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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 230 · 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 dice are rolled together. What is the probability that the two numbers add up to 9? (a) 5/36 (b) 4/11 (c) 1/9 (d) 1/11
  2. 2.The mean of 6 numbers is 17. When the number 24 is added to them, what is the new mean? (a) 19 (b) 17 (c) 20 (d) 18
  3. 3.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
  4. 4.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 24 (b) 36 (c) 37 (d) 25
  5. 5.A cuboid is 7 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 70 sq cm (b) 118 sq cm (c) 236 sq cm (d) 59 sq cm
  6. 6.What is the mean of 4, 4, 7, 15 and 15? (a) 9 (b) 11 (c) 10 (d) 8
  7. 7.A bag has 8 white, 7 red and 6 green balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/2 (b) 2/3 (c) 1/3 (d) 8/21
  8. 8.If a + b = 13 and ab = 40, what is a² + b²? (a) 249 (b) 89 (c) 169 (d) 129
  9. 9.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 75 (b) 540 (c) 504 (d) 1008
  10. 10.What is the midpoint of the line joining (8, 7) and (18, 1)? (a) (13, 4) (b) (4, 13) (c) (26, 8) (d) (5, 3)
  11. 11.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 46 (b) 196 (c) 392 (d) 217
  12. 12.5 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 35 (b) 70 (c) 12 (d) 40
  13. 13.What is the sum of the roots of x² − 7x + 12 = 0? (a) 8 (b) 6 (c) 7 (d) 12
  14. 14.A bag has 5 red balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 6 (b) 9 (c) 2 (d) 7
  15. 15.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  16. 16.What is the 10th term of the AP 18, 22, 26, 30, …? (a) 58 (b) 36 (c) 54 (d) 40
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 21 (b) 9 (c) 20 (d) 19
  18. 18.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 144 (c) 16 (d) 48
  19. 19.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/36 (b) 1/11 (c) 1/12 (d) 1/18
  20. 20.What is the midpoint of the line joining (4, 0) and (14, 4)? (a) (2, 9) (b) (18, 4) (c) (5, 2) (d) (9, 2)
  21. 21.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 125 sq cm (c) 150 sq cm (d) 25 sq cm
  22. 22.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  23. 23.A canteen sells 7 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 14 (b) 56 (c) 49 (d) 98
  24. 24.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
  25. 25.A bag has 2 blue, 7 yellow and 4 red balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 2/13 (b) 1/3 (c) 12/13 (d) 11/13
  26. 26.Which term of the AP 2, 8, 14, 20, … is 218? (a) 37th (b) 36th (c) 38th (d) 39th
  27. 27.Two angles of a triangle are 50° and 40°. What is the third angle? (a) 270° (b) 140° (c) 90° (d) 130°
  28. 28.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 105 (c) 210 (d) 225
  29. 29.What is the smallest prime factor of 33? (a) 3 (b) 11 (c) 2 (d) 1
  30. 30.What is the missing term in the AP 11, ?, 25, 32, 39? (a) 17 (b) 25 (c) 19 (d) 18
  31. 31.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 30° (c) 60° (d) 150°
  32. 32.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
  33. 33.There are 6 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 48 (b) 84 (c) 42 (d) 13
  34. 34.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
  35. 35.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 1/2 (c) 2/3 (d) 1/3
  36. 36.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 20 (c) 25 (d) 11
  37. 37.What is the mode of 16, 9, 1, 10, 10, 1 and 10? (a) 16 (b) 9 (c) 1 (d) 10
  38. 38.What is the midpoint of the line joining (8, 5) and (16, 11)? (a) (24, 16) (b) (8, 12) (c) (4, 3) (d) (12, 8)
  39. 39.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 145° (b) 100° (c) 115° (d) 35°
  40. 40.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6

Answer key

  1. 1/9
  2. 18
  3. 220 cm
  4. 25
  5. 118 sq cm
  6. 9
  7. 1/3
  8. 89
  9. 504
  10. (13, 4)
  11. 196
  12. 35
  13. 7
  14. 7
  15. 20
  16. 54
  17. 20
  18. 48
  19. 1/36
  20. (9, 2)
  21. 150 sq cm
  22. 17
  23. 49
  24. 44 cm
  25. 11/13
  26. 37th
  27. 90°
  28. 105
  29. 3
  30. 18
  31. 75°
  32. 154 sq cm
  33. 42
  34. 176 cm
  35. 1/2
  36. 10
  37. 10
  38. (12, 8)
  39. 35°
  40. 1/2

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