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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 754 · 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.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  2. 2.What is the smallest prime factor of 319? (a) 29 (b) 2 (c) 11 (d) 1
  3. 3.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 90 (c) 20 (d) 45
  4. 4.In a class of 47 children, 28 like cricket, 28 like football and 12 like both. How many like neither? (a) 12 (b) 4 (c) 15 (d) 3
  5. 5.What is the mode of 14, 19, 17, 14, 17, 14 and 1? (a) 17 (b) 1 (c) 19 (d) 14
  6. 6.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 2070 (c) 1035 (d) 990
  7. 7.A drawer has lots of blue, red, white and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 2 (c) 5 (d) 4
  8. 8.What is the mode of 6, 15, 8, 11, 8, 6 and 8? (a) 11 (b) 8 (c) 6 (d) 15
  9. 9.Using (a + b)² = a² + 2ab + b², what is 81²? (a) 6401 (b) 6561 (c) 6571 (d) 6241
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 4 (b) 6 (c) 3 (d) 5
  11. 11.A cuboid is 9 cm long, 5 cm wide and 3 cm high. What is its total surface area? (a) 174 sq cm (b) 348 sq cm (c) 135 sq cm (d) 87 sq cm
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 91? (a) 9 (b) 10 (c) 12 (d) 11
  13. 13.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 35° (c) 25° (d) 50°
  14. 14.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 24 (c) 216 (d) 75
  15. 15.In a class of 46 children, 23 like cricket, 25 like football and 10 like neither. How many like both? (a) 12 (b) 36 (c) 2 (d) 10
  16. 16.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/4 (c) 2/3 (d) 1/3
  17. 17.What is the smallest prime factor of 133? (a) 2 (b) 1 (c) 19 (d) 7
  18. 18.Using (a + b)² = a² + 2ab + b², what is 82²? (a) 6084 (b) 6404 (c) 6734 (d) 6724
  19. 19.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 65° (c) 25° (d) 50°
  20. 20.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 125° (b) 120° (c) 115° (d) 55°
  21. 21.What is the prime factorisation of 120? (a) 2 × 3 × 5³ (b) 2⁴ × 3 × 5 (c) 2³ × 3 × 5 (d) 2² × 3 × 5
  22. 22.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 28 (c) 49 (d) 42
  23. 23.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 37 (c) 361 (d) 380
  24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 5/36 (b) 4/11 (c) 1/9 (d) 1/11
  25. 25.What is the missing term in the AP 6, ?, 24, 33, 42? (a) 14 (b) 16 (c) 24 (d) 15
  26. 26.6 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) 42 (b) 84 (c) 13 (d) 48
  27. 27.What is the mode of 14, 5, 12, 16, 16, 16 and 12? (a) 16 (b) 14 (c) 12 (d) 5
  28. 28.Using (a − b)² = a² − 2ab + b², what is 58²? (a) 3364 (b) 3844 (c) 3596 (d) 3374
  29. 29.What is the mean of 20, 3, 19, 19 and 9? (a) 15 (b) 14 (c) 16 (d) 13
  30. 30.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/2 (c) 1/3 (d) 1/4
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 1 (b) 4 (c) 2 (d) 3
  32. 32.A bag has 4 yellow, 2 red and 3 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 4/9 (b) 5/9 (c) 4/5 (d) 1/3
  33. 33.What is the midpoint of the line joining (0, 5) and (6, 17)? (a) (6, 22) (b) (11, 3) (c) (3, 11) (d) (3, 6)
  34. 34.4 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 6 (b) 8 (c) 12 (d) 16
  35. 35.What is the midpoint of the line joining (8, 1) and (12, 3)? (a) (2, 1) (b) (10, 2) (c) (2, 10) (d) (20, 4)
  36. 36.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
  37. 37.How many prime numbers are there between 20 and 40? (a) 5 (b) 6 (c) 3 (d) 4
  38. 38.What is the sum of the first 8 terms of the AP 6, 9, 12, …? (a) 27 (b) 144 (c) 264 (d) 132
  39. 39.In a class of 32 children, 16 like mangoes, 19 like bananas and 7 like both. How many like neither? (a) 7 (b) 4 (c) 11 (d) 5
  40. 40.What is the product of the roots of x² − 16x + 63 = 0? (a) 16 (b) 62 (c) 64 (d) 63

Answer key

  1. 17
  2. 11
  3. 90
  4. 3
  5. 14
  6. 1035
  7. 5
  8. 8
  9. 6561
  10. 5
  11. 174 sq cm
  12. 11
  13. 25°
  14. 72
  15. 12
  16. 1/2
  17. 7
  18. 6724
  19. 50°
  20. 125°
  21. 2³ × 3 × 5
  22. 21
  23. 361
  24. 1/9
  25. 15
  26. 42
  27. 16
  28. 3364
  29. 14
  30. 3/4
  31. 3
  32. 4/9
  33. (3, 11)
  34. 8
  35. (10, 2)
  36. 1/3
  37. 4
  38. 132
  39. 4
  40. 63

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