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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 32 · 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.Which is the correct factorisation of x² + 13x + 36? (a) (x + 1)(x + 12) (b) (x + 1)(x + 36) (c) (x − 4)(x − 9) (d) (x + 4)(x + 9)
  2. 2.What is the 22nd term of the AP 2, 10, 18, 26, …? (a) 178 (b) 168 (c) 170 (d) 176
  3. 3.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2⁵ × 3 (c) 2³ × 3 (d) 2⁴ × 3
  4. 4.What is the prime factorisation of 180? (a) 2 × 3² × 5² (b) 2² × 3² × 5 (c) 2 × 3² × 5 (d) 2³ × 3² × 5
  5. 5.In which quadrant does the point (1, 3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  6. 6.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 50° (c) 40° (d) 100°
  7. 7.What is the mode of 11, 5, 11, 10, 5, 20 and 11? (a) 11 (b) 10 (c) 20 (d) 5
  8. 8.A bag has 3 red, 4 green and 5 yellow balls. One ball is taken out without looking. What is the probability that it is not red? (a) 3/4 (b) 1/3 (c) 1/4 (d) 5/6
  9. 9.What is the mode of 18, 11, 11, 17, 15, 11 and 17? (a) 18 (b) 11 (c) 17 (d) 15
  10. 10.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 290 (b) 160 (c) 28 (d) 145
  11. 11.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
  12. 12.Which is the correct factorisation of x² + 15x + 54? (a) (x + 6)(x + 9) (b) (x + 1)(x + 54) (c) (x + 1)(x + 14) (d) (x − 6)(x − 9)
  13. 13.What is the median of 9, 23, 3, 39 and 14? (a) 9 (b) 14 (c) 3 (d) 23
  14. 14.What is the mean of 6, 15, 4, 12 and 3? (a) 9 (b) 8 (c) 10 (d) 7
  15. 15.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 25° (c) 50° (d) 115°
  16. 16.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 145° (c) 35° (d) 55°
  17. 17.In a league, 11 teams each play every other team once. How many matches are played? (a) 55 (b) 121 (c) 110 (d) 66
  18. 18.In a class of 27 children, 14 like mangoes, 17 like bananas and 8 like both. How many like at least one of the two? (a) 15 (b) 31 (c) 23 (d) 27
  19. 19.What is the sum of the first 11 terms of the AP 9, 10, 11, …? (a) 155 (b) 19 (c) 154 (d) 308
  20. 20.What is the 14th term of the AP 7, 16, 25, 34, …? (a) 133 (b) 126 (c) 124 (d) 117
  21. 21.Using (a − b)² = a² − 2ab + b², what is 75²? (a) 7225 (b) 5635 (c) 6375 (d) 5625
  22. 22.What is the mode of 4, 8, 15, 4, 15, 20 and 15? (a) 15 (b) 8 (c) 20 (d) 4
  23. 23.Using (a − b)² = a² − 2ab + b², what is 69²? (a) 4771 (b) 5041 (c) 4761 (d) 4899
  24. 24.There are 5 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 20 (b) 40 (c) 9 (d) 25
  25. 25.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
  26. 26.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 110° (c) 45° (d) 35°
  27. 27.What is the distance between the points (2, 8) and (18, 20)? (a) 21 (b) 28 (c) 20 (d) 400
  28. 28.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 196 (c) 105 (d) 27
  29. 29.What is the product of the roots of x² − 12x + 35 = 0? (a) 12 (b) 36 (c) 34 (d) 35
  30. 30.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 70° (b) 290° (c) 20° (d) 110°
  31. 31.7 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 10 (b) 28 (c) 21 (d) 42
  32. 32.What is the sum of the roots of x² − 16x + 63 = 0? (a) 63 (b) 17 (c) 15 (d) 16
  33. 33.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 20 (c) 60 (d) 180
  34. 34.In a class of 35 children, 18 like maths, 15 like science and 4 like both. How many like only maths? (a) 20 (b) 14 (c) 18 (d) 11
  35. 35.If a + b = 15 and ab = 44, what is (a − b)²? (a) 137 (b) 49 (c) 7 (d) 225
  36. 36.The mean of 9 numbers is 24. When the number 44 is added to them, what is the new mean? (a) 27 (b) 34 (c) 26 (d) 24
  37. 37.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 4/11 (b) 1/11 (c) 1/9 (d) 5/36
  38. 38.What is the distance between the points (1, 16) and (10, 4)? (a) 225 (b) 16 (c) 21 (d) 15
  39. 39.A cuboid is 7 cm long, 5 cm wide and 10 cm high. What is its total surface area? (a) 155 sq cm (b) 620 sq cm (c) 310 sq cm (d) 350 sq cm
  40. 40.In a class of 38 children, 15 like maths, 27 like science and 12 like both. How many like at least one of the two? (a) 18 (b) 30 (c) 42 (d) 38

Answer key

  1. (x + 4)(x + 9)
  2. 170
  3. 2⁴ × 3
  4. 2² × 3² × 5
  5. First quadrant
  6. 40°
  7. 11
  8. 3/4
  9. 11
  10. 145
  11. 25
  12. (x + 6)(x + 9)
  13. 14
  14. 8
  15. 50°
  16. 110°
  17. 55
  18. 23
  19. 154
  20. 124
  21. 5625
  22. 15
  23. 4761
  24. 20
  25. 64 times
  26. 35°
  27. 20
  28. 196
  29. 35
  30. 110°
  31. 21
  32. 16
  33. 60
  34. 14
  35. 49
  36. 26
  37. 1/9
  38. 15
  39. 310 sq cm
  40. 30

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