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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 337 · 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.How many factors does 90 have? (a) 10 (b) 13 (c) 11 (d) 12
  2. 2.Using (a + b)² = a² + 2ab + b², what is 95²? (a) 9025 (b) 8125 (c) 7225 (d) 9035
  3. 3.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
  4. 4.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  5. 5.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  6. 6.A bag has 8 blue balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 12 (c) 2 (d) 19
  7. 7.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 1/4 (c) 1/2 (d) 2/3
  8. 8.Which is the correct factorisation of x² + 15x + 54? (a) (x + 1)(x + 54) (b) (x − 6)(x − 9) (c) (x + 1)(x + 14) (d) (x + 6)(x + 9)
  9. 9.What is the distance between the points (7, 7) and (10, 3)? (a) 25 (b) 6 (c) 7 (d) 5
  10. 10.What is the mode of 15, 18, 18, 1, 10, 15 and 18? (a) 1 (b) 15 (c) 18 (d) 10
  11. 11.A drawer has lots of green and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 5 (c) 2 (d) 3
  12. 12.What is the sum of all the whole numbers from 1 to 51? (a) 2652 (b) 1326 (c) 1327 (d) 1275
  13. 13.Two angles of a triangle are 25° and 110°. What is the third angle? (a) 155° (b) 45° (c) 70° (d) 135°
  14. 14.In a class of 43 children, 17 like mangoes, 28 like bananas and 10 like neither. How many like both? (a) 33 (b) 2 (c) 12 (d) 10
  15. 15.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  16. 16.What is the mean of 15, 8, 17, 5 and 5? (a) 12 (b) 9 (c) 10 (d) 11
  17. 17.What is the missing term in the AP 16, 18, 20, ?, 24? (a) 24 (b) 21 (c) 22 (d) 23
  18. 18.Two angles of a triangle are 25° and 25°. What is the third angle? (a) 155° (b) 310° (c) 50° (d) 130°
  19. 19.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 1/18 (c) 1/12 (d) 2/11
  20. 20.In a class of 33 children, 11 like tea, 27 like coffee and 8 like both. How many like at least one of the two? (a) 38 (b) 22 (c) 33 (d) 30
  21. 21.How many factors does 28 have? (a) 7 (b) 6 (c) 5 (d) 4
  22. 22.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  23. 23.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 120 (c) 210 (d) 225
  24. 24.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/3 (b) 1/5 (c) 5/6 (d) 1/6
  25. 25.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 120° (c) 30° (d) 60°
  26. 26.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  27. 27.What is the missing term in the AP 16, 18, ?, 22, 24? (a) 22 (b) 19 (c) 21 (d) 20
  28. 28.What is the mode of 11, 15, 11, 3, 3, 19 and 3? (a) 11 (b) 3 (c) 19 (d) 15
  29. 29.What is the smallest prime factor of 145? (a) 2 (b) 1 (c) 5 (d) 29
  30. 30.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) 14 (b) 8 (c) 15 (d) 7
  31. 31.Which is the correct factorisation of x² + 9x + 14? (a) (x + 2)(x + 7) (b) (x + 1)(x + 14) (c) (x − 2)(x − 7) (d) (x + 1)(x + 8)
  32. 32.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  33. 33.What is the distance between the points (4, 14) and (16, 5)? (a) 16 (b) 225 (c) 15 (d) 21
  34. 34.What is the missing term in the AP 7, ?, 15, 19, 23? (a) 12 (b) 15 (c) 11 (d) 10
  35. 35.What is the sum of the roots of x² − 12x + 35 = 0? (a) 35 (b) 11 (c) 12 (d) 13
  36. 36.In a class of 37 children, 11 like cricket, 22 like football and 8 like neither. How many like both? (a) 8 (b) 5 (c) 29 (d) 4
  37. 37.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  38. 38.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  39. 39.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 110 (c) 22 (d) 55
  40. 40.What is the sum of the first 7 terms of the AP 3, 8, 13, …? (a) 131 (b) 33 (c) 126 (d) 252

Answer key

  1. 12
  2. 9025
  3. 88 cm
  4. 5
  5. 25
  6. 12
  7. 1/2
  8. (x + 6)(x + 9)
  9. 5
  10. 18
  11. 3
  12. 1326
  13. 45°
  14. 12
  15. 5
  16. 10
  17. 22
  18. 130°
  19. 1/18
  20. 30
  21. 6
  22. 5
  23. 105
  24. 5/6
  25. 60°
  26. 24
  27. 20
  28. 3
  29. 5
  30. 8
  31. (x + 2)(x + 7)
  32. 15
  33. 15
  34. 11
  35. 12
  36. 4
  37. 5
  38. 6
  39. 55
  40. 126

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