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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 234 · 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.A bag has 4 yellow balls and 5 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 6 (c) 9 (d) 5
  2. 2.A bag has 9 white balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 20 (b) 10 (c) 12 (d) 2
  3. 3.What is the distance between the points (2, 0) and (11, 12)? (a) 15 (b) 225 (c) 16 (d) 21
  4. 4.What is the 38th term of the AP 1, 8, 15, 22, …? (a) 266 (b) 267 (c) 260 (d) 259
  5. 5.A bag has 4 red, 7 yellow and 2 white balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 4/13 (c) 4/9 (d) 9/13
  6. 6.A bag has 8 white, 4 green and 7 yellow balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/3 (b) 15/19 (c) 4/15 (d) 4/19
  7. 7.What is the 12th term of the AP 6, 9, 12, 15, …? (a) 39 (b) 33 (c) 42 (d) 36
  8. 8.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 51 (c) 16 (d) 144
  9. 9.If a + b = 13 and ab = 40, what is (a − b)²? (a) 89 (b) 3 (c) 169 (d) 9
  10. 10.What is the 27th term of the AP 20, 25, 30, 35, …? (a) 130 (b) 150 (c) 155 (d) 135
  11. 11.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 156 (c) 91 (d) 169
  12. 12.In a class of 28 children, 15 like tea, 11 like coffee and 8 like both. How many like neither? (a) 18 (b) 2 (c) 8 (d) 10
  13. 13.How many prime numbers are there between 20 and 40? (a) 6 (b) 5 (c) 3 (d) 4
  14. 14.Two angles of a triangle are 50° and 70°. What is the exterior angle at the third corner? (a) 130° (b) 120° (c) 60° (d) 110°
  15. 15.What is the prime factorisation of 126? (a) 2² × 3² × 7 (b) 2³ × 3² × 7 (c) 2 × 3² × 7 (d) 2 × 3² × 7²
  16. 16.What is the prime factorisation of 28? (a) 2² × 7 (b) 2 × 7² (c) 2³ × 7 (d) 2 × 7
  17. 17.How many factors does 103 have? (a) 4 (b) 1 (c) 2 (d) 3
  18. 18.How many factors does 22 have? (a) 4 (b) 2 (c) 5 (d) 3
  19. 19.Which term of the AP 20, 29, 38, 47, … is 137? (a) 16th (b) 13th (c) 15th (d) 14th
  20. 20.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
  21. 21.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/5 (b) 5/6 (c) 1/6 (d) 1/3
  22. 22.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/8 (c) 3/8 (d) 3/4
  23. 23.A bag has 8 blue balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 9 (b) 13 (c) 2 (d) 10
  24. 24.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 25° (c) 130° (d) 65°
  25. 25.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 1/12 (c) 1/18 (d) 2/11
  26. 26.Two angles of a triangle are 30° and 30°. What is the third angle? (a) 60° (b) 150° (c) 120° (d) 300°
  27. 27.What is the distance between the points (7, 1) and (22, 9)? (a) 18 (b) 289 (c) 17 (d) 23
  28. 28.What is the 30th term of the AP 4, 7, 10, 13, …? (a) 87 (b) 91 (c) 90 (d) 94
  29. 29.In a class of 14 children, 8 like maths, 8 like science and 5 like both. How many like at least one of the two? (a) 6 (b) 11 (c) 16 (d) 14
  30. 30.Using (a − b)² = a² − 2ab + b², what is 15²? (a) 625 (b) 375 (c) 235 (d) 225
  31. 31.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 35° (c) 145° (d) 110°
  32. 32.What is the prime factorisation of 40? (a) 2² × 5 (b) 2³ × 5 (c) 2 × 5³ (d) 2⁴ × 5
  33. 33.What is the median of 39, 29, 2, 7 and 12? (a) 29 (b) 7 (c) 2 (d) 12
  34. 34.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 7/8 (b) 1/7 (c) 1/8 (d) 1/4
  35. 35.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/3 (c) 3/4 (d) 1/2
  36. 36.What is the midpoint of the line joining (4, 16) and (6, 8)? (a) (10, 24) (b) (12, 5) (c) (5, 12) (d) (1, 4)
  37. 37.What is the distance between the points (1, 12) and (13, 7)? (a) 17 (b) 169 (c) 13 (d) 14
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 60° (b) 150° (c) 30° (d) 31°
  39. 39.Using (a + b)² = a² + 2ab + b², what is 44²? (a) 1936 (b) 1946 (c) 1296 (d) 1616
  40. 40.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 155° (b) 110° (c) 95° (d) 85°

Answer key

  1. 6
  2. 12
  3. 15
  4. 260
  5. 4/13
  6. 4/19
  7. 39
  8. 48
  9. 9
  10. 150
  11. 78
  12. 10
  13. 4
  14. 120°
  15. 2 × 3² × 7
  16. 2² × 7
  17. 2
  18. 4
  19. 14th
  20. 132 cm
  21. 5/6
  22. 3/4
  23. 10
  24. 130°
  25. 1/18
  26. 120°
  27. 17
  28. 91
  29. 11
  30. 225
  31. 110°
  32. 2³ × 5
  33. 12
  34. 1/8
  35. 1/4
  36. (5, 12)
  37. 13
  38. 30°
  39. 1936
  40. 95°

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