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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 451 · 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.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 75° (b) 105° (c) 140° (d) 145°
  2. 2.In which quadrant does the point (−6, −2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  3. 3.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 191 (c) 190 (d) 380
  4. 4.What is the distance between the points (7, 8) and (12, 20)? (a) 169 (b) 17 (c) 14 (d) 13
  5. 5.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 64 (d) 72
  6. 6.A bag has 6 green, 8 white and 3 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 6/17 (c) 11/17 (d) 12/17
  7. 7.In a class of 36 children, 12 like dance, 16 like music and 2 like both. How many like neither? (a) 2 (b) 8 (c) 12 (d) 10
  8. 8.What is the sum of all the whole numbers from 1 to 13? (a) 91 (b) 78 (c) 92 (d) 182
  9. 9.What is the sum of the first 6 terms of the AP 8, 10, 12, …? (a) 156 (b) 84 (c) 18 (d) 78
  10. 10.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 90° (c) 45° (d) 55°
  11. 11.A bag has 8 green, 7 white and 2 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 15/17 (b) 1/3 (c) 2/15 (d) 2/17
  12. 12.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 64 times (d) 4 times
  13. 13.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 130° (c) 80° (d) 40°
  14. 14.In a class of 33 children, 12 like mangoes, 23 like bananas and 8 like both. How many like at least one of the two? (a) 19 (b) 33 (c) 35 (d) 27
  15. 15.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/8 (b) 1/4 (c) 3/8 (d) 3/4
  16. 16.A drawer has lots of white, green and blue 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) 3 (c) 6 (d) 2
  17. 17.What is the mean of 6, 11, 9, 7 and 17? (a) 11 (b) 9 (c) 12 (d) 10
  18. 18.In a class of 45 children, 24 like dance, 29 like music and 1 like neither. How many like both? (a) 9 (b) 8 (c) 44 (d) 1
  19. 19.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
  20. 20.What is the sum of all the whole numbers from 1 to 29? (a) 406 (b) 435 (c) 870 (d) 436
  21. 21.What is the sum of all the whole numbers from 1 to 77? (a) 2926 (b) 3004 (c) 6006 (d) 3003
  22. 22.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 14) (b) (x + 1)(x + 56) (c) (x − 7)(x − 8) (d) (x + 7)(x + 8)
  23. 23.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) 24 (b) 12 (c) 16 (d) 7
  24. 24.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 5/6 (c) 1/4 (d) 2/3
  25. 25.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 24 (b) 34 (c) 42 (d) 33
  26. 26.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 4 times (d) 2 times
  27. 27.A bag has 4 yellow balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 10 (b) 5 (c) 2 (d) 6
  28. 28.Two angles of a triangle are 40° and 95°. What is the third angle? (a) 140° (b) 135° (c) 85° (d) 45°
  29. 29.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  30. 30.What is the mean of 15, 10, 7 and 12? (a) 12 (b) 13 (c) 10 (d) 11
  31. 31.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
  32. 32.What is the median of 40, 3, 18, 32, 37, 14 and 12? (a) 32 (b) 19 (c) 18 (d) 14
  33. 33.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  34. 34.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 64 (c) 16 (d) 56
  35. 35.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
  36. 36.What is the sum of all the whole numbers from 1 to 82? (a) 3362 (b) 3321 (c) 6806 (d) 3403
  37. 37.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/11 (b) 1/6 (c) 6/11 (d) 7/36
  38. 38.Which term of the AP 4, 13, 22, 31, … is 211? (a) 24th (b) 25th (c) 26th (d) 23rd
  39. 39.Using (a − b)² = a² − 2ab + b², what is 36²? (a) 1936 (b) 1296 (c) 1306 (d) 1584
  40. 40.The mean of 4 numbers is 17. When the number 27 is added to them, what is the new mean? (a) 22 (b) 19 (c) 17 (d) 20

Answer key

  1. 105°
  2. Third quadrant
  3. 190
  4. 13
  5. 64
  6. 11/17
  7. 10
  8. 91
  9. 78
  10. 45°
  11. 2/17
  12. 16 times
  13. 80°
  14. 27
  15. 3/4
  16. 4
  17. 10
  18. 9
  19. 2464 sq cm
  20. 435
  21. 3003
  22. (x + 7)(x + 8)
  23. 12
  24. 2/3
  25. 33
  26. 4 times
  27. 6
  28. 45°
  29. 5
  30. 11
  31. 88 cm
  32. 18
  33. 17
  34. 56
  35. 25 times
  36. 3403
  37. 1/6
  38. 24th
  39. 1296
  40. 19

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