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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 350 · 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.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 216 sq cm (c) 36 sq cm (d) 144 sq cm
  2. 2.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 25° (b) 155° (c) 205° (d) 26°
  3. 3.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
  4. 4.How many factors does 49 have? (a) 2 (b) 1 (c) 4 (d) 3
  5. 5.7 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 13 (b) 42 (c) 49 (d) 84
  6. 6.In a class of 26 children, 15 like tea, 16 like coffee and 11 like both. How many like only tea? (a) 5 (b) 15 (c) 4 (d) 10
  7. 7.If a + b = 19 and ab = 90, what is (a − b)²? (a) 271 (b) 181 (c) 361 (d) 1
  8. 8.What is the sum of the roots of x² − 9x + 14 = 0? (a) 8 (b) 10 (c) 14 (d) 9
  9. 9.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 50° (c) 25° (d) 115°
  10. 10.What is the smallest prime factor of 91? (a) 7 (b) 1 (c) 13 (d) 2
  11. 11.The mean of 4 numbers is 22. When the number 37 is added to them, what is the new mean? (a) 25 (b) 26 (c) 22 (d) 24
  12. 12.In a class of 35 children, 19 like cricket, 20 like football and 10 like both. How many like neither? (a) 16 (b) 7 (c) 10 (d) 6
  13. 13.What is the mean of 19, 15, 17 and 9? (a) 12 (b) 20 (c) 15 (d) 16
  14. 14.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 15 (b) 14 (c) 7 (d) 8
  15. 15.If a + b = 10 and ab = 9, what is a² + b²? (a) 91 (b) 118 (c) 100 (d) 82
  16. 16.Two angles of a triangle are 35° and 25°. What is the third angle? (a) 155° (b) 145° (c) 60° (d) 120°
  17. 17.In which quadrant does the point (−5, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  18. 18.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 24 (c) 48 (d) 12
  19. 19.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/12 (c) 1/11 (d) 1/18
  20. 20.In a class of 35 children, 25 like maths, 19 like science and 2 like neither. How many like both? (a) 9 (b) 33 (c) 11 (d) 2
  21. 21.How many factors does 88 have? (a) 6 (b) 9 (c) 8 (d) 7
  22. 22.A bag has 4 yellow balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 12 (c) 5 (d) 2
  23. 23.What is the distance between the points (2, 23) and (14, 7)? (a) 400 (b) 28 (c) 21 (d) 20
  24. 24.What is the 21st term of the AP 18, 27, 36, 45, …? (a) 198 (b) 180 (c) 189 (d) 207
  25. 25.A bag has 7 red, 3 yellow and 5 white balls. One ball is taken out without looking. What is the probability that it is red? (a) 7/15 (b) 1/3 (c) 8/15 (d) 7/8
  26. 26.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  27. 27.What is the missing term in the AP 18, ?, 30, 36, 42? (a) 30 (b) 23 (c) 24 (d) 25
  28. 28.A bag has 6 blue balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 7 (c) 15 (d) 8
  29. 29.How many prime numbers are there between 60 and 80? (a) 6 (b) 4 (c) 7 (d) 5
  30. 30.In which quadrant does the point (8, 7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  31. 31.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 115° (b) 270° (c) 90° (d) 155°
  32. 32.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 145° (d) 110°
  33. 33.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
  34. 34.What is the prime factorisation of 168? (a) 2² × 3 × 7 (b) 2 × 3 × 7³ (c) 2³ × 3 × 7 (d) 2⁴ × 3 × 7
  35. 35.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
  36. 36.How many prime numbers are there between 10 and 20? (a) 6 (b) 3 (c) 4 (d) 5
  37. 37.What is the prime factorisation of 20? (a) 2 × 5² (b) 2 × 5 (c) 2³ × 5 (d) 2² × 5
  38. 38.In a class of 29 children, 19 like dance, 16 like music and 12 like both. How many like only dance? (a) 4 (b) 13 (c) 19 (d) 7
  39. 39.In a class of 30 children, 15 like tea, 7 like coffee and 2 like both. How many like at least one of the two? (a) 20 (b) 22 (c) 18 (d) 30
  40. 40.In a class of 47 children, 26 like cricket, 25 like football and 12 like both. How many like at least one of the two? (a) 47 (b) 39 (c) 51 (d) 27

Answer key

  1. 216 sq cm
  2. 25°
  3. 132 cm
  4. 3
  5. 42
  6. 4
  7. 1
  8. 9
  9. 50°
  10. 7
  11. 25
  12. 6
  13. 15
  14. 8
  15. 82
  16. 120°
  17. Third quadrant
  18. 24
  19. 1/18
  20. 11
  21. 8
  22. 9
  23. 20
  24. 198
  25. 7/15
  26. 2
  27. 24
  28. 8
  29. 5
  30. First quadrant
  31. 90°
  32. 105°
  33. 20
  34. 2³ × 3 × 7
  35. 154 sq cm
  36. 4
  37. 2² × 5
  38. 7
  39. 20
  40. 39

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