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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 927 · 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.What is the 28th term of the AP 5, 14, 23, 32, …? (a) 257 (b) 252 (c) 248 (d) 243
  2. 2.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 90 (b) 10 (c) 45 (d) 48
  3. 3.What is the mean of 2, 19, 16, 20, 4 and 11? (a) 13 (b) 12 (c) 14 (d) 11
  4. 4.A bag has 9 red balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 10 (b) 2 (c) 11 (d) 13
  5. 5.A bag has 5 blue balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 2 (c) 11 (d) 15
  6. 6.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
  7. 7.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 10 (d) 7
  8. 8.What is the distance between the points (0, 13) and (5, 1)? (a) 14 (b) 13 (c) 169 (d) 17
  9. 9.What is the prime factorisation of 21? (a) 3³ × 7 (b) 3 × 7 (c) 3 × 7² (d) 3² × 7
  10. 10.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/2 (c) 1/4 (d) 1/3
  11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/36 (c) 1/18 (d) 1/11
  12. 12.In a class of 27 children, 19 like dance, 7 like music and 4 like both. How many like at least one of the two? (a) 22 (b) 18 (c) 26 (d) 27
  13. 13.What is the mode of 20, 12, 12, 12, 20, 10 and 19? (a) 12 (b) 20 (c) 19 (d) 10
  14. 14.Two angles of a triangle are 65° and 20°. What is the third angle? (a) 85° (b) 95° (c) 115° (d) 160°
  15. 15.A bag has 4 white, 9 red and 4 blue balls. One ball is taken out without looking. What is the probability that it is white? (a) 13/17 (b) 1/3 (c) 4/13 (d) 4/17
  16. 16.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/12 (b) 1/9 (c) 3/11 (d) 1/11
  17. 17.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
  18. 18.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 49 (c) 58 (d) 40
  19. 19.What is the sum of all the whole numbers from 1 to 75? (a) 2775 (b) 5700 (c) 2851 (d) 2850
  20. 20.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 80° (c) 40° (d) 50°
  21. 21.What is the 27th term of the AP 3, 9, 15, 21, …? (a) 156 (b) 159 (c) 165 (d) 162
  22. 22.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  23. 23.What is the mode of 13, 2, 13, 13, 17, 5 and 5? (a) 2 (b) 13 (c) 17 (d) 5
  24. 24.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  25. 25.If a + b = 17 and ab = 70, what is a² + b²? (a) 289 (b) 429 (c) 219 (d) 149
  26. 26.Which term of the AP 15, 24, 33, 42, … is 204? (a) 22nd (b) 23rd (c) 24th (d) 21st
  27. 27.What is the mode of 11, 2, 9, 2, 6, 11 and 2? (a) 6 (b) 11 (c) 2 (d) 9
  28. 28.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 20 (b) 154 (c) 80 (d) 77
  29. 29.What is the 37th term of the AP 9, 16, 23, 30, …? (a) 252 (b) 268 (c) 259 (d) 261
  30. 30.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 16 (d) 4
  31. 31.In a class of 29 children, 19 like cricket, 10 like football and 4 like both. How many like at least one of the two? (a) 21 (b) 29 (c) 25 (d) 26
  32. 32.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 135° (b) 75° (c) 120° (d) 105°
  33. 33.In a class of 51 children, 28 like maths, 30 like science and 12 like both. How many like neither? (a) 12 (b) 6 (c) 17 (d) 5
  34. 34.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 21° (b) 200° (c) 20° (d) 160°
  35. 35.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) 56 (b) 15 (c) 64 (d) 112
  36. 36.What is the mean of 13, 6, 7, 5, 19 and 22? (a) 12 (b) 11 (c) 13 (d) 14
  37. 37.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 567 (b) 577 (c) 456 (d) 576
  38. 38.How many prime numbers are there between 40 and 70? (a) 7 (b) 9 (c) 8 (d) 6
  39. 39.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) 22 (c) 21 (d) 29
  40. 40.What is the 29th term of the AP 18, 24, 30, 36, …? (a) 186 (b) 192 (c) 168 (d) 174

Answer key

  1. 248
  2. 45
  3. 12
  4. 11
  5. 11
  6. 16 times
  7. 8
  8. 13
  9. 3 × 7
  10. 3/4
  11. 1/36
  12. 22
  13. 12
  14. 95°
  15. 4/17
  16. 1/12
  17. 1386 sq cm
  18. 49
  19. 2850
  20. 80°
  21. 159
  22. 120
  23. 13
  24. 5
  25. 149
  26. 22nd
  27. 2
  28. 77
  29. 261
  30. 4
  31. 25
  32. 75°
  33. 5
  34. 20°
  35. 56
  36. 12
  37. 576
  38. 7
  39. 22
  40. 186

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