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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 441 · 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 many prime numbers are there between 80 and 90? (a) 2 (b) 4 (c) 3 (d) 1
  2. 2.In which quadrant does the point (−1, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  3. 3.What is the sum of the roots of x² − 13x + 40 = 0? (a) 13 (b) 14 (c) 12 (d) 40
  4. 4.What is the prime factorisation of 60? (a) 2 × 3 × 5² (b) 2³ × 3 × 5 (c) 2 × 3 × 5 (d) 2² × 3 × 5
  5. 5.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 64 times (c) 4 times (d) 8 times
  6. 6.5 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) 20 (b) 15 (c) 10 (d) 7
  7. 7.How many factors does 78 have? (a) 9 (b) 7 (c) 6 (d) 8
  8. 8.What is the midpoint of the line joining (0, 3) and (2, 7)? (a) (5, 1) (b) (1, 2) (c) (1, 5) (d) (2, 10)
  9. 9.What is the distance between the points (3, 17) and (9, 9)? (a) 14 (b) 10 (c) 11 (d) 100
  10. 10.In a class of 54 children, 29 like mangoes, 30 like bananas and 12 like both. How many like neither? (a) 7 (b) 8 (c) 12 (d) 19
  11. 11.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 3 (b) 1 (c) 4 (d) 2
  13. 13.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  14. 14.What is the distance between the points (0, 5) and (6, 13)? (a) 14 (b) 11 (c) 10 (d) 100
  15. 15.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/2 (c) 1/3 (d) 3/4
  16. 16.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
  17. 17.What is the 34th term of the AP 4, 10, 16, 22, …? (a) 204 (b) 208 (c) 202 (d) 198
  18. 18.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
  19. 19.In which quadrant does the point (7, 6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  20. 20.A cuboid is 7 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 190 cu cm (b) 18 cu cm (c) 126 cu cm (d) 14 cu cm
  21. 21.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 75° (b) 105° (c) 76° (d) 255°
  22. 22.What is the smallest prime factor of 121? (a) 1 (b) 2 (c) 11 (d) 3
  23. 23.What is the 15th term of the AP 2, 7, 12, 17, …? (a) 70 (b) 72 (c) 75 (d) 77
  24. 24.What is the prime factorisation of 210? (a) 2³ × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2 × 3 × 5 × 7 (d) 2² × 3 × 5 × 7
  25. 25.What is the prime factorisation of 168? (a) 2² × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7³ (d) 2⁴ × 3 × 7
  26. 26.What is the sum of the roots of x² − 15x + 56 = 0? (a) 16 (b) 15 (c) 14 (d) 56
  27. 27.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
  28. 28.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  29. 29.How many prime numbers are there between 10 and 20? (a) 4 (b) 5 (c) 3 (d) 6
  30. 30.What is the sum of the first 7 terms of the AP 10, 12, 14, …? (a) 22 (b) 119 (c) 112 (d) 224
  31. 31.What is the mode of 3, 1, 19, 19, 11, 11 and 11? (a) 19 (b) 11 (c) 3 (d) 1
  32. 32.What is the distance between the points (9, 0) and (13, 3)? (a) 7 (b) 6 (c) 5 (d) 25
  33. 33.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 64 (c) 28 (d) 16
  34. 34.The mean of 3 numbers is 23. When the number 19 is added to them, what is the new mean? (a) 21 (b) 23 (c) 24 (d) 22
  35. 35.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 88 cm (d) 22 cm
  36. 36.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 28 (b) 108 (c) 186 (d) 93
  37. 37.What is the mean of 16, 11, 20, 3, 5 and 17? (a) 11 (b) 12 (c) 14 (d) 13
  38. 38.A bag has 3 yellow, 5 red and 3 white balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 3/8 (b) 3/11 (c) 1/3 (d) 8/11
  39. 39.A drawer has lots of green and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 5 (c) 3 (d) 2
  40. 40.In a class of 17 children, 11 like dance, 10 like music and 5 like both. How many like neither? (a) 5 (b) 2 (c) 1 (d) 6

Answer key

  1. 2
  2. Third quadrant
  3. 13
  4. 2² × 3 × 5
  5. 16 times
  6. 10
  7. 8
  8. (1, 5)
  9. 10
  10. 7
  11. 120
  12. 3
  13. 5
  14. 10
  15. 3/4
  16. 88 cm
  17. 202
  18. 44 cm
  19. First quadrant
  20. 126 cu cm
  21. 75°
  22. 11
  23. 72
  24. 2 × 3 × 5 × 7
  25. 2³ × 3 × 7
  26. 15
  27. 2
  28. 17
  29. 4
  30. 112
  31. 11
  32. 5
  33. 56
  34. 22
  35. 44 cm
  36. 93
  37. 12
  38. 3/11
  39. 3
  40. 1

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