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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 901 · 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 drawer has lots of yellow, green, red and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 8 (c) 5 (d) 4
  2. 2.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 70 (b) 11 (c) 35 (d) 40
  3. 3.What is the 27th term of the AP 8, 12, 16, 20, …? (a) 108 (b) 104 (c) 116 (d) 112
  4. 4.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 45 (c) 90 (d) 55
  5. 5.Using (a − b)² = a² − 2ab + b², what is 96²? (a) 9226 (b) 9216 (c) 10816 (d) 9984
  6. 6.Which is the correct factorisation of x² + 14x + 48? (a) (x + 1)(x + 48) (b) (x − 6)(x − 8) (c) (x + 1)(x + 13) (d) (x + 6)(x + 8)
  7. 7.What is the mode of 19, 2, 15, 18, 15, 2 and 15? (a) 2 (b) 18 (c) 15 (d) 19
  8. 8.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
  9. 9.In a class of 23 children, 14 like mangoes, 10 like bananas and 2 like both. How many like neither? (a) 3 (b) 1 (c) 2 (d) 0
  10. 10.What is the sum of all the whole numbers from 1 to 88? (a) 7832 (b) 3916 (c) 3828 (d) 3872
  11. 11.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 125° (b) 145° (c) 55° (d) 160°
  12. 12.A cuboid is 12 cm long, 6 cm wide and 4 cm high. What is its volume? (a) 72 cu cm (b) 22 cu cm (c) 288 cu cm (d) 289 cu cm
  13. 13.A bag has 11 white balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 6 (c) 16 (d) 12
  14. 14.Which is the correct factorisation of x² + 7x + 12? (a) (x − 3)(x − 4) (b) (x + 1)(x + 12) (c) (x + 1)(x + 6) (d) (x + 3)(x + 4)
  15. 15.A canteen sells 6 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 72 (b) 36 (c) 42 (d) 12
  16. 16.3 T-shirts and 7 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) 21 (c) 10 (d) 24
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 6 (b) 8 (c) 5 (d) 7
  18. 18.What are the roots of x² − 14x + 48 = 0? (a) 1 and 13 (b) 2 and 24 (c) 6 and 8 (d) 1 and 48
  19. 19.What is the 17th term of the AP 2, 8, 14, 20, …? (a) 104 (b) 96 (c) 98 (d) 102
  20. 20.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 24 (b) 25 (c) 37 (d) 36
  21. 21.What is the distance between the points (3, 5) and (18, 13)? (a) 17 (b) 289 (c) 23 (d) 18
  22. 22.Using (a + b)² = a² + 2ab + b², what is 41²? (a) 1681 (b) 1601 (c) 1521 (d) 1691
  23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/12 (c) 1/11 (d) 1/9
  24. 24.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  25. 25.What is the median of 38, 9, 34, 35, 31, 13 and 16? (a) 35 (b) 31 (c) 34 (d) 16
  26. 26.In which quadrant does the point (8, −5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  27. 27.What is the prime factorisation of 40? (a) 2 × 5³ (b) 2² × 5 (c) 2⁴ × 5 (d) 2³ × 5
  28. 28.A drawer has lots of green, blue and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 6 (c) 4 (d) 2
  29. 29.What is the distance between the points (8, 11) and (16, 5)? (a) 14 (b) 11 (c) 10 (d) 100
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 21° (b) 20° (c) 160° (d) 40°
  31. 31.In a class of 38 children, 28 like dance, 13 like music and 10 like both. How many like only dance? (a) 18 (b) 28 (c) 3 (d) 25
  32. 32.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 47 (c) 300 (d) 576
  33. 33.How many factors does 115 have? (a) 2 (b) 3 (c) 4 (d) 5
  34. 34.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 4 times (d) 8 times
  35. 35.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  36. 36.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 132 (c) 144 (d) 78
  37. 37.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 10 (b) 33 (c) 90 (d) 30
  38. 38.What is the product of the roots of x² − 10x + 21 = 0? (a) 21 (b) 20 (c) 22 (d) 10
  39. 39.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/2 (c) 1/6 (d) 2/3
  40. 40.A drawer has lots of blue and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 3 (c) 2 (d) 5

Answer key

  1. 5
  2. 35
  3. 112
  4. 45
  5. 9216
  6. (x + 6)(x + 8)
  7. 15
  8. 1386 sq cm
  9. 1
  10. 3916
  11. 125°
  12. 288 cu cm
  13. 12
  14. (x + 3)(x + 4)
  15. 36
  16. 21
  17. 7
  18. 6 and 8
  19. 98
  20. 25
  21. 17
  22. 1681
  23. 1/12
  24. 5
  25. 31
  26. Fourth quadrant
  27. 2³ × 5
  28. 4
  29. 10
  30. 20°
  31. 18
  32. 576
  33. 4
  34. 16 times
  35. 15
  36. 66
  37. 30
  38. 21
  39. 1/2
  40. 3

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