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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 75 · 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 a class of 40 children, 18 like maths, 21 like science and 3 like both. How many like at least one of the two? (a) 39 (b) 40 (c) 36 (d) 33
  2. 2.Using (a + b)² = a² + 2ab + b², what is 23²? (a) 409 (b) 289 (c) 539 (d) 529
  3. 3.What is the smallest prime factor of 95? (a) 5 (b) 1 (c) 19 (d) 2
  4. 4.What is the sum of the roots of x² − 14x + 48 = 0? (a) 15 (b) 13 (c) 48 (d) 14
  5. 5.A bag has 3 red balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 9 (b) 5 (c) 2 (d) 4
  6. 6.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
  7. 7.What is the product of the roots of x² − 11x + 24 = 0? (a) 11 (b) 23 (c) 25 (d) 24
  8. 8.How many factors does 56 have? (a) 7 (b) 6 (c) 8 (d) 9
  9. 9.What is the mean of 5, 4, 2 and 17? (a) 8 (b) 7 (c) 6 (d) 9
  10. 10.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 125° (b) 235° (c) 56° (d) 55°
  11. 11.The mean of 5 numbers is 27. When the number 45 is added to them, what is the new mean? (a) 36 (b) 27 (c) 31 (d) 30
  12. 12.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 18 (c) 81 (d) 72
  13. 13.The mean of 4 numbers is 22. When the number 37 is added to them, what is the new mean? (a) 24 (b) 25 (c) 26 (d) 22
  14. 14.What is the smallest prime factor of 187? (a) 17 (b) 11 (c) 1 (d) 2
  15. 15.What is the mean of 9, 11, 20, 2, 2 and 16? (a) 9 (b) 12 (c) 11 (d) 10
  16. 16.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
  17. 17.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) 21 (b) 14 (c) 15 (d) 22
  18. 18.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 155° (b) 26° (c) 205° (d) 25°
  19. 19.What is the mean of 12, 14, 20, 5, 6 and 15? (a) 11 (b) 13 (c) 12 (d) 14
  20. 20.A bag has 5 blue balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 7 (b) 6 (c) 8 (d) 2
  21. 21.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  22. 22.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
  23. 23.In a class of 22 children, 13 like mangoes, 9 like bananas and 3 like both. How many like only mangoes? (a) 3 (b) 6 (c) 13 (d) 10
  24. 24.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/8 (b) 1/4 (c) 7/8 (d) 3/8
  25. 25.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 405 (c) 342 (d) 406
  26. 26.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 60° (c) 120° (d) 30°
  27. 27.In a class of 29 children, 21 like maths, 11 like science and 5 like neither. How many like both? (a) 8 (b) 24 (c) 3 (d) 5
  28. 28.How many factors does 68 have? (a) 7 (b) 6 (c) 5 (d) 4
  29. 29.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 135° (b) 105° (c) 150° (d) 75°
  30. 30.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  31. 31.Which is the correct factorisation of x² + 8x + 12? (a) (x + 1)(x + 12) (b) (x + 1)(x + 7) (c) (x + 2)(x + 6) (d) (x − 2)(x − 6)
  32. 32.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 537 (c) 528 (d) 538
  33. 33.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 132 (c) 78 (d) 144
  34. 34.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
  35. 35.Two angles of a triangle are 55° and 60°. What is the exterior angle at the third corner? (a) 115° (b) 125° (c) 120° (d) 65°
  36. 36.If a + b = 6 and ab = 8, what is a² + b²? (a) 36 (b) 52 (c) 20 (d) 28
  37. 37.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm
  38. 38.In which quadrant does the point (2, 6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  39. 39.The mean of 4 numbers is 24. When the number 9 is added to them, what is the new mean? (a) 21 (b) 20 (c) 22 (d) 24
  40. 40.What is the prime factorisation of 70? (a) 2³ × 5 × 7 (b) 2 × 5 × 7² (c) 2 × 5 × 7 (d) 2² × 5 × 7

Answer key

  1. 36
  2. 529
  3. 5
  4. 14
  5. 5
  6. 1/3
  7. 24
  8. 8
  9. 7
  10. 55°
  11. 30
  12. 36
  13. 25
  14. 11
  15. 10
  16. 1/2
  17. 15
  18. 25°
  19. 12
  20. 7
  21. 120
  22. 2464 sq cm
  23. 10
  24. 7/8
  25. 405
  26. 60°
  27. 8
  28. 6
  29. 75°
  30. 120
  31. (x + 2)(x + 6)
  32. 537
  33. 66
  34. 154 sq cm
  35. 115°
  36. 20
  37. 88 cm
  38. First quadrant
  39. 21
  40. 2 × 5 × 7

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