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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 316 · 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, 1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  2. 2.Which is the correct factorisation of x² + 12x + 35? (a) (x + 1)(x + 11) (b) (x − 5)(x − 7) (c) (x + 5)(x + 7) (d) (x + 1)(x + 35)
  3. 3.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 40° (b) 50° (c) 140° (d) 320°
  4. 4.A bag has 11 green balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 12 (c) 2 (d) 5
  5. 5.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
  6. 6.A bag has 5 blue balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 6 (c) 2 (d) 4
  7. 7.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 130° (b) 50° (c) 51° (d) 230°
  8. 8.Which term of the AP 3, 10, 17, 24, … is 199? (a) 29th (b) 28th (c) 31st (d) 30th
  9. 9.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 70° (c) 55° (d) 20°
  10. 10.In a class of 51 children, 27 like dance, 27 like music and 10 like both. How many like at least one of the two? (a) 51 (b) 54 (c) 34 (d) 44
  11. 11.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 80° (b) 160° (c) 70° (d) 20°
  12. 12.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 36 (c) 18 (d) 72
  13. 13.What is the prime factorisation of 126? (a) 2 × 3² × 7² (b) 2³ × 3² × 7 (c) 2 × 3² × 7 (d) 2² × 3² × 7
  14. 14.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  15. 15.Two angles of a triangle are 65° and 50°. What is the third angle? (a) 65° (b) 130° (c) 115° (d) 245°
  16. 16.What is the sum of the first 12 terms of the AP 6, 7, 8, …? (a) 144 (b) 138 (c) 276 (d) 17
  17. 17.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 7 (d) 5
  18. 18.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
  19. 19.How many factors does 115 have? (a) 5 (b) 3 (c) 2 (d) 4
  20. 20.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
  21. 21.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 13 (c) 39 (d) 42
  22. 22.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 198 (c) 66 (d) 22
  23. 23.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 55° (c) 35° (d) 145°
  24. 24.What is the mode of 12, 16, 17, 12, 18, 16 and 16? (a) 17 (b) 18 (c) 16 (d) 12
  25. 25.In a class of 28 children, 20 like tea, 7 like coffee and 2 like both. How many like at least one of the two? (a) 23 (b) 27 (c) 25 (d) 28
  26. 26.Two angles of a triangle are 40° and 110°. What is the exterior angle at the third corner? (a) 150° (b) 30° (c) 70° (d) 140°
  27. 27.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/11 (b) 6/11 (c) 1/6 (d) 7/36
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 9 (b) 18 (c) 20 (d) 19
  29. 29.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 55 (c) 121 (d) 22
  30. 30.What is the smallest prime factor of 35? (a) 2 (b) 1 (c) 7 (d) 5
  31. 31.What is the midpoint of the line joining (0, 9) and (6, 15)? (a) (12, 3) (b) (3, 12) (c) (6, 24) (d) (3, 3)
  32. 32.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 63) (b) (x − 7)(x − 9) (c) (x + 1)(x + 15) (d) (x + 7)(x + 9)
  33. 33.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
  34. 34.A cuboid is 12 cm long, 9 cm wide and 2 cm high. What is its volume? (a) 23 cu cm (b) 108 cu cm (c) 216 cu cm (d) 300 cu cm
  35. 35.How many factors does 103 have? (a) 3 (b) 4 (c) 2 (d) 1
  36. 36.What is the mode of 17, 8, 3, 16, 3, 17 and 17? (a) 16 (b) 3 (c) 8 (d) 17
  37. 37.What is the mean of 19, 3, 7 and 15? (a) 13 (b) 12 (c) 11 (d) 10
  38. 38.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/8 (c) 1/7 (d) 7/8
  39. 39.How many factors does 86 have? (a) 3 (b) 4 (c) 2 (d) 5
  40. 40.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3

Answer key

  1. First quadrant
  2. (x + 5)(x + 7)
  3. 140°
  4. 12
  5. 9 times
  6. 6
  7. 50°
  8. 29th
  9. 55°
  10. 44
  11. 80°
  12. 72
  13. 2 × 3² × 7
  14. 15
  15. 65°
  16. 138
  17. 6
  18. 17
  19. 4
  20. 132 cm
  21. 39
  22. 66
  23. 110°
  24. 16
  25. 25
  26. 150°
  27. 1/6
  28. 19
  29. 55
  30. 5
  31. (3, 12)
  32. (x + 7)(x + 9)
  33. 154 sq cm
  34. 216 cu cm
  35. 2
  36. 17
  37. 11
  38. 1/8
  39. 4
  40. 1/2

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