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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 455 · 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.In which quadrant does the point (−9, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  2. 2.What is the mode of 3, 1, 3, 3, 11, 8 and 8? (a) 11 (b) 1 (c) 8 (d) 3
  3. 3.A cuboid is 11 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 296 sq cm (b) 88 sq cm (c) 148 sq cm (d) 74 sq cm
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 5 (b) 3 (c) 2 (d) 4
  5. 5.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 22 (b) 31 (c) 32 (d) 40
  6. 6.In a league, 10 teams each play every other team once. How many matches are played? (a) 90 (b) 45 (c) 100 (d) 55
  7. 7.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  8. 8.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 145° (b) 60° (c) 120° (d) 155°
  9. 9.Using (a − b)² = a² − 2ab + b², what is 45²? (a) 2475 (b) 2035 (c) 2025 (d) 3025
  10. 10.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 42 (c) 28 (d) 21
  11. 11.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 15 (c) 30 (d) 36
  12. 12.In a class of 33 children, 21 like maths, 20 like science and 12 like both. How many like neither? (a) 12 (b) 4 (c) 5 (d) 16
  13. 13.A bag has 9 green balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 8 (c) 16 (d) 2
  14. 14.A cuboid is 11 cm long, 8 cm wide and 5 cm high. What is its total surface area? (a) 366 sq cm (b) 183 sq cm (c) 440 sq cm (d) 732 sq cm
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 75? (a) 5 (b) 6 (c) 7 (d) 8
  16. 16.How many factors does 43 have? (a) 2 (b) 3 (c) 4 (d) 1
  17. 17.What is the smallest prime factor of 39? (a) 1 (b) 3 (c) 13 (d) 2
  18. 18.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/6 (b) 1/5 (c) 1/3 (d) 5/6
  19. 19.If a + b = 14 and ab = 40, what is a² + b²? (a) 276 (b) 196 (c) 116 (d) 156
  20. 20.What is the distance between the points (6, 2) and (10, 5)? (a) 7 (b) 6 (c) 25 (d) 5
  21. 21.A bag has 6 red, 8 yellow and 7 white balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 8/13 (b) 1/3 (c) 13/21 (d) 8/21
  22. 22.What is the distance between the points (3, 18) and (15, 2)? (a) 400 (b) 28 (c) 21 (d) 20
  23. 23.A bag has 9 red, 7 yellow and 3 green balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 7/19 (b) 13/19 (c) 1/3 (d) 12/19
  24. 24.If a + b = 18 and ab = 72, what is (a − b)²? (a) 6 (b) 180 (c) 324 (d) 36
  25. 25.What is the median of 10, 19, 13, 11, 33, 17 and 27? (a) 11 (b) 19 (c) 13 (d) 17
  26. 26.6 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 36 (b) 60 (c) 30 (d) 11
  27. 27.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 15 (c) 25 (d) 20
  28. 28.What is the mode of 15, 18, 14, 7, 15, 7 and 7? (a) 14 (b) 7 (c) 18 (d) 15
  29. 29.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 7/8 (c) 1/8 (d) 1/7
  30. 30.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
  31. 31.What is the mean of 11, 15, 18 and 8? (a) 12 (b) 13 (c) 14 (d) 15
  32. 32.In which quadrant does the point (−2, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  33. 33.If a + b = 12 and ab = 11, what is (a − b)²? (a) 122 (b) 10 (c) 144 (d) 100
  34. 34.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 726 cu cm (c) 1331 cu cm (d) 33 cu cm
  35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/18 (c) 1/36 (d) 1/12
  36. 36.What is the median of 25, 23, 14, 32 and 38? (a) 32 (b) 14 (c) 23 (d) 25
  37. 37.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 616 cm (d) 44 cm
  38. 38.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  39. 39.A cuboid is 6 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 336 sq cm (b) 168 sq cm (c) 108 sq cm (d) 84 sq cm
  40. 40.In a class of 23 children, 8 like dance, 14 like music and 3 like both. How many like neither? (a) 3 (b) 1 (c) 4 (d) 7

Answer key

  1. Second quadrant
  2. 3
  3. 148 sq cm
  4. 4
  5. 31
  6. 45
  7. 120
  8. 120°
  9. 2025
  10. 21
  11. 30
  12. 4
  13. 10
  14. 366 sq cm
  15. 7
  16. 2
  17. 3
  18. 1/6
  19. 116
  20. 5
  21. 8/21
  22. 20
  23. 12/19
  24. 36
  25. 17
  26. 30
  27. 10
  28. 7
  29. 1/8
  30. 44 cm
  31. 13
  32. Third quadrant
  33. 100
  34. 1331 cu cm
  35. 1/36
  36. 25
  37. 88 cm
  38. 25
  39. 168 sq cm
  40. 4

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