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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 752 · 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 how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  2. 2.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 45° (b) 100° (c) 125° (d) 135°
  3. 3.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 85° (b) 135° (c) 95° (d) 130°
  4. 4.A cube has edges of 8 cm. What is its total surface area? (a) 384 sq cm (b) 512 sq cm (c) 64 sq cm (d) 256 sq cm
  5. 5.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 3 (d) 2
  6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 5/36 (b) 1/11 (c) 4/11 (d) 1/9
  7. 7.If a + b = 7 and ab = 12, what is a² + b²? (a) 49 (b) 37 (c) 73 (d) 25
  8. 8.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6
  9. 9.In a class of 36 children, 9 like mangoes, 24 like bananas and 5 like both. How many like only mangoes? (a) 19 (b) 4 (c) 9 (d) 12
  10. 10.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 28 (c) 16 (d) 64
  11. 11.What is the mean of 10, 7, 6, 10 and 12? (a) 10 (b) 9 (c) 8 (d) 11
  12. 12.In which quadrant does the point (3, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  13. 13.A bag has 3 red, 5 green and 5 white balls. One ball is taken out without looking. What is the probability that it is not green? (a) 9/13 (b) 1/3 (c) 5/13 (d) 8/13
  14. 14.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
  15. 15.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 7 (d) 8
  16. 16.Which term of the AP 16, 25, 34, 43, … is 268? (a) 28th (b) 31st (c) 29th (d) 30th
  17. 17.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 121 (c) 132 (d) 21
  18. 18.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 100 (c) 45 (d) 20
  19. 19.A drawer has lots of red, black, yellow, 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) 10 (b) 2 (c) 6 (d) 5
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 56° (b) 110° (c) 125° (d) 55°
  21. 21.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/18 (b) 1/12 (c) 1/36 (d) 1/11
  22. 22.In a class of 19 children, 11 like tea, 12 like coffee and 8 like both. How many like neither? (a) 5 (b) 8 (c) 4 (d) 12
  23. 23.What is the prime factorisation of 120? (a) 2 × 3 × 5³ (b) 2³ × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2² × 3 × 5
  24. 24.In a class of 30 children, 12 like maths, 16 like science and 7 like neither. How many like both? (a) 6 (b) 7 (c) 23 (d) 5
  25. 25.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 6 (b) 54 (c) 18 (d) 21
  26. 26.A bag has 7 white balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 11 (c) 8 (d) 2
  27. 27.What is the 18th term of the AP 6, 11, 16, 21, …? (a) 91 (b) 85 (c) 96 (d) 90
  28. 28.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 21 (b) 15 (c) 22 (d) 14
  29. 29.What is the 31st term of the AP 10, 16, 22, 28, …? (a) 186 (b) 196 (c) 180 (d) 190
  30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/18 (b) 1/11 (c) 1/12 (d) 2/11
  31. 31.How many factors does 40 have? (a) 8 (b) 6 (c) 9 (d) 7
  32. 32.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 41? (a) 5 (b) 4 (c) 2 (d) 3
  34. 34.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 225 (c) 210 (d) 105
  35. 35.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 1/3 (c) 3/4 (d) 1/4
  36. 36.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  37. 37.There are 8 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 112 (b) 56 (c) 15 (d) 64
  38. 38.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 48 (b) 49 (c) 37 (d) 36
  39. 39.What is the mean of 18, 12, 10, 2 and 8? (a) 12 (b) 11 (c) 9 (d) 10
  40. 40.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 500 (b) 270 (c) 43 (d) 250

Answer key

  1. 120
  2. 135°
  3. 85°
  4. 384 sq cm
  5. 3
  6. 1/9
  7. 25
  8. 7
  9. 4
  10. 56
  11. 9
  12. First quadrant
  13. 8/13
  14. 4
  15. 8
  16. 29th
  17. 121
  18. 45
  19. 6
  20. 55°
  21. 1/36
  22. 4
  23. 2³ × 3 × 5
  24. 5
  25. 18
  26. 8
  27. 91
  28. 15
  29. 190
  30. 1/18
  31. 8
  32. 120
  33. 4
  34. 105
  35. 3/4
  36. 20
  37. 56
  38. 37
  39. 10
  40. 250

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