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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 931 · 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 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) 5
  2. 2.A bag has 7 red balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 11 (b) 8 (c) 2 (d) 9
  3. 3.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 140 (b) 70 (c) 85 (d) 26
  4. 4.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  5. 5.How many factors does 66 have? (a) 8 (b) 7 (c) 9 (d) 6
  6. 6.In which quadrant does the point (−1, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  7. 7.How many prime numbers are there between 50 and 70? (a) 6 (b) 3 (c) 4 (d) 5
  8. 8.A drawer has lots of black, white, green 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) 5 (b) 4 (c) 2 (d) 8
  9. 9.A bag has 5 red, 2 yellow and 7 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 5/7 (b) 9/14 (c) 5/14 (d) 1/3
  10. 10.What is the mean of 17, 2, 9, 20, 18 and 12? (a) 14 (b) 15 (c) 12 (d) 13
  11. 11.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
  12. 12.A drawer has lots of blue, white, green 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) 2 (b) 5 (c) 4 (d) 8
  13. 13.What is the prime factorisation of 180? (a) 2 × 3² × 5² (b) 2 × 3² × 5 (c) 2² × 3² × 5 (d) 2³ × 3² × 5
  14. 14.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 2/3 (c) 1/4 (d) 1/3
  15. 15.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 25 (c) 11 (d) 20
  16. 16.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 45° (b) 70° (c) 155° (d) 135°
  17. 17.What is the prime factorisation of 35? (a) 5 × 7² (b) 5 × 7 (c) 5³ × 7 (d) 5² × 7
  18. 18.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 260° (b) 80° (c) 50° (d) 130°
  19. 19.In which quadrant does the point (−2, 2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  20. 20.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 16 (c) 24 (d) 12
  21. 21.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
  22. 22.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 125° (b) 25° (c) 155° (d) 80°
  23. 23.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 70 (b) 36 (c) 35 (d) 8
  24. 24.How many factors does 49 have? (a) 1 (b) 3 (c) 4 (d) 2
  25. 25.What is the mean of 2, 2, 19, 7 and 5? (a) 9 (b) 7 (c) 6 (d) 8
  26. 26.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 36 (c) 12 (d) 30
  27. 27.What is the prime factorisation of 140? (a) 2³ × 5 × 7 (b) 2 × 5 × 7² (c) 2 × 5 × 7 (d) 2² × 5 × 7
  28. 28.A bag has 7 yellow balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 8 (b) 13 (c) 2 (d) 9
  29. 29.What is the 13th term of the AP 4, 8, 12, 16, …? (a) 52 (b) 48 (c) 53 (d) 56
  30. 30.A bag has 3 black balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 4 (b) 2 (c) 7 (d) 5
  31. 31.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  32. 32.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 72 (c) 81 (d) 36
  33. 33.The mean of 3 numbers is 22. When the number 14 is added to them, what is the new mean? (a) 18 (b) 21 (c) 22 (d) 20
  34. 34.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 22 (b) 21 (c) 28 (d) 29
  35. 35.A cuboid is 4 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 10 cu cm (b) 36 cu cm (c) 66 cu cm (d) 12 cu cm
  36. 36.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2³ × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7³
  37. 37.A cuboid is 5 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 15 cu cm (b) 10 cu cm (c) 62 cu cm (d) 30 cu cm
  38. 38.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  39. 39.What is the product of the roots of x² − 17x + 72 = 0? (a) 17 (b) 73 (c) 72 (d) 71
  40. 40.There are 5 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 70 (b) 35 (c) 40 (d) 12

Answer key

  1. 3
  2. 9
  3. 70
  4. 15
  5. 8
  6. Third quadrant
  7. 4
  8. 5
  9. 9/14
  10. 13
  11. 154 sq cm
  12. 5
  13. 2² × 3² × 5
  14. 1/2
  15. 10
  16. 135°
  17. 5 × 7
  18. 130°
  19. Second quadrant
  20. 24
  21. 154 sq cm
  22. 25°
  23. 35
  24. 3
  25. 7
  26. 15
  27. 2² × 5 × 7
  28. 9
  29. 52
  30. 5
  31. 120
  32. 36
  33. 20
  34. 22
  35. 36 cu cm
  36. 2³ × 5 × 7
  37. 30 cu cm
  38. 17
  39. 72
  40. 35

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