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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 43 · 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. 1.7 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) 21 (b) 42 (c) 28 (d) 10
  2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 1/11 (c) 1/9 (d) 5/36
  3. 3.What is the product of the roots of x² − 7x + 10 = 0? (a) 11 (b) 9 (c) 10 (d) 7
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 5 (b) 7 (c) 10 (d) 9
  5. 5.Using (a + b)² = a² + 2ab + b², what is 94²? (a) 8116 (b) 7396 (c) 8836 (d) 8846
  6. 6.In which quadrant does the point (−8, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  7. 7.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 3/4 (c) 1/4 (d) 1/2
  8. 8.What is the distance between the points (7, 8) and (11, 11)? (a) 5 (b) 6 (c) 25 (d) 7
  9. 9.What is the sum of all the whole numbers from 1 to 36? (a) 648 (b) 1332 (c) 666 (d) 630
  10. 10.There are 6 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 18 (b) 24 (c) 8 (d) 12
  11. 11.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  12. 12.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 294 (c) 268 (d) 295
  13. 13.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  14. 14.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 25 (c) 11 (d) 10
  15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/18 (b) 1/11 (c) 1/36 (d) 1/12
  16. 16.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
  17. 17.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
  18. 18.What is the mean of 15, 6, 9 and 18? (a) 16 (b) 13 (c) 12 (d) 11
  19. 19.Using (a + b)² = a² + 2ab + b², what is 85²? (a) 5625 (b) 7235 (c) 6425 (d) 7225
  20. 20.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 100° (b) 45° (c) 135° (d) 125°
  21. 21.What is the sum of all the whole numbers from 1 to 65? (a) 4290 (b) 2146 (c) 2080 (d) 2145
  22. 22.A bag has 8 white balls and 5 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 10 (b) 2 (c) 9 (d) 13
  23. 23.Which is the correct factorisation of x² + 5x + 6? (a) (x + 1)(x + 6) (b) (x + 1)(x + 4) (c) (x + 2)(x + 3) (d) (x − 2)(x − 3)
  24. 24.What is the median of 14, 23, 31, 38 and 29? (a) 31 (b) 29 (c) 27 (d) 23
  25. 25.Which is the correct factorisation of x² + 6x + 8? (a) (x − 2)(x − 4) (b) (x + 1)(x + 8) (c) (x + 1)(x + 5) (d) (x + 2)(x + 4)
  26. 26.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
  27. 27.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 12 sq cm (b) 64 sq cm (c) 16 sq cm (d) 32 sq cm
  28. 28.Two angles of a triangle are 80° and 50°. What is the third angle? (a) 230° (b) 50° (c) 100° (d) 130°
  29. 29.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) 21 (b) 28 (c) 22 (d) 29
  30. 30.What is the mean of 9, 6, 19, 5, 9 and 18? (a) 13 (b) 11 (c) 12 (d) 10
  31. 31.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
  32. 32.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 66 (c) 55 (d) 110
  33. 33.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 729 (c) 756 (d) 378
  34. 34.What is the sum of the first 11 terms of the AP 3, 6, 9, …? (a) 201 (b) 198 (c) 396 (d) 33
  35. 35.How many factors does 85 have? (a) 3 (b) 5 (c) 4 (d) 2
  36. 36.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
  37. 37.What is the mean of 14, 17, 10, 13 and 21? (a) 15 (b) 17 (c) 16 (d) 14
  38. 38.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 28 (c) 56 (d) 36
  39. 39.In a class of 39 children, 14 like dance, 23 like music and 3 like both. How many like at least one of the two? (a) 31 (b) 34 (c) 39 (d) 37
  40. 40.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 144 (c) 24 (d) 66

Answer key

  1. 21
  2. 1/9
  3. 10
  4. 9
  5. 8836
  6. Second quadrant
  7. 3/4
  8. 5
  9. 666
  10. 12
  11. 24
  12. 294
  13. 120
  14. 10
  15. 1/36
  16. 616 sq cm
  17. 132 cm
  18. 12
  19. 7225
  20. 45°
  21. 2145
  22. 10
  23. (x + 2)(x + 3)
  24. 29
  25. (x + 2)(x + 4)
  26. 1/2
  27. 32 sq cm
  28. 50°
  29. 22
  30. 11
  31. 16 times
  32. 55
  33. 729
  34. 198
  35. 4
  36. 154 sq cm
  37. 15
  38. 28
  39. 34
  40. 66

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