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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 194 · 40 questions
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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 65° and 60°. What is the third angle? (a) 125° (b) 55° (c) 115° (d) 120°
  2. 2.In a class of 36 children, 19 like tea, 15 like coffee and 8 like both. How many like only tea? (a) 11 (b) 7 (c) 21 (d) 19
  3. 3.What is the prime factorisation of 210? (a) 2³ × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2² × 3 × 5 × 7 (d) 2 × 3 × 5 × 7
  4. 4.In which quadrant does the point (−8, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  5. 5.What is the distance between the points (5, 17) and (17, 1)? (a) 400 (b) 21 (c) 28 (d) 20
  6. 6.Two angles of a triangle are 50° and 80°. What is the exterior angle at the third corner? (a) 230° (b) 100° (c) 130° (d) 50°
  7. 7.What is the smallest prime factor of 143? (a) 2 (b) 1 (c) 13 (d) 11
  8. 8.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
  9. 9.Which term of the AP 16, 21, 26, 31, … is 96? (a) 19th (b) 16th (c) 18th (d) 17th
  10. 10.What is the mode of 17, 4, 2, 1, 17, 2 and 17? (a) 1 (b) 2 (c) 4 (d) 17
  11. 11.How many factors does 23 have? (a) 1 (b) 2 (c) 4 (d) 3
  12. 12.What is the distance between the points (3, 12) and (7, 9)? (a) 5 (b) 25 (c) 7 (d) 6
  13. 13.What is the smallest prime factor of 115? (a) 2 (b) 23 (c) 1 (d) 5
  14. 14.What is the smallest prime factor of 253? (a) 2 (b) 23 (c) 1 (d) 11
  15. 15.Which is the correct factorisation of x² + 14x + 48? (a) (x + 1)(x + 13) (b) (x + 6)(x + 8) (c) (x + 1)(x + 48) (d) (x − 6)(x − 8)
  16. 16.A bag has 5 yellow balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 6 (b) 2 (c) 16 (d) 7
  17. 17.How many prime numbers are there between 50 and 80? (a) 8 (b) 6 (c) 9 (d) 7
  18. 18.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 20 (c) 25 (d) 240
  19. 19.What is the median of 21, 22, 34, 4, 6, 17 and 29? (a) 19 (b) 4 (c) 22 (d) 21
  20. 20.A cuboid is 10 cm long, 4 cm wide and 2 cm high. What is its volume? (a) 80 cu cm (b) 136 cu cm (c) 16 cu cm (d) 40 cu cm
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 9 (b) 21 (c) 19 (d) 20
  22. 22.In a class of 45 children, 22 like tea, 18 like coffee and 5 like both. How many like at least one of the two? (a) 45 (b) 40 (c) 30 (d) 35
  23. 23.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
  24. 24.Which is the correct factorisation of x² + 8x + 12? (a) (x + 1)(x + 7) (b) (x − 2)(x − 6) (c) (x + 2)(x + 6) (d) (x + 1)(x + 12)
  25. 25.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/11 (b) 5/11 (c) 1/6 (d) 5/36
  26. 26.If a + b = 19 and ab = 90, what is (a − b)²? (a) 271 (b) 1 (c) 361 (d) 181
  27. 27.In which quadrant does the point (3, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  28. 28.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 8 cu cm (c) 24 cu cm (d) 6 cu cm
  29. 29.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 154 (c) 153 (d) 136
  30. 30.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
  31. 31.What is the missing term in the AP 18, 20, 22, ?, 26? (a) 26 (b) 24 (c) 23 (d) 25
  32. 32.In which quadrant does the point (2, 9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  33. 33.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 36 (c) 30 (d) 15
  34. 34.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 28 (c) 56 (d) 36
  35. 35.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 50° (b) 230° (c) 100° (d) 130°
  36. 36.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
  37. 37.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 40° (b) 310° (c) 130° (d) 50°
  38. 38.A drawer has lots of yellow, 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) 6 (b) 3 (c) 4 (d) 2
  39. 39.Which is the correct factorisation of x² + 17x + 72? (a) (x + 8)(x + 9) (b) (x + 1)(x + 72) (c) (x − 8)(x − 9) (d) (x + 1)(x + 16)
  40. 40.How many factors does 66 have? (a) 6 (b) 7 (c) 9 (d) 8

Answer key

  1. 55°
  2. 11
  3. 2 × 3 × 5 × 7
  4. Second quadrant
  5. 20
  6. 130°
  7. 11
  8. 88 cm
  9. 17th
  10. 17
  11. 2
  12. 5
  13. 5
  14. 11
  15. (x + 6)(x + 8)
  16. 7
  17. 7
  18. 120
  19. 21
  20. 80 cu cm
  21. 20
  22. 35
  23. 616 sq cm
  24. (x + 2)(x + 6)
  25. 5/36
  26. 1
  27. First quadrant
  28. 8 cu cm
  29. 153
  30. 25 times
  31. 24
  32. First quadrant
  33. 15
  34. 28
  35. 50°
  36. 2464 sq cm
  37. 130°
  38. 4
  39. (x + 8)(x + 9)
  40. 8

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