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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 226 · 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.A drawer has lots of white 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) 3 (b) 4 (c) 5 (d) 2
  2. 2.What is the prime factorisation of 40? (a) 2⁴ × 5 (b) 2³ × 5 (c) 2² × 5 (d) 2 × 5³
  3. 3.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 81 (c) 18 (d) 36
  4. 4.What is the mean of 8, 3, 13 and 16? (a) 11 (b) 8 (c) 9 (d) 10
  5. 5.What is the product of the roots of x² − 12x + 27 = 0? (a) 28 (b) 27 (c) 26 (d) 12
  6. 6.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 105° (b) 135° (c) 120° (d) 60°
  7. 7.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 18 (d) 1
  8. 8.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 215° (b) 70° (c) 145° (d) 35°
  9. 9.A bag has 8 blue balls and 9 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) 17 (c) 2 (d) 10
  10. 10.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 120 (b) 102 (c) 204 (d) 32
  11. 11.A drawer has lots of yellow and red 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) 5 (c) 3 (d) 2
  12. 12.What is the 11th term of the AP 20, 23, 26, 29, …? (a) 50 (b) 33 (c) 30 (d) 53
  13. 13.What is the smallest prime factor of 253? (a) 2 (b) 11 (c) 1 (d) 23
  14. 14.What is the smallest prime factor of 35? (a) 7 (b) 1 (c) 2 (d) 5
  15. 15.What is the mode of 14, 14, 9, 14, 20, 20 and 11? (a) 20 (b) 14 (c) 11 (d) 9
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 20° (b) 11° (c) 170° (d) 10°
  17. 17.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 144 sq cm (c) 1728 sq cm (d) 576 sq cm
  18. 18.A drawer has lots of white, green, red, black 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) 5 (b) 6 (c) 10 (d) 2
  19. 19.What is the mean of 10, 4, 17, 6, 7 and 10? (a) 10 (b) 8 (c) 11 (d) 9
  20. 20.What is the median of 26, 4, 28, 25 and 14? (a) 25 (b) 28 (c) 26 (d) 14
  21. 21.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 55° (b) 125° (c) 35° (d) 305°
  22. 22.What is the distance between the points (1, 18) and (10, 6)? (a) 16 (b) 21 (c) 225 (d) 15
  23. 23.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 52 (c) 51 (d) 60
  24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/9 (b) 5/36 (c) 1/11 (d) 4/11
  25. 25.In which quadrant does the point (−5, −6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  26. 26.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 10 (c) 15 (d) 20
  27. 27.What is the missing term in the AP 15, 23, ?, 39, 47? (a) 32 (b) 39 (c) 31 (d) 30
  28. 28.Two angles of a triangle are 40° and 65°. What is the third angle? (a) 115° (b) 140° (c) 105° (d) 75°
  29. 29.Using (a + b)² = a² + 2ab + b², what is 54²? (a) 2516 (b) 2926 (c) 2916 (d) 2116
  30. 30.How many factors does 76 have? (a) 7 (b) 5 (c) 6 (d) 4
  31. 31.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 110° (b) 250° (c) 70° (d) 71°
  32. 32.What is the 19th term of the AP 1, 3, 5, 7, …? (a) 38 (b) 39 (c) 36 (d) 37
  33. 33.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
  34. 34.What is the prime factorisation of 90? (a) 2 × 3² × 5² (b) 2³ × 3² × 5 (c) 2² × 3² × 5 (d) 2 × 3² × 5
  35. 35.5 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 40 (b) 25 (c) 20 (d) 9
  36. 36.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 1/18 (c) 1/12 (d) 2/11
  37. 37.What is the sum of the first 9 terms of the AP 7, 12, 17, …? (a) 486 (b) 248 (c) 243 (d) 47
  38. 38.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
  39. 39.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 1/3 (c) 3/4 (d) 1/4
  40. 40.What is the distance between the points (1, 5) and (8, 29)? (a) 25 (b) 31 (c) 26 (d) 625

Answer key

  1. 3
  2. 2³ × 5
  3. 36
  4. 10
  5. 27
  6. 60°
  7. 2
  8. 35°
  9. 10
  10. 102
  11. 3
  12. 50
  13. 11
  14. 5
  15. 14
  16. 10°
  17. 864 sq cm
  18. 6
  19. 9
  20. 25
  21. 125°
  22. 15
  23. 51
  24. 1/9
  25. Third quadrant
  26. 10
  27. 31
  28. 75°
  29. 2916
  30. 6
  31. 70°
  32. 37
  33. 154 sq cm
  34. 2 × 3² × 5
  35. 20
  36. 1/18
  37. 243
  38. 2464 sq cm
  39. 1/4
  40. 25

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