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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 494 · 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 prime numbers are there between 40 and 50? (a) 5 (b) 2 (c) 3 (d) 4
  2. 2.In a class of 30 children, 25 like mangoes, 13 like bananas and 9 like both. How many like neither? (a) 1 (b) 2 (c) 10 (d) 9
  3. 3.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 60° (b) 300° (c) 30° (d) 120°
  4. 4.The mean of 3 numbers is 29. When the number 25 is added to them, what is the new mean? (a) 29 (b) 28 (c) 30 (d) 27
  5. 5.What is the sum of all the whole numbers from 1 to 52? (a) 1326 (b) 1378 (c) 1352 (d) 2756
  6. 6.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 24 (c) 37 (d) 25
  7. 7.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 5/6 (b) 1/4 (c) 2/3 (d) 1/3
  8. 8.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 45° (c) 46° (d) 55°
  9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/18 (b) 1/11 (c) 1/12 (d) 1/36
  10. 10.A bag has 5 yellow balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 12 (c) 6 (d) 8
  11. 11.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 2/3 (c) 1/2 (d) 1/3
  12. 12.What is the 21st term of the AP 20, 22, 24, 26, …? (a) 40 (b) 60 (c) 42 (d) 62
  13. 13.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) 13 (b) 84 (c) 42 (d) 49
  14. 14.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
  15. 15.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  16. 16.What is the distance between the points (4, 2) and (9, 14)? (a) 13 (b) 14 (c) 169 (d) 17
  17. 17.What is the sum of all the whole numbers from 1 to 71? (a) 2556 (b) 2557 (c) 2485 (d) 5112
  18. 18.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 10 (d) 6
  19. 19.In a class of 42 children, 19 like cricket, 19 like football and 2 like both. How many like neither? (a) 8 (b) 4 (c) 6 (d) 2
  20. 20.Which is the correct factorisation of x² + 14x + 45? (a) (x + 1)(x + 13) (b) (x − 5)(x − 9) (c) (x + 5)(x + 9) (d) (x + 1)(x + 45)
  21. 21.Which term of the AP 1, 10, 19, 28, … is 64? (a) 9th (b) 8th (c) 10th (d) 7th
  22. 22.What is the sum of the roots of x² − 8x + 12 = 0? (a) 8 (b) 9 (c) 7 (d) 12
  23. 23.What is the smallest prime factor of 133? (a) 1 (b) 2 (c) 19 (d) 7
  24. 24.What is the distance between the points (3, 21) and (19, 9)? (a) 400 (b) 28 (c) 20 (d) 21
  25. 25.What is the mode of 10, 13, 20, 13, 10, 10 and 3? (a) 10 (b) 13 (c) 20 (d) 3
  26. 26.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 21 (c) 22 (d) 29
  27. 27.If a + b = 9 and ab = 8, what is a² + b²? (a) 73 (b) 65 (c) 81 (d) 97
  28. 28.What is the distance between the points (8, 2) and (32, 9)? (a) 26 (b) 25 (c) 625 (d) 31
  29. 29.If a + b = 12 and ab = 11, what is (a − b)²? (a) 100 (b) 122 (c) 144 (d) 10
  30. 30.A drawer has lots of blue, yellow, white and red 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) 8 (c) 5 (d) 2
  31. 31.What is the mean of 7, 13, 5 and 11? (a) 12 (b) 8 (c) 9 (d) 10
  32. 32.What is the sum of the roots of x² − 11x + 30 = 0? (a) 12 (b) 30 (c) 11 (d) 10
  33. 33.In a league, 14 teams each play every other team once. How many matches are played? (a) 196 (b) 182 (c) 91 (d) 105
  34. 34.What is the 32nd term of the AP 19, 28, 37, 46, …? (a) 298 (b) 307 (c) 279 (d) 288
  35. 35.4 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 7 (b) 16 (c) 12 (d) 24
  36. 36.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 5 times (c) 4 times (d) 2 times
  37. 37.What is the median of 30, 14, 34, 7 and 11? (a) 34 (b) 11 (c) 14 (d) 30
  38. 38.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  39. 39.A bag has 8 blue, 6 green and 9 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 6/17 (b) 6/23 (c) 17/23 (d) 1/3
  40. 40.If a + b = 8 and ab = 12, what is a² + b²? (a) 52 (b) 88 (c) 40 (d) 64

Answer key

  1. 3
  2. 1
  3. 120°
  4. 28
  5. 1378
  6. 25
  7. 2/3
  8. 45°
  9. 1/36
  10. 8
  11. 1/2
  12. 60
  13. 42
  14. 616 sq cm
  15. 6
  16. 13
  17. 2556
  18. 5
  19. 6
  20. (x + 5)(x + 9)
  21. 8th
  22. 8
  23. 7
  24. 20
  25. 10
  26. 22
  27. 65
  28. 25
  29. 100
  30. 5
  31. 9
  32. 11
  33. 91
  34. 298
  35. 12
  36. 4 times
  37. 14
  38. 7
  39. 6/23
  40. 40

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