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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 133 · 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.What is the midpoint of the line joining (0, 3) and (12, 15)? (a) (6, 9) (b) (9, 6) (c) (12, 18) (d) (6, 6)
  2. 2.A bag has 12 red balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 22 (b) 13 (c) 2 (d) 14
  3. 3.In a class of 43 children, 24 like maths, 23 like science and 11 like both. How many like at least one of the two? (a) 47 (b) 25 (c) 36 (d) 43
  4. 4.How many prime numbers are there between 30 and 40? (a) 1 (b) 4 (c) 3 (d) 2
  5. 5.What is the midpoint of the line joining (2, 0) and (8, 4)? (a) (2, 5) (b) (3, 2) (c) (5, 2) (d) (10, 4)
  6. 6.In a class of 30 children, 18 like dance, 10 like music and 2 like both. How many like only dance? (a) 20 (b) 8 (c) 16 (d) 18
  7. 7.Two angles of a triangle are 25° and 125°. What is the third angle? (a) 30° (b) 155° (c) 55° (d) 150°
  8. 8.In a class of 46 children, 18 like dance, 23 like music and 8 like neither. How many like both? (a) 8 (b) 4 (c) 38 (d) 3
  9. 9.Which is the correct factorisation of x² + 12x + 35? (a) (x + 1)(x + 35) (b) (x + 1)(x + 11) (c) (x − 5)(x − 7) (d) (x + 5)(x + 7)
  10. 10.How many factors does 59 have? (a) 1 (b) 4 (c) 2 (d) 3
  11. 11.What is the sum of the first 9 terms of the AP 10, 15, 20, …? (a) 275 (b) 50 (c) 540 (d) 270
  12. 12.5 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) 40 (b) 70 (c) 35 (d) 12
  13. 13.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 294 (c) 334 (d) 333
  14. 14.What is the sum of all the whole numbers from 1 to 96? (a) 4608 (b) 4560 (c) 9312 (d) 4656
  15. 15.In a class of 25 children, 17 like dance, 15 like music and 9 like both. How many like only dance? (a) 6 (b) 8 (c) 10 (d) 17
  16. 16.What is the smallest prime factor of 69? (a) 1 (b) 2 (c) 23 (d) 3
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 91? (a) 19 (b) 9 (c) 20 (d) 18
  18. 18.A drawer has lots of green, blue 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) 3 (d) 6
  19. 19.What is the midpoint of the line joining (4, 10) and (8, 0)? (a) (6, 5) (b) (5, 6) (c) (12, 10) (d) (2, 5)
  20. 20.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 3 (c) 6 (d) 9
  21. 21.Using (a + b)² = a² + 2ab + b², what is 85²? (a) 5625 (b) 7235 (c) 6425 (d) 7225
  22. 22.The mean of 6 numbers is 26. When the number 33 is added to them, what is the new mean? (a) 27 (b) 26 (c) 28 (d) 29
  23. 23.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 4 times (d) 5 times
  24. 24.In a class of 20 children, 14 like maths, 13 like science and 9 like both. How many like at least one of the two? (a) 18 (b) 20 (c) 9 (d) 27
  25. 25.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
  26. 26.What are the roots of x² − 9x + 14 = 0? (a) 2 and 7 (b) 3 and 6 (c) 1 and 8 (d) 1 and 14
  27. 27.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  28. 28.The mean of 3 numbers is 10. When the number 22 is added to them, what is the new mean? (a) 10 (b) 14 (c) 16 (d) 13
  29. 29.How many prime numbers are there between 40 and 50? (a) 5 (b) 4 (c) 2 (d) 3
  30. 30.A drawer has lots of blue, 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) 4 (b) 3 (c) 2 (d) 6
  31. 31.How many factors does 112 have? (a) 11 (b) 9 (c) 10 (d) 8
  32. 32.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 135° (c) 45° (d) 90°
  33. 33.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
  34. 34.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 21 (c) 42 (d) 49
  35. 35.The mean of 4 numbers is 25. When the number 10 is added to them, what is the new mean? (a) 25 (b) 21 (c) 23 (d) 22
  36. 36.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  37. 37.Using (a − b)² = a² − 2ab + b², what is 27²? (a) 739 (b) 729 (c) 1089 (d) 891
  38. 38.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 265° (c) 85° (d) 86°
  39. 39.What is the smallest prime factor of 95? (a) 19 (b) 5 (c) 2 (d) 1
  40. 40.In a class of 39 children, 22 like maths, 16 like science and 7 like neither. How many like both? (a) 32 (b) 6 (c) 7 (d) 5

Answer key

  1. (6, 9)
  2. 14
  3. 36
  4. 2
  5. (5, 2)
  6. 16
  7. 30°
  8. 3
  9. (x + 5)(x + 7)
  10. 2
  11. 270
  12. 35
  13. 333
  14. 4656
  15. 8
  16. 3
  17. 19
  18. 4
  19. (6, 5)
  20. 6
  21. 7225
  22. 27
  23. 4 times
  24. 18
  25. 125 times
  26. 2 and 7
  27. 120
  28. 13
  29. 3
  30. 4
  31. 10
  32. 90°
  33. 1/3
  34. 21
  35. 22
  36. 7
  37. 729
  38. 85°
  39. 5
  40. 6

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