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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 761 · 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, 7) and (10, 9)? (a) (5, 1) (b) (8, 5) (c) (10, 16) (d) (5, 8)
  2. 2.Two angles of a triangle are 35° and 65°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 115° (d) 145°
  3. 3.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
  4. 4.Two angles of a triangle are 80° and 65°. What is the third angle? (a) 35° (b) 145° (c) 115° (d) 100°
  5. 5.In a class of 45 children, 32 like dance, 20 like music and 12 like both. How many like only dance? (a) 8 (b) 32 (c) 25 (d) 20
  6. 6.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  7. 7.What is the smallest prime factor of 217? (a) 1 (b) 7 (c) 31 (d) 2
  8. 8.In a league, 11 teams each play every other team once. How many matches are played? (a) 66 (b) 110 (c) 121 (d) 55
  9. 9.In which quadrant does the point (−1, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  10. 10.Two angles of a triangle are 40° and 75°. What is the exterior angle at the third corner? (a) 140° (b) 65° (c) 115° (d) 105°
  11. 11.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
  12. 12.How many factors does 94 have? (a) 5 (b) 4 (c) 2 (d) 3
  13. 13.What is the sum of all the whole numbers from 1 to 88? (a) 7832 (b) 3916 (c) 3872 (d) 3828
  14. 14.What is the mode of 5, 3, 3, 5, 6, 5 and 20? (a) 6 (b) 3 (c) 5 (d) 20
  15. 15.A bag has 3 green, 2 white and 3 yellow balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 7/8 (c) 3/4 (d) 1/4
  16. 16.If a + b = 12 and ab = 20, what is a² + b²? (a) 124 (b) 104 (c) 144 (d) 184
  17. 17.In a class of 34 children, 17 like mangoes, 24 like bananas and 4 like neither. How many like both? (a) 11 (b) 4 (c) 7 (d) 30
  18. 18.In which quadrant does the point (8, −1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  19. 19.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 121 (c) 22 (d) 110
  20. 20.What is the distance between the points (3, 6) and (11, 21)? (a) 23 (b) 289 (c) 18 (d) 17
  21. 21.What is the midpoint of the line joining (1, 13) and (5, 9)? (a) (3, 11) (b) (6, 22) (c) (11, 3) (d) (2, 2)
  22. 22.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
  23. 23.A bag has 4 yellow, 4 blue and 4 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 2/3 (b) 3/4 (c) 1/12 (d) 1/3
  24. 24.A drawer has lots of white, green 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) 2 (b) 4 (c) 6 (d) 3
  25. 25.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) 21 (b) 14 (c) 15 (d) 22
  26. 26.Using (a − b)² = a² − 2ab + b², what is 39²? (a) 1531 (b) 1681 (c) 1521 (d) 1599
  27. 27.What is the mean of 10, 16, 7 and 7? (a) 9 (b) 8 (c) 11 (d) 10
  28. 28.Using (a − b)² = a² − 2ab + b², what is 65²? (a) 5625 (b) 4875 (c) 4235 (d) 4225
  29. 29.What is the prime factorisation of 14? (a) 2³ × 7 (b) 2 × 7² (c) 2 × 7 (d) 2² × 7
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 18 (b) 7 (c) 17 (d) 19
  31. 31.A bag has 5 yellow, 4 red and 2 green balls. One ball is taken out without looking. What is the probability that it is red? (a) 4/7 (b) 1/3 (c) 4/11 (d) 7/11
  32. 32.What is the mean of 11, 15, 8, 2 and 9? (a) 10 (b) 9 (c) 11 (d) 8
  33. 33.What is the mean of 10, 20, 8, 7, 10 and 5? (a) 11 (b) 9 (c) 12 (d) 10
  34. 34.What is the mean of 19, 15, 2, 20 and 19? (a) 16 (b) 15 (c) 14 (d) 17
  35. 35.What is the distance between the points (4, 5) and (28, 12)? (a) 26 (b) 625 (c) 25 (d) 31
  36. 36.What is the smallest prime factor of 299? (a) 1 (b) 2 (c) 13 (d) 23
  37. 37.What is the 25th term of the AP 17, 20, 23, 26, …? (a) 92 (b) 75 (c) 89 (d) 72
  38. 38.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  39. 39.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 28 (c) 21 (d) 42
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 1 (b) 2 (c) 3 (d) 4

Answer key

  1. (5, 8)
  2. 100°
  3. 1/3
  4. 35°
  5. 20
  6. 5
  7. 7
  8. 55
  9. Second quadrant
  10. 115°
  11. 2464 sq cm
  12. 4
  13. 3916
  14. 5
  15. 3/4
  16. 104
  17. 11
  18. Fourth quadrant
  19. 55
  20. 17
  21. (3, 11)
  22. 88 cm
  23. 2/3
  24. 4
  25. 15
  26. 1521
  27. 10
  28. 4225
  29. 2 × 7
  30. 18
  31. 4/11
  32. 9
  33. 10
  34. 15
  35. 25
  36. 13
  37. 89
  38. 120
  39. 21
  40. 3

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