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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 158 · 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.In which quadrant does the point (1, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  2. 2.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  3. 3.What is the product of the roots of x² − 17x + 72 = 0? (a) 71 (b) 72 (c) 17 (d) 73
  4. 4.In a class of 33 children, 18 like dance, 15 like music and 7 like neither. How many like both? (a) 26 (b) 8 (c) 7 (d) 6
  5. 5.What is the midpoint of the line joining (2, 3) and (8, 5)? (a) (10, 8) (b) (5, 4) (c) (3, 1) (d) (4, 5)
  6. 6.The mean of 7 numbers is 19. When the number 3 is added to them, what is the new mean? (a) 18 (b) 11 (c) 17 (d) 19
  7. 7.What is the product of the roots of x² − 11x + 30 = 0? (a) 31 (b) 11 (c) 29 (d) 30
  8. 8.If a + b = 13 and ab = 40, what is a² + b²? (a) 249 (b) 169 (c) 89 (d) 129
  9. 9.What is the median of 5, 30, 36, 8, 24, 2 and 19? (a) 24 (b) 20 (c) 8 (d) 19
  10. 10.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 171 (b) 60 (c) 19 (d) 57
  11. 11.How many factors does 38 have? (a) 2 (b) 4 (c) 5 (d) 3
  12. 12.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
  13. 13.If a + b = 10 and ab = 9, what is (a − b)²? (a) 64 (b) 82 (c) 100 (d) 8
  14. 14.The mean of 7 numbers is 33. When the number 49 is added to them, what is the new mean? (a) 33 (b) 36 (c) 41 (d) 35
  15. 15.A bag has 2 white, 7 green and 4 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 7/13 (b) 1/3 (c) 6/13 (d) 6/7
  16. 16.In a class of 38 children, 31 like mangoes, 16 like bananas and 12 like both. How many like at least one of the two? (a) 23 (b) 35 (c) 38 (d) 47
  17. 17.A bag has 8 green balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 10 (b) 9 (c) 2 (d) 20
  18. 18.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 140° (c) 50° (d) 100°
  19. 19.Which is the correct factorisation of x² + 10x + 24? (a) (x + 1)(x + 9) (b) (x + 4)(x + 6) (c) (x − 4)(x − 6) (d) (x + 1)(x + 24)
  20. 20.What is the smallest prime factor of 91? (a) 1 (b) 13 (c) 7 (d) 2
  21. 21.A drawer has lots of blue, yellow, green, red 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) 5 (b) 6 (c) 10 (d) 2
  22. 22.How many prime numbers are there between 90 and 100? (a) 3 (b) 2 (c) 1 (d) 0
  23. 23.What is the midpoint of the line joining (0, 1) and (6, 7)? (a) (3, 3) (b) (4, 3) (c) (3, 4) (d) (6, 8)
  24. 24.A drawer has lots of red and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 2 (c) 4 (d) 5
  25. 25.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 66 (c) 132 (d) 78
  26. 26.What is the missing term in the AP 8, 15, ?, 29, 36? (a) 23 (b) 29 (c) 21 (d) 22
  27. 27.How many prime numbers are there between 20 and 50? (a) 9 (b) 8 (c) 7 (d) 6
  28. 28.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 36 (c) 15 (d) 30
  29. 29.What is the mode of 12, 11, 12, 9, 9, 18 and 9? (a) 18 (b) 11 (c) 9 (d) 12
  30. 30.8 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 56 (b) 48 (c) 96 (d) 14
  31. 31.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 169 (c) 14 (d) 17
  32. 32.A bag has 9 yellow balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 10 (b) 12 (c) 11 (d) 2
  33. 33.Which term of the AP 8, 11, 14, 17, … is 77? (a) 26th (b) 24th (c) 23rd (d) 25th
  34. 34.What is the sum of the first 11 terms of the AP 4, 10, 16, …? (a) 407 (b) 748 (c) 374 (d) 64
  35. 35.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
  36. 36.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 75 (b) 24 (c) 140 (d) 70
  37. 37.In a class of 39 children, 24 like dance, 21 like music and 10 like both. How many like neither? (a) 10 (b) 14 (c) 4 (d) 5
  38. 38.What is the 23rd term of the AP 5, 12, 19, 26, …? (a) 166 (b) 154 (c) 161 (d) 159
  39. 39.A drawer has lots of blue, yellow 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) 3 (b) 6 (c) 2 (d) 4
  40. 40.A drawer has lots of green and red 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) 2 (c) 5 (d) 3

Answer key

  1. First quadrant
  2. 6
  3. 72
  4. 7
  5. (5, 4)
  6. 17
  7. 30
  8. 89
  9. 19
  10. 57
  11. 4
  12. 1/2
  13. 64
  14. 35
  15. 6/13
  16. 35
  17. 10
  18. 100°
  19. (x + 4)(x + 6)
  20. 7
  21. 6
  22. 1
  23. (3, 4)
  24. 3
  25. 66
  26. 22
  27. 7
  28. 15
  29. 9
  30. 48
  31. 13
  32. 11
  33. 24th
  34. 374
  35. 176 cm
  36. 70
  37. 4
  38. 159
  39. 4
  40. 3

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