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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 733 · 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 23 children, 13 like tea, 8 like coffee and 4 like both. How many like only tea? (a) 9 (b) 13 (c) 4 (d) 15
  2. 2.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 28 (c) 21 (d) 49
  3. 3.Using (a − b)² = a² − 2ab + b², what is 87²? (a) 8649 (b) 7569 (c) 8091 (d) 7579
  4. 4.Using (a + b)² = a² + 2ab + b², what is 61²? (a) 3721 (b) 3601 (c) 3731 (d) 3481
  5. 5.A bag has 5 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) 15 (d) 6
  6. 6.What is the prime factorisation of 240? (a) 2⁴ × 3 × 5 (b) 2 × 3 × 5⁴ (c) 2⁵ × 3 × 5 (d) 2³ × 3 × 5
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 140° (b) 160° (c) 20° (d) 320°
  8. 8.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
  9. 9.What is the 26th term of the AP 8, 12, 16, 20, …? (a) 108 (b) 100 (c) 112 (d) 104
  10. 10.A bag has 5 blue, 9 green and 6 white balls. One ball is taken out without looking. What is the probability that it is blue? (a) 3/10 (b) 1/3 (c) 1/4 (d) 3/4
  11. 11.A bag has 9 yellow, 8 green and 6 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 9/14 (b) 14/23 (c) 1/3 (d) 9/23
  12. 12.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 75° (b) 105° (c) 130° (d) 125°
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 15 (b) 14 (c) 4 (d) 16
  14. 14.What is the mean of 20, 3, 6 and 7? (a) 8 (b) 10 (c) 12 (d) 9
  15. 15.A bag has 3 red, 2 white and 2 yellow balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 3/7 (c) 4/7 (d) 5/7
  16. 16.What is the smallest prime factor of 77? (a) 1 (b) 11 (c) 7 (d) 2
  17. 17.How many prime numbers are there between 30 and 50? (a) 6 (b) 4 (c) 5 (d) 7
  18. 18.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
  19. 19.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/3 (b) 5/6 (c) 1/5 (d) 1/6
  20. 20.There are 4 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 10 (b) 28 (c) 48 (d) 24
  21. 21.In a class of 35 children, 15 like maths, 25 like science and 6 like both. How many like only maths? (a) 15 (b) 9 (c) 19 (d) 10
  22. 22.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 130° (c) 50° (d) 65°
  23. 23.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 55 (b) 54 (c) 108 (d) 10
  24. 24.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  25. 25.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 28 (d) 49
  26. 26.There are 3 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) 8 (b) 18 (c) 30 (d) 15
  27. 27.What is the 18th term of the AP 15, 18, 21, 24, …? (a) 54 (b) 51 (c) 66 (d) 69
  28. 28.In which quadrant does the point (−7, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  29. 29.Using (a − b)² = a² − 2ab + b², what is 17²? (a) 299 (b) 289 (c) 529 (d) 391
  30. 30.Using (a + b)² = a² + 2ab + b², what is 105²? (a) 11025 (b) 9025 (c) 10025 (d) 11035
  31. 31.A drawer has lots of blue, red, 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) 5 (b) 2 (c) 8 (d) 4
  32. 32.What is the 33rd term of the AP 1, 9, 17, 25, …? (a) 256 (b) 265 (c) 264 (d) 257
  33. 33.A bag has 9 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) 10 (d) 19
  34. 34.In which quadrant does the point (−4, 7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  35. 35.What is the prime factorisation of 45? (a) 3³ × 5 (b) 3² × 5 (c) 3 × 5 (d) 3 × 5²
  36. 36.What is the prime factorisation of 112? (a) 2³ × 7 (b) 2⁵ × 7 (c) 2⁴ × 7 (d) 2 × 7⁴
  37. 37.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 2 (b) 4 (c) 3 (d) 5
  39. 39.What is the sum of the first 10 terms of the AP 2, 6, 10, …? (a) 200 (b) 38 (c) 400 (d) 220
  40. 40.If a + b = 16 and ab = 60, what is (a − b)²? (a) 16 (b) 4 (c) 136 (d) 256

Answer key

  1. 9
  2. 21
  3. 7569
  4. 3721
  5. 11
  6. 2⁴ × 3 × 5
  7. 160°
  8. 1386 sq cm
  9. 108
  10. 1/4
  11. 9/23
  12. 75°
  13. 15
  14. 9
  15. 4/7
  16. 7
  17. 5
  18. 2464 sq cm
  19. 5/6
  20. 24
  21. 9
  22. 65°
  23. 54
  24. 5
  25. 49
  26. 15
  27. 66
  28. Second quadrant
  29. 289
  30. 11025
  31. 5
  32. 257
  33. 11
  34. Second quadrant
  35. 3² × 5
  36. 2⁴ × 7
  37. 1386 sq cm
  38. 4
  39. 200
  40. 16

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