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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 514 · 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 5 yellow balls and 6 blue 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) 11 (d) 7
  2. 2.What is the smallest prime factor of 85? (a) 2 (b) 1 (c) 17 (d) 5
  3. 3.In a class of 44 children, 20 like maths, 25 like science and 6 like both. How many like at least one of the two? (a) 33 (b) 39 (c) 45 (d) 44
  4. 4.A drawer has lots of yellow 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) 5 (b) 2 (c) 4 (d) 3
  5. 5.What is the median of 30, 34, 1, 15, 6, 5 and 28? (a) 6 (b) 28 (c) 17 (d) 15
  6. 6.What is the 25th term of the AP 14, 17, 20, 23, …? (a) 89 (b) 75 (c) 86 (d) 72
  7. 7.In a class of 39 children, 27 like tea, 18 like coffee and 3 like neither. How many like both? (a) 36 (b) 6 (c) 3 (d) 9
  8. 8.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 10° (b) 11° (c) 20° (d) 170°
  9. 9.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
  10. 10.What is the prime factorisation of 80? (a) 2⁵ × 5 (b) 2⁴ × 5 (c) 2 × 5⁴ (d) 2³ × 5
  11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/9 (c) 1/12 (d) 1/11
  12. 12.What is the median of 19, 32, 24, 40 and 10? (a) 24 (b) 25 (c) 19 (d) 32
  13. 13.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 13 (c) 42 (d) 39
  14. 14.In a class of 23 children, 12 like cricket, 12 like football and 2 like both. How many like only cricket? (a) 12 (b) 10 (c) 11 (d) 2
  15. 15.How many factors does 77 have? (a) 2 (b) 3 (c) 4 (d) 5
  16. 16.What is the mean of 16, 14, 8, 13, 8 and 13? (a) 13 (b) 14 (c) 12 (d) 11
  17. 17.In a class of 33 children, 19 like tea, 12 like coffee and 2 like both. How many like only tea? (a) 19 (b) 21 (c) 10 (d) 17
  18. 18.A drawer has lots of blue, yellow and white 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) 2 (c) 3 (d) 6
  19. 19.How many prime numbers are there between 30 and 40? (a) 2 (b) 4 (c) 1 (d) 3
  20. 20.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
  21. 21.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 65° (c) 100° (d) 145°
  22. 22.What is the mode of 20, 9, 18, 20, 15, 20 and 15? (a) 20 (b) 9 (c) 15 (d) 18
  23. 23.What are the roots of x² − 17x + 72 = 0? (a) 1 and 16 (b) 1 and 72 (c) 2 and 36 (d) 8 and 9
  24. 24.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 45 (c) 36 (d) 81
  25. 25.What is the distance between the points (4, 4) and (13, 16)? (a) 225 (b) 16 (c) 21 (d) 15
  26. 26.A drawer has lots of white and red 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) 5 (d) 2
  27. 27.In a class of 45 children, 24 like mangoes, 30 like bananas and 12 like both. How many like only mangoes? (a) 12 (b) 15 (c) 24 (d) 18
  28. 28.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 50° (b) 40° (c) 310° (d) 130°
  29. 29.What is the median of 6, 37, 31, 16, 40, 30 and 24? (a) 30 (b) 24 (c) 16 (d) 31
  30. 30.In which quadrant does the point (−7, 7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  31. 31.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 49 (b) 13 (c) 98 (d) 56
  32. 32.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  33. 33.A bag has 4 yellow, 3 red and 7 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 1/14 (c) 1/2 (d) 4/7
  34. 34.3 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) 21 (b) 10 (c) 24 (d) 42
  35. 35.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
  36. 36.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 49 (c) 42 (d) 14
  37. 37.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 306 (c) 153 (d) 33
  38. 38.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
  39. 39.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
  40. 40.In a class of 43 children, 24 like dance, 24 like music and 11 like both. How many like neither? (a) 11 (b) 7 (c) 6 (d) 17

Answer key

  1. 7
  2. 5
  3. 39
  4. 3
  5. 15
  6. 86
  7. 9
  8. 10°
  9. 9 times
  10. 2⁴ × 5
  11. 1/12
  12. 24
  13. 39
  14. 10
  15. 4
  16. 12
  17. 17
  18. 4
  19. 2
  20. 1/2
  21. 115°
  22. 20
  23. 8 and 9
  24. 36
  25. 15
  26. 3
  27. 12
  28. 130°
  29. 30
  30. Second quadrant
  31. 49
  32. 120
  33. 1/2
  34. 21
  35. 88 cm
  36. 42
  37. 289
  38. 25
  39. 4 times
  40. 6

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