Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 567 · 40 questions

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.

1. 1.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
2. 2.In a class of 43 children, 20 like dance, 21 like music and 4 like both. How many like neither? (a) 10 (b) 4 (c) 2 (d) 6
3. 3.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 51° (b) 130° (c) 230° (d) 50°
4. 4.The mean of 6 numbers is 32. When the number 39 is added to them, what is the new mean? (a) 32 (b) 33 (c) 35 (d) 34
5. 5.Two angles of a triangle are 50° and 70°. What is the third angle? (a) 130° (b) 60° (c) 120° (d) 110°
6. 6.A drawer has lots of red, green 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) 4 (c) 3 (d) 6
7. 7.A bag has 2 red, 3 yellow and 3 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 7/8 (c) 3/4 (d) 1/4
8. 8.What is the smallest prime factor of 299? (a) 2 (b) 1 (c) 23 (d) 13
9. 9.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm
10. 10.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 100° (b) 80° (c) 150° (d) 110°
11. 11.What is the product of the roots of x² − 12x + 32 = 0? (a) 12 (b) 33 (c) 31 (d) 32
12. 12.A cuboid is 11 cm long, 6 cm wide and 6 cm high. What is its volume? (a) 23 cu cm (b) 336 cu cm (c) 66 cu cm (d) 396 cu cm
13. 13.What is the mode of 11, 5, 5, 2, 17, 17 and 17? (a) 5 (b) 2 (c) 11 (d) 17
14. 14.In a class of 38 children, 24 like tea, 20 like coffee and 9 like both. How many like at least one of the two? (a) 38 (b) 44 (c) 26 (d) 35
15. 15.A bag has 10 blue balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 14 (b) 2 (c) 5 (d) 11
16. 16.What is the smallest prime factor of 377? (a) 1 (b) 29 (c) 2 (d) 13
17. 17.How many factors does 34 have? (a) 4 (b) 3 (c) 5 (d) 2
18. 18.Two angles of a triangle are 35° and 85°. What is the third angle? (a) 60° (b) 95° (c) 145° (d) 120°
19. 19.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 616 cm (d) 44 cm
20. 20.A drawer has lots of red and white 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) 2 (c) 5 (d) 4
21. 21.In a class of 33 children, 6 like maths, 21 like science and 9 like neither. How many like both? (a) 4 (b) 24 (c) 9 (d) 3
22. 22.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 20 (b) 70 (c) 140 (d) 73
23. 23.What is the 13th term of the AP 2, 6, 10, 14, …? (a) 50 (b) 48 (c) 52 (d) 54
24. 24.In which quadrant does the point (7, −3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 17 (b) 18 (c) 7 (d) 19
26. 26.What is the median of 21, 35, 10, 15 and 8? (a) 15 (b) 16 (c) 10 (d) 21
27. 27.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 70° (c) 140° (d) 40°
28. 28.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
29. 29.What is the smallest prime factor of 209? (a) 1 (b) 11 (c) 2 (d) 19
30. 30.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/2 (c) 1/3 (d) 1/4
31. 31.A bag has 12 yellow balls and 3 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) 4 (c) 13 (d) 15
32. 32.Using (a − b)² = a² − 2ab + b², what is 87²? (a) 8649 (b) 8091 (c) 7569 (d) 7579
33. 33.A bag has 12 yellow balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 20 (c) 14 (d) 13
34. 34.What is the mean of 5, 14, 15 and 2? (a) 8 (b) 9 (c) 10 (d) 12
35. 35.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
36. 36.There are 8 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 48 (b) 80 (c) 13 (d) 40
37. 37.What is the mode of 9, 9, 15, 15, 18, 14 and 9? (a) 18 (b) 15 (c) 9 (d) 14
38. 38.In a class of 39 children, 25 like tea, 17 like coffee and 3 like neither. How many like both? (a) 36 (b) 3 (c) 7 (d) 6
39. 39.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) 33 (b) 90 (c) 10 (d) 30
40. 40.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 90° (b) 45° (c) 46° (d) 135°

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