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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 69 · 40 questions
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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.In a class of 35 children, 16 like tea, 16 like coffee and 6 like both. How many like only tea? (a) 19 (b) 6 (c) 10 (d) 16
  2. 2.How many factors does 12 have? (a) 7 (b) 6 (c) 4 (d) 5
  3. 3.How many factors does 78 have? (a) 7 (b) 8 (c) 9 (d) 6
  4. 4.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 15 cu cm (b) 6 cu cm (c) 112 cu cm (d) 60 cu cm
  5. 5.In which quadrant does the point (9, 8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  6. 6.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 120 (c) 20 (d) 240
  7. 7.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
  8. 8.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
  9. 9.How many prime numbers are there between 70 and 90? (a) 7 (b) 6 (c) 5 (d) 4
  10. 10.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 676 (c) 702 (d) 51
  11. 11.In a class of 49 children, 29 like mangoes, 28 like bananas and 9 like both. How many like neither? (a) 2 (b) 1 (c) 10 (d) 9
  12. 12.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 21 (c) 63 (d) 7
  13. 13.A drawer has lots of green, black 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) 2 (b) 4 (c) 3 (d) 6
  14. 14.Two angles of a triangle are 40° and 25°. What is the exterior angle at the third corner? (a) 65° (b) 155° (c) 115° (d) 140°
  15. 15.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 80 (b) 41 (c) 10 (d) 40
  16. 16.What is the prime factorisation of 14? (a) 2 × 7² (b) 2² × 7 (c) 2³ × 7 (d) 2 × 7
  17. 17.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  18. 18.A bag has 10 white balls and 12 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 12 (b) 22 (c) 2 (d) 11
  19. 19.5 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) 12 (b) 35 (c) 40 (d) 70
  20. 20.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 16° (b) 195° (c) 165° (d) 15°
  21. 21.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 14 (b) 15 (c) 8 (d) 7
  22. 22.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 14 (c) 42 (d) 49
  23. 23.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
  24. 24.The mean of 9 numbers is 23. When the number 63 is added to them, what is the new mean? (a) 27 (b) 28 (c) 43 (d) 23
  25. 25.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 3 (c) 6 (d) 9
  26. 26.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
  27. 27.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 5 (d) 14
  28. 28.The mean of 6 numbers is 10. When the number 3 is added to them, what is the new mean? (a) 9 (b) 8 (c) 10 (d) 11
  29. 29.What is the sum of all the whole numbers from 1 to 46? (a) 1081 (b) 1035 (c) 2162 (d) 1058
  30. 30.What is the sum of the roots of x² − 14x + 45 = 0? (a) 14 (b) 13 (c) 15 (d) 45
  31. 31.Using (a − b)² = a² − 2ab + b², what is 37²? (a) 1849 (b) 1591 (c) 1379 (d) 1369
  32. 32.What is the median of 3, 7, 16, 27 and 32? (a) 7 (b) 27 (c) 17 (d) 16
  33. 33.Two angles of a triangle are 65° and 35°. What is the third angle? (a) 115° (b) 80° (c) 145° (d) 100°
  34. 34.3 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 18 (b) 12 (c) 6 (d) 9
  35. 35.What is the mode of 8, 9, 8, 2, 8, 4 and 9? (a) 4 (b) 2 (c) 9 (d) 8
  36. 36.Two angles of a triangle are 60° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 120° (c) 45° (d) 135°
  37. 37.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 36 cu cm (c) 27 cu cm (d) 54 cu cm
  38. 38.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 216 cu cm (c) 144 cu cm (d) 18 cu cm
  39. 39.In a class of 36 children, 23 like cricket, 20 like football and 9 like both. How many like at least one of the two? (a) 36 (b) 25 (c) 34 (d) 43
  40. 40.Using (a − b)² = a² − 2ab + b², what is 99²? (a) 10201 (b) 9801 (c) 9999 (d) 9811

Answer key

  1. 10
  2. 6
  3. 8
  4. 60 cu cm
  5. First quadrant
  6. 120
  7. 88 cm
  8. 20
  9. 5
  10. 676
  11. 1
  12. 21
  13. 4
  14. 65°
  15. 40
  16. 2 × 7
  17. 5
  18. 12
  19. 35
  20. 15°
  21. 8
  22. 21
  23. 9 times
  24. 27
  25. 6
  26. 3/4
  27. 6
  28. 9
  29. 1081
  30. 14
  31. 1369
  32. 16
  33. 80°
  34. 9
  35. 8
  36. 135°
  37. 27 cu cm
  38. 216 cu cm
  39. 34
  40. 9801

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