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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 397 · 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.A bag has 3 white, 8 red and 7 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 7/18 (b) 11/18 (c) 1/3 (d) 2/3
  2. 2.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
  3. 3.How many factors does 19 have? (a) 4 (b) 1 (c) 3 (d) 2
  4. 4.A cuboid is 10 cm long, 8 cm wide and 4 cm high. What is its total surface area? (a) 608 sq cm (b) 320 sq cm (c) 304 sq cm (d) 152 sq cm
  5. 5.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 2 times (c) 6 times (d) 8 times
  6. 6.What is the smallest prime factor of 377? (a) 1 (b) 13 (c) 2 (d) 29
  7. 7.Using (a + b)² = a² + 2ab + b², what is 91²? (a) 8101 (b) 7921 (c) 8291 (d) 8281
  8. 8.What is the smallest prime factor of 209? (a) 19 (b) 11 (c) 2 (d) 1
  9. 9.What is the median of 39, 12, 28, 10, 15, 22 and 13? (a) 13 (b) 22 (c) 15 (d) 10
  10. 10.In a class of 39 children, 22 like maths, 11 like science and 2 like both. How many like neither? (a) 2 (b) 6 (c) 10 (d) 8
  11. 11.The mean of 8 numbers is 21. When the number 30 is added to them, what is the new mean? (a) 24 (b) 21 (c) 22 (d) 23
  12. 12.In a class of 19 children, 7 like cricket, 8 like football and 8 like neither. How many like both? (a) 8 (b) 4 (c) 5 (d) 11
  13. 13.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  14. 14.What is the midpoint of the line joining (2, 1) and (6, 9)? (a) (8, 10) (b) (4, 5) (c) (5, 4) (d) (2, 4)
  15. 15.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) 22 (c) 14 (d) 15
  16. 16.What is the midpoint of the line joining (10, 3) and (18, 9)? (a) (6, 14) (b) (14, 6) (c) (28, 12) (d) (4, 3)
  17. 17.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
  18. 18.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 44 cm (d) 176 cm
  19. 19.What is the sum of the first 7 terms of the AP 9, 11, 13, …? (a) 210 (b) 105 (c) 21 (d) 112
  20. 20.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  21. 21.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 150° (c) 60° (d) 75°
  22. 22.If a + b = 11 and ab = 28, what is a² + b²? (a) 177 (b) 121 (c) 93 (d) 65
  23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 7/36 (b) 1/6 (c) 6/11 (d) 1/11
  24. 24.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) 37 (b) 25 (c) 24 (d) 36
  25. 25.In which quadrant does the point (−7, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  26. 26.What is the 33rd term of the AP 20, 24, 28, 32, …? (a) 152 (b) 132 (c) 128 (d) 148
  27. 27.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 72 (b) 81 (c) 18 (d) 36
  28. 28.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
  29. 29.How many factors does 42 have? (a) 6 (b) 9 (c) 7 (d) 8
  30. 30.In a league, 11 teams each play every other team once. How many matches are played? (a) 66 (b) 110 (c) 121 (d) 55
  31. 31.5 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) 70 (b) 40 (c) 12 (d) 35
  32. 32.What is the sum of the roots of x² − 11x + 30 = 0? (a) 11 (b) 10 (c) 12 (d) 30
  33. 33.Using (a + b)² = a² + 2ab + b², what is 21²? (a) 401 (b) 451 (c) 441 (d) 361
  34. 34.What is the median of 2, 12, 5, 26 and 11? (a) 5 (b) 12 (c) 10 (d) 11
  35. 35.A bag has 7 green balls and 12 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 8 (c) 19 (d) 13
  36. 36.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 189 (b) 66 (c) 63 (d) 21
  37. 37.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 493 (c) 492 (d) 400
  38. 38.How many factors does 22 have? (a) 3 (b) 4 (c) 2 (d) 5
  39. 39.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 155° (b) 95° (c) 110° (d) 85°
  40. 40.6 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 36 (b) 9 (c) 18 (d) 24

Answer key

  1. 11/18
  2. 1/2
  3. 2
  4. 304 sq cm
  5. 8 times
  6. 13
  7. 8281
  8. 11
  9. 15
  10. 8
  11. 22
  12. 4
  13. 120
  14. (4, 5)
  15. 15
  16. (14, 6)
  17. 1386 sq cm
  18. 88 cm
  19. 105
  20. 15
  21. 75°
  22. 65
  23. 1/6
  24. 25
  25. Third quadrant
  26. 148
  27. 72
  28. 10
  29. 8
  30. 55
  31. 35
  32. 11
  33. 441
  34. 11
  35. 13
  36. 63
  37. 492
  38. 4
  39. 85°
  40. 18

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