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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 620 · 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 times is the digit 2 written when you write all the numbers from 1 to 36? (a) 3 (b) 15 (c) 13 (d) 14
  2. 2.What is the midpoint of the line joining (0, 3) and (10, 5)? (a) (4, 5) (b) (10, 8) (c) (5, 4) (d) (5, 1)
  3. 3.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  4. 4.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 169 (c) 78 (d) 91
  5. 5.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
  6. 6.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 28 (c) 56 (d) 36
  7. 7.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
  8. 8.What is the distance between the points (0, 19) and (8, 4)? (a) 289 (b) 18 (c) 17 (d) 23
  9. 9.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 81? (a) 18 (b) 8 (c) 19 (d) 17
  11. 11.In a class of 48 children, 24 like tea, 27 like coffee and 8 like both. How many like only tea? (a) 16 (b) 21 (c) 19 (d) 24
  12. 12.How many prime numbers are there between 20 and 30? (a) 1 (b) 4 (c) 3 (d) 2
  13. 13.Two angles of a triangle are 25° and 130°. What is the third angle? (a) 155° (b) 205° (c) 25° (d) 50°
  14. 14.What is the mode of 20, 20, 13, 20, 11, 4 and 11? (a) 20 (b) 4 (c) 13 (d) 11
  15. 15.How many factors does 105 have? (a) 6 (b) 9 (c) 8 (d) 7
  16. 16.What is the 23rd term of the AP 2, 5, 8, 11, …? (a) 71 (b) 66 (c) 69 (d) 68
  17. 17.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 294 cu cm (c) 21 cu cm (d) 343 cu cm
  18. 18.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
  19. 19.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/12 (c) 1/11 (d) 1/9
  20. 20.What is the distance between the points (6, 3) and (10, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  21. 21.Which is the correct factorisation of x² + 8x + 15? (a) (x − 3)(x − 5) (b) (x + 1)(x + 15) (c) (x + 3)(x + 5) (d) (x + 1)(x + 7)
  22. 22.In a class of 44 children, 15 like maths, 23 like science and 4 like both. How many like only maths? (a) 11 (b) 15 (c) 21 (d) 19
  23. 23.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
  24. 24.In a class of 36 children, 21 like maths, 17 like science and 11 like both. How many like only maths? (a) 10 (b) 19 (c) 6 (d) 21
  25. 25.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
  26. 26.A drawer has lots of blue and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 4 (c) 2 (d) 5
  27. 27.What is the 26th term of the AP 2, 4, 6, 8, …? (a) 53 (b) 52 (c) 54 (d) 50
  28. 28.In a class of 32 children, 12 like maths, 22 like science and 4 like both. How many like at least one of the two? (a) 34 (b) 32 (c) 26 (d) 30
  29. 29.Using (a − b)² = a² − 2ab + b², what is 87²? (a) 7579 (b) 8091 (c) 8649 (d) 7569
  30. 30.In a class of 42 children, 13 like mangoes, 24 like bananas and 5 like both. How many like at least one of the two? (a) 37 (b) 42 (c) 27 (d) 32
  31. 31.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 216 (b) 109 (c) 108 (d) 16
  32. 32.What is the mean of 15, 16, 7, 4, 15 and 15? (a) 13 (b) 11 (c) 12 (d) 14
  33. 33.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) 29 (d) 22
  34. 34.What is the mode of 14, 3, 2, 20, 20, 20 and 3? (a) 20 (b) 14 (c) 2 (d) 3
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 125° (b) 56° (c) 110° (d) 55°
  36. 36.A bag has 8 black balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 14 (b) 2 (c) 10 (d) 9
  37. 37.A cuboid is 10 cm long, 7 cm wide and 9 cm high. What is its total surface area? (a) 446 sq cm (b) 892 sq cm (c) 223 sq cm (d) 630 sq cm
  38. 38.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 99 (b) 108 (c) 198 (d) 19
  39. 39.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
  40. 40.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5

Answer key

  1. 14
  2. (5, 4)
  3. 7
  4. 78
  5. 2/3
  6. 28
  7. 1/8
  8. 17
  9. 120
  10. 18
  11. 16
  12. 2
  13. 25°
  14. 20
  15. 8
  16. 68
  17. 343 cu cm
  18. 1/2
  19. 1/12
  20. 5
  21. (x + 3)(x + 5)
  22. 11
  23. 1/2
  24. 10
  25. 1386 sq cm
  26. 3
  27. 52
  28. 30
  29. 7569
  30. 32
  31. 108
  32. 12
  33. 22
  34. 20
  35. 55°
  36. 10
  37. 446 sq cm
  38. 99
  39. 1/2
  40. 5

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