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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 873 · 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.What is the smallest prime factor of 145? (a) 1 (b) 29 (c) 2 (d) 5
  2. 2.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  3. 3.How many prime numbers are there between 40 and 60? (a) 6 (b) 7 (c) 4 (d) 5
  4. 4.Two angles of a triangle are 20° and 50°. What is the third angle? (a) 160° (b) 130° (c) 70° (d) 110°
  5. 5.What is the product of the roots of x² − 11x + 30 = 0? (a) 11 (b) 29 (c) 30 (d) 31
  6. 6.How many factors does 53 have? (a) 1 (b) 4 (c) 2 (d) 3
  7. 7.In a class of 48 children, 25 like cricket, 20 like football and 7 like both. How many like at least one of the two? (a) 31 (b) 45 (c) 48 (d) 38
  8. 8.Which is the correct factorisation of x² + 16x + 63? (a) (x + 7)(x + 9) (b) (x + 1)(x + 15) (c) (x − 7)(x − 9) (d) (x + 1)(x + 63)
  9. 9.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 245° (b) 66° (c) 115° (d) 65°
  10. 10.What is the sum of all the whole numbers from 1 to 34? (a) 561 (b) 578 (c) 1190 (d) 595
  11. 11.What is the smallest prime factor of 91? (a) 1 (b) 2 (c) 13 (d) 7
  12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/11 (b) 7/36 (c) 6/11 (d) 1/6
  13. 13.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
  14. 14.In a class of 34 children, 21 like mangoes, 10 like bananas and 5 like both. How many like neither? (a) 8 (b) 3 (c) 13 (d) 5
  15. 15.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 60 (c) 68 (d) 59
  16. 16.In a class of 30 children, 22 like dance, 18 like music and 11 like both. How many like only dance? (a) 11 (b) 7 (c) 12 (d) 22
  17. 17.What is the 36th term of the AP 8, 11, 14, 17, …? (a) 108 (b) 113 (c) 116 (d) 105
  18. 18.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 27 sq cm (c) 36 sq cm (d) 54 sq cm
  19. 19.What is the mode of 8, 15, 9, 8, 2, 8 and 15? (a) 15 (b) 8 (c) 9 (d) 2
  20. 20.In a class of 24 children, 6 like tea, 19 like coffee and 2 like neither. How many like both? (a) 1 (b) 2 (c) 22 (d) 3
  21. 21.A bag has 8 red, 6 green and 6 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 3/4 (c) 3/10 (d) 7/10
  22. 22.What is the 23rd term of the AP 12, 21, 30, 39, …? (a) 198 (b) 210 (c) 207 (d) 219
  23. 23.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
  24. 24.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 80° (c) 10° (d) 100°
  25. 25.Which is the correct factorisation of x² + 13x + 40? (a) (x + 1)(x + 40) (b) (x + 5)(x + 8) (c) (x + 1)(x + 12) (d) (x − 5)(x − 8)
  26. 26.What is the sum of the first 7 terms of the AP 9, 15, 21, …? (a) 210 (b) 378 (c) 45 (d) 189
  27. 27.A drawer has lots of green, white, black, 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) 10 (b) 6 (c) 2 (d) 5
  28. 28.In a class of 34 children, 18 like mangoes, 22 like bananas and 2 like neither. How many like both? (a) 32 (b) 8 (c) 6 (d) 2
  29. 29.A cube has edges of 12 cm. What is its total surface area? (a) 1728 sq cm (b) 864 sq cm (c) 576 sq cm (d) 144 sq cm
  30. 30.If a + b = 19 and ab = 90, what is a² + b²? (a) 271 (b) 541 (c) 181 (d) 361
  31. 31.A bag has 5 black balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 2 (c) 11 (d) 15
  32. 32.What is the mode of 7, 7, 1, 20, 6, 20 and 7? (a) 6 (b) 7 (c) 1 (d) 20
  33. 33.What is the smallest prime factor of 65? (a) 1 (b) 5 (c) 2 (d) 13
  34. 34.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/12 (c) 1/9 (d) 1/11
  35. 35.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 28 (c) 21 (d) 49
  36. 36.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 100° (b) 120° (c) 140° (d) 60°
  37. 37.A bag has 8 yellow, 4 blue and 5 green balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 8/9 (b) 8/17 (c) 9/17 (d) 1/3
  38. 38.A canteen sells 3 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 36 (b) 21 (c) 9 (d) 18
  39. 39.In a class of 22 children, 9 like maths, 16 like science and 4 like both. How many like at least one of the two? (a) 22 (b) 17 (c) 25 (d) 21
  40. 40.A bag has 7 blue, 4 red and 8 green balls. One ball is taken out without looking. What is the probability that it is blue? (a) 12/19 (b) 7/12 (c) 1/3 (d) 7/19

Answer key

  1. 5
  2. 10
  3. 5
  4. 110°
  5. 30
  6. 2
  7. 38
  8. (x + 7)(x + 9)
  9. 65°
  10. 595
  11. 7
  12. 1/6
  13. 1386 sq cm
  14. 8
  15. 59
  16. 11
  17. 113
  18. 54 sq cm
  19. 8
  20. 3
  21. 7/10
  22. 210
  23. 176 cm
  24. 20°
  25. (x + 5)(x + 8)
  26. 189
  27. 6
  28. 8
  29. 864 sq cm
  30. 181
  31. 11
  32. 7
  33. 5
  34. 1/12
  35. 21
  36. 60°
  37. 8/17
  38. 18
  39. 21
  40. 7/19

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