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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 596 · 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 sum of the first 12 terms of the AP 3, 8, 13, …? (a) 732 (b) 396 (c) 366 (d) 58
  2. 2.What is the mode of 7, 7, 19, 16, 7, 3 and 3? (a) 16 (b) 3 (c) 19 (d) 7
  3. 3.What is the sum of all the whole numbers from 1 to 38? (a) 722 (b) 741 (c) 1482 (d) 703
  4. 4.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 40 (c) 9 (d) 20
  5. 5.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 50° (c) 140° (d) 40°
  6. 6.If a + b = 20 and ab = 99, what is a² + b²? (a) 202 (b) 598 (c) 400 (d) 301
  7. 7.In a class of 33 children, 24 like tea, 20 like coffee and 12 like both. How many like at least one of the two? (a) 44 (b) 20 (c) 33 (d) 32
  8. 8.Which term of the AP 4, 13, 22, 31, … is 139? (a) 17th (b) 16th (c) 15th (d) 18th
  9. 9.How many factors does 65 have? (a) 2 (b) 3 (c) 4 (d) 5
  10. 10.What is the mode of 19, 4, 1, 1, 1, 19 and 6? (a) 6 (b) 4 (c) 1 (d) 19
  11. 11.3 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) 15 (b) 30 (c) 8 (d) 18
  12. 12.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 16 (c) 24 (d) 12
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 2 (b) 5 (c) 3 (d) 4
  14. 14.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 36 (c) 54 (d) 45
  15. 15.If a + b = 6 and ab = 5, what is (a − b)²? (a) 4 (b) 26 (c) 36 (d) 16
  16. 16.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/8 (c) 7/8 (d) 3/8
  17. 17.In which quadrant does the point (3, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 4 (b) 14 (c) 16 (d) 15
  19. 19.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/11 (b) 1/9 (c) 1/12 (d) 3/11
  20. 20.What is the distance between the points (4, 25) and (11, 1)? (a) 31 (b) 26 (c) 25 (d) 625
  21. 21.In which quadrant does the point (3, −4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  22. 22.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
  23. 23.In a class of 38 children, 19 like tea, 24 like coffee and 10 like both. How many like neither? (a) 10 (b) 15 (c) 5 (d) 6
  24. 24.What is the mean of 6, 5, 5, 15 and 19? (a) 11 (b) 9 (c) 12 (d) 10
  25. 25.Using (a − b)² = a² − 2ab + b², what is 79²? (a) 6251 (b) 6399 (c) 6241 (d) 6561
  26. 26.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 85° (b) 130° (c) 95° (d) 145°
  27. 27.Using (a − b)² = a² − 2ab + b², what is 99²? (a) 9999 (b) 9801 (c) 10201 (d) 9811
  28. 28.What is the mean of 6, 4, 15, 14, 13 and 20? (a) 12 (b) 13 (c) 14 (d) 11
  29. 29.What is the midpoint of the line joining (1, 1) and (7, 11)? (a) (8, 12) (b) (4, 6) (c) (3, 5) (d) (6, 4)
  30. 30.Two angles of a triangle are 60° and 75°. What is the third angle? (a) 105° (b) 45° (c) 135° (d) 120°
  31. 31.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
  32. 32.In which quadrant does the point (−7, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  33. 33.In which quadrant does the point (−3, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  34. 34.A drawer has lots of yellow and green 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) 3 (d) 5
  35. 35.In a class of 37 children, 15 like dance, 25 like music and 4 like neither. How many like both? (a) 3 (b) 7 (c) 33 (d) 4
  36. 36.What is the 19th term of the AP 4, 12, 20, 28, …? (a) 148 (b) 152 (c) 144 (d) 156
  37. 37.What is the mode of 9, 1, 9, 12, 12, 16 and 12? (a) 16 (b) 12 (c) 1 (d) 9
  38. 38.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  39. 39.A drawer has lots of red, blue, green 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) 8 (b) 5 (c) 4 (d) 2
  40. 40.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm

Answer key

  1. 366
  2. 7
  3. 741
  4. 20
  5. 100°
  6. 202
  7. 32
  8. 16th
  9. 4
  10. 1
  11. 15
  12. 24
  13. 4
  14. 45
  15. 16
  16. 7/8
  17. First quadrant
  18. 15
  19. 1/12
  20. 25
  21. Fourth quadrant
  22. 154 sq cm
  23. 5
  24. 10
  25. 6241
  26. 95°
  27. 9801
  28. 12
  29. (4, 6)
  30. 45°
  31. 616 sq cm
  32. Third quadrant
  33. Second quadrant
  34. 3
  35. 7
  36. 148
  37. 12
  38. 17
  39. 5
  40. 132 cm

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