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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 558 · 40 questions
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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.If a + b = 15 and ab = 36, what is (a − b)²? (a) 225 (b) 81 (c) 9 (d) 153
  2. 2.7 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 42 (b) 12 (c) 70 (d) 35
  3. 3.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 7 (d) 14
  4. 4.The mean of 8 numbers is 15. When the number 42 is added to them, what is the new mean? (a) 19 (b) 17 (c) 15 (d) 18
  5. 5.A bag has 9 red balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 10 (b) 2 (c) 20 (d) 11
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 5 (d) 4
  7. 7.How many factors does 26 have? (a) 2 (b) 5 (c) 4 (d) 3
  8. 8.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 6 (d) 13
  9. 9.Two angles of a triangle are 50° and 55°. What is the third angle? (a) 130° (b) 105° (c) 125° (d) 75°
  10. 10.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 350 (c) 418 (d) 417
  11. 11.What is the mean of 17, 13, 15 and 15? (a) 12 (b) 20 (c) 15 (d) 16
  12. 12.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
  13. 13.What is the missing term in the AP 8, 17, 26, ?, 44? (a) 36 (b) 35 (c) 44 (d) 34
  14. 14.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 145° (b) 105° (c) 110° (d) 70°
  15. 15.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  16. 16.What is the sum of all the whole numbers from 1 to 65? (a) 2146 (b) 4290 (c) 2080 (d) 2145
  17. 17.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  18. 18.A cuboid is 12 cm long, 4 cm wide and 9 cm high. What is its volume? (a) 432 cu cm (b) 384 cu cm (c) 25 cu cm (d) 48 cu cm
  19. 19.What is the product of the roots of x² − 8x + 12 = 0? (a) 11 (b) 12 (c) 8 (d) 13
  20. 20.What is the midpoint of the line joining (8, 10) and (20, 14)? (a) (14, 12) (b) (6, 2) (c) (12, 14) (d) (28, 24)
  21. 21.What is the 22nd term of the AP 2, 6, 10, 14, …? (a) 90 (b) 88 (c) 84 (d) 86
  22. 22.What is the mean of 7, 2, 5, 19, 3 and 18? (a) 8 (b) 9 (c) 10 (d) 11
  23. 23.The mean of 9 numbers is 16. When the number 46 is added to them, what is the new mean? (a) 20 (b) 31 (c) 19 (d) 16
  24. 24.In a class of 35 children, 13 like cricket, 23 like football and 4 like both. How many like at least one of the two? (a) 28 (b) 36 (c) 32 (d) 35
  25. 25.If a + b = 14 and ab = 40, what is (a − b)²? (a) 196 (b) 6 (c) 116 (d) 36
  26. 26.What is the prime factorisation of 15? (a) 3 × 5² (b) 3 × 5 (c) 3³ × 5 (d) 3² × 5
  27. 27.The mean of 8 numbers is 38. When the number 29 is added to them, what is the new mean? (a) 38 (b) 36 (c) 37 (d) 39
  28. 28.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
  29. 29.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 1/4 (b) 5/6 (c) 1/3 (d) 2/3
  30. 30.In a class of 29 children, 19 like dance, 11 like music and 7 like both. How many like neither? (a) 13 (b) 7 (c) 6 (d) 5
  31. 31.In a class of 39 children, 17 like cricket, 22 like football and 7 like neither. How many like both? (a) 6 (b) 7 (c) 8 (d) 32
  32. 32.In a class of 26 children, 12 like tea, 16 like coffee and 9 like both. How many like neither? (a) 8 (b) 7 (c) 9 (d) 16
  33. 33.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 388 (c) 475 (d) 465
  34. 34.What is the product of the roots of x² − 12x + 35 = 0? (a) 12 (b) 34 (c) 35 (d) 36
  35. 35.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 49 (c) 13 (d) 28
  36. 36.In which quadrant does the point (6, 7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  37. 37.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 105° (b) 115° (c) 65° (d) 140°
  38. 38.What is the 19th term of the AP 3, 12, 21, 30, …? (a) 171 (b) 165 (c) 162 (d) 174
  39. 39.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 12 (c) 16 (d) 24
  40. 40.A cuboid is 11 cm long, 6 cm wide and 10 cm high. What is its volume? (a) 660 cu cm (b) 27 cu cm (c) 472 cu cm (d) 66 cu cm

Answer key

  1. 81
  2. 35
  3. 6
  4. 18
  5. 11
  6. 5
  7. 4
  8. 7
  9. 75°
  10. 417
  11. 15
  12. 1386 sq cm
  13. 35
  14. 70°
  15. 17
  16. 2145
  17. 10
  18. 432 cu cm
  19. 12
  20. (14, 12)
  21. 86
  22. 9
  23. 19
  24. 32
  25. 36
  26. 3 × 5
  27. 37
  28. 132 cm
  29. 2/3
  30. 6
  31. 7
  32. 7
  33. 474
  34. 35
  35. 49
  36. First quadrant
  37. 65°
  38. 165
  39. 24
  40. 660 cu cm

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