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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 605 · 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 34 children, 10 like tea, 17 like coffee and 2 like both. How many like neither? (a) 2 (b) 9 (c) 11 (d) 7
  2. 2.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 48 (c) 12 (d) 24
  3. 3.What is the distance between the points (7, 7) and (15, 13)? (a) 10 (b) 14 (c) 11 (d) 100
  4. 4.What is the smallest prime factor of 51? (a) 3 (b) 2 (c) 17 (d) 1
  5. 5.What is the sum of the first 10 terms of the AP 4, 9, 14, …? (a) 49 (b) 530 (c) 265 (d) 290
  6. 6.If a + b = 19 and ab = 90, what is a² + b²? (a) 541 (b) 361 (c) 271 (d) 181
  7. 7.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
  8. 8.What is the smallest prime factor of 65? (a) 13 (b) 2 (c) 5 (d) 1
  9. 9.A bag has 7 blue, 8 green and 3 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 8/9 (b) 5/6 (c) 1/6 (d) 1/3
  10. 10.What is the distance between the points (4, 16) and (19, 8)? (a) 17 (b) 23 (c) 289 (d) 18
  11. 11.A bag has 8 blue balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 18 (c) 11 (d) 2
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 16° (b) 165° (c) 30° (d) 15°
  13. 13.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 3850 cm (d) 440 cm
  14. 14.Which is the correct factorisation of x² + 7x + 10? (a) (x + 1)(x + 10) (b) (x + 1)(x + 6) (c) (x − 2)(x − 5) (d) (x + 2)(x + 5)
  15. 15.What is the 15th term of the AP 2, 8, 14, 20, …? (a) 86 (b) 92 (c) 84 (d) 90
  16. 16.What is the mean of 2, 2, 4, 18 and 9? (a) 8 (b) 9 (c) 6 (d) 7
  17. 17.What is the smallest prime factor of 33? (a) 1 (b) 11 (c) 2 (d) 3
  18. 18.What is the mode of 19, 2, 3, 19, 2, 1 and 2? (a) 19 (b) 3 (c) 2 (d) 1
  19. 19.Using (a − b)² = a² − 2ab + b², what is 38²? (a) 1454 (b) 1596 (c) 1764 (d) 1444
  20. 20.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  21. 21.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 36 (c) 18 (d) 72
  22. 22.A bag has 10 blue balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 11 (c) 12 (d) 21
  23. 23.Using (a + b)² = a² + 2ab + b², what is 31²? (a) 901 (b) 971 (c) 841 (d) 961
  24. 24.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 6 (c) 3 (d) 9
  25. 25.In which quadrant does the point (−4, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  26. 26.What is the smallest prime factor of 247? (a) 1 (b) 2 (c) 19 (d) 13
  27. 27.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 36 (b) 9 (c) 18 (d) 24
  28. 28.The mean of 7 numbers is 37. When the number 5 is added to them, what is the new mean? (a) 33 (b) 21 (c) 37 (d) 34
  29. 29.If a + b = 13 and ab = 22, what is (a − b)²? (a) 81 (b) 169 (c) 125 (d) 9
  30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/11 (b) 1/11 (c) 1/6 (d) 5/36
  31. 31.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 992 (c) 497 (d) 496
  32. 32.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/6 (b) 1/3 (c) 1/5 (d) 5/6
  33. 33.A bag has 10 green balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 11 (c) 4 (d) 2
  34. 34.Which term of the AP 18, 27, 36, 45, … is 162? (a) 18th (b) 16th (c) 19th (d) 17th
  35. 35.Two angles of a triangle are 70° and 65°. What is the third angle? (a) 135° (b) 115° (c) 110° (d) 45°
  36. 36.How many prime numbers are there between 80 and 90? (a) 2 (b) 4 (c) 1 (d) 3
  37. 37.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 28 (c) 13 (d) 49
  38. 38.A bag has 3 green balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 4 (b) 11 (c) 5 (d) 2
  39. 39.How many factors does 42 have? (a) 9 (b) 7 (c) 8 (d) 6
  40. 40.A bag has 3 white, 8 green and 2 yellow balls. One ball is taken out without looking. What is the probability that it is white? (a) 10/13 (b) 1/3 (c) 3/10 (d) 3/13

Answer key

  1. 9
  2. 24
  3. 10
  4. 3
  5. 265
  6. 181
  7. 1/2
  8. 5
  9. 5/6
  10. 17
  11. 11
  12. 15°
  13. 220 cm
  14. (x + 2)(x + 5)
  15. 86
  16. 7
  17. 3
  18. 2
  19. 1444
  20. 24
  21. 72
  22. 12
  23. 961
  24. 6
  25. Third quadrant
  26. 13
  27. 18
  28. 33
  29. 81
  30. 5/36
  31. 496
  32. 5/6
  33. 11
  34. 17th
  35. 45°
  36. 2
  37. 49
  38. 5
  39. 8
  40. 3/13

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