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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 372 · 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.Two angles of a triangle are 40° and 90°. What is the third angle? (a) 130° (b) 140° (c) 50° (d) 90°
  2. 2.What is the mode of 1, 10, 10, 15, 1, 18 and 1? (a) 1 (b) 10 (c) 18 (d) 15
  3. 3.If a + b = 9 and ab = 18, what is (a − b)²? (a) 3 (b) 45 (c) 81 (d) 9
  4. 4.A bag has 3 red balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 2 (c) 9 (d) 4
  5. 5.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 14 (c) 42 (d) 21
  6. 6.What is the mean of 19, 19, 15, 16, 2 and 13? (a) 12 (b) 14 (c) 15 (d) 13
  7. 7.In a class of 27 children, 14 like cricket, 14 like football and 6 like both. How many like only cricket? (a) 14 (b) 8 (c) 13 (d) 6
  8. 8.What is the 35th term of the AP 10, 15, 20, 25, …? (a) 180 (b) 170 (c) 175 (d) 185
  9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/12 (c) 1/11 (d) 1/18
  10. 10.What is the product of the roots of x² − 8x + 15 = 0? (a) 8 (b) 16 (c) 15 (d) 14
  11. 11.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 60° (c) 70° (d) 120°
  12. 12.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  13. 13.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) 22 (b) 15 (c) 21 (d) 14
  14. 14.How many factors does 76 have? (a) 5 (b) 4 (c) 6 (d) 7
  15. 15.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  16. 16.What is the mean of 4, 10, 9, 10, 3 and 6? (a) 6 (b) 8 (c) 7 (d) 9
  17. 17.What is the sum of all the whole numbers from 1 to 36? (a) 666 (b) 648 (c) 1332 (d) 630
  18. 18.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 374 (b) 444 (c) 454 (d) 453
  19. 19.What is the mean of 12, 19, 18, 14 and 7? (a) 16 (b) 13 (c) 14 (d) 15
  20. 20.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
  21. 21.How many factors does 84 have? (a) 10 (b) 12 (c) 11 (d) 13
  22. 22.A bag has 3 red, 5 green and 5 blue balls. One ball is taken out without looking. What is the probability that it is not green? (a) 9/13 (b) 5/13 (c) 1/3 (d) 8/13
  23. 23.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 1/4 (c) 1/2 (d) 3/4
  24. 24.Which is the correct factorisation of x² + 12x + 32? (a) (x − 4)(x − 8) (b) (x + 1)(x + 11) (c) (x + 4)(x + 8) (d) (x + 1)(x + 32)
  25. 25.A bag has 5 blue balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 13 (b) 7 (c) 6 (d) 2
  26. 26.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 5 times (d) 8 times
  27. 27.What is the median of 24, 39, 29, 10, 1, 26 and 36? (a) 29 (b) 24 (c) 10 (d) 26
  28. 28.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 55° (c) 125° (d) 70°
  29. 29.What are the roots of x² − 13x + 42 = 0? (a) 1 and 12 (b) 2 and 21 (c) 1 and 42 (d) 6 and 7
  30. 30.7 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 21 (b) 42 (c) 10 (d) 28
  31. 31.What is the midpoint of the line joining (3, 9) and (13, 13)? (a) (11, 8) (b) (5, 2) (c) (16, 22) (d) (8, 11)
  32. 32.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  33. 33.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
  34. 34.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 512 (c) 496 (d) 528
  35. 35.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 10 (d) 7
  36. 36.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  37. 37.A drawer has lots of black and green 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) 2 (c) 3 (d) 5
  38. 38.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 12 (c) 30 (d) 15
  39. 39.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
  40. 40.What is the missing term in the AP 14, ?, 22, 26, 30? (a) 18 (b) 17 (c) 22 (d) 19

Answer key

  1. 50°
  2. 1
  3. 9
  4. 7
  5. 42
  6. 14
  7. 8
  8. 180
  9. 1/18
  10. 15
  11. 60°
  12. 6
  13. 15
  14. 6
  15. 5
  16. 7
  17. 666
  18. 453
  19. 14
  20. 9 times
  21. 12
  22. 8/13
  23. 3/4
  24. (x + 4)(x + 8)
  25. 7
  26. 4 times
  27. 26
  28. 70°
  29. 6 and 7
  30. 21
  31. (8, 11)
  32. 7
  33. 1386 sq cm
  34. 528
  35. 8
  36. 5
  37. 3
  38. 30
  39. 17
  40. 18

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