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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 998 · 40 questions
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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 distance between the points (3, 9) and (11, 15)? (a) 11 (b) 10 (c) 14 (d) 100
  2. 2.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
  3. 3.The mean of 7 numbers is 30. When the number 6 is added to them, what is the new mean? (a) 18 (b) 30 (c) 27 (d) 28
  4. 4.What is the median of 34, 3, 27, 40, 4, 23 and 1? (a) 4 (b) 27 (c) 40 (d) 23
  5. 5.What is the prime factorisation of 35? (a) 5³ × 7 (b) 5² × 7 (c) 5 × 7 (d) 5 × 7²
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 3 (b) 14 (c) 13 (d) 15
  7. 7.What is the mode of 16, 13, 16, 16, 5, 12 and 13? (a) 5 (b) 12 (c) 13 (d) 16
  8. 8.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 240 (c) 20 (d) 25
  9. 9.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 290° (b) 145° (c) 70° (d) 110°
  10. 10.In a class of 38 children, 17 like dance, 24 like music and 9 like both. How many like at least one of the two? (a) 23 (b) 38 (c) 41 (d) 32
  11. 11.In which quadrant does the point (−4, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  12. 12.Which is the correct factorisation of x² + 8x + 15? (a) (x + 1)(x + 15) (b) (x + 1)(x + 7) (c) (x + 3)(x + 5) (d) (x − 3)(x − 5)
  13. 13.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 64 times (c) 4 times (d) 8 times
  14. 14.The mean of 5 numbers is 10. When the number 16 is added to them, what is the new mean? (a) 10 (b) 13 (c) 11 (d) 12
  15. 15.A cuboid is 9 cm long, 6 cm wide and 6 cm high. What is its volume? (a) 288 cu cm (b) 324 cu cm (c) 54 cu cm (d) 21 cu cm
  16. 16.A bag has 9 white balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 17 (c) 10 (d) 11
  17. 17.A bag has 12 blue balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 13 (c) 9 (d) 20
  18. 18.8 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) 24 (b) 11 (c) 32 (d) 48
  19. 19.What is the missing term in the AP 8, 14, ?, 26, 32? (a) 19 (b) 26 (c) 20 (d) 21
  20. 20.What is the median of 23, 19, 9, 14, 27, 30 and 12? (a) 20 (b) 23 (c) 19 (d) 14
  21. 21.What is the midpoint of the line joining (7, 15) and (11, 3)? (a) (9, 9) (b) (2, 6) (c) (10, 9) (d) (18, 18)
  22. 22.What is the prime factorisation of 336? (a) 2³ × 3 × 7 (b) 2 × 3 × 7⁴ (c) 2⁵ × 3 × 7 (d) 2⁴ × 3 × 7
  23. 23.In a class of 49 children, 28 like cricket, 30 like football and 11 like both. How many like neither? (a) 11 (b) 3 (c) 2 (d) 13
  24. 24.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 162 (c) 54 (d) 18
  25. 25.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 97 sq cm (c) 64 sq cm (d) 96 sq cm
  26. 26.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 2 (d) 4
  27. 27.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 110° (b) 150° (c) 100° (d) 80°
  28. 28.In a class of 21 children, 11 like maths, 12 like science and 7 like both. How many like at least one of the two? (a) 23 (b) 9 (c) 21 (d) 16
  29. 29.In which quadrant does the point (7, −6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  30. 30.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  31. 31.What is the mean of 12, 20, 2 and 10? (a) 11 (b) 10 (c) 13 (d) 12
  32. 32.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 91 (c) 169 (d) 78
  33. 33.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 3 (c) 9 (d) 12
  34. 34.If a + b = 18 and ab = 80, what is (a − b)²? (a) 2 (b) 324 (c) 4 (d) 164
  35. 35.A cuboid is 9 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 294 cu cm (b) 27 cu cm (c) 270 cu cm (d) 22 cu cm
  36. 36.What is the distance between the points (9, 2) and (13, 5)? (a) 7 (b) 25 (c) 6 (d) 5
  37. 37.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  38. 38.8 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 15 (b) 112 (c) 56 (d) 64
  39. 39.What is the mean of 5, 19, 19 and 13? (a) 15 (b) 13 (c) 16 (d) 14
  40. 40.Using (a + b)² = a² + 2ab + b², what is 25²? (a) 635 (b) 425 (c) 225 (d) 625

Answer key

  1. 10
  2. 1/2
  3. 27
  4. 23
  5. 5 × 7
  6. 14
  7. 16
  8. 120
  9. 110°
  10. 32
  11. Third quadrant
  12. (x + 3)(x + 5)
  13. 16 times
  14. 11
  15. 324 cu cm
  16. 11
  17. 13
  18. 24
  19. 20
  20. 19
  21. (9, 9)
  22. 2⁴ × 3 × 7
  23. 2
  24. 54
  25. 96 sq cm
  26. 3
  27. 80°
  28. 16
  29. Fourth quadrant
  30. 24
  31. 11
  32. 78
  33. 6
  34. 4
  35. 270 cu cm
  36. 5
  37. 6
  38. 56
  39. 14
  40. 625

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