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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 502 · 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.How many factors does 14 have? (a) 2 (b) 3 (c) 5 (d) 4
  2. 2.What is the product of the roots of x² − 13x + 42 = 0? (a) 42 (b) 13 (c) 43 (d) 41
  3. 3.How many factors does 18 have? (a) 7 (b) 5 (c) 6 (d) 4
  4. 4.In a class of 25 children, 17 like mangoes, 14 like bananas and 7 like both. How many like only mangoes? (a) 11 (b) 10 (c) 7 (d) 17
  5. 5.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 21 (d) 225
  6. 6.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 42 (c) 14 (d) 21
  7. 7.What is the smallest prime factor of 143? (a) 13 (b) 11 (c) 2 (d) 1
  8. 8.In a class of 22 children, 14 like mangoes, 7 like bananas and 4 like both. How many like at least one of the two? (a) 22 (b) 13 (c) 17 (d) 21
  9. 9.In a class of 30 children, 9 like cricket, 25 like football and 6 like both. How many like at least one of the two? (a) 30 (b) 28 (c) 22 (d) 34
  10. 10.In a class of 42 children, 18 like tea, 23 like coffee and 4 like neither. How many like both? (a) 38 (b) 4 (c) 3 (d) 2
  11. 11.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 190° (b) 95° (c) 10° (d) 85°
  12. 12.What is the distance between the points (1, 14) and (13, 5)? (a) 21 (b) 16 (c) 225 (d) 15
  13. 13.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 54 sq cm (c) 36 sq cm (d) 27 sq cm
  14. 14.What is the mode of 13, 4, 4, 11, 13, 13 and 9? (a) 13 (b) 11 (c) 4 (d) 9
  15. 15.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
  16. 16.What is the product of the roots of x² − 9x + 18 = 0? (a) 9 (b) 19 (c) 18 (d) 17
  17. 17.In which quadrant does the point (5, −9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  18. 18.In a class of 38 children, 11 like tea, 21 like coffee and 4 like both. How many like only tea? (a) 17 (b) 11 (c) 7 (d) 4
  19. 19.What is the mode of 6, 8, 15, 8, 3, 15 and 15? (a) 6 (b) 3 (c) 8 (d) 15
  20. 20.What is the 34th term of the AP 16, 23, 30, 37, …? (a) 254 (b) 238 (c) 247 (d) 231
  21. 21.How many prime numbers are there between 50 and 70? (a) 4 (b) 3 (c) 5 (d) 6
  22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 58? (a) 15 (b) 17 (c) 5 (d) 16
  23. 23.A bag has 7 green, 8 white and 9 blue balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/3 (b) 1/2 (c) 3/8 (d) 2/3
  24. 24.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
  25. 25.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 10 (d) 9
  26. 26.What is the median of 29, 23, 20, 40, 28, 13 and 16? (a) 23 (b) 20 (c) 28 (d) 40
  27. 27.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
  28. 28.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 387 (c) 388 (d) 330
  29. 29.What is the distance between the points (7, 8) and (10, 4)? (a) 6 (b) 7 (c) 25 (d) 5
  30. 30.The mean of 8 numbers is 16. When the number 25 is added to them, what is the new mean? (a) 18 (b) 17 (c) 19 (d) 16
  31. 31.What is the 17th term of the AP 5, 11, 17, 23, …? (a) 102 (b) 101 (c) 96 (d) 107
  32. 32.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
  33. 33.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  34. 34.What is the mean of 15, 2, 2, 17, 7 and 23? (a) 12 (b) 10 (c) 13 (d) 11
  35. 35.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 125° (b) 120° (c) 115° (d) 60°
  36. 36.There are 8 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 40 (b) 80 (c) 13 (d) 48
  37. 37.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 2/3 (c) 1/4 (d) 5/6
  38. 38.A bag has 4 green balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 5 (c) 14 (d) 6
  39. 39.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 110 cm (d) 440 cm
  40. 40.In a class of 46 children, 26 like maths, 24 like science and 6 like neither. How many like both? (a) 10 (b) 40 (c) 4 (d) 6

Answer key

  1. 4
  2. 42
  3. 6
  4. 10
  5. 15
  6. 42
  7. 11
  8. 17
  9. 28
  10. 3
  11. 95°
  12. 15
  13. 54 sq cm
  14. 13
  15. 88 cm
  16. 18
  17. Fourth quadrant
  18. 7
  19. 15
  20. 247
  21. 4
  22. 16
  23. 1/3
  24. 2464 sq cm
  25. 8
  26. 23
  27. 2464 sq cm
  28. 387
  29. 5
  30. 17
  31. 101
  32. 4 times
  33. 6
  34. 11
  35. 60°
  36. 40
  37. 2/3
  38. 6
  39. 220 cm
  40. 10

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