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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 739 · 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.Which term of the AP 15, 17, 19, 21, … is 75? (a) 33rd (b) 32nd (c) 31st (d) 30th
  2. 2.What is the mean of 13, 7, 7, 14 and 19? (a) 15 (b) 10 (c) 13 (d) 12
  3. 3.A bag has 12 red balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 18 (c) 13 (d) 14
  4. 4.In a class of 23 children, 14 like dance, 19 like music and 11 like both. How many like at least one of the two? (a) 33 (b) 23 (c) 11 (d) 22
  5. 5.What is the mean of 3, 2, 6 and 17? (a) 7 (b) 6 (c) 9 (d) 8
  6. 6.Using (a + b)² = a² + 2ab + b², what is 104²? (a) 10016 (b) 10826 (c) 10816 (d) 9216
  7. 7.What is the 34th term of the AP 9, 18, 27, 36, …? (a) 315 (b) 297 (c) 306 (d) 307
  8. 8.What is the smallest prime factor of 377? (a) 1 (b) 13 (c) 2 (d) 29
  9. 9.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/2 (c) 1/3 (d) 1/4
  10. 10.In which quadrant does the point (8, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  11. 11.What is the midpoint of the line joining (0, 11) and (4, 1)? (a) (2, 6) (b) (4, 12) (c) (2, 5) (d) (6, 2)
  12. 12.What is the median of 33, 37, 27, 12, 17, 32 and 34? (a) 33 (b) 27 (c) 12 (d) 32
  13. 13.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 24 (c) 72 (d) 75
  14. 14.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
  15. 15.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 32 (b) 264 (c) 504 (d) 252
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 130° (c) 115° (d) 66°
  17. 17.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 125° (c) 70° (d) 55°
  18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/18 (b) 1/12 (c) 1/11 (d) 1/36
  19. 19.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  20. 20.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 12 (b) 10 (c) 9 (d) 8
  21. 21.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 18 (c) 15 (d) 8
  22. 22.What is the sum of all the whole numbers from 1 to 62? (a) 1891 (b) 1953 (c) 3906 (d) 1922
  23. 23.How many factors does 56 have? (a) 6 (b) 8 (c) 9 (d) 7
  24. 24.How many prime numbers are there between 10 and 20? (a) 4 (b) 3 (c) 5 (d) 6
  25. 25.What is the mode of 18, 2, 6, 2, 14, 2 and 14? (a) 2 (b) 6 (c) 18 (d) 14
  26. 26.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 30 (c) 36 (d) 15
  27. 27.What is the median of 34, 3, 15, 12 and 24? (a) 16 (b) 24 (c) 15 (d) 12
  28. 28.How many factors does 16 have? (a) 4 (b) 5 (c) 6 (d) 3
  29. 29.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 50° (b) 140° (c) 10° (d) 170°
  30. 30.If a + b = 18 and ab = 72, what is a² + b²? (a) 468 (b) 252 (c) 180 (d) 324
  31. 31.A cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 144 sq cm (c) 217 sq cm (d) 36 sq cm
  32. 32.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 1/4 (c) 1/8 (d) 7/8
  33. 33.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 23 (c) 72 (d) 69
  34. 34.A bag has 5 white, 2 green and 3 yellow balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/5 (b) 1/3 (c) 4/5 (d) 9/10
  35. 35.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 36 (c) 30 (d) 21
  36. 36.What is the 15th term of the AP 18, 27, 36, 45, …? (a) 153 (b) 126 (c) 144 (d) 135
  37. 37.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  38. 38.What is the 11th term of the AP 6, 13, 20, 27, …? (a) 76 (b) 70 (c) 83 (d) 77
  39. 39.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 22 (b) 198 (c) 66 (d) 69
  40. 40.How many factors does 17 have? (a) 4 (b) 1 (c) 2 (d) 3

Answer key

  1. 31st
  2. 12
  3. 14
  4. 22
  5. 7
  6. 10816
  7. 306
  8. 13
  9. 3/4
  10. Fourth quadrant
  11. (2, 6)
  12. 32
  13. 72
  14. 4
  15. 252
  16. 65°
  17. 70°
  18. 1/36
  19. 25
  20. 9
  21. 15
  22. 1953
  23. 8
  24. 4
  25. 2
  26. 15
  27. 15
  28. 5
  29. 10°
  30. 180
  31. 216 sq cm
  32. 1/8
  33. 69
  34. 4/5
  35. 15
  36. 144
  37. 24
  38. 76
  39. 66
  40. 2

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