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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 98 · 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.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
  2. 2.In a class of 34 children, 18 like maths, 14 like science and 4 like both. How many like only maths? (a) 14 (b) 18 (c) 20 (d) 10
  3. 3.What is the smallest prime factor of 247? (a) 1 (b) 19 (c) 2 (d) 13
  4. 4.What is the smallest prime factor of 299? (a) 23 (b) 2 (c) 1 (d) 13
  5. 5.What is the median of 25, 34, 7, 1 and 24? (a) 7 (b) 23 (c) 25 (d) 24
  6. 6.What is the midpoint of the line joining (2, 14) and (4, 10)? (a) (1, 2) (b) (12, 3) (c) (3, 12) (d) (6, 24)
  7. 7.Which is the correct factorisation of x² + 5x + 6? (a) (x − 2)(x − 3) (b) (x + 2)(x + 3) (c) (x + 1)(x + 4) (d) (x + 1)(x + 6)
  8. 8.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 15 (b) 184 (c) 96 (d) 92
  9. 9.In a class of 31 children, 17 like mangoes, 16 like bananas and 12 like both. How many like neither? (a) 22 (b) 10 (c) 11 (d) 12
  10. 10.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
  11. 11.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 135° (b) 130° (c) 85° (d) 95°
  12. 12.A drawer has lots of blue, 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) 6 (b) 2 (c) 4 (d) 3
  13. 13.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 125° (b) 35° (c) 90° (d) 145°
  14. 14.How many prime numbers are there between 90 and 100? (a) 3 (b) 1 (c) 2 (d) 0
  15. 15.7 T-shirts and 5 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) 70 (c) 35 (d) 12
  16. 16.What is the 12th term of the AP 6, 9, 12, 15, …? (a) 42 (b) 33 (c) 36 (d) 39
  17. 17.What are the roots of x² − 9x + 18 = 0? (a) 1 and 8 (b) 1 and 18 (c) 2 and 9 (d) 3 and 6
  18. 18.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 120 (c) 240 (d) 25
  19. 19.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
  20. 20.How many factors does 47 have? (a) 2 (b) 3 (c) 4 (d) 1
  21. 21.What is the mode of 9, 16, 9, 20, 20, 20 and 4? (a) 4 (b) 9 (c) 20 (d) 16
  22. 22.A drawer has lots of white 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) 3 (c) 5 (d) 2
  23. 23.What is the median of 37, 9, 34, 33 and 40? (a) 34 (b) 33 (c) 37 (d) 35
  24. 24.In a class of 45 children, 21 like cricket, 24 like football and 5 like both. How many like neither? (a) 0 (b) 5 (c) 6 (d) 10
  25. 25.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
  26. 26.If a + b = 8 and ab = 15, what is a² + b²? (a) 49 (b) 94 (c) 34 (d) 64
  27. 27.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 115° (b) 65° (c) 245° (d) 66°
  28. 28.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
  29. 29.What is the 17th term of the AP 9, 18, 27, 36, …? (a) 154 (b) 153 (c) 144 (d) 162
  30. 30.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
  31. 31.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 3 times (c) 27 times (d) 6 times
  32. 32.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) 36 (c) 37 (d) 25
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 67? (a) 15 (b) 6 (c) 16 (d) 14
  34. 34.A bag has 8 green balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 20 (b) 13 (c) 9 (d) 2
  35. 35.What is the distance between the points (6, 9) and (12, 17)? (a) 11 (b) 10 (c) 100 (d) 14
  36. 36.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 36 sq cm (c) 144 sq cm (d) 216 sq cm
  37. 37.What is the prime factorisation of 40? (a) 2² × 5 (b) 2⁴ × 5 (c) 2 × 5³ (d) 2³ × 5
  38. 38.In a class of 35 children, 21 like maths, 16 like science and 4 like both. How many like at least one of the two? (a) 29 (b) 33 (c) 35 (d) 37
  39. 39.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 9 (c) 6 (d) 12
  40. 40.Two angles of a triangle are 50° and 25°. What is the third angle? (a) 75° (b) 105° (c) 130° (d) 155°

Answer key

  1. 132 cm
  2. 14
  3. 13
  4. 13
  5. 24
  6. (3, 12)
  7. (x + 2)(x + 3)
  8. 92
  9. 10
  10. 1/3
  11. 85°
  12. 4
  13. 145°
  14. 1
  15. 35
  16. 39
  17. 3 and 6
  18. 120
  19. 1/3
  20. 2
  21. 20
  22. 3
  23. 34
  24. 5
  25. 88 cm
  26. 34
  27. 65°
  28. 616 sq cm
  29. 153
  30. 220 cm
  31. 27 times
  32. 25
  33. 15
  34. 13
  35. 10
  36. 216 sq cm
  37. 2³ × 5
  38. 33
  39. 6
  40. 105°

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