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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 333 · 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.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 9 (d) 12
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 6 (b) 17 (c) 18 (d) 16
  3. 3.What is the mode of 3, 18, 16, 1, 18, 18 and 3? (a) 3 (b) 1 (c) 18 (d) 16
  4. 4.What is the median of 31, 28, 6, 11, 21, 32 and 1? (a) 22 (b) 11 (c) 28 (d) 21
  5. 5.What is the median of 18, 14, 9, 21, 8, 23 and 16? (a) 18 (b) 14 (c) 16 (d) 21
  6. 6.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 55° (b) 150° (c) 155° (d) 25°
  7. 7.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  8. 8.In which quadrant does the point (3, 8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  9. 9.A bag has 7 red, 8 green and 8 white balls. One ball is taken out without looking. What is the probability that it is not green? (a) 16/23 (b) 1/3 (c) 8/23 (d) 15/23
  10. 10.What is the midpoint of the line joining (5, 10) and (7, 16)? (a) (13, 6) (b) (12, 26) (c) (1, 3) (d) (6, 13)
  11. 11.What is the distance between the points (9, 4) and (15, 12)? (a) 100 (b) 10 (c) 14 (d) 11
  12. 12.What is the 17th term of the AP 12, 21, 30, 39, …? (a) 165 (b) 144 (c) 156 (d) 153
  13. 13.A cuboid is 6 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 120 sq cm (b) 184 sq cm (c) 368 sq cm (d) 92 sq cm
  14. 14.A bag has 8 green balls and 9 red 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) 10 (c) 17 (d) 2
  15. 15.A bag has 8 green balls and 11 red 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) 12 (c) 2 (d) 19
  16. 16.Using (a − b)² = a² − 2ab + b², what is 69²? (a) 4899 (b) 5041 (c) 4771 (d) 4761
  17. 17.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 726 cu cm (c) 1331 cu cm (d) 484 cu cm
  18. 18.A canteen sells 6 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 13 (c) 42 (d) 84
  19. 19.Which is the correct factorisation of x² + 12x + 32? (a) (x − 4)(x − 8) (b) (x + 1)(x + 32) (c) (x + 1)(x + 11) (d) (x + 4)(x + 8)
  20. 20.If a + b = 7 and ab = 10, what is (a − b)²? (a) 9 (b) 49 (c) 3 (d) 29
  21. 21.Which term of the AP 6, 8, 10, 12, … is 22? (a) 11th (b) 9th (c) 8th (d) 10th
  22. 22.A drawer has lots of white, blue, yellow 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) 8 (b) 4 (c) 5 (d) 2
  23. 23.In which quadrant does the point (2, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  24. 24.What is the distance between the points (6, 13) and (14, 7)? (a) 10 (b) 100 (c) 14 (d) 11
  25. 25.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 3 (d) 18
  26. 26.A bag has 5 red, 7 green and 8 blue balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 3/4 (c) 1/4 (d) 3/10
  27. 27.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/18 (b) 1/11 (c) 2/11 (d) 1/12
  28. 28.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) 25 (b) 24 (c) 36 (d) 37
  29. 29.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 120 (c) 240 (d) 20
  30. 30.What is the mean of 7, 17, 7, 15 and 9? (a) 11 (b) 13 (c) 10 (d) 12
  31. 31.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 182 (c) 91 (d) 25
  32. 32.What is the smallest prime factor of 69? (a) 23 (b) 2 (c) 1 (d) 3
  33. 33.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) 14 (d) 8
  34. 34.What is the median of 20, 13, 30, 19, 35, 5 and 36? (a) 21 (b) 20 (c) 30 (d) 19
  35. 35.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 70° (c) 110° (d) 45°
  36. 36.What is the mean of 4, 17, 11 and 4? (a) 8 (b) 12 (c) 10 (d) 9
  37. 37.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
  38. 38.In a class of 31 children, 25 like dance, 14 like music and 1 like neither. How many like both? (a) 30 (b) 9 (c) 8 (d) 1
  39. 39.5 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) 12 (b) 40 (c) 35 (d) 70
  40. 40.The mean of 4 numbers is 35. When the number 50 is added to them, what is the new mean? (a) 35 (b) 37 (c) 38 (d) 39

Answer key

  1. 6
  2. 17
  3. 18
  4. 21
  5. 16
  6. 25°
  7. 13
  8. First quadrant
  9. 15/23
  10. (6, 13)
  11. 10
  12. 156
  13. 184 sq cm
  14. 10
  15. 12
  16. 4761
  17. 1331 cu cm
  18. 42
  19. (x + 4)(x + 8)
  20. 9
  21. 9th
  22. 5
  23. First quadrant
  24. 10
  25. 2
  26. 1/4
  27. 1/18
  28. 25
  29. 120
  30. 11
  31. 169
  32. 3
  33. 8
  34. 20
  35. 35°
  36. 9
  37. 1386 sq cm
  38. 9
  39. 35
  40. 38

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