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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 738 · 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 30th term of the AP 10, 19, 28, 37, …? (a) 271 (b) 270 (c) 280 (d) 261
  2. 2.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  3. 3.What is the 40th term of the AP 3, 9, 15, 21, …? (a) 237 (b) 243 (c) 234 (d) 240
  4. 4.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 48 (b) 42 (c) 84 (d) 12
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 7 (d) 18
  6. 6.How many factors does 32 have? (a) 4 (b) 5 (c) 7 (d) 6
  7. 7.What is the smallest prime factor of 51? (a) 1 (b) 17 (c) 2 (d) 3
  8. 8.What is the prime factorisation of 35? (a) 5 × 7 (b) 5 × 7² (c) 5³ × 7 (d) 5² × 7
  9. 9.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 110 (c) 121 (d) 22
  10. 10.What is the distance between the points (1, 25) and (8, 1)? (a) 26 (b) 31 (c) 25 (d) 625
  11. 11.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 145° (c) 270° (d) 90°
  12. 12.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
  13. 13.What is the sum of all the whole numbers from 1 to 51? (a) 1327 (b) 1275 (c) 2652 (d) 1326
  14. 14.How many factors does 109 have? (a) 2 (b) 3 (c) 1 (d) 4
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 20 (b) 19 (c) 18 (d) 9
  16. 16.What is the median of 30, 25, 4, 16 and 37? (a) 4 (b) 25 (c) 16 (d) 30
  17. 17.If a + b = 14 and ab = 40, what is (a − b)²? (a) 196 (b) 116 (c) 36 (d) 6
  18. 18.A bag has 6 green, 7 blue and 4 red balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 11/17 (b) 7/17 (c) 1/3 (d) 10/17
  19. 19.What are the roots of x² − 7x + 10 = 0? (a) 1 and 10 (b) 1 and 6 (c) 3 and 4 (d) 2 and 5
  20. 20.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3 × 5 × 7 (c) 3² × 5 × 7 (d) 3 × 5 × 7²
  21. 21.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 10 (d) 8
  22. 22.What is the smallest prime factor of 253? (a) 11 (b) 1 (c) 23 (d) 2
  23. 23.A bag has 2 green, 2 yellow and 7 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 4/11 (b) 1/3 (c) 7/11 (d) 8/11
  24. 24.There are 5 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) 40 (b) 25 (c) 20 (d) 9
  25. 25.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
  26. 26.What is the median of 34, 8, 16, 2 and 27? (a) 27 (b) 16 (c) 8 (d) 17
  27. 27.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
  28. 28.What are the roots of x² − 13x + 40 = 0? (a) 1 and 40 (b) 5 and 8 (c) 1 and 12 (d) 2 and 20
  29. 29.How many factors does 45 have? (a) 6 (b) 7 (c) 5 (d) 4
  30. 30.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 46° (b) 45° (c) 135° (d) 90°
  32. 32.In a class of 43 children, 21 like maths, 18 like science and 2 like both. How many like only maths? (a) 16 (b) 19 (c) 21 (d) 25
  33. 33.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 4 times (c) 16 times (d) 8 times
  34. 34.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
  35. 35.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 25° (c) 65° (d) 115°
  36. 36.How many prime numbers are there between 20 and 30? (a) 1 (b) 2 (c) 3 (d) 4
  37. 37.How many prime numbers are there between 80 and 110? (a) 7 (b) 8 (c) 6 (d) 9
  38. 38.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
  39. 39.What is the prime factorisation of 30? (a) 2 × 3 × 5 (b) 2³ × 3 × 5 (c) 2 × 3 × 5² (d) 2² × 3 × 5
  40. 40.The mean of 3 numbers is 10. When the number 6 is added to them, what is the new mean? (a) 10 (b) 11 (c) 9 (d) 8

Answer key

  1. 271
  2. 120
  3. 237
  4. 42
  5. 18
  6. 6
  7. 3
  8. 5 × 7
  9. 55
  10. 25
  11. 90°
  12. 1/2
  13. 1326
  14. 2
  15. 19
  16. 25
  17. 36
  18. 10/17
  19. 2 and 5
  20. 3² × 5 × 7
  21. 9
  22. 11
  23. 7/11
  24. 20
  25. 7
  26. 16
  27. 176 cm
  28. 5 and 8
  29. 6
  30. 2
  31. 45°
  32. 19
  33. 16 times
  34. 25 times
  35. 50°
  36. 2
  37. 7
  38. 1/2
  39. 2 × 3 × 5
  40. 9

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