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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 444 · 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.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 110° (c) 35° (d) 55°
  2. 2.What is the midpoint of the line joining (10, 13) and (16, 9)? (a) (13, 11) (b) (11, 13) (c) (26, 22) (d) (3, 2)
  3. 3.What is the product of the roots of x² − 15x + 56 = 0? (a) 55 (b) 57 (c) 15 (d) 56
  4. 4.What is the product of the roots of x² − 9x + 14 = 0? (a) 14 (b) 13 (c) 15 (d) 9
  5. 5.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 200° (b) 160° (c) 21° (d) 20°
  6. 6.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 130° (b) 51° (c) 50° (d) 230°
  7. 7.Which term of the AP 13, 17, 21, 25, … is 61? (a) 12th (b) 15th (c) 14th (d) 13th
  8. 8.In which quadrant does the point (−5, −7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  9. 9.What is the prime factorisation of 140? (a) 2³ × 5 × 7 (b) 2 × 5 × 7² (c) 2 × 5 × 7 (d) 2² × 5 × 7
  10. 10.What is the prime factorisation of 36? (a) 2³ × 3² (b) 2² × 3² (c) 2² × 3³ (d) 2 × 3²
  11. 11.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/8 (b) 3/8 (c) 1/4 (d) 3/4
  12. 12.Two angles of a triangle are 40° and 60°. What is the third angle? (a) 120° (b) 100° (c) 140° (d) 80°
  13. 13.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
  14. 14.The mean of 3 numbers is 20. When the number 12 is added to them, what is the new mean? (a) 19 (b) 18 (c) 20 (d) 16
  15. 15.What is the distance between the points (2, 0) and (10, 6)? (a) 11 (b) 100 (c) 10 (d) 14
  16. 16.What is the sum of all the whole numbers from 1 to 18? (a) 342 (b) 153 (c) 162 (d) 171
  17. 17.A bag has 12 blue balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 13 (b) 2 (c) 22 (d) 14
  18. 18.Two angles of a triangle are 30° and 65°. What is the exterior angle at the third corner? (a) 150° (b) 115° (c) 85° (d) 95°
  19. 19.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
  20. 20.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
  21. 21.What is the mean of 12, 2, 19 and 3? (a) 12 (b) 10 (c) 9 (d) 8
  22. 22.In a class of 22 children, 11 like tea, 12 like coffee and 7 like both. How many like neither? (a) 7 (b) 13 (c) 5 (d) 6
  23. 23.What is the mean of 10, 18, 5, 18 and 9? (a) 10 (b) 12 (c) 13 (d) 15
  24. 24.What is the 13th term of the AP 19, 24, 29, 34, …? (a) 65 (b) 60 (c) 79 (d) 84
  25. 25.A drawer has lots of yellow and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 5 (c) 3 (d) 4
  26. 26.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3 × 5 × 7² (c) 3² × 5 × 7 (d) 3 × 5 × 7
  27. 27.In a class of 44 children, 26 like maths, 23 like science and 7 like both. How many like at least one of the two? (a) 42 (b) 35 (c) 49 (d) 44
  28. 28.What is the mean of 15, 17, 19, 16, 15 and 14? (a) 18 (b) 15 (c) 16 (d) 17
  29. 29.What is the mode of 6, 20, 1, 20, 12, 12 and 20? (a) 1 (b) 12 (c) 20 (d) 6
  30. 30.If a + b = 13 and ab = 40, what is (a − b)²? (a) 89 (b) 9 (c) 169 (d) 3
  31. 31.What is the 15th term of the AP 20, 24, 28, 32, …? (a) 76 (b) 56 (c) 60 (d) 80
  32. 32.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
  33. 33.What is the prime factorisation of 420? (a) 2 × 3 × 5 × 7² (b) 2² × 3 × 5 × 7 (c) 2³ × 3 × 5 × 7 (d) 2 × 3 × 5 × 7
  34. 34.What is the distance between the points (3, 17) and (15, 1)? (a) 28 (b) 21 (c) 20 (d) 400
  35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 2/11 (b) 1/11 (c) 1/12 (d) 1/18
  36. 36.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
  37. 37.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) 12 (b) 24 (c) 7 (d) 16
  38. 38.A bag has 5 red balls and 11 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 16 (b) 2 (c) 6 (d) 12
  39. 39.What is the 35th term of the AP 6, 10, 14, 18, …? (a) 146 (b) 136 (c) 140 (d) 142
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 50° (b) 100° (c) 130° (d) 51°

Answer key

  1. 110°
  2. (13, 11)
  3. 56
  4. 14
  5. 20°
  6. 50°
  7. 13th
  8. Third quadrant
  9. 2² × 5 × 7
  10. 2² × 3²
  11. 3/4
  12. 80°
  13. 1/2
  14. 18
  15. 10
  16. 171
  17. 14
  18. 95°
  19. 1386 sq cm
  20. 176 cm
  21. 9
  22. 6
  23. 12
  24. 79
  25. 3
  26. 3² × 5 × 7
  27. 42
  28. 16
  29. 20
  30. 9
  31. 76
  32. 154 sq cm
  33. 2² × 3 × 5 × 7
  34. 20
  35. 1/18
  36. 1/2
  37. 12
  38. 12
  39. 142
  40. 50°

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