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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 284 · 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 median of 24, 15, 6, 5 and 22? (a) 15 (b) 22 (c) 6 (d) 16
  2. 2.Two angles of a triangle are 55° and 85°. What is the third angle? (a) 95° (b) 140° (c) 40° (d) 125°
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 13 (b) 15 (c) 3 (d) 14
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 51° (b) 100° (c) 130° (d) 50°
  5. 5.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
  6. 6.What is the sum of the first 7 terms of the AP 4, 8, 12, …? (a) 112 (b) 126 (c) 224 (d) 28
  7. 7.What is the midpoint of the line joining (7, 7) and (15, 11)? (a) (11, 9) (b) (22, 18) (c) (9, 11) (d) (4, 2)
  8. 8.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 30° (c) 120° (d) 61°
  9. 9.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) 36 (b) 49 (c) 37 (d) 48
  10. 10.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 24 (c) 132 (d) 144
  11. 11.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 60° (c) 30° (d) 150°
  12. 12.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 65° (b) 295° (c) 25° (d) 115°
  13. 13.What is the smallest prime factor of 33? (a) 3 (b) 2 (c) 11 (d) 1
  14. 14.The mean of 6 numbers is 25. When the number 46 is added to them, what is the new mean? (a) 27 (b) 25 (c) 29 (d) 28
  15. 15.A canteen sells 8 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 40 (b) 48 (c) 80 (d) 13
  16. 16.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 9 times (c) 27 times (d) 3 times
  17. 17.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 726 cu cm (c) 1331 cu cm (d) 484 cu cm
  18. 18.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 3 (c) 9 (d) 12
  19. 19.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  20. 20.A drawer has lots of black and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 2 (c) 4 (d) 3
  21. 21.What is the 10th term of the AP 1, 8, 15, 22, …? (a) 70 (b) 71 (c) 63 (d) 64
  22. 22.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 20° (c) 30° (d) 140°
  23. 23.What is the 16th term of the AP 18, 27, 36, 45, …? (a) 144 (b) 162 (c) 135 (d) 153
  24. 24.What is the distance between the points (6, 14) and (14, 8)? (a) 11 (b) 10 (c) 14 (d) 100
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 51? (a) 6 (b) 4 (c) 3 (d) 5
  26. 26.A bag has 7 white balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 18 (b) 2 (c) 12 (d) 8
  27. 27.What is the mean of 5, 9, 8, 10, 9 and 13? (a) 11 (b) 10 (c) 9 (d) 8
  28. 28.What is the mode of 20, 8, 20, 12, 12, 4 and 12? (a) 12 (b) 20 (c) 8 (d) 4
  29. 29.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 225° (b) 45° (c) 46° (d) 135°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 86° (c) 85° (d) 170°
  31. 31.In a class of 41 children, 29 like maths, 14 like science and 11 like both. How many like at least one of the two? (a) 43 (b) 32 (c) 41 (d) 21
  32. 32.Using (a + b)² = a² + 2ab + b², what is 83²? (a) 5929 (b) 6899 (c) 6409 (d) 6889
  33. 33.What is the missing term in the AP 10, 17, ?, 31, 38? (a) 31 (b) 23 (c) 25 (d) 24
  34. 34.What is the mean of 20, 9, 20 and 11? (a) 15 (b) 12 (c) 16 (d) 20
  35. 35.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 270° (b) 145° (c) 90° (d) 125°
  36. 36.What is the median of 24, 12, 37, 26, 7, 35 and 34? (a) 26 (b) 25 (c) 34 (d) 24
  37. 37.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 6 cu cm (c) 16 cu cm (d) 8 cu cm
  38. 38.How many prime numbers are there between 50 and 60? (a) 1 (b) 4 (c) 2 (d) 3
  39. 39.In which quadrant does the point (6, 6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  40. 40.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6

Answer key

  1. 15
  2. 40°
  3. 14
  4. 50°
  5. 1/2
  6. 112
  7. (11, 9)
  8. 60°
  9. 37
  10. 132
  11. 75°
  12. 115°
  13. 3
  14. 28
  15. 40
  16. 27 times
  17. 1331 cu cm
  18. 6
  19. 15
  20. 3
  21. 64
  22. 20°
  23. 153
  24. 10
  25. 5
  26. 12
  27. 9
  28. 12
  29. 45°
  30. 85°
  31. 32
  32. 6889
  33. 24
  34. 15
  35. 90°
  36. 26
  37. 8 cu cm
  38. 2
  39. First quadrant
  40. 6

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