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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 622 · 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.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/9 (b) 5/36 (c) 1/11 (d) 4/11
  2. 2.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  3. 3.A canteen sells 5 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 25 (c) 40 (d) 20
  4. 4.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 180 (c) 20 (d) 63
  5. 5.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 55° (b) 56° (c) 125° (d) 235°
  6. 6.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 42 (b) 12 (c) 84 (d) 48
  7. 7.In which quadrant does the point (−8, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  8. 8.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 100° (c) 50° (d) 140°
  9. 9.A drawer has lots of white, red and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 6 (c) 4 (d) 3
  10. 10.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
  11. 11.In a class of 34 children, 10 like cricket, 26 like football and 6 like both. How many like at least one of the two? (a) 24 (b) 36 (c) 34 (d) 30
  12. 12.Two angles of a triangle are 45° and 85°. What is the third angle? (a) 130° (b) 95° (c) 135° (d) 50°
  13. 13.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
  14. 14.In a class of 23 children, 10 like tea, 8 like coffee and 7 like neither. How many like both? (a) 16 (b) 3 (c) 2 (d) 7
  15. 15.What is the mean of 13, 13, 17, 15, 9 and 11? (a) 14 (b) 12 (c) 15 (d) 13
  16. 16.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 265° (c) 86° (d) 85°
  17. 17.How many prime numbers are there between 40 and 70? (a) 9 (b) 6 (c) 8 (d) 7
  18. 18.What is the median of 17, 9, 12, 11 and 3? (a) 11 (b) 9 (c) 12 (d) 10
  19. 19.In a class of 35 children, 26 like tea, 9 like coffee and 6 like both. How many like at least one of the two? (a) 35 (b) 30 (c) 29 (d) 23
  20. 20.How many factors does 54 have? (a) 9 (b) 7 (c) 8 (d) 6
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 94? (a) 21 (b) 19 (c) 20 (d) 9
  22. 22.What is the mode of 19, 13, 7, 19, 19, 13 and 8? (a) 8 (b) 7 (c) 19 (d) 13
  23. 23.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 36 (b) 48 (c) 37 (d) 49
  24. 24.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 30° (b) 75° (c) 135° (d) 150°
  25. 25.What is the 15th term of the AP 2, 8, 14, 20, …? (a) 90 (b) 84 (c) 92 (d) 86
  26. 26.In a class of 41 children, 16 like dance, 27 like music and 6 like neither. How many like both? (a) 2 (b) 6 (c) 8 (d) 35
  27. 27.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 108 (c) 36 (d) 12
  28. 28.A cuboid is 11 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 22 cu cm (b) 44 cu cm (c) 308 cu cm (d) 298 cu cm
  29. 29.Which term of the AP 11, 15, 19, 23, … is 47? (a) 11th (b) 10th (c) 12th (d) 9th
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 4 (b) 3 (c) 5 (d) 6
  31. 31.A bag has 10 yellow balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 11 (b) 2 (c) 17 (d) 12
  32. 32.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 48 (b) 88 (c) 9 (d) 44
  33. 33.What is the smallest prime factor of 91? (a) 2 (b) 1 (c) 7 (d) 13
  34. 34.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 10 (c) 21 (d) 24
  35. 35.What is the prime factorisation of 140? (a) 2² × 5 × 7 (b) 2 × 5 × 7 (c) 2 × 5 × 7² (d) 2³ × 5 × 7
  36. 36.What is the smallest prime factor of 39? (a) 1 (b) 2 (c) 3 (d) 13
  37. 37.What is the distance between the points (1, 16) and (17, 4)? (a) 20 (b) 21 (c) 400 (d) 28
  38. 38.In which quadrant does the point (−4, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  39. 39.In a class of 37 children, 13 like cricket, 28 like football and 8 like both. How many like neither? (a) 12 (b) 8 (c) 4 (d) 5
  40. 40.Which term of the AP 1, 5, 9, 13, … is 73? (a) 20th (b) 18th (c) 21st (d) 19th

Answer key

  1. 1/9
  2. 24
  3. 20
  4. 60
  5. 55°
  6. 42
  7. Second quadrant
  8. 100°
  9. 4
  10. 20
  11. 30
  12. 50°
  13. 88 cm
  14. 2
  15. 13
  16. 85°
  17. 7
  18. 11
  19. 29
  20. 8
  21. 20
  22. 19
  23. 37
  24. 150°
  25. 86
  26. 8
  27. 36
  28. 308 cu cm
  29. 10th
  30. 5
  31. 12
  32. 44
  33. 7
  34. 21
  35. 2² × 5 × 7
  36. 3
  37. 20
  38. Third quadrant
  39. 4
  40. 19th

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