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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 72 · 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.In a class of 29 children, 11 like mangoes, 17 like bananas and 5 like both. How many like neither? (a) 6 (b) 11 (c) 5 (d) 1
  2. 2.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
  3. 3.How many prime numbers are there between 80 and 100? (a) 3 (b) 4 (c) 2 (d) 5
  4. 4.There are 8 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 56 (b) 96 (c) 14 (d) 48
  5. 5.If a + b = 18 and ab = 77, what is (a − b)²? (a) 4 (b) 16 (c) 324 (d) 170
  6. 6.What is the 33rd term of the AP 19, 25, 31, 37, …? (a) 198 (b) 211 (c) 192 (d) 217
  7. 7.In a class of 29 children, 20 like cricket, 12 like football and 7 like both. How many like only cricket? (a) 20 (b) 5 (c) 13 (d) 17
  8. 8.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 90 (c) 45 (d) 20
  9. 9.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 726 sq cm (c) 121 sq cm (d) 484 sq cm
  10. 10.What is the sum of all the whole numbers from 1 to 22? (a) 506 (b) 253 (c) 231 (d) 242
  11. 11.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 57 (c) 19 (d) 171
  12. 12.In a class of 36 children, 21 like cricket, 15 like football and 4 like both. How many like only cricket? (a) 11 (b) 17 (c) 4 (d) 21
  13. 13.Which is the correct factorisation of x² + 12x + 32? (a) (x − 4)(x − 8) (b) (x + 1)(x + 32) (c) (x + 4)(x + 8) (d) (x + 1)(x + 11)
  14. 14.How many prime numbers are there between 30 and 50? (a) 6 (b) 4 (c) 5 (d) 7
  15. 15.How many factors does 105 have? (a) 8 (b) 6 (c) 7 (d) 9
  16. 16.What is the median of 18, 5, 29, 4 and 24? (a) 18 (b) 16 (c) 24 (d) 29
  17. 17.What is the distance between the points (9, 8) and (17, 14)? (a) 14 (b) 100 (c) 10 (d) 11
  18. 18.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 20 (c) 90 (d) 45
  19. 19.Two angles of a triangle are 25° and 135°. What is the third angle? (a) 160° (b) 45° (c) 155° (d) 20°
  20. 20.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
  21. 21.A drawer has lots of yellow 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) 4 (c) 3 (d) 2
  22. 22.What is the smallest prime factor of 51? (a) 17 (b) 2 (c) 1 (d) 3
  23. 23.In which quadrant does the point (7, 4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  24. 24.Which is the correct factorisation of x² + 8x + 15? (a) (x − 3)(x − 5) (b) (x + 1)(x + 15) (c) (x + 3)(x + 5) (d) (x + 1)(x + 7)
  25. 25.Two angles of a triangle are 30° and 30°. What is the third angle? (a) 120° (b) 150° (c) 60° (d) 300°
  26. 26.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  27. 27.What is the midpoint of the line joining (4, 12) and (16, 0)? (a) (6, 10) (b) (6, 6) (c) (10, 6) (d) (20, 12)
  28. 28.A canteen sells 6 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 13 (b) 84 (c) 48 (d) 42
  29. 29.In a class of 23 children, 15 like dance, 16 like music and 12 like both. How many like only dance? (a) 3 (b) 7 (c) 4 (d) 15
  30. 30.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 48 (b) 12 (c) 84 (d) 42
  31. 31.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) 13 (b) 12 (c) 24 (d) 25
  32. 32.If a + b = 16 and ab = 60, what is (a − b)²? (a) 16 (b) 256 (c) 136 (d) 4
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 79? (a) 17 (b) 18 (c) 7 (d) 19
  34. 34.Which is the correct factorisation of x² + 17x + 72? (a) (x + 8)(x + 9) (b) (x − 8)(x − 9) (c) (x + 1)(x + 72) (d) (x + 1)(x + 16)
  35. 35.Which term of the AP 7, 15, 23, 31, … is 135? (a) 16th (b) 17th (c) 18th (d) 19th
  36. 36.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 100° (c) 45° (d) 135°
  37. 37.How many factors does 59 have? (a) 2 (b) 3 (c) 1 (d) 4
  38. 38.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  39. 39.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
  40. 40.A bag has 9 white, 7 blue and 8 red balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 3/4 (b) 7/24 (c) 17/24 (d) 1/3

Answer key

  1. 6
  2. 5
  3. 3
  4. 48
  5. 16
  6. 211
  7. 13
  8. 45
  9. 726 sq cm
  10. 253
  11. 57
  12. 17
  13. (x + 4)(x + 8)
  14. 5
  15. 8
  16. 18
  17. 10
  18. 90
  19. 20°
  20. 16 times
  21. 3
  22. 3
  23. First quadrant
  24. (x + 3)(x + 5)
  25. 120°
  26. 3
  27. (10, 6)
  28. 42
  29. 3
  30. 42
  31. 13
  32. 16
  33. 18
  34. (x + 8)(x + 9)
  35. 17th
  36. 135°
  37. 2
  38. 120
  39. 13
  40. 17/24

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