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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 76 · 40 questions
TalentJR

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.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 170° (c) 86° (d) 95°
  2. 2.In a class of 46 children, 25 like dance, 25 like music and 5 like both. How many like only dance? (a) 20 (b) 5 (c) 25 (d) 21
  3. 3.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 10 (d) 8
  4. 4.What is the mode of 6, 6, 10, 19, 6, 15 and 15? (a) 15 (b) 19 (c) 6 (d) 10
  5. 5.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 80° (b) 120° (c) 100° (d) 160°
  6. 6.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 25° (c) 130° (d) 155°
  7. 7.The mean of 5 numbers is 31. When the number 25 is added to them, what is the new mean? (a) 30 (b) 29 (c) 31 (d) 28
  8. 8.What is the product of the roots of x² − 15x + 56 = 0? (a) 15 (b) 56 (c) 57 (d) 55
  9. 9.What is the distance between the points (1, 2) and (10, 14)? (a) 21 (b) 225 (c) 15 (d) 16
  10. 10.What is the 38th term of the AP 9, 15, 21, 27, …? (a) 228 (b) 222 (c) 237 (d) 231
  11. 11.In a class of 27 children, 6 like cricket, 21 like football and 3 like neither. How many like both? (a) 4 (b) 2 (c) 24 (d) 3
  12. 12.A drawer has lots of black, red, white and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 4 (c) 5 (d) 2
  13. 13.What is the mean of 15, 5, 13 and 7? (a) 8 (b) 11 (c) 9 (d) 10
  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) 8 (b) 7 (c) 14 (d) 15
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 18 (b) 19 (c) 7 (d) 17
  16. 16.In a class of 38 children, 20 like maths, 15 like science and 5 like neither. How many like both? (a) 3 (b) 33 (c) 2 (d) 5
  17. 17.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
  18. 18.Which term of the AP 9, 11, 13, 15, … is 79? (a) 38th (b) 35th (c) 36th (d) 37th
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 15 (b) 16 (c) 14 (d) 4
  20. 20.What is the mode of 7, 5, 20, 6, 7, 20 and 7? (a) 5 (b) 20 (c) 6 (d) 7
  21. 21.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
  22. 22.How many prime numbers are there between 40 and 70? (a) 8 (b) 6 (c) 9 (d) 7
  23. 23.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/4 (c) 1/2 (d) 1/3
  24. 24.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 78 (c) 144 (d) 66
  25. 25.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  26. 26.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  27. 27.3 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) 7 (b) 24 (c) 15 (d) 12
  28. 28.In which quadrant does the point (9, −9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  29. 29.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 110° (c) 55° (d) 35°
  30. 30.A drawer has lots of white, blue, black 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) 8 (b) 5 (c) 4 (d) 2
  31. 31.What is the sum of the roots of x² − 16x + 63 = 0? (a) 16 (b) 63 (c) 17 (d) 15
  32. 32.How many prime numbers are there between 30 and 50? (a) 7 (b) 6 (c) 4 (d) 5
  33. 33.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
  34. 34.How many prime numbers are there between 10 and 30? (a) 7 (b) 5 (c) 6 (d) 8
  35. 35.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 15 (c) 36 (d) 30
  36. 36.A drawer has lots of 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) 4 (b) 5 (c) 3 (d) 2
  37. 37.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 22 (b) 28 (c) 29 (d) 21
  38. 38.In a class of 31 children, 5 like dance, 22 like music and 2 like both. How many like only dance? (a) 20 (b) 3 (c) 9 (d) 5
  39. 39.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
  40. 40.If a + b = 14 and ab = 33, what is (a − b)²? (a) 196 (b) 130 (c) 64 (d) 8

Answer key

  1. 85°
  2. 20
  3. 7
  4. 6
  5. 100°
  6. 130°
  7. 30
  8. 56
  9. 15
  10. 231
  11. 3
  12. 5
  13. 10
  14. 8
  15. 18
  16. 2
  17. 2464 sq cm
  18. 36th
  19. 15
  20. 7
  21. 1/2
  22. 7
  23. 1/2
  24. 66
  25. 15
  26. 120
  27. 12
  28. Fourth quadrant
  29. 110°
  30. 5
  31. 16
  32. 5
  33. 16 times
  34. 6
  35. 15
  36. 3
  37. 22
  38. 3
  39. 125 times
  40. 64

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