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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 686 · 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.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 70° (b) 220° (c) 40° (d) 110°
  2. 2.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 63? (a) 16 (b) 15 (c) 6 (d) 17
  4. 4.In a class of 22 children, 10 like mangoes, 12 like bananas and 7 like both. How many like only mangoes? (a) 3 (b) 7 (c) 10 (d) 5
  5. 5.What is the mode of 19, 19, 2, 8, 6, 19 and 8? (a) 8 (b) 19 (c) 2 (d) 6
  6. 6.In a class of 42 children, 26 like tea, 14 like coffee and 7 like both. How many like neither? (a) 7 (b) 9 (c) 16 (d) 2
  7. 7.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) 8 (b) 7 (c) 15 (d) 14
  8. 8.A drawer has lots of yellow, green, red and blue 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) 8 (c) 4 (d) 5
  9. 9.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 3/8 (c) 1/4 (d) 5/8
  10. 10.What is the mode of 14, 15, 15, 17, 15, 12 and 14? (a) 14 (b) 12 (c) 17 (d) 15
  11. 11.What is the midpoint of the line joining (0, 7) and (2, 19)? (a) (1, 13) (b) (2, 26) (c) (1, 6) (d) (13, 1)
  12. 12.If a + b = 13 and ab = 12, what is a² + b²? (a) 145 (b) 169 (c) 193 (d) 157
  13. 13.What is the mode of 3, 5, 5, 15, 16, 16 and 16? (a) 15 (b) 5 (c) 3 (d) 16
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 35? (a) 4 (b) 2 (c) 3 (d) 1
  15. 15.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 75° (b) 255° (c) 105° (d) 150°
  16. 16.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/2 (c) 1/3 (d) 3/4
  17. 17.What is the mode of 16, 18, 16, 13, 18, 9 and 18? (a) 13 (b) 18 (c) 16 (d) 9
  18. 18.What is the distance between the points (0, 13) and (8, 7)? (a) 14 (b) 100 (c) 10 (d) 11
  19. 19.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
  20. 20.What is the mode of 5, 3, 11, 3, 3, 11 and 2? (a) 11 (b) 5 (c) 3 (d) 2
  21. 21.Two angles of a triangle are 25° and 45°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 155° (d) 135°
  22. 22.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 24 sq cm (b) 104 sq cm (c) 26 sq cm (d) 52 sq cm
  23. 23.What are the roots of x² − 17x + 72 = 0? (a) 2 and 36 (b) 8 and 9 (c) 1 and 72 (d) 1 and 16
  24. 24.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 10 (c) 20 (d) 11
  25. 25.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 12 (c) 15 (d) 30
  26. 26.What is the midpoint of the line joining (2, 2) and (10, 14)? (a) (6, 8) (b) (8, 6) (c) (4, 6) (d) (12, 16)
  27. 27.Using (a + b)² = a² + 2ab + b², what is 72²? (a) 5194 (b) 4904 (c) 5184 (d) 4624
  28. 28.What is the midpoint of the line joining (7, 7) and (13, 17)? (a) (20, 24) (b) (3, 5) (c) (10, 12) (d) (12, 10)
  29. 29.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 198 (b) 69 (c) 66 (d) 22
  30. 30.What are the roots of x² − 12x + 27 = 0? (a) 2 and 10 (b) 1 and 27 (c) 1 and 11 (d) 3 and 9
  31. 31.How many factors does 34 have? (a) 4 (b) 2 (c) 3 (d) 5
  32. 32.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 30 (c) 15 (d) 36
  33. 33.How many prime numbers are there between 80 and 90? (a) 2 (b) 1 (c) 4 (d) 3
  34. 34.In a class of 39 children, 20 like dance, 13 like music and 4 like both. How many like only dance? (a) 26 (b) 20 (c) 9 (d) 16
  35. 35.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 6 (c) 12 (d) 3
  36. 36.A cuboid is 12 cm long, 5 cm wide and 5 cm high. What is its volume? (a) 290 cu cm (b) 22 cu cm (c) 300 cu cm (d) 60 cu cm
  37. 37.In a class of 38 children, 25 like cricket, 16 like football and 11 like both. How many like neither? (a) 11 (b) 8 (c) 19 (d) 9
  38. 38.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 1/11 (c) 3/11 (d) 1/9
  39. 39.What is the sum of the roots of x² − 8x + 12 = 0? (a) 9 (b) 12 (c) 8 (d) 7
  40. 40.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 42 (c) 21 (d) 28

Answer key

  1. 110°
  2. 176 cm
  3. 16
  4. 3
  5. 19
  6. 9
  7. 8
  8. 5
  9. 3/8
  10. 15
  11. (1, 13)
  12. 145
  13. 16
  14. 3
  15. 105°
  16. 1/4
  17. 18
  18. 10
  19. 9 times
  20. 3
  21. 70°
  22. 52 sq cm
  23. 8 and 9
  24. 10
  25. 15
  26. (6, 8)
  27. 5184
  28. (10, 12)
  29. 66
  30. 3 and 9
  31. 4
  32. 30
  33. 2
  34. 16
  35. 6
  36. 300 cu cm
  37. 8
  38. 1/12
  39. 8
  40. 21

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