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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 173 · 40 questions
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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 sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 190 (c) 37 (d) 380
  2. 2.A drawer has lots of blue, red and yellow 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
  3. 3.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  4. 4.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
  5. 5.Two angles of a triangle are 35° and 85°. What is the third angle? (a) 120° (b) 145° (c) 95° (d) 60°
  6. 6.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 90 (c) 100 (d) 45
  7. 7.Which term of the AP 4, 8, 12, 16, … is 80? (a) 20th (b) 21st (c) 19th (d) 22nd
  8. 8.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
  9. 9.What is the product of the roots of x² − 8x + 12 = 0? (a) 13 (b) 8 (c) 11 (d) 12
  10. 10.8 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 16 (b) 10 (c) 24 (d) 32
  11. 11.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
  12. 12.The mean of 5 numbers is 27. When the number 9 is added to them, what is the new mean? (a) 24 (b) 18 (c) 25 (d) 27
  13. 13.Using (a − b)² = a² − 2ab + b², what is 89²? (a) 7931 (b) 8099 (c) 8281 (d) 7921
  14. 14.What is the prime factorisation of 140? (a) 2 × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7² (d) 2² × 5 × 7
  15. 15.What is the 35th term of the AP 8, 17, 26, 35, …? (a) 314 (b) 323 (c) 315 (d) 306
  16. 16.What is the distance between the points (7, 25) and (14, 1)? (a) 26 (b) 25 (c) 31 (d) 625
  17. 17.What is the smallest prime factor of 121? (a) 1 (b) 11 (c) 2 (d) 3
  18. 18.How many prime numbers are there between 30 and 50? (a) 6 (b) 7 (c) 5 (d) 4
  19. 19.There are 4 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 6 (b) 16 (c) 12 (d) 8
  20. 20.Using (a − b)² = a² − 2ab + b², what is 15²? (a) 625 (b) 375 (c) 225 (d) 235
  21. 21.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 5/8 (c) 3/8 (d) 1/4
  22. 22.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 23 (c) 207 (d) 69
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 40° (b) 80° (c) 41° (d) 140°
  24. 24.What is the midpoint of the line joining (3, 22) and (9, 10)? (a) (6, 16) (b) (12, 32) (c) (16, 6) (d) (3, 6)
  25. 25.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/36 (b) 1/12 (c) 1/18 (d) 1/11
  26. 26.What is the product of the roots of x² − 7x + 12 = 0? (a) 11 (b) 12 (c) 7 (d) 13
  27. 27.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 90 (c) 20 (d) 100
  28. 28.A drawer has lots of white, yellow 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) 2 (b) 6 (c) 4 (d) 3
  29. 29.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 20° (c) 10° (d) 100°
  30. 30.A bag has 8 red balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 10 (b) 9 (c) 2 (d) 19
  31. 31.A bag has 2 red, 2 green and 7 blue balls. One ball is taken out without looking. What is the probability that it is green? (a) 9/11 (b) 2/11 (c) 2/9 (d) 1/3
  32. 32.What is the distance between the points (9, 8) and (17, 14)? (a) 100 (b) 11 (c) 14 (d) 10
  33. 33.What is the distance between the points (1, 13) and (9, 7)? (a) 14 (b) 10 (c) 100 (d) 11
  34. 34.6 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) 12 (b) 36 (c) 42 (d) 72
  35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 5/36 (b) 4/11 (c) 1/9 (d) 1/11
  36. 36.A bag has 4 blue, 2 red and 8 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 4/7 (c) 3/7 (d) 3/4
  37. 37.What is the sum of all the whole numbers from 1 to 88? (a) 7832 (b) 3872 (c) 3828 (d) 3916
  38. 38.In a class of 31 children, 19 like mangoes, 6 like bananas and 2 like both. How many like at least one of the two? (a) 23 (b) 25 (c) 31 (d) 21
  39. 39.A bag has 6 blue balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 7 (c) 10 (d) 2
  40. 40.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 23 (b) 150 (c) 85 (d) 75

Answer key

  1. 361
  2. 4
  3. 120
  4. 88 cm
  5. 60°
  6. 45
  7. 20th
  8. 1/3
  9. 12
  10. 16
  11. 1/2
  12. 24
  13. 7921
  14. 2² × 5 × 7
  15. 314
  16. 25
  17. 11
  18. 5
  19. 8
  20. 225
  21. 3/8
  22. 69
  23. 40°
  24. (6, 16)
  25. 1/36
  26. 12
  27. 45
  28. 4
  29. 20°
  30. 10
  31. 2/11
  32. 10
  33. 10
  34. 36
  35. 1/9
  36. 3/7
  37. 3916
  38. 23
  39. 7
  40. 75

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