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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 404 · 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.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 75° (b) 285° (c) 105° (d) 15°
  2. 2.How many factors does 17 have? (a) 3 (b) 1 (c) 4 (d) 2
  3. 3.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 125° (b) 120° (c) 115° (d) 60°
  4. 4.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/11 (b) 6/11 (c) 7/36 (d) 1/6
  5. 5.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) 37 (b) 36 (c) 48 (d) 49
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 90° (b) 46° (c) 45° (d) 135°
  7. 7.In which quadrant does the point (−3, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  8. 8.What is the sum of the first 9 terms of the AP 1, 4, 7, …? (a) 117 (b) 25 (c) 234 (d) 120
  9. 9.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 22 (b) 21 (c) 15 (d) 14
  10. 10.In a class of 25 children, 19 like maths, 16 like science and 12 like both. How many like only maths? (a) 7 (b) 19 (c) 9 (d) 4
  11. 11.A bag has 3 green, 6 red and 2 yellow balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 2/9 (b) 2/11 (c) 9/11 (d) 1/3
  12. 12.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 125° (b) 235° (c) 55° (d) 56°
  13. 13.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 64 times (c) 4 times (d) 16 times
  14. 14.How many prime numbers are there between 10 and 40? (a) 9 (b) 10 (c) 7 (d) 8
  15. 15.Using (a + b)² = a² + 2ab + b², what is 25²? (a) 635 (b) 225 (c) 425 (d) 625
  16. 16.In a class of 41 children, 18 like dance, 21 like music and 7 like both. How many like neither? (a) 7 (b) 9 (c) 2 (d) 16
  17. 17.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 70° (c) 35° (d) 110°
  18. 18.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 120° (b) 140° (c) 100° (d) 80°
  19. 19.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
  20. 20.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 115° (b) 30° (c) 95° (d) 150°
  21. 21.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 6 times (c) 9 times (d) 3 times
  22. 22.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 45° (b) 135° (c) 105° (d) 120°
  23. 23.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 130° (b) 155° (c) 105° (d) 75°
  24. 24.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 15 cu cm (c) 100 cu cm (d) 150 cu cm
  25. 25.What is the distance between the points (0, 3) and (3, 7)? (a) 7 (b) 5 (c) 25 (d) 6
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 85? (a) 15 (b) 12 (c) 8 (d) 14
  27. 27.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 11 (c) 20 (d) 10
  28. 28.What is the midpoint of the line joining (2, 22) and (14, 10)? (a) (16, 32) (b) (6, 6) (c) (8, 16) (d) (16, 8)
  29. 29.A drawer has lots of white and blue 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) 3 (d) 4
  30. 30.In which quadrant does the point (−1, −5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  31. 31.What is the distance between the points (6, 8) and (10, 5)? (a) 25 (b) 5 (c) 7 (d) 6
  32. 32.How many prime numbers are there between 30 and 60? (a) 6 (b) 7 (c) 8 (d) 9
  33. 33.What is the distance between the points (9, 1) and (25, 13)? (a) 28 (b) 20 (c) 21 (d) 400
  34. 34.What is the midpoint of the line joining (5, 9) and (13, 21)? (a) (15, 9) (b) (4, 6) (c) (18, 30) (d) (9, 15)
  35. 35.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 132 cm (d) 264 cm
  36. 36.What is the mean of 12, 8, 9, 2 and 9? (a) 10 (b) 8 (c) 9 (d) 7
  37. 37.What is the median of 34, 35, 36, 27, 29, 13 and 21? (a) 34 (b) 29 (c) 30 (d) 27
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 97? (a) 21 (b) 20 (c) 9 (d) 19
  39. 39.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
  40. 40.In a class of 43 children, 16 like maths, 28 like science and 9 like both. How many like at least one of the two? (a) 35 (b) 44 (c) 26 (d) 43

Answer key

  1. 105°
  2. 2
  3. 60°
  4. 1/6
  5. 37
  6. 45°
  7. Second quadrant
  8. 117
  9. 15
  10. 7
  11. 2/11
  12. 55°
  13. 16 times
  14. 8
  15. 625
  16. 9
  17. 35°
  18. 80°
  19. 88 cm
  20. 30°
  21. 9 times
  22. 45°
  23. 75°
  24. 125 cu cm
  25. 5
  26. 14
  27. 10
  28. (8, 16)
  29. 3
  30. Third quadrant
  31. 5
  32. 7
  33. 20
  34. (9, 15)
  35. 132 cm
  36. 8
  37. 29
  38. 20
  39. 25
  40. 35

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