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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 921 · 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.What is the 28th term of the AP 9, 14, 19, 24, …? (a) 144 (b) 140 (c) 135 (d) 149
  2. 2.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
  3. 3.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 125 times (c) 5 times (d) 10 times
  4. 4.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 120 (c) 225 (d) 105
  5. 5.A drawer has lots of green, black, 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) 2 (b) 8 (c) 5 (d) 4
  6. 6.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 49 (b) 36 (c) 37 (d) 48
  7. 7.What is the mode of 18, 9, 9, 20, 18, 18 and 5? (a) 18 (b) 20 (c) 9 (d) 5
  8. 8.A canteen sells 6 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 84 (b) 42 (c) 48 (d) 13
  9. 9.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 85° (c) 125° (d) 95°
  10. 10.How many prime numbers are there between 30 and 40? (a) 2 (b) 4 (c) 1 (d) 3
  11. 11.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
  12. 12.A bag has 7 green balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 5 (c) 2 (d) 11
  13. 13.Using (a + b)² = a² + 2ab + b², what is 74²? (a) 5476 (b) 5486 (c) 4356 (d) 4916
  14. 14.The mean of 5 numbers is 12. When the number 18 is added to them, what is the new mean? (a) 13 (b) 14 (c) 12 (d) 15
  15. 15.What is the 14th term of the AP 7, 13, 19, 25, …? (a) 85 (b) 91 (c) 84 (d) 78
  16. 16.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 140° (c) 40° (d) 50°
  17. 17.What is the 37th term of the AP 3, 6, 9, 12, …? (a) 111 (b) 108 (c) 112 (d) 114
  18. 18.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 3 (c) 6 (d) 9
  19. 19.What is the prime factorisation of 60? (a) 2² × 3 × 5 (b) 2 × 3 × 5 (c) 2³ × 3 × 5 (d) 2 × 3 × 5²
  20. 20.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 24 (c) 37 (d) 25
  21. 21.A bag has 3 green, 7 white and 5 yellow balls. One ball is taken out without looking. What is the probability that it is not green? (a) 13/15 (b) 4/5 (c) 1/3 (d) 1/5
  22. 22.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 1/4 (c) 3/4 (d) 1/3
  23. 23.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  24. 24.What is the mean of 7, 18, 14, 4, 18 and 11? (a) 13 (b) 14 (c) 11 (d) 12
  25. 25.3 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) 18 (b) 12 (c) 9 (d) 6
  26. 26.In a class of 43 children, 27 like mangoes, 22 like bananas and 2 like neither. How many like both? (a) 41 (b) 6 (c) 2 (d) 8
  27. 27.What is the distance between the points (7, 31) and (14, 7)? (a) 625 (b) 31 (c) 26 (d) 25
  28. 28.What is the mode of 2, 1, 2, 1, 15, 1 and 20? (a) 2 (b) 1 (c) 20 (d) 15
  29. 29.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 40° (c) 50° (d) 80°
  30. 30.Two angles of a triangle are 55° and 85°. What is the third angle? (a) 140° (b) 125° (c) 95° (d) 40°
  31. 31.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 15° (c) 75° (d) 30°
  32. 32.What is the 10th term of the AP 15, 20, 25, 30, …? (a) 65 (b) 45 (c) 50 (d) 60
  33. 33.What is the missing term in the AP 16, 25, ?, 43, 52? (a) 34 (b) 35 (c) 43 (d) 33
  34. 34.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7² (b) 2 × 3 × 5 × 7 (c) 2³ × 3 × 5 × 7 (d) 2² × 3 × 5 × 7
  35. 35.In which quadrant does the point (6, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  36. 36.Two angles of a triangle are 45° and 35°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 145° (d) 135°
  37. 37.What is the mean of 5, 7, 19, 15, 9 and 5? (a) 11 (b) 12 (c) 10 (d) 9
  38. 38.What is the 14th term of the AP 8, 16, 24, 32, …? (a) 113 (b) 120 (c) 104 (d) 112
  39. 39.In which quadrant does the point (8, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  40. 40.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3

Answer key

  1. 144
  2. 220 cm
  3. 25 times
  4. 105
  5. 5
  6. 37
  7. 18
  8. 42
  9. 85°
  10. 2
  11. 1/3
  12. 8
  13. 5476
  14. 13
  15. 85
  16. 100°
  17. 111
  18. 6
  19. 2² × 3 × 5
  20. 25
  21. 4/5
  22. 3/4
  23. 4
  24. 12
  25. 9
  26. 8
  27. 25
  28. 1
  29. 80°
  30. 40°
  31. 30°
  32. 60
  33. 34
  34. 2 × 3 × 5 × 7
  35. First quadrant
  36. 80°
  37. 10
  38. 112
  39. Fourth quadrant
  40. 1/2

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