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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 592 · 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 30° and 105°. What is the exterior angle at the third corner? (a) 150° (b) 75° (c) 45° (d) 135°
  2. 2.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
  3. 3.Using (a − b)² = a² − 2ab + b², what is 27²? (a) 739 (b) 891 (c) 1089 (d) 729
  4. 4.How many factors does 55 have? (a) 4 (b) 2 (c) 3 (d) 5
  5. 5.What is the mean of 10, 13, 3, 16, 13 and 5? (a) 11 (b) 9 (c) 12 (d) 10
  6. 6.A cuboid is 10 cm long, 8 cm wide and 3 cm high. What is its total surface area? (a) 134 sq cm (b) 268 sq cm (c) 536 sq cm (d) 240 sq cm
  7. 7.Using (a + b)² = a² + 2ab + b², what is 71²? (a) 5051 (b) 4901 (c) 5041 (d) 4761
  8. 8.A drawer has lots of white, red, blue 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) 8 (c) 5 (d) 2
  9. 9.In a class of 31 children, 17 like tea, 9 like coffee and 3 like both. How many like neither? (a) 8 (b) 11 (c) 3 (d) 5
  10. 10.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 1/2 (c) 1/4 (d) 3/4
  11. 11.What is the midpoint of the line joining (1, 10) and (3, 20)? (a) (1, 5) (b) (15, 2) (c) (4, 30) (d) (2, 15)
  12. 12.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 36 (c) 45 (d) 81
  13. 13.What is the mean of 15, 3, 11, 8 and 18? (a) 10 (b) 13 (c) 11 (d) 12
  14. 14.What is the mean of 2, 18, 12 and 16? (a) 16 (b) 11 (c) 13 (d) 12
  15. 15.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 55 (c) 66 (d) 121
  16. 16.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 900 (c) 930 (d) 465
  17. 17.A bag has 5 blue, 4 red and 2 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 2/11 (c) 9/11 (d) 10/11
  18. 18.In a class of 45 children, 26 like dance, 27 like music and 9 like both. How many like only dance? (a) 18 (b) 26 (c) 17 (d) 9
  19. 19.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 125° (b) 55° (c) 130° (d) 105°
  20. 20.Using (a − b)² = a² − 2ab + b², what is 48²? (a) 2496 (b) 2314 (c) 2304 (d) 2704
  21. 21.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 160° (b) 130° (c) 70° (d) 110°
  22. 22.A bag has 4 yellow balls and 9 green 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) 10 (c) 5 (d) 13
  23. 23.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 64 (c) 56 (d) 16
  24. 24.What is the prime factorisation of 252? (a) 2² × 3² × 7 (b) 2 × 3² × 7 (c) 2³ × 3² × 7 (d) 2 × 3² × 7²
  25. 25.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 20° (b) 110° (c) 290° (d) 70°
  26. 26.A bag has 11 green balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 13 (b) 2 (c) 16 (d) 12
  27. 27.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 7 (c) 14 (d) 15
  28. 28.What is the smallest prime factor of 221? (a) 13 (b) 1 (c) 2 (d) 17
  29. 29.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 145° (b) 105° (c) 75° (d) 140°
  30. 30.If a + b = 9 and ab = 20, what is (a − b)²? (a) 41 (b) 1 (c) 61 (d) 81
  31. 31.Two angles of a triangle are 25° and 110°. What is the third angle? (a) 45° (b) 155° (c) 135° (d) 70°
  32. 32.What is the midpoint of the line joining (0, 4) and (8, 6)? (a) (8, 10) (b) (4, 5) (c) (4, 1) (d) (5, 4)
  33. 33.What is the missing term in the AP 2, 6, 10, ?, 18? (a) 15 (b) 18 (c) 13 (d) 14
  34. 34.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
  35. 35.How many prime numbers are there between 70 and 100? (a) 7 (b) 6 (c) 8 (d) 5
  36. 36.7 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 98 (b) 14 (c) 56 (d) 49
  37. 37.In a class of 41 children, 12 like tea, 23 like coffee and 4 like both. How many like at least one of the two? (a) 31 (b) 27 (c) 35 (d) 41
  38. 38.Two angles of a triangle are 70° and 80°. What is the third angle? (a) 30° (b) 110° (c) 100° (d) 150°
  39. 39.A drawer has lots of green, 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) 3 (b) 4 (c) 2 (d) 6
  40. 40.What is the distance between the points (8, 0) and (20, 5)? (a) 169 (b) 14 (c) 13 (d) 17

Answer key

  1. 135°
  2. 220 cm
  3. 729
  4. 4
  5. 10
  6. 268 sq cm
  7. 5041
  8. 5
  9. 8
  10. 3/4
  11. (2, 15)
  12. 36
  13. 11
  14. 12
  15. 55
  16. 900
  17. 9/11
  18. 17
  19. 55°
  20. 2304
  21. 70°
  22. 10
  23. 56
  24. 2² × 3² × 7
  25. 110°
  26. 13
  27. 8
  28. 13
  29. 105°
  30. 1
  31. 45°
  32. (4, 5)
  33. 14
  34. 88 cm
  35. 6
  36. 49
  37. 31
  38. 30°
  39. 4
  40. 13

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