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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 568 · 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 team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 132 (c) 144 (d) 66
  2. 2.Two angles of a triangle are 55° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 95° (c) 85° (d) 125°
  3. 3.Which is the correct factorisation of x² + 9x + 20? (a) (x − 4)(x − 5) (b) (x + 1)(x + 8) (c) (x + 4)(x + 5) (d) (x + 1)(x + 20)
  4. 4.In a class of 42 children, 18 like mangoes, 27 like bananas and 5 like neither. How many like both? (a) 5 (b) 37 (c) 8 (d) 3
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 85° (b) 10° (c) 190° (d) 95°
  6. 6.Which is the correct factorisation of x² + 17x + 72? (a) (x + 8)(x + 9) (b) (x − 8)(x − 9) (c) (x + 1)(x + 72) (d) (x + 1)(x + 16)
  7. 7.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 15 (d) 30
  8. 8.A drawer has lots of black 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) 2 (b) 5 (c) 3 (d) 4
  9. 9.What is the sum of the first 8 terms of the AP 2, 7, 12, …? (a) 156 (b) 176 (c) 37 (d) 312
  10. 10.How many factors does 62 have? (a) 3 (b) 2 (c) 5 (d) 4
  11. 11.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 112 (c) 103 (d) 104
  12. 12.How many prime numbers are there between 50 and 80? (a) 6 (b) 7 (c) 9 (d) 8
  13. 13.Which term of the AP 6, 14, 22, 30, … is 62? (a) 10th (b) 8th (c) 7th (d) 9th
  14. 14.A bag has 9 yellow balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 18 (c) 11 (d) 10
  15. 15.What is the prime factorisation of 63? (a) 3 × 7 (b) 3 × 7² (c) 3² × 7 (d) 3³ × 7
  16. 16.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 302 (c) 346 (d) 345
  17. 17.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 64 (c) 16 (d) 28
  18. 18.What is the prime factorisation of 45? (a) 3 × 5² (b) 3³ × 5 (c) 3 × 5 (d) 3² × 5
  19. 19.How many factors does 90 have? (a) 13 (b) 10 (c) 11 (d) 12
  20. 20.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 220 cm (d) 110 cm
  21. 21.There are 8 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) 80 (b) 48 (c) 40 (d) 13
  22. 22.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
  23. 23.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 155° (d) 110°
  24. 24.The mean of 3 numbers is 25. When the number 41 is added to them, what is the new mean? (a) 30 (b) 29 (c) 25 (d) 33
  25. 25.What are the roots of x² − 17x + 72 = 0? (a) 2 and 36 (b) 1 and 16 (c) 8 and 9 (d) 1 and 72
  26. 26.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 63 (c) 21 (d) 7
  27. 27.Two angles of a triangle are 80° and 85°. What is the third angle? (a) 100° (b) 165° (c) 15° (d) 95°
  28. 28.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 64 (b) 11 (c) 120 (d) 60
  29. 29.What is the smallest prime factor of 65? (a) 1 (b) 13 (c) 5 (d) 2
  30. 30.A bag has 6 red balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 2 (c) 7 (d) 16
  31. 31.How many prime numbers are there between 70 and 100? (a) 7 (b) 8 (c) 6 (d) 5
  32. 32.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 49 (c) 21 (d) 42
  33. 33.A canteen sells 5 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 10 (c) 20 (d) 15
  34. 34.A bag has 9 red balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 10 (b) 13 (c) 11 (d) 2
  35. 35.If a + b = 10 and ab = 21, what is a² + b²? (a) 79 (b) 142 (c) 58 (d) 100
  36. 36.There are 8 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) 15 (b) 56 (c) 64 (d) 112
  37. 37.In which quadrant does the point (9, 6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 170° (c) 85° (d) 95°
  39. 39.What is the median of 4, 10, 14, 15, 22, 26 and 9? (a) 10 (b) 13 (c) 15 (d) 14
  40. 40.What is the mode of 1, 8, 1, 4, 1, 8 and 17? (a) 17 (b) 1 (c) 4 (d) 8

Answer key

  1. 66
  2. 95°
  3. (x + 4)(x + 5)
  4. 8
  5. 95°
  6. (x + 8)(x + 9)
  7. 25
  8. 3
  9. 156
  10. 4
  11. 103
  12. 7
  13. 8th
  14. 11
  15. 3² × 7
  16. 345
  17. 28
  18. 3² × 5
  19. 12
  20. 220 cm
  21. 40
  22. 154 sq cm
  23. 95°
  24. 29
  25. 8 and 9
  26. 21
  27. 15°
  28. 60
  29. 5
  30. 11
  31. 6
  32. 42
  33. 10
  34. 11
  35. 58
  36. 56
  37. First quadrant
  38. 85°
  39. 14
  40. 1

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