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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 468 · 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.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
  2. 2.The mean of 3 numbers is 31. When the number 39 is added to them, what is the new mean? (a) 33 (b) 34 (c) 35 (d) 31
  3. 3.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 14) (b) (x − 7)(x − 8) (c) (x + 7)(x + 8) (d) (x + 1)(x + 56)
  4. 4.What is the midpoint of the line joining (10, 5) and (14, 9)? (a) (12, 7) (b) (24, 14) (c) (2, 2) (d) (7, 12)
  5. 5.How many prime numbers are there between 90 and 100? (a) 3 (b) 0 (c) 2 (d) 1
  6. 6.How many factors does 42 have? (a) 9 (b) 6 (c) 8 (d) 7
  7. 7.A bag has 10 black balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 12 (b) 2 (c) 21 (d) 11
  8. 8.In a class of 33 children, 11 like mangoes, 23 like bananas and 5 like both. How many like at least one of the two? (a) 34 (b) 33 (c) 24 (d) 29
  9. 9.What is the median of 10, 25, 2, 21 and 33? (a) 25 (b) 2 (c) 10 (d) 21
  10. 10.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
  11. 11.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 6 (c) 12 (d) 3
  12. 12.If a + b = 4 and ab = 3, what is a² + b²? (a) 13 (b) 10 (c) 22 (d) 16
  13. 13.A bag has 6 black balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 8 (b) 2 (c) 7 (d) 16
  14. 14.How many prime numbers are there between 30 and 50? (a) 7 (b) 5 (c) 4 (d) 6
  15. 15.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 15 (b) 22 (c) 14 (d) 21
  16. 16.What is the mode of 1, 2, 4, 13, 1, 13 and 13? (a) 13 (b) 2 (c) 1 (d) 4
  17. 17.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 132 (c) 24 (d) 144
  18. 18.What is the smallest prime factor of 93? (a) 1 (b) 2 (c) 31 (d) 3
  19. 19.What is the prime factorisation of 15? (a) 3 × 5 (b) 3² × 5 (c) 3 × 5² (d) 3³ × 5
  20. 20.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  21. 21.A bag has 12 black balls and 9 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 21 (b) 2 (c) 10 (d) 13
  22. 22.In a class of 43 children, 21 like mangoes, 27 like bananas and 8 like both. How many like neither? (a) 11 (b) 8 (c) 4 (d) 3
  23. 23.In a class of 36 children, 20 like mangoes, 20 like bananas and 6 like both. How many like neither? (a) 8 (b) 3 (c) 2 (d) 6
  24. 24.How many factors does 99 have? (a) 7 (b) 6 (c) 5 (d) 4
  25. 25.In a class of 39 children, 20 like maths, 19 like science and 9 like neither. How many like both? (a) 10 (b) 30 (c) 9 (d) 8
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 56° (b) 55° (c) 110° (d) 125°
  27. 27.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 5 times (c) 125 times (d) 25 times
  28. 28.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2⁵ × 3 (c) 2³ × 3 (d) 2⁴ × 3
  29. 29.A bag has 8 green balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 17 (b) 10 (c) 9 (d) 2
  30. 30.There are 6 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 48 (b) 42 (c) 84 (d) 13
  31. 31.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 16) (c) (x + 8)(x + 9) (d) (x + 1)(x + 72)
  32. 32.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 256 (c) 31 (d) 272
  33. 33.What is the median of 13, 34, 21, 14, 38, 25 and 18? (a) 18 (b) 21 (c) 25 (d) 14
  34. 34.A bag has 4 yellow balls and 12 blue 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) 5 (c) 13 (d) 16
  35. 35.If a + b = 18 and ab = 80, what is (a − b)²? (a) 324 (b) 4 (c) 164 (d) 2
  36. 36.In a class of 35 children, 11 like tea, 28 like coffee and 8 like both. How many like only tea? (a) 7 (b) 20 (c) 11 (d) 3
  37. 37.There are 6 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 11 (b) 36 (c) 30 (d) 60
  38. 38.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
  39. 39.What is the 39th term of the AP 7, 13, 19, 25, …? (a) 234 (b) 235 (c) 228 (d) 241
  40. 40.In a class of 26 children, 19 like maths, 11 like science and 6 like both. How many like at least one of the two? (a) 26 (b) 18 (c) 30 (d) 24

Answer key

  1. 2
  2. 33
  3. (x + 7)(x + 8)
  4. (12, 7)
  5. 1
  6. 8
  7. 12
  8. 29
  9. 21
  10. 1/2
  11. 6
  12. 10
  13. 8
  14. 5
  15. 15
  16. 13
  17. 66
  18. 3
  19. 3 × 5
  20. 20
  21. 13
  22. 3
  23. 2
  24. 6
  25. 9
  26. 55°
  27. 25 times
  28. 2⁴ × 3
  29. 10
  30. 42
  31. (x + 8)(x + 9)
  32. 256
  33. 21
  34. 13
  35. 4
  36. 3
  37. 30
  38. 1/2
  39. 235
  40. 24

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