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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 459 · 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.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 270 (b) 135 (c) 140 (d) 18
  2. 2.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  3. 3.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 1/8 (c) 3/8 (d) 1/4
  4. 4.In a class of 34 children, 21 like mangoes, 15 like bananas and 10 like both. How many like at least one of the two? (a) 36 (b) 16 (c) 34 (d) 26
  5. 5.What is the midpoint of the line joining (2, 10) and (6, 0)? (a) (8, 10) (b) (4, 5) (c) (2, 5) (d) (5, 4)
  6. 6.What is the mean of 12, 17, 3 and 8? (a) 8 (b) 10 (c) 9 (d) 11
  7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/36 (b) 1/6 (c) 5/11 (d) 1/11
  8. 8.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 117 (b) 31 (c) 224 (d) 112
  9. 9.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 50° (c) 80° (d) 40°
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 80? (a) 8 (b) 18 (c) 19 (d) 17
  11. 11.A bag has 6 yellow, 2 green and 6 white balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/3 (b) 4/7 (c) 9/14 (d) 3/7
  12. 12.The mean of 4 numbers is 37. When the number 57 is added to them, what is the new mean? (a) 42 (b) 47 (c) 37 (d) 41
  13. 13.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 25 (b) 12 (c) 24 (d) 13
  14. 14.What is the mean of 4, 7, 9, 15 and 20? (a) 12 (b) 10 (c) 13 (d) 11
  15. 15.In a class of 30 children, 12 like cricket, 19 like football and 7 like both. How many like at least one of the two? (a) 30 (b) 31 (c) 24 (d) 17
  16. 16.If a + b = 15 and ab = 54, what is (a − b)²? (a) 225 (b) 9 (c) 117 (d) 3
  17. 17.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  18. 18.What is the sum of the first 8 terms of the AP 8, 11, 14, …? (a) 296 (b) 160 (c) 29 (d) 148
  19. 19.A canteen sells 7 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 11 (c) 28 (d) 35
  20. 20.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 96 sq cm (c) 16 sq cm (d) 97 sq cm
  21. 21.How many factors does 27 have? (a) 4 (b) 2 (c) 5 (d) 3
  22. 22.In a class of 36 children, 23 like tea, 9 like coffee and 6 like both. How many like only tea? (a) 27 (b) 3 (c) 17 (d) 23
  23. 23.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 14 (d) 7
  24. 24.What is the missing term in the AP 3, ?, 21, 30, 39? (a) 12 (b) 13 (c) 21 (d) 11
  25. 25.If a + b = 18 and ab = 80, what is (a − b)²? (a) 164 (b) 2 (c) 4 (d) 324
  26. 26.In a class of 43 children, 15 like dance, 29 like music and 8 like neither. How many like both? (a) 8 (b) 9 (c) 1 (d) 35
  27. 27.What are the roots of x² − 12x + 35 = 0? (a) 1 and 11 (b) 1 and 35 (c) 2 and 10 (d) 5 and 7
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 100° (b) 130° (c) 51° (d) 50°
  29. 29.How many prime numbers are there between 60 and 90? (a) 9 (b) 6 (c) 7 (d) 8
  30. 30.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) 63 (c) 20 (d) 180
  31. 31.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 3/11 (c) 1/11 (d) 1/9
  32. 32.In a class of 30 children, 16 like cricket, 22 like football and 9 like both. How many like only cricket? (a) 7 (b) 13 (c) 8 (d) 16
  33. 33.What is the mean of 16, 15, 6 and 11? (a) 11 (b) 16 (c) 12 (d) 13
  34. 34.A canteen sells 4 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 24 (c) 12 (d) 16
  35. 35.What is the 26th term of the AP 18, 22, 26, 30, …? (a) 118 (b) 100 (c) 104 (d) 122
  36. 36.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
  37. 37.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
  38. 38.In a class of 28 children, 9 like mangoes, 19 like bananas and 3 like both. How many like only mangoes? (a) 9 (b) 3 (c) 6 (d) 16
  39. 39.What is the prime factorisation of 20? (a) 2 × 5 (b) 2 × 5² (c) 2² × 5 (d) 2³ × 5
  40. 40.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 110° (b) 130° (c) 120° (d) 50°

Answer key

  1. 135
  2. 24
  3. 3/4
  4. 26
  5. (4, 5)
  6. 10
  7. 5/36
  8. 112
  9. 40°
  10. 18
  11. 4/7
  12. 41
  13. 13
  14. 11
  15. 24
  16. 9
  17. 15
  18. 148
  19. 28
  20. 96 sq cm
  21. 4
  22. 17
  23. 6
  24. 12
  25. 4
  26. 9
  27. 5 and 7
  28. 50°
  29. 7
  30. 60
  31. 1/12
  32. 7
  33. 12
  34. 12
  35. 118
  36. 88 cm
  37. 1/3
  38. 6
  39. 2² × 5
  40. 130°

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