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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 841 · 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.What is the prime factorisation of 42? (a) 2² × 3 × 7 (b) 2 × 3 × 7² (c) 2³ × 3 × 7 (d) 2 × 3 × 7
  2. 2.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 5/6 (c) 1/3 (d) 2/3
  3. 3.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
  4. 4.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/5 (b) 1/6 (c) 1/3 (d) 5/6
  5. 5.How many factors does 19 have? (a) 3 (b) 4 (c) 2 (d) 1
  6. 6.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 240 (c) 20 (d) 25
  7. 7.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 520 (b) 519 (c) 418 (d) 510
  8. 8.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
  9. 9.What is the smallest prime factor of 33? (a) 3 (b) 11 (c) 1 (d) 2
  10. 10.Using (a + b)² = a² + 2ab + b², what is 42²? (a) 1764 (b) 1774 (c) 1604 (d) 1444
  11. 11.What is the mode of 2, 14, 2, 13, 13, 17 and 13? (a) 2 (b) 17 (c) 13 (d) 14
  12. 12.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 78 (c) 23 (d) 144
  13. 13.What is the 23rd term of the AP 2, 6, 10, 14, …? (a) 88 (b) 90 (c) 92 (d) 94
  14. 14.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
  15. 15.What is the 22nd term of the AP 11, 19, 27, 35, …? (a) 168 (b) 179 (c) 187 (d) 176
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 4 (b) 2 (c) 3 (d) 5
  17. 17.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 13 (b) 117 (c) 42 (d) 39
  18. 18.In which quadrant does the point (7, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  19. 19.What is the 12th term of the AP 20, 26, 32, 38, …? (a) 86 (b) 66 (c) 92 (d) 72
  20. 20.If a + b = 18 and ab = 77, what is (a − b)²? (a) 170 (b) 16 (c) 324 (d) 4
  21. 21.What is the mean of 15, 20, 19, 8 and 13? (a) 17 (b) 15 (c) 16 (d) 14
  22. 22.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 3850 cm (d) 440 cm
  23. 23.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 16 cu cm (c) 6 cu cm (d) 24 cu cm
  24. 24.Which is the correct factorisation of x² + 6x + 8? (a) (x + 2)(x + 4) (b) (x + 1)(x + 5) (c) (x + 1)(x + 8) (d) (x − 2)(x − 4)
  25. 25.What is the prime factorisation of 60? (a) 2 × 3 × 5 (b) 2² × 3 × 5 (c) 2 × 3 × 5² (d) 2³ × 3 × 5
  26. 26.What is the median of 16, 10, 31, 22, 13, 12 and 37? (a) 16 (b) 13 (c) 17 (d) 22
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 16 (b) 5 (c) 15 (d) 17
  28. 28.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 15° (b) 16° (c) 195° (d) 165°
  29. 29.What is the median of 31, 22, 8, 6 and 25? (a) 25 (b) 23 (c) 22 (d) 8
  30. 30.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 110° (b) 155° (c) 25° (d) 95°
  31. 31.A bag has 5 blue balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 6 (b) 7 (c) 2 (d) 11
  32. 32.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) 48 (b) 144 (c) 51 (d) 16
  33. 33.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
  34. 34.What are the roots of x² − 14x + 48 = 0? (a) 1 and 13 (b) 6 and 8 (c) 1 and 48 (d) 2 and 24
  35. 35.What is the mean of 12, 6, 2, 11 and 9? (a) 8 (b) 7 (c) 10 (d) 9
  36. 36.3 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 12 (b) 7 (c) 24 (d) 15
  37. 37.Two angles of a triangle are 40° and 95°. What is the third angle? (a) 85° (b) 135° (c) 45° (d) 140°
  38. 38.What is the prime factorisation of 180? (a) 2 × 3² × 5² (b) 2² × 3² × 5 (c) 2 × 3² × 5 (d) 2³ × 3² × 5
  39. 39.What is the distance between the points (3, 0) and (15, 9)? (a) 21 (b) 15 (c) 225 (d) 16
  40. 40.What is the smallest prime factor of 145? (a) 29 (b) 5 (c) 2 (d) 1

Answer key

  1. 2 × 3 × 7
  2. 2/3
  3. 132 cm
  4. 5/6
  5. 2
  6. 120
  7. 519
  8. 154 sq cm
  9. 3
  10. 1764
  11. 13
  12. 144
  13. 90
  14. 88 cm
  15. 179
  16. 4
  17. 39
  18. First quadrant
  19. 86
  20. 16
  21. 15
  22. 220 cm
  23. 8 cu cm
  24. (x + 2)(x + 4)
  25. 2² × 3 × 5
  26. 16
  27. 16
  28. 15°
  29. 22
  30. 25°
  31. 7
  32. 48
  33. 154 sq cm
  34. 6 and 8
  35. 8
  36. 12
  37. 45°
  38. 2² × 3² × 5
  39. 15
  40. 5

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