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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 276 · 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 prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2³ × 3 × 7 (c) 2² × 3 × 7 (d) 2⁴ × 3 × 7
  2. 2.In a class of 39 children, 24 like tea, 15 like coffee and 6 like neither. How many like both? (a) 7 (b) 33 (c) 6 (d) 5
  3. 3.What is the distance between the points (3, 23) and (11, 8)? (a) 289 (b) 23 (c) 17 (d) 18
  4. 4.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
  5. 5.What is the midpoint of the line joining (9, 3) and (11, 5)? (a) (4, 10) (b) (20, 8) (c) (1, 1) (d) (10, 4)
  6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/11 (b) 1/9 (c) 3/11 (d) 1/12
  7. 7.What is the smallest prime factor of 203? (a) 7 (b) 29 (c) 1 (d) 2
  8. 8.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 176 sq cm
  9. 9.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 12 (b) 108 (c) 36 (d) 39
  10. 10.Two angles of a triangle are 20° and 110°. What is the third angle? (a) 50° (b) 130° (c) 70° (d) 160°
  11. 11.In a class of 35 children, 21 like mangoes, 17 like bananas and 5 like both. How many like neither? (a) 5 (b) 2 (c) 7 (d) 3
  12. 12.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 1/8 (c) 1/4 (d) 7/8
  13. 13.What is the distance between the points (9, 26) and (16, 2)? (a) 26 (b) 31 (c) 25 (d) 625
  14. 14.Which term of the AP 8, 11, 14, 17, … is 71? (a) 21st (b) 22nd (c) 23rd (d) 24th
  15. 15.Which is the correct factorisation of x² + 15x + 54? (a) (x + 1)(x + 14) (b) (x + 6)(x + 9) (c) (x − 6)(x − 9) (d) (x + 1)(x + 54)
  16. 16.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/18 (b) 1/11 (c) 1/36 (d) 1/12
  17. 17.In a class of 46 children, 26 like cricket, 20 like football and 8 like both. How many like neither? (a) 0 (b) 8 (c) 16 (d) 9
  18. 18.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 26 (b) 85 (c) 80 (d) 160
  19. 19.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 1/3 (c) 3/4 (d) 1/4
  20. 20.What is the missing term in the AP 7, 13, ?, 25, 31? (a) 18 (b) 19 (c) 25 (d) 20
  21. 21.What is the prime factorisation of 42? (a) 2 × 3 × 7 (b) 2² × 3 × 7 (c) 2 × 3 × 7² (d) 2³ × 3 × 7
  22. 22.In a class of 44 children, 21 like mangoes, 22 like bananas and 10 like neither. How many like both? (a) 8 (b) 9 (c) 10 (d) 34
  23. 23.A drawer has lots of black, white 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) 3 (b) 4 (c) 2 (d) 6
  24. 24.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 90 (d) 81
  25. 25.What is the median of 17, 1, 15, 9, 14, 5 and 10? (a) 14 (b) 9 (c) 11 (d) 10
  26. 26.What is the midpoint of the line joining (6, 6) and (12, 8)? (a) (9, 7) (b) (18, 14) (c) (7, 9) (d) (3, 1)
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 13 (b) 12 (c) 11 (d) 3
  28. 28.What is the median of 23, 14, 3, 2, 40, 5 and 21? (a) 21 (b) 2 (c) 5 (d) 14
  29. 29.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 24 sq cm (b) 26 sq cm (c) 52 sq cm (d) 104 sq cm
  30. 30.How many factors does 27 have? (a) 2 (b) 5 (c) 3 (d) 4
  31. 31.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 1/6 (c) 7/36 (d) 1/11
  32. 32.There are 5 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 70 (b) 40 (c) 12 (d) 35
  33. 33.A drawer has lots of green, yellow, red 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) 5 (b) 4 (c) 2 (d) 8
  34. 34.In which quadrant does the point (−1, −3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  35. 35.How many factors does 65 have? (a) 4 (b) 2 (c) 3 (d) 5
  36. 36.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  37. 37.What is the missing term in the AP 15, 22, 29, ?, 43? (a) 37 (b) 35 (c) 43 (d) 36
  38. 38.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 55 (c) 45 (d) 90
  39. 39.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 12 (c) 3 (d) 6
  40. 40.A bag has 9 white balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 10 (b) 11 (c) 13 (d) 2

Answer key

  1. 2³ × 3 × 7
  2. 6
  3. 17
  4. 1/2
  5. (10, 4)
  6. 1/12
  7. 7
  8. 2464 sq cm
  9. 36
  10. 50°
  11. 2
  12. 1/8
  13. 25
  14. 22nd
  15. (x + 6)(x + 9)
  16. 1/36
  17. 8
  18. 80
  19. 1/4
  20. 19
  21. 2 × 3 × 7
  22. 9
  23. 4
  24. 81
  25. 10
  26. (9, 7)
  27. 12
  28. 14
  29. 52 sq cm
  30. 4
  31. 1/6
  32. 35
  33. 5
  34. Third quadrant
  35. 4
  36. 5
  37. 36
  38. 45
  39. 6
  40. 11

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