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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 162 · 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 midpoint of the line joining (1, 7) and (3, 11)? (a) (2, 9) (b) (4, 18) (c) (9, 2) (d) (1, 2)
  2. 2.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 28 (c) 21 (d) 49
  3. 3.Which is the correct factorisation of x² + 9x + 20? (a) (x + 4)(x + 5) (b) (x + 1)(x + 8) (c) (x + 1)(x + 20) (d) (x − 4)(x − 5)
  4. 4.6 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 48 (b) 42 (c) 13 (d) 84
  5. 5.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 14 (d) 5
  6. 6.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
  7. 7.What is the smallest prime factor of 133? (a) 1 (b) 7 (c) 2 (d) 19
  8. 8.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
  9. 9.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 12 (d) 9
  10. 10.A bag has 5 red balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 2 (c) 10 (d) 14
  11. 11.In a class of 25 children, 13 like tea, 14 like coffee and 7 like both. How many like neither? (a) 7 (b) 5 (c) 6 (d) 12
  12. 12.What is the smallest prime factor of 377? (a) 2 (b) 1 (c) 29 (d) 13
  13. 13.What is the median of 24, 36, 25, 2 and 4? (a) 23 (b) 24 (c) 4 (d) 25
  14. 14.What is the smallest prime factor of 33? (a) 11 (b) 1 (c) 3 (d) 2
  15. 15.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 2/3 (b) 5/6 (c) 1/3 (d) 1/4
  16. 16.What is the mean of 5, 17, 3 and 11? (a) 12 (b) 9 (c) 10 (d) 8
  17. 17.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 28 (c) 21 (d) 42
  18. 18.In a class of 31 children, 23 like cricket, 15 like football and 3 like neither. How many like both? (a) 3 (b) 10 (c) 28 (d) 7
  19. 19.Using (a − b)² = a² − 2ab + b², what is 87²? (a) 7579 (b) 8649 (c) 8091 (d) 7569
  20. 20.Three coins are tossed together. What is the probability of getting at least one head? (a) 7/8 (b) 1/8 (c) 3/8 (d) 1/4
  21. 21.In a class of 36 children, 21 like cricket, 24 like football and 11 like both. How many like only cricket? (a) 12 (b) 13 (c) 21 (d) 10
  22. 22.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 26 (b) 44 (c) 36 (d) 35
  23. 23.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 45 (c) 46 (d) 36
  24. 24.The mean of 4 numbers is 13. When the number 3 is added to them, what is the new mean? (a) 12 (b) 13 (c) 8 (d) 11
  25. 25.Which is the correct factorisation of x² + 15x + 56? (a) (x + 7)(x + 8) (b) (x + 1)(x + 14) (c) (x − 7)(x − 8) (d) (x + 1)(x + 56)
  26. 26.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 16 cu cm (c) 8 cu cm (d) 6 cu cm
  27. 27.What is the distance between the points (6, 8) and (9, 4)? (a) 7 (b) 25 (c) 6 (d) 5
  28. 28.How many prime numbers are there between 30 and 50? (a) 4 (b) 7 (c) 6 (d) 5
  29. 29.What is the midpoint of the line joining (3, 7) and (5, 9)? (a) (8, 16) (b) (1, 1) (c) (8, 4) (d) (4, 8)
  30. 30.Two angles of a triangle are 45° and 50°. What is the exterior angle at the third corner? (a) 85° (b) 135° (c) 130° (d) 95°
  31. 31.Which is the correct factorisation of x² + 12x + 27? (a) (x + 3)(x + 9) (b) (x + 1)(x + 27) (c) (x + 1)(x + 11) (d) (x − 3)(x − 9)
  32. 32.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  33. 33.What is the 33rd term of the AP 8, 11, 14, 17, …? (a) 107 (b) 96 (c) 99 (d) 104
  34. 34.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 100° (b) 125° (c) 135° (d) 80°
  35. 35.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
  36. 36.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 253 (b) 43 (c) 275 (d) 506
  37. 37.In a class of 28 children, 14 like mangoes, 14 like bananas and 9 like both. How many like at least one of the two? (a) 10 (b) 20 (c) 28 (d) 19
  38. 38.The mean of 8 numbers is 14. When the number 41 is added to them, what is the new mean? (a) 16 (b) 14 (c) 17 (d) 18
  39. 39.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 5/6 (b) 2/3 (c) 1/4 (d) 1/3
  40. 40.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 70° (b) 110° (c) 55° (d) 20°

Answer key

  1. (2, 9)
  2. 21
  3. (x + 4)(x + 5)
  4. 42
  5. 6
  6. 7
  7. 7
  8. 220 cm
  9. 8
  10. 10
  11. 5
  12. 13
  13. 24
  14. 3
  15. 2/3
  16. 9
  17. 21
  18. 10
  19. 7569
  20. 7/8
  21. 10
  22. 35
  23. 45
  24. 11
  25. (x + 7)(x + 8)
  26. 8 cu cm
  27. 5
  28. 5
  29. (4, 8)
  30. 95°
  31. (x + 3)(x + 9)
  32. 10
  33. 104
  34. 80°
  35. 44 cm
  36. 253
  37. 19
  38. 17
  39. 2/3
  40. 55°

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