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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 125 · 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.Which term of the AP 16, 24, 32, 40, … is 200? (a) 23rd (b) 25th (c) 26th (d) 24th
  2. 2.What is the 18th term of the AP 3, 6, 9, 12, …? (a) 51 (b) 55 (c) 54 (d) 57
  3. 3.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
  4. 4.A canteen sells 8 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 80 (b) 40 (c) 48 (d) 13
  5. 5.What is the product of the roots of x² − 6x + 8 = 0? (a) 6 (b) 8 (c) 7 (d) 9
  6. 6.How many prime numbers are there between 20 and 50? (a) 6 (b) 9 (c) 8 (d) 7
  7. 7.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
  8. 8.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
  9. 9.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 30 (c) 36 (d) 15
  10. 10.Two angles of a triangle are 60° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 120° (c) 95° (d) 85°
  11. 11.What is the 19th term of the AP 12, 14, 16, 18, …? (a) 36 (b) 48 (c) 50 (d) 38
  12. 12.How many factors does 23 have? (a) 2 (b) 1 (c) 3 (d) 4
  13. 13.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
  14. 14.If a + b = 18 and ab = 77, what is (a − b)²? (a) 170 (b) 4 (c) 324 (d) 16
  15. 15.There are 7 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 42 (b) 84 (c) 13 (d) 49
  16. 16.What is the prime factorisation of 180? (a) 2³ × 3² × 5 (b) 2 × 3² × 5 (c) 2² × 3² × 5 (d) 2 × 3² × 5²
  17. 17.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 132 (c) 66 (d) 78
  18. 18.There are 7 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 42 (b) 21 (c) 28 (d) 10
  19. 19.How many factors does 66 have? (a) 7 (b) 8 (c) 9 (d) 6
  20. 20.What is the smallest prime factor of 221? (a) 2 (b) 13 (c) 1 (d) 17
  21. 21.What is the sum of the first 7 terms of the AP 3, 7, 11, …? (a) 27 (b) 105 (c) 119 (d) 210
  22. 22.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) 12 (c) 24 (d) 15
  23. 23.What is the median of 35, 22, 31, 21 and 5? (a) 21 (b) 22 (c) 31 (d) 23
  24. 24.What is the mean of 5, 13, 5, 5 and 7? (a) 7 (b) 9 (c) 8 (d) 6
  25. 25.A bag has 8 yellow 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) 10 (c) 9 (d) 2
  26. 26.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 6 times (c) 4 times (d) 8 times
  27. 27.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 35° (b) 145° (c) 325° (d) 55°
  28. 28.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
  29. 29.Using (a + b)² = a² + 2ab + b², what is 21²? (a) 451 (b) 401 (c) 441 (d) 361
  30. 30.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 72 (b) 36 (c) 40 (d) 8
  31. 31.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 60° (c) 150° (d) 30°
  32. 32.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  33. 33.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 10° (c) 20° (d) 160°
  34. 34.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) 16 (b) 24 (c) 12 (d) 7
  35. 35.A bag has 3 white balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 4 (c) 13 (d) 2
  36. 36.If a + b = 19 and ab = 84, what is a² + b²? (a) 361 (b) 193 (c) 529 (d) 277
  37. 37.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
  38. 38.How many prime numbers are there between 60 and 70? (a) 2 (b) 1 (c) 4 (d) 3
  39. 39.What is the sum of the first 6 terms of the AP 8, 11, 14, …? (a) 102 (b) 186 (c) 23 (d) 93
  40. 40.How many factors does 74 have? (a) 2 (b) 5 (c) 4 (d) 3

Answer key

  1. 24th
  2. 54
  3. 616 sq cm
  4. 40
  5. 8
  6. 7
  7. 1386 sq cm
  8. 4 times
  9. 15
  10. 85°
  11. 48
  12. 2
  13. 154 sq cm
  14. 16
  15. 42
  16. 2² × 3² × 5
  17. 66
  18. 21
  19. 8
  20. 13
  21. 105
  22. 12
  23. 22
  24. 7
  25. 10
  26. 8 times
  27. 145°
  28. 44 cm
  29. 441
  30. 36
  31. 120°
  32. 24
  33. 10°
  34. 12
  35. 11
  36. 193
  37. 1386 sq cm
  38. 2
  39. 93
  40. 4

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