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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 715 · 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.How many factors does 24 have? (a) 9 (b) 8 (c) 7 (d) 6
  2. 2.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
  3. 3.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 18 (b) 140 (c) 270 (d) 135
  4. 4.What is the smallest prime factor of 35? (a) 2 (b) 5 (c) 1 (d) 7
  5. 5.A drawer has lots of green 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) 2 (b) 3 (c) 5 (d) 4
  6. 6.There are 7 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 11 (b) 35 (c) 56 (d) 28
  7. 7.What is the mode of 3, 10, 3, 3, 1, 1 and 12? (a) 10 (b) 12 (c) 3 (d) 1
  8. 8.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 55° (c) 305° (d) 125°
  9. 9.A bag has 5 yellow balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 8 (c) 2 (d) 6
  10. 10.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 70° (c) 140° (d) 50°
  11. 11.What is the smallest prime factor of 21? (a) 3 (b) 2 (c) 7 (d) 1
  12. 12.How many prime numbers are there between 10 and 40? (a) 7 (b) 10 (c) 8 (d) 9
  13. 13.What is the mode of 6, 19, 10, 1, 19, 19 and 10? (a) 6 (b) 1 (c) 19 (d) 10
  14. 14.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
  15. 15.If a + b = 4 and ab = 3, what is (a − b)²? (a) 2 (b) 16 (c) 10 (d) 4
  16. 16.A bag has 4 white balls and 8 yellow 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) 5 (c) 2 (d) 12
  17. 17.What is the distance between the points (3, 9) and (7, 6)? (a) 6 (b) 7 (c) 5 (d) 25
  18. 18.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 9 (c) 6 (d) 3
  19. 19.What is the mean of 5, 7, 15 and 21? (a) 13 (b) 16 (c) 12 (d) 11
  20. 20.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 6 cu cm (c) 8 cu cm (d) 16 cu cm
  21. 21.How many prime numbers are there between 60 and 70? (a) 3 (b) 1 (c) 4 (d) 2
  22. 22.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
  23. 23.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 42) (b) (x + 6)(x + 7) (c) (x − 6)(x − 7) (d) (x + 1)(x + 12)
  24. 24.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
  25. 25.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
  26. 26.There are 5 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 11 (b) 60 (c) 35 (d) 30
  27. 27.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) 7 (c) 8 (d) 14
  28. 28.What is the smallest prime factor of 85? (a) 2 (b) 1 (c) 17 (d) 5
  29. 29.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 135° (b) 45° (c) 136° (d) 315°
  30. 30.There are 4 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 24 (b) 7 (c) 12 (d) 16
  31. 31.What is the sum of the first 8 terms of the AP 10, 13, 16, …? (a) 328 (b) 31 (c) 164 (d) 176
  32. 32.In which quadrant does the point (5, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  33. 33.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 4 (b) 2 (c) 3 (d) 5
  35. 35.How many factors does 48 have? (a) 11 (b) 8 (c) 10 (d) 9
  36. 36.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 1/4 (c) 3/5 (d) 5/8
  37. 37.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 24 (c) 48 (d) 12
  38. 38.What is the median of 13, 5, 1, 8 and 20? (a) 5 (b) 8 (c) 13 (d) 1
  39. 39.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 49 (b) 48 (c) 37 (d) 36
  40. 40.Which term of the AP 12, 18, 24, 30, … is 60? (a) 11th (b) 10th (c) 9th (d) 8th

Answer key

  1. 8
  2. 2464 sq cm
  3. 135
  4. 5
  5. 3
  6. 28
  7. 3
  8. 125°
  9. 8
  10. 70°
  11. 3
  12. 8
  13. 19
  14. 1386 sq cm
  15. 4
  16. 9
  17. 5
  18. 6
  19. 12
  20. 8 cu cm
  21. 2
  22. 6
  23. (x + 6)(x + 7)
  24. 154 sq cm
  25. 4
  26. 30
  27. 8
  28. 5
  29. 135°
  30. 12
  31. 164
  32. First quadrant
  33. 154 sq cm
  34. 4
  35. 10
  36. 3/8
  37. 24
  38. 8
  39. 37
  40. 9th

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