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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 862 · 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 captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 144 (c) 66 (d) 132
  2. 2.What is the prime factorisation of 168? (a) 2⁴ × 3 × 7 (b) 2 × 3 × 7³ (c) 2² × 3 × 7 (d) 2³ × 3 × 7
  3. 3.What is the median of 17, 30, 6, 38 and 40? (a) 17 (b) 6 (c) 30 (d) 38
  4. 4.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
  5. 5.The mean of 3 numbers is 22. When the number 14 is added to them, what is the new mean? (a) 18 (b) 21 (c) 20 (d) 22
  6. 6.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  7. 7.In a class of 30 children, 19 like mangoes, 10 like bananas and 5 like both. How many like at least one of the two? (a) 24 (b) 30 (c) 19 (d) 29
  8. 8.In a class of 39 children, 19 like mangoes, 20 like bananas and 2 like both. How many like only mangoes? (a) 17 (b) 19 (c) 18 (d) 2
  9. 9.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 41° (c) 80° (d) 40°
  11. 11.What is the distance between the points (8, 3) and (17, 15)? (a) 225 (b) 15 (c) 16 (d) 21
  12. 12.What is the prime factorisation of 30? (a) 2² × 3 × 5 (b) 2 × 3 × 5² (c) 2 × 3 × 5 (d) 2³ × 3 × 5
  13. 13.In a class of 45 children, 26 like dance, 22 like music and 7 like both. How many like only dance? (a) 23 (b) 26 (c) 15 (d) 19
  14. 14.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 4 (b) 3 (c) 2 (d) 5
  16. 16.A cuboid is 5 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 10 cu cm (b) 100 cu cm (c) 160 cu cm (d) 17 cu cm
  17. 17.The mean of 7 numbers is 30. When the number 22 is added to them, what is the new mean? (a) 30 (b) 29 (c) 28 (d) 26
  18. 18.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  19. 19.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 70° (c) 120° (d) 60°
  20. 20.In a class of 32 children, 8 like maths, 24 like science and 4 like both. How many like neither? (a) 8 (b) 0 (c) 4 (d) 5
  21. 21.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 121 (c) 110 (d) 22
  22. 22.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 11 (c) 21 (d) 36
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 80° (b) 20° (c) 100° (d) 200°
  24. 24.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
  25. 25.3 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) 24 (b) 12 (c) 7 (d) 15
  26. 26.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 1/8 (c) 1/4 (d) 7/8
  27. 27.What is the median of 6, 30, 11, 28 and 29? (a) 27 (b) 11 (c) 29 (d) 28
  28. 28.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 5/36 (c) 1/9 (d) 4/11
  29. 29.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 65° (c) 115° (d) 50°
  30. 30.Using (a − b)² = a² − 2ab + b², what is 37²? (a) 1849 (b) 1379 (c) 1591 (d) 1369
  31. 31.In a class of 23 children, 11 like dance, 10 like music and 7 like both. How many like neither? (a) 2 (b) 7 (c) 16 (d) 9
  32. 32.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
  33. 33.If a + b = 14 and ab = 24, what is a² + b²? (a) 244 (b) 196 (c) 172 (d) 148
  34. 34.A cube has edges of 5 cm. What is its total surface area? (a) 125 sq cm (b) 25 sq cm (c) 150 sq cm (d) 100 sq cm
  35. 35.How many prime numbers are there between 90 and 120? (a) 7 (b) 8 (c) 6 (d) 5
  36. 36.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 42 (c) 21 (d) 14
  37. 37.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 70 (c) 62 (d) 61
  38. 38.Which term of the AP 6, 10, 14, 18, … is 38? (a) 9th (b) 8th (c) 10th (d) 11th
  39. 39.In which quadrant does the point (−3, 5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  40. 40.In a class of 39 children, 17 like maths, 26 like science and 10 like both. How many like neither? (a) 6 (b) 7 (c) 10 (d) 16

Answer key

  1. 132
  2. 2³ × 3 × 7
  3. 30
  4. 1/3
  5. 20
  6. 17
  7. 24
  8. 17
  9. 1/2
  10. 40°
  11. 15
  12. 2 × 3 × 5
  13. 19
  14. 8
  15. 4
  16. 100 cu cm
  17. 29
  18. 24
  19. 60°
  20. 4
  21. 55
  22. 36
  23. 100°
  24. 1/3
  25. 12
  26. 1/8
  27. 28
  28. 1/9
  29. 50°
  30. 1369
  31. 9
  32. 132 cm
  33. 148
  34. 150 sq cm
  35. 6
  36. 21
  37. 61
  38. 9th
  39. Second quadrant
  40. 6

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