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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 693 · 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.A bag has 3 white balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 4 (c) 7 (d) 5
  2. 2.A cuboid is 6 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 360 sq cm (b) 180 sq cm (c) 144 sq cm (d) 90 sq cm
  3. 3.Two angles of a triangle are 35° and 125°. What is the third angle? (a) 55° (b) 160° (c) 145° (d) 20°
  4. 4.What is the 38th term of the AP 14, 17, 20, 23, …? (a) 111 (b) 125 (c) 128 (d) 114
  5. 5.What is the product of the roots of x² − 16x + 63 = 0? (a) 63 (b) 64 (c) 16 (d) 62
  6. 6.If a + b = 14 and ab = 48, what is (a − b)²? (a) 100 (b) 4 (c) 196 (d) 2
  7. 7.What is the distance between the points (5, 15) and (17, 6)? (a) 16 (b) 225 (c) 15 (d) 21
  8. 8.Which is the correct factorisation of x² + 14x + 48? (a) (x + 6)(x + 8) (b) (x + 1)(x + 48) (c) (x − 6)(x − 8) (d) (x + 1)(x + 13)
  9. 9.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  10. 10.What is the sum of all the whole numbers from 1 to 18? (a) 171 (b) 153 (c) 162 (d) 342
  11. 11.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 14 (b) 8 (c) 7 (d) 15
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 69? (a) 18 (b) 6 (c) 17 (d) 16
  13. 13.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 4 times (c) 16 times (d) 8 times
  14. 14.What is the midpoint of the line joining (1, 3) and (5, 1)? (a) (6, 4) (b) (2, 1) (c) (3, 2) (d) (2, 3)
  15. 15.How many factors does 12 have? (a) 4 (b) 7 (c) 6 (d) 5
  16. 16.Two angles of a triangle are 20° and 95°. What is the third angle? (a) 65° (b) 85° (c) 115° (d) 160°
  17. 17.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) 49 (b) 37 (c) 48 (d) 36
  18. 18.What is the midpoint of the line joining (8, 0) and (18, 6)? (a) (3, 13) (b) (13, 3) (c) (5, 3) (d) (26, 6)
  19. 19.In a class of 44 children, 28 like dance, 17 like music and 11 like both. How many like neither? (a) 10 (b) 21 (c) 9 (d) 11
  20. 20.What is the mode of 13, 11, 18, 5, 13, 5 and 5? (a) 18 (b) 13 (c) 5 (d) 11
  21. 21.Which term of the AP 5, 13, 21, 29, … is 317? (a) 42nd (b) 39th (c) 41st (d) 40th
  22. 22.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 576 (c) 600 (d) 300
  23. 23.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 6 (c) 54 (d) 21
  24. 24.What is the distance between the points (6, 13) and (18, 8)? (a) 13 (b) 169 (c) 17 (d) 14
  25. 25.What is the sum of the roots of x² − 5x + 6 = 0? (a) 5 (b) 6 (c) 4 (d) 7
  26. 26.Using (a − b)² = a² − 2ab + b², what is 76²? (a) 7056 (b) 6384 (c) 5786 (d) 5776
  27. 27.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
  28. 28.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
  29. 29.What is the 20th term of the AP 20, 22, 24, 26, …? (a) 60 (b) 40 (c) 38 (d) 58
  30. 30.What is the prime factorisation of 21? (a) 3² × 7 (b) 3 × 7 (c) 3³ × 7 (d) 3 × 7²
  31. 31.Using (a + b)² = a² + 2ab + b², what is 75²? (a) 5635 (b) 5625 (c) 4225 (d) 4925
  32. 32.What is the median of 6, 4, 27, 14, 16, 20 and 18? (a) 15 (b) 18 (c) 14 (d) 16
  33. 33.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 19 (d) 100
  34. 34.A cuboid is 6 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 240 sq cm (b) 72 sq cm (c) 60 sq cm (d) 120 sq cm
  35. 35.Two angles of a triangle are 65° and 50°. What is the exterior angle at the third corner? (a) 245° (b) 130° (c) 115° (d) 65°
  36. 36.How many factors does 110 have? (a) 9 (b) 6 (c) 7 (d) 8
  37. 37.What is the sum of all the whole numbers from 1 to 36? (a) 630 (b) 648 (c) 1332 (d) 666
  38. 38.What is the mean of 19, 14, 5, 4 and 3? (a) 8 (b) 9 (c) 10 (d) 11
  39. 39.What is the mode of 12, 19, 15, 5, 19, 12 and 19? (a) 12 (b) 5 (c) 15 (d) 19
  40. 40.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 3/11 (b) 1/11 (c) 1/9 (d) 1/12

Answer key

  1. 5
  2. 180 sq cm
  3. 20°
  4. 125
  5. 63
  6. 4
  7. 15
  8. (x + 6)(x + 8)
  9. 24
  10. 171
  11. 8
  12. 17
  13. 64 times
  14. (3, 2)
  15. 6
  16. 65°
  17. 37
  18. (13, 3)
  19. 10
  20. 5
  21. 40th
  22. 576
  23. 18
  24. 13
  25. 5
  26. 5776
  27. 88 cm
  28. 1/2
  29. 58
  30. 3 × 7
  31. 5625
  32. 16
  33. 100
  34. 120 sq cm
  35. 115°
  36. 8
  37. 666
  38. 9
  39. 19
  40. 1/12

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