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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 965 · 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 midpoint of the line joining (0, 17) and (6, 5)? (a) (3, 11) (b) (3, 6) (c) (6, 22) (d) (11, 3)
  2. 2.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 24 (c) 12 (d) 48
  3. 3.How many prime numbers are there between 70 and 90? (a) 6 (b) 5 (c) 4 (d) 7
  4. 4.In which quadrant does the point (−5, 1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  5. 5.What is the prime factorisation of 72? (a) 2² × 3² (b) 2⁴ × 3² (c) 2² × 3³ (d) 2³ × 3²
  6. 6.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 135° (c) 160° (d) 45°
  7. 7.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 48 (c) 15 (d) 45
  8. 8.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/4 (c) 1/2 (d) 1/3
  9. 9.How many prime numbers are there between 30 and 40? (a) 4 (b) 3 (c) 2 (d) 1
  10. 10.In a class of 38 children, 18 like dance, 21 like music and 6 like both. How many like at least one of the two? (a) 27 (b) 38 (c) 39 (d) 33
  11. 11.What is the midpoint of the line joining (3, 7) and (13, 1)? (a) (8, 4) (b) (16, 8) (c) (4, 8) (d) (5, 3)
  12. 12.What is the mode of 11, 10, 11, 17, 10, 10 and 12? (a) 11 (b) 17 (c) 10 (d) 12
  13. 13.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 150° (c) 75° (d) 30°
  14. 14.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
  15. 15.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
  16. 16.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  17. 17.A bag has 9 blue, 7 red and 3 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 3/16 (b) 3/19 (c) 16/19 (d) 1/3
  18. 18.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 19 (b) 171 (c) 60 (d) 57
  19. 19.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 14 (b) 15 (c) 7 (d) 8
  20. 20.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 14 (d) 169
  21. 21.What is the smallest prime factor of 143? (a) 1 (b) 11 (c) 13 (d) 2
  22. 22.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 72) (b) (x + 8)(x + 9) (c) (x + 1)(x + 16) (d) (x − 8)(x − 9)
  23. 23.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 3 (d) 2
  24. 24.A drawer has lots of blue 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) 5 (b) 2 (c) 3 (d) 4
  25. 25.What is the distance between the points (3, 11) and (18, 3)? (a) 23 (b) 18 (c) 289 (d) 17
  26. 26.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 9 sq cm (c) 54 sq cm (d) 36 sq cm
  27. 27.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/36 (b) 5/11 (c) 1/6 (d) 1/11
  28. 28.What is the distance between the points (0, 16) and (24, 9)? (a) 26 (b) 31 (c) 25 (d) 625
  29. 29.What is the 14th term of the AP 17, 22, 27, 32, …? (a) 70 (b) 87 (c) 65 (d) 82
  30. 30.What is the midpoint of the line joining (6, 7) and (16, 9)? (a) (11, 8) (b) (22, 16) (c) (5, 1) (d) (8, 11)
  31. 31.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
  32. 32.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 25 (c) 10 (d) 15
  33. 33.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
  34. 34.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/12 (b) 1/11 (c) 1/18 (d) 2/11
  35. 35.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 132 (c) 66 (d) 144
  36. 36.What is the distance between the points (5, 9) and (12, 33)? (a) 625 (b) 25 (c) 26 (d) 31
  37. 37.What is the sum of all the whole numbers from 1 to 95? (a) 4465 (b) 4561 (c) 9120 (d) 4560
  38. 38.Two angles of a triangle are 80° and 70°. What is the third angle? (a) 30° (b) 100° (c) 150° (d) 110°
  39. 39.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 72 (c) 36 (d) 45
  40. 40.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 45 (c) 46 (d) 54

Answer key

  1. (3, 11)
  2. 24
  3. 5
  4. Second quadrant
  5. 2³ × 3²
  6. 45°
  7. 45
  8. 3/4
  9. 2
  10. 33
  11. (8, 4)
  12. 10
  13. 75°
  14. 1386 sq cm
  15. 154 sq cm
  16. 10
  17. 3/19
  18. 57
  19. 8
  20. 13
  21. 11
  22. (x + 8)(x + 9)
  23. 2
  24. 3
  25. 17
  26. 54 sq cm
  27. 5/36
  28. 25
  29. 82
  30. (11, 8)
  31. 25 times
  32. 10
  33. 20
  34. 1/18
  35. 66
  36. 25
  37. 4560
  38. 30°
  39. 36
  40. 45

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