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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 113 · 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.There are 7 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) 49 (b) 13 (c) 84 (d) 42
  2. 2.What is the midpoint of the line joining (7, 5) and (11, 9)? (a) (9, 7) (b) (18, 14) (c) (7, 9) (d) (2, 2)
  3. 3.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 130° (d) 160°
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 57? (a) 17 (b) 16 (c) 15 (d) 5
  5. 5.Which is the correct factorisation of x² + 17x + 72? (a) (x + 8)(x + 9) (b) (x − 8)(x − 9) (c) (x + 1)(x + 16) (d) (x + 1)(x + 72)
  6. 6.In a class of 24 children, 16 like maths, 11 like science and 4 like both. How many like at least one of the two? (a) 24 (b) 23 (c) 27 (d) 19
  7. 7.How many prime numbers are there between 50 and 70? (a) 4 (b) 3 (c) 5 (d) 6
  8. 8.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
  9. 9.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
  10. 10.What is the 14th term of the AP 9, 17, 25, 33, …? (a) 104 (b) 113 (c) 112 (d) 121
  11. 11.How many factors does 18 have? (a) 7 (b) 5 (c) 6 (d) 4
  12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 2/11 (b) 1/12 (c) 1/18 (d) 1/11
  13. 13.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
  14. 14.What is the distance between the points (8, 32) and (15, 8)? (a) 625 (b) 26 (c) 31 (d) 25
  15. 15.What is the midpoint of the line joining (1, 3) and (3, 7)? (a) (5, 2) (b) (2, 5) (c) (4, 10) (d) (1, 2)
  16. 16.There are 4 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) 10 (b) 24 (c) 28 (d) 48
  17. 17.Using (a + b)² = a² + 2ab + b², what is 42²? (a) 1444 (b) 1774 (c) 1764 (d) 1604
  18. 18.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 25 (c) 21 (d) 10
  19. 19.What is the smallest prime factor of 247? (a) 2 (b) 19 (c) 13 (d) 1
  20. 20.What is the distance between the points (1, 7) and (6, 19)? (a) 14 (b) 169 (c) 17 (d) 13
  21. 21.A bag has 3 white balls and 11 black 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) 14 (c) 4 (d) 2
  22. 22.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  23. 23.What is the mode of 20, 20, 8, 8, 8, 2 and 5? (a) 2 (b) 20 (c) 8 (d) 5
  24. 24.What is the smallest prime factor of 299? (a) 1 (b) 2 (c) 13 (d) 23
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 6 (b) 18 (c) 17 (d) 16
  26. 26.What is the 10th term of the AP 19, 26, 33, 40, …? (a) 89 (b) 82 (c) 70 (d) 63
  27. 27.If a + b = 8 and ab = 12, what is a² + b²? (a) 52 (b) 40 (c) 88 (d) 64
  28. 28.In which quadrant does the point (−1, −9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/6 (b) 1/11 (c) 6/11 (d) 7/36
  30. 30.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 120° (b) 60° (c) 140° (d) 100°
  31. 31.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 115° (b) 155° (c) 90° (d) 270°
  32. 32.In which quadrant does the point (8, −4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  33. 33.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
  34. 34.If a + b = 8 and ab = 12, what is (a − b)²? (a) 40 (b) 64 (c) 4 (d) 16
  35. 35.In a class of 43 children, 29 like dance, 23 like music and 3 like neither. How many like both? (a) 3 (b) 9 (c) 12 (d) 40
  36. 36.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 32 (c) 20 (d) 16
  37. 37.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 91 (c) 105 (d) 196
  38. 38.What is the sum of the roots of x² − 16x + 63 = 0? (a) 17 (b) 15 (c) 63 (d) 16
  39. 39.How many factors does 23 have? (a) 1 (b) 3 (c) 2 (d) 4
  40. 40.A bag has 8 green balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 9 (c) 11 (d) 10

Answer key

  1. 42
  2. (9, 7)
  3. 70°
  4. 16
  5. (x + 8)(x + 9)
  6. 23
  7. 4
  8. 1/2
  9. 176 cm
  10. 113
  11. 6
  12. 1/18
  13. 44 cm
  14. 25
  15. (2, 5)
  16. 24
  17. 1764
  18. 20
  19. 13
  20. 13
  21. 12
  22. 120
  23. 8
  24. 13
  25. 17
  26. 82
  27. 40
  28. Third quadrant
  29. 1/6
  30. 60°
  31. 90°
  32. Fourth quadrant
  33. 2
  34. 16
  35. 12
  36. 16
  37. 91
  38. 16
  39. 2
  40. 10

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