) 2
  17. 17.What is the smallest prime factor of 21? (a) 7 (b) 3 (c) 2 (d) 1
  18. 18.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 8 times (c) 4 times (d) 16 times
  19. 19.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
  20. 20.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
  21. 21.What is the median of 33, 24, 10, 1 and 14? (a) 14 (b) 24 (c) 15 (d) 10
  22. 22.A drawer has lots of yellow, 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) 2 (b) 5 (c) 4 (d) 8
  23. 23.What is the product of the roots of x² − 13x + 42 = 0? (a) 41 (b) 43 (c) 13 (d) 42
  24. 24.What is the midpoint of the line joining (5, 9) and (7, 19)? (a) (14, 6) (b) (12, 28) (c) (1, 5) (d) (6, 14)
  25. 25.A canteen sells 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 35 (c) 70 (d) 42
  26. 26.A bag has 11 yellow balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 13 (b) 12 (c) 2 (d) 15
  27. 27.What is the prime factorisation of 36? (a) 2² × 3³ (b) 2² × 3² (c) 2 × 3² (d) 2³ × 3²
  28. 28.What is the 13th term of the AP 20, 29, 38, 47, …? (a) 137 (b) 108 (c) 117 (d) 128
  29. 29.What is the distance between the points (2, 0) and (9, 24)? (a) 26 (b) 625 (c) 25 (d) 31
  30. 30.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 5 times (c) 8 times (d) 4 times
  31. 31.Which term of the AP 5, 13, 21, 29, … is 197? (a) 26th (b) 25th (c) 27th (d) 24th
  32. 32.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 100° (b) 50° (c) 130° (d) 51°
  33. 33.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 110° (c) 35° (d) 45°
  34. 34.What is the mode of 4, 1, 4, 18, 4, 5 and 1? (a) 5 (b) 1 (c) 4 (d) 18
  35. 35.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 50° (c) 130° (d) 65°
  36. 36.A bag has 6 black balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 7 (b) 11 (c) 8 (d) 2
  37. 37.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 15 (c) 25 (d) 20
  38. 38.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 156 (c) 78 (d) 91
  39. 39.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) 36 (c) 24 (d) 37
  40. 40.Which is the correct factorisation of x² + 9x + 20? (a) (x − 4)(x − 5) (b) (x + 1)(x + 20) (c) (x + 4)(x + 5) (d) (x + 1)(x + 8)

Answer key

  1. 8
  2. 558
  3. 13
  4. 57
  5. 8
  6. 154 sq cm
  7. 8
  8. (14, 12)
  9. 35°
  10. 3/4
  11. 15
  12. 10
  13. 176 cm
  14. 7
  15. 109
  16. 4
  17. 3
  18. 16 times
  19. 25
  20. 125 times
  21. 14
  22. 5
  23. 42
  24. (6, 14)
  25. 35
  26. 13
  27. 2² × 3²
  28. 128
  29. 25
  30. 4 times
  31. 25th
  32. 50°
  33. 35°
  34. 4
  35. 65°
  36. 8
  37. 10
  38. 78
  39. 25
  40. (x + 4)(x + 5)

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