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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 126 · 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 (6, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  2. 2.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 36 (b) 72 (c) 40 (d) 8
  3. 3.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 7/8 (c) 1/8 (d) 1/4
  4. 4.In a class of 42 children, 25 like maths, 13 like science and 6 like both. How many like at least one of the two? (a) 42 (b) 26 (c) 32 (d) 38
  5. 5.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) 14 (b) 22 (c) 15 (d) 21
  6. 6.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 8 (d) 7
  7. 7.3 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 21 (c) 10 (d) 42
  8. 8.What is the mean of 10, 19, 9, 9, 12 and 7? (a) 10 (b) 11 (c) 12 (d) 13
  9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/36 (c) 1/12 (d) 1/18
  10. 10.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 160° (c) 60° (d) 120°
  11. 11.There are 8 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) 16 (b) 10 (c) 32 (d) 24
  12. 12.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 1/4 (c) 3/4 (d) 1/3
  13. 13.What is the mean of 2, 16, 2 and 12? (a) 10 (b) 8 (c) 9 (d) 7
  14. 14.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 25 (c) 20 (d) 11
  15. 15.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 75 (b) 216 (c) 24 (d) 72
  16. 16.What is the 24th term of the AP 7, 15, 23, 31, …? (a) 184 (b) 191 (c) 199 (d) 192
  17. 17.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 5 (d) 4
  18. 18.In a class of 48 children, 22 like cricket, 31 like football and 11 like both. How many like only cricket? (a) 17 (b) 11 (c) 20 (d) 22
  19. 19.Which is the correct factorisation of x² + 12x + 32? (a) (x + 1)(x + 11) (b) (x − 4)(x − 8) (c) (x + 4)(x + 8) (d) (x + 1)(x + 32)
  20. 20.What is the 32nd term of the AP 8, 10, 12, 14, …? (a) 64 (b) 62 (c) 70 (d) 72
  21. 21.A bag has 9 yellow, 4 red and 9 blue balls. One ball is taken out without looking. What is the probability that it is red? (a) 9/11 (b) 1/3 (c) 2/9 (d) 2/11
  22. 22.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 34 (c) 24 (d) 33
  23. 23.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 55° (b) 125° (c) 145° (d) 160°
  24. 24.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 85° (b) 105° (c) 160° (d) 95°
  25. 25.The mean of 3 numbers is 29. When the number 41 is added to them, what is the new mean? (a) 33 (b) 35 (c) 32 (d) 29
  26. 26.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 88 cm (d) 22 cm
  27. 27.What is the distance between the points (7, 24) and (14, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  28. 28.In a class of 32 children, 8 like cricket, 22 like football and 4 like both. How many like neither? (a) 6 (b) 10 (c) 2 (d) 4
  29. 29.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 2/3 (c) 1/3 (d) 1/4
  30. 30.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 1/4 (c) 1/3 (d) 3/4
  31. 31.Using (a + b)² = a² + 2ab + b², what is 95²? (a) 8125 (b) 9025 (c) 9035 (d) 7225
  32. 32.What is the smallest prime factor of 69? (a) 23 (b) 1 (c) 2 (d) 3
  33. 33.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
  34. 34.What is the prime factorisation of 504? (a) 2² × 3² × 7 (b) 2 × 3² × 7³ (c) 2³ × 3² × 7 (d) 2⁴ × 3² × 7
  35. 35.What is the sum of the first 11 terms of the AP 5, 7, 9, …? (a) 330 (b) 25 (c) 176 (d) 165
  36. 36.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 5/6 (b) 1/6 (c) 1/3 (d) 1/5
  37. 37.How many prime numbers are there between 80 and 110? (a) 6 (b) 9 (c) 7 (d) 8
  38. 38.What is the 34th term of the AP 3, 8, 13, 18, …? (a) 170 (b) 168 (c) 173 (d) 165
  39. 39.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 12 (c) 6 (d) 18
  40. 40.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times

Answer key

  1. First quadrant
  2. 36
  3. 7/8
  4. 32
  5. 15
  6. 8
  7. 21
  8. 11
  9. 1/36
  10. 60°
  11. 16
  12. 1/4
  13. 8
  14. 10
  15. 72
  16. 191
  17. 5
  18. 11
  19. (x + 4)(x + 8)
  20. 70
  21. 2/11
  22. 33
  23. 125°
  24. 95°
  25. 32
  26. 44 cm
  27. 25
  28. 6
  29. 2/3
  30. 3/4
  31. 9025
  32. 3
  33. 1/3
  34. 2³ × 3² × 7
  35. 165
  36. 1/6
  37. 7
  38. 168
  39. 9
  40. 9 times

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