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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 220 · 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.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
  2. 2.4 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) 9 (b) 24 (c) 20 (d) 40
  3. 3.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/4 (c) 1/3 (d) 2/3
  4. 4.A bag has 9 blue balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 2 (c) 10 (d) 21
  5. 5.What is the prime factorisation of 35? (a) 5 × 7 (b) 5 × 7² (c) 5³ × 7 (d) 5² × 7
  6. 6.What is the median of 33, 38, 5, 32 and 4? (a) 31 (b) 5 (c) 33 (d) 32
  7. 7.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 708 (b) 384 (c) 354 (d) 57
  8. 8.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 96 cu cm (c) 65 cu cm (d) 64 cu cm
  9. 9.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 7 (b) 14 (c) 8 (d) 15
  10. 10.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  11. 11.How many prime numbers are there between 50 and 80? (a) 9 (b) 6 (c) 8 (d) 7
  12. 12.In which quadrant does the point (6, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  13. 13.A cuboid is 7 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 100 sq cm (b) 200 sq cm (c) 50 sq cm (d) 56 sq cm
  14. 14.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 180 (b) 26 (c) 340 (d) 170
  15. 15.Two angles of a triangle are 60° and 25°. What is the exterior angle at the third corner? (a) 95° (b) 120° (c) 155° (d) 85°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 25° (c) 50° (d) 130°
  17. 17.What is the sum of the roots of x² − 6x + 8 = 0? (a) 5 (b) 8 (c) 7 (d) 6
  18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 2/11 (c) 1/12 (d) 1/18
  19. 19.Using (a + b)² = a² + 2ab + b², what is 95²? (a) 9025 (b) 9035 (c) 8125 (d) 7225
  20. 20.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 2 times (d) 5 times
  21. 21.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 30° (b) 60° (c) 300° (d) 120°
  22. 22.What is the product of the roots of x² − 9x + 20 = 0? (a) 9 (b) 21 (c) 19 (d) 20
  23. 23.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
  24. 24.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
  25. 25.Which term of the AP 7, 12, 17, 22, … is 127? (a) 24th (b) 25th (c) 27th (d) 26th
  26. 26.What is the distance between the points (6, 29) and (13, 5)? (a) 625 (b) 26 (c) 25 (d) 31
  27. 27.Using (a − b)² = a² − 2ab + b², what is 99²? (a) 9999 (b) 9811 (c) 9801 (d) 10201
  28. 28.What is the distance between the points (6, 4) and (22, 16)? (a) 28 (b) 21 (c) 400 (d) 20
  29. 29.What is the mode of 14, 14, 18, 18, 2, 18 and 13? (a) 14 (b) 13 (c) 2 (d) 18
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 4 (b) 2 (c) 1 (d) 3
  31. 31.In a class of 40 children, 24 like mangoes, 17 like bananas and 10 like both. How many like neither? (a) 8 (b) 9 (c) 19 (d) 10
  32. 32.What is the median of 16, 5, 32, 39 and 1? (a) 17 (b) 32 (c) 16 (d) 5
  33. 33.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/8 (c) 3/8 (d) 7/8
  34. 34.What is the mean of 6, 19, 18 and 17? (a) 15 (b) 12 (c) 20 (d) 16
  35. 35.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  36. 36.What is the distance between the points (3, 20) and (19, 8)? (a) 28 (b) 21 (c) 400 (d) 20
  37. 37.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 324 (c) 217 (d) 216
  38. 38.What is the distance between the points (0, 0) and (24, 7)? (a) 25 (b) 26 (c) 625 (d) 31
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 16 (b) 5 (c) 14 (d) 15
  40. 40.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 160° (d) 260°

Answer key

  1. 1/2
  2. 20
  3. 1/2
  4. 13
  5. 5 × 7
  6. 32
  7. 354
  8. 64 cu cm
  9. 8
  10. 6
  11. 7
  12. First quadrant
  13. 100 sq cm
  14. 170
  15. 85°
  16. 25°
  17. 6
  18. 1/18
  19. 9025
  20. 4 times
  21. 120°
  22. 20
  23. 132 cm
  24. 176 cm
  25. 25th
  26. 25
  27. 9801
  28. 20
  29. 18
  30. 3
  31. 9
  32. 16
  33. 7/8
  34. 15
  35. 5
  36. 20
  37. 216
  38. 25
  39. 15
  40. 100°

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