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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 10 · 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 7 red, 9 blue and 4 white balls. One ball is taken out without looking. What is the probability that it is red? (a) 7/13 (b) 1/3 (c) 7/20 (d) 13/20
  2. 2.A bag has 3 yellow, 6 white and 8 blue balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 3/17 (b) 1/3 (c) 15/17 (d) 14/17
  3. 3.What is the sum of the first 12 terms of the AP 10, 15, 20, …? (a) 480 (b) 450 (c) 65 (d) 900
  4. 4.What is the smallest prime factor of 77? (a) 7 (b) 11 (c) 1 (d) 2
  5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/11 (b) 3/11 (c) 1/12 (d) 1/9
  6. 6.What is the 19th term of the AP 12, 15, 18, 21, …? (a) 57 (b) 66 (c) 54 (d) 69
  7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 2/11 (c) 1/18 (d) 1/12
  8. 8.What is the smallest prime factor of 121? (a) 1 (b) 2 (c) 3 (d) 11
  9. 9.In a class of 40 children, 12 like dance, 27 like music and 8 like neither. How many like both? (a) 8 (b) 6 (c) 32 (d) 7
  10. 10.What is the mean of 13, 12, 4, 20, 16 and 19? (a) 12 (b) 14 (c) 13 (d) 15
  11. 11.How many prime numbers are there between 10 and 40? (a) 8 (b) 9 (c) 10 (d) 7
  12. 12.What is the prime factorisation of 84? (a) 2² × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7² (d) 2 × 3 × 7
  13. 13.In a class of 43 children, 22 like cricket, 19 like football and 3 like both. How many like neither? (a) 3 (b) 8 (c) 5 (d) 2
  14. 14.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
  15. 15.Which term of the AP 14, 16, 18, 20, … is 64? (a) 25th (b) 26th (c) 32nd (d) 27th
  16. 16.In which quadrant does the point (−3, 8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  17. 17.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
  18. 18.What is the distance between the points (3, 3) and (15, 19)? (a) 400 (b) 21 (c) 20 (d) 28
  19. 19.Which term of the AP 1, 7, 13, 19, … is 175? (a) 31st (b) 29th (c) 32nd (d) 30th
  20. 20.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
  21. 21.What is the prime factorisation of 60? (a) 2 × 3 × 5² (b) 2 × 3 × 5 (c) 2³ × 3 × 5 (d) 2² × 3 × 5
  22. 22.What is the median of 23, 30, 17, 40 and 1? (a) 30 (b) 17 (c) 23 (d) 24
  23. 23.Which is the correct factorisation of x² + 11x + 24? (a) (x + 1)(x + 24) (b) (x + 3)(x + 8) (c) (x − 3)(x − 8) (d) (x + 1)(x + 10)
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 14 (b) 16 (c) 15 (d) 4
  25. 25.A bag has 4 black balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 6 (c) 9 (d) 5
  26. 26.What is the smallest prime factor of 247? (a) 2 (b) 19 (c) 13 (d) 1
  27. 27.What is the midpoint of the line joining (6, 8) and (18, 14)? (a) (24, 22) (b) (11, 12) (c) (6, 3) (d) (12, 11)
  28. 28.A drawer has lots of yellow, green and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 3 (c) 2 (d) 6
  29. 29.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
  30. 30.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 37 (b) 25 (c) 24 (d) 36
  31. 31.If a + b = 20 and ab = 99, what is (a − b)²? (a) 400 (b) 202 (c) 4 (d) 2
  32. 32.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/6 (b) 5/11 (c) 1/11 (d) 5/36
  33. 33.A bag has 6 black balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 14 (b) 7 (c) 8 (d) 2
  34. 34.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 20 (c) 240 (d) 25
  35. 35.What is the sum of all the whole numbers from 1 to 70? (a) 2415 (b) 4970 (c) 2450 (d) 2485
  36. 36.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/36 (b) 1/12 (c) 1/11 (d) 1/18
  37. 37.What is the mode of 10, 2, 5, 6, 10, 5 and 10? (a) 6 (b) 2 (c) 10 (d) 5
  38. 38.In a class of 41 children, 12 like cricket, 27 like football and 8 like both. How many like at least one of the two? (a) 23 (b) 31 (c) 39 (d) 41
  39. 39.What is the median of 14, 6, 5, 30 and 18? (a) 5 (b) 6 (c) 14 (d) 18
  40. 40.What is the smallest prime factor of 119? (a) 2 (b) 7 (c) 17 (d) 1

Answer key

  1. 7/20
  2. 14/17
  3. 450
  4. 7
  5. 1/12
  6. 66
  7. 1/18
  8. 11
  9. 7
  10. 14
  11. 8
  12. 2² × 3 × 7
  13. 5
  14. 13
  15. 26th
  16. Second quadrant
  17. 1386 sq cm
  18. 20
  19. 30th
  20. 5
  21. 2² × 3 × 5
  22. 23
  23. (x + 3)(x + 8)
  24. 15
  25. 6
  26. 13
  27. (12, 11)
  28. 4
  29. 1/2
  30. 25
  31. 4
  32. 5/36
  33. 8
  34. 120
  35. 2485
  36. 1/36
  37. 10
  38. 31
  39. 14
  40. 7

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