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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 203 · 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.Which term of the AP 15, 21, 27, 33, … is 129? (a) 21st (b) 22nd (c) 20th (d) 19th
  2. 2.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 96 (b) 84 (c) 168 (d) 24
  3. 3.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 10° (c) 80° (d) 20°
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 38? (a) 3 (b) 5 (c) 4 (d) 2
  5. 5.In a class of 33 children, 8 like tea, 20 like coffee and 10 like neither. How many like both? (a) 23 (b) 5 (c) 10 (d) 6
  6. 6.What is the median of 35, 31, 13, 8 and 33? (a) 33 (b) 24 (c) 13 (d) 31
  7. 7.What is the smallest prime factor of 203? (a) 29 (b) 2 (c) 1 (d) 7
  8. 8.How many prime numbers are there between 60 and 70? (a) 3 (b) 4 (c) 2 (d) 1
  9. 9.A drawer has lots of white 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) 2 (c) 5 (d) 3
  10. 10.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 5° (c) 10° (d) 85°
  11. 11.A bag has 3 blue, 7 yellow and 5 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/2 (b) 2/5 (c) 2/3 (d) 1/3
  12. 12.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  13. 13.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/11 (b) 3/11 (c) 1/12 (d) 1/9
  14. 14.Two angles of a triangle are 40° and 50°. What is the third angle? (a) 130° (b) 270° (c) 140° (d) 90°
  15. 15.What is the 15th term of the AP 11, 15, 19, 23, …? (a) 67 (b) 60 (c) 71 (d) 56
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 43? (a) 5 (b) 3 (c) 4 (d) 2
  17. 17.What is the sum of the first 6 terms of the AP 7, 12, 17, …? (a) 117 (b) 32 (c) 234 (d) 132
  18. 18.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 140° (b) 80° (c) 280° (d) 100°
  19. 19.In a class of 39 children, 22 like tea, 14 like coffee and 5 like both. How many like at least one of the two? (a) 39 (b) 31 (c) 26 (d) 36
  20. 20.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 6 (d) 7
  21. 21.Two angles of a triangle are 25° and 20°. What is the third angle? (a) 160° (b) 135° (c) 155° (d) 45°
  22. 22.A drawer has lots of black, red and white 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) 6 (c) 4 (d) 2
  23. 23.In which quadrant does the point (−2, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  24. 24.How many prime numbers are there between 50 and 70? (a) 5 (b) 3 (c) 4 (d) 6
  25. 25.How many prime numbers are there between 40 and 70? (a) 8 (b) 7 (c) 9 (d) 6
  26. 26.What is the mode of 17, 17, 5, 2, 2, 15 and 17? (a) 17 (b) 5 (c) 2 (d) 15
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 85° (b) 10° (c) 95° (d) 190°
  28. 28.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 70° (b) 145° (c) 35° (d) 215°
  29. 29.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/4 (c) 1/3 (d) 1/2
  30. 30.How many prime numbers are there between 80 and 90? (a) 1 (b) 2 (c) 3 (d) 4
  31. 31.What is the missing term in the AP 1, 4, 7, ?, 13? (a) 13 (b) 9 (c) 10 (d) 11
  32. 32.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 25 (b) 24 (c) 13 (d) 12
  33. 33.3 T-shirts and 5 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) 15 (c) 8 (d) 30
  34. 34.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 18 (b) 19 (c) 8 (d) 20
  36. 36.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 75 (b) 66 (c) 76 (d) 84
  37. 37.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
  38. 38.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
  39. 39.In a class of 35 children, 13 like maths, 23 like science and 9 like both. How many like at least one of the two? (a) 35 (b) 27 (c) 36 (d) 18
  40. 40.A bag has 4 blue balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 9 (c) 2 (d) 6

Answer key

  1. 20th
  2. 84
  3. 20°
  4. 4
  5. 5
  6. 31
  7. 7
  8. 2
  9. 3
  10. 10°
  11. 1/3
  12. 120
  13. 1/12
  14. 90°
  15. 67
  16. 4
  17. 117
  18. 100°
  19. 31
  20. 7
  21. 135°
  22. 4
  23. Second quadrant
  24. 4
  25. 7
  26. 17
  27. 95°
  28. 145°
  29. 3/4
  30. 2
  31. 10
  32. 13
  33. 15
  34. 176 cm
  35. 19
  36. 75
  37. 1/2
  38. 1/2
  39. 27
  40. 6

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