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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 537 · 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.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 25 (c) 11 (d) 10
  2. 2.What are the roots of x² − 8x + 12 = 0? (a) 2 and 6 (b) 3 and 4 (c) 1 and 7 (d) 1 and 12
  3. 3.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 65 cu cm (c) 96 cu cm (d) 64 cu cm
  4. 4.A drawer has lots of white, 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) 2 (b) 4 (c) 3 (d) 6
  5. 5.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2² × 3 × 7 (c) 2 × 3 × 7 (d) 2³ × 3 × 7
  6. 6.Which is the correct factorisation of x² + 13x + 40? (a) (x + 1)(x + 12) (b) (x + 1)(x + 40) (c) (x − 5)(x − 8) (d) (x + 5)(x + 8)
  7. 7.Two angles of a triangle are 55° and 105°. What is the third angle? (a) 125° (b) 75° (c) 160° (d) 20°
  8. 8.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 4 times (d) 5 times
  9. 9.What is the sum of all the whole numbers from 1 to 34? (a) 578 (b) 561 (c) 595 (d) 1190
  10. 10.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 16 cu cm (c) 6 cu cm (d) 8 cu cm
  11. 11.What is the midpoint of the line joining (0, 9) and (4, 21)? (a) (2, 15) (b) (4, 30) (c) (2, 6) (d) (15, 2)
  12. 12.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 22 (c) 21 (d) 15
  13. 13.Two angles of a triangle are 55° and 30°. What is the third angle? (a) 150° (b) 85° (c) 125° (d) 95°
  14. 14.There are 5 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 15 (b) 7 (c) 20 (d) 10
  15. 15.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) 37 (c) 36 (d) 24
  16. 16.What is the sum of the roots of x² − 11x + 24 = 0? (a) 11 (b) 24 (c) 10 (d) 12
  17. 17.What is the mean of 13, 3, 18, 3 and 3? (a) 8 (b) 7 (c) 9 (d) 10
  18. 18.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 13 (c) 56 (d) 28
  19. 19.How many prime numbers are there between 30 and 60? (a) 6 (b) 7 (c) 9 (d) 8
  20. 20.What is the missing term in the AP 9, ?, 15, 18, 21? (a) 11 (b) 13 (c) 15 (d) 12
  21. 21.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
  22. 22.If a + b = 8 and ab = 15, what is a² + b²? (a) 94 (b) 34 (c) 49 (d) 64
  23. 23.A bag has 4 green, 3 yellow and 2 blue balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/3 (b) 2/3 (c) 1/9 (d) 7/9
  24. 24.What is the prime factorisation of 12? (a) 2² × 3 (b) 2³ × 3 (c) 2 × 3² (d) 2 × 3
  25. 25.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 25 (b) 24 (c) 12 (d) 13
  26. 26.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  27. 27.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 170° (c) 85° (d) 86°
  29. 29.4 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) 24 (b) 28 (c) 48 (d) 10
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 19 (b) 17 (c) 18 (d) 7
  31. 31.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 169 (c) 91 (d) 78
  32. 32.What is the midpoint of the line joining (10, 0) and (18, 4)? (a) (28, 4) (b) (2, 14) (c) (14, 2) (d) (4, 2)
  33. 33.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)
  34. 34.If a + b = 11 and ab = 18, what is a² + b²? (a) 103 (b) 157 (c) 85 (d) 121
  35. 35.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 15 (d) 25
  36. 36.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
  37. 37.Two angles of a triangle are 20° and 65°. What is the third angle? (a) 115° (b) 85° (c) 95° (d) 160°
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 2 (b) 3 (c) 4 (d) 1
  39. 39.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 61° (c) 120° (d) 30°
  40. 40.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) 14 (c) 15 (d) 8

Answer key

  1. 10
  2. 2 and 6
  3. 64 cu cm
  4. 4
  5. 2² × 3 × 7
  6. (x + 5)(x + 8)
  7. 20°
  8. 4 times
  9. 595
  10. 8 cu cm
  11. (2, 15)
  12. 15
  13. 95°
  14. 10
  15. 25
  16. 11
  17. 8
  18. 49
  19. 7
  20. 12
  21. 1/2
  22. 34
  23. 2/3
  24. 2² × 3
  25. 13
  26. 6
  27. 25
  28. 85°
  29. 24
  30. 18
  31. 78
  32. (14, 2)
  33. (x + 4)(x + 5)
  34. 85
  35. 25
  36. 1/2
  37. 95°
  38. 3
  39. 60°
  40. 8

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