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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 947 · 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.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  2. 2.In a class of 23 children, 18 like tea, 13 like coffee and 1 like neither. How many like both? (a) 8 (b) 9 (c) 22 (d) 1
  3. 3.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 91 (c) 78 (d) 156
  4. 4.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 486 cu cm (c) 324 cu cm (d) 729 cu cm
  5. 5.What is the smallest prime factor of 33? (a) 3 (b) 1 (c) 11 (d) 2
  6. 6.What is the midpoint of the line joining (3, 10) and (5, 22)? (a) (1, 6) (b) (8, 32) (c) (16, 4) (d) (4, 16)
  7. 7.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/5 (c) 5/8 (d) 3/8
  8. 8.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 64 sq cm (c) 97 sq cm (d) 96 sq cm
  9. 9.What is the median of 13, 23, 35, 3 and 9? (a) 13 (b) 9 (c) 23 (d) 35
  10. 10.7 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 35 (b) 56 (c) 11 (d) 28
  11. 11.How many factors does 88 have? (a) 9 (b) 7 (c) 8 (d) 6
  12. 12.What is the 36th term of the AP 18, 26, 34, 42, …? (a) 280 (b) 288 (c) 306 (d) 298
  13. 13.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 1/4 (c) 5/6 (d) 2/3
  14. 14.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 216 cu cm (c) 18 cu cm (d) 144 cu cm
  15. 15.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2⁴ × 7 (c) 2³ × 7 (d) 2² × 7
  16. 16.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 40° (c) 130° (d) 80°
  17. 17.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  18. 18.Using (a − b)² = a² − 2ab + b², what is 67²? (a) 4489 (b) 4891 (c) 4499 (d) 5329
  19. 19.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 4 (b) 5 (c) 6 (d) 3
  21. 21.How many factors does 32 have? (a) 7 (b) 4 (c) 5 (d) 6
  22. 22.Two angles of a triangle are 40° and 50°. What is the third angle? (a) 270° (b) 130° (c) 90° (d) 140°
  23. 23.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
  24. 24.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 35° (c) 110° (d) 55°
  25. 25.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 70° (c) 40° (d) 20°
  26. 26.What is the midpoint of the line joining (8, 22) and (10, 10)? (a) (16, 9) (b) (9, 16) (c) (1, 6) (d) (18, 32)
  27. 27.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 226 (b) 232 (c) 231 (d) 222
  28. 28.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 70° (c) 50° (d) 40°
  29. 29.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 171 (c) 60 (d) 19
  30. 30.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 75 (b) 504 (c) 1008 (d) 540
  31. 31.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 14 (d) 5
  32. 32.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
  33. 33.What is the distance between the points (2, 18) and (10, 3)? (a) 23 (b) 289 (c) 18 (d) 17
  34. 34.What is the prime factorisation of 84? (a) 2² × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7 (d) 2 × 3 × 7²
  35. 35.What is the missing term in the AP 17, 22, ?, 32, 37? (a) 27 (b) 32 (c) 28 (d) 26
  36. 36.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 30° (c) 60° (d) 120°
  37. 37.A bag has 12 white balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 13 (b) 2 (c) 17 (d) 14
  38. 38.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 343 (b) 300 (c) 342 (d) 333
  39. 39.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  40. 40.What is the 16th term of the AP 13, 19, 25, 31, …? (a) 96 (b) 90 (c) 103 (d) 109

Answer key

  1. 9
  2. 9
  3. 78
  4. 729 cu cm
  5. 3
  6. (4, 16)
  7. 3/8
  8. 96 sq cm
  9. 13
  10. 28
  11. 8
  12. 298
  13. 2/3
  14. 216 cu cm
  15. 2³ × 7
  16. 80°
  17. 24
  18. 4489
  19. 154 sq cm
  20. 5
  21. 6
  22. 90°
  23. 4 times
  24. 110°
  25. 40°
  26. (9, 16)
  27. 231
  28. 70°
  29. 57
  30. 504
  31. 6
  32. 1/12
  33. 17
  34. 2² × 3 × 7
  35. 27
  36. 60°
  37. 14
  38. 342
  39. 120
  40. 103

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