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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 4 · 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 area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
  2. 2.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 23 (b) 72 (c) 69 (d) 207
  3. 3.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 51° (b) 50° (c) 230° (d) 130°
  4. 4.What is the 28th term of the AP 17, 26, 35, 44, …? (a) 243 (b) 252 (c) 260 (d) 269
  5. 5.In a class of 21 children, 11 like tea, 10 like coffee and 5 like both. How many like at least one of the two? (a) 21 (b) 11 (c) 17 (d) 16
  6. 6.The mean of 6 numbers is 25. When the number 32 is added to them, what is the new mean? (a) 28 (b) 25 (c) 26 (d) 27
  7. 7.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
  8. 8.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  9. 9.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 42 (b) 9 (c) 78 (d) 39
  10. 10.What is the mean of 15, 10, 8, 19 and 8? (a) 13 (b) 15 (c) 12 (d) 10
  11. 11.What is the mean of 8, 4, 2 and 6? (a) 6 (b) 7 (c) 4 (d) 5
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 8 (d) 10
  13. 13.In a class of 33 children, 19 like mangoes, 20 like bananas and 11 like both. How many like at least one of the two? (a) 39 (b) 17 (c) 33 (d) 28
  14. 14.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) 63 (b) 7 (c) 24 (d) 21
  15. 15.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
  16. 16.In a class of 28 children, 14 like cricket, 19 like football and 4 like neither. How many like both? (a) 5 (b) 24 (c) 4 (d) 9
  17. 17.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 12 (c) 3 (d) 6
  18. 18.In a class of 48 children, 24 like maths, 24 like science and 6 like both. How many like at least one of the two? (a) 43 (b) 42 (c) 48 (d) 36
  19. 19.How many factors does 106 have? (a) 4 (b) 2 (c) 5 (d) 3
  20. 20.What is the smallest prime factor of 85? (a) 5 (b) 17 (c) 2 (d) 1
  21. 21.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/6 (b) 5/11 (c) 1/11 (d) 5/36
  22. 22.What is the mode of 6, 6, 10, 6, 5, 3 and 5? (a) 6 (b) 10 (c) 3 (d) 5
  23. 23.What is the mode of 2, 12, 12, 6, 6, 6 and 8? (a) 12 (b) 2 (c) 6 (d) 8
  24. 24.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
  25. 25.A cube has edges of 12 cm. What is its volume? (a) 36 cu cm (b) 864 cu cm (c) 576 cu cm (d) 1728 cu cm
  26. 26.What is the missing term in the AP 13, ?, 21, 25, 29? (a) 16 (b) 18 (c) 17 (d) 21
  27. 27.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
  28. 28.A bag has 3 green balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 5 (b) 2 (c) 4 (d) 7
  29. 29.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
  30. 30.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 30 cu cm (c) 1000 cu cm (d) 400 cu cm
  31. 31.What are the roots of x² − 11x + 28 = 0? (a) 2 and 14 (b) 1 and 10 (c) 4 and 7 (d) 1 and 28
  32. 32.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) 4 times (c) 2 times (d) 5 times
  33. 33.There are 3 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 7 (b) 15 (c) 12 (d) 24
  34. 34.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  35. 35.Using (a − b)² = a² − 2ab + b², what is 29²? (a) 899 (b) 961 (c) 841 (d) 851
  36. 36.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 30° (c) 40° (d) 60°
  37. 37.What is the mean of 5, 7, 3 and 13? (a) 6 (b) 9 (c) 8 (d) 7
  38. 38.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 40° (c) 100° (d) 140°
  39. 39.Which is the correct factorisation of x² + 11x + 28? (a) (x + 1)(x + 10) (b) (x + 4)(x + 7) (c) (x − 4)(x − 7) (d) (x + 1)(x + 28)
  40. 40.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) 12 (b) 25 (c) 24 (d) 13

Answer key

  1. 1386 sq cm
  2. 69
  3. 50°
  4. 260
  5. 16
  6. 26
  7. 13
  8. 5
  9. 39
  10. 12
  11. 5
  12. 9
  13. 28
  14. 21
  15. 20
  16. 9
  17. 6
  18. 42
  19. 4
  20. 5
  21. 5/36
  22. 6
  23. 6
  24. 176 cm
  25. 1728 cu cm
  26. 17
  27. 13
  28. 5
  29. 1/2
  30. 1000 cu cm
  31. 4 and 7
  32. 4 times
  33. 12
  34. 17
  35. 841
  36. 30°
  37. 7
  38. 100°
  39. (x + 4)(x + 7)
  40. 13

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