Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 795 · 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.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 19 (b) 17 (c) 7 (d) 18
2. 2.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 308 sq cm
3. 3.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 1/3 (c) 3/4 (d) 1/4
4. 4.What is the median of 25, 8, 7, 24 and 30? (a) 8 (b) 24 (c) 25 (d) 7
5. 5.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 7 (b) 24 (c) 63 (d) 21
6. 6.In a class of 39 children, 12 like tea, 23 like coffee and 4 like both. How many like neither? (a) 4 (b) 9 (c) 8 (d) 12
7. 7.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
8. 8.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 240° (b) 61° (c) 60° (d) 120°
9. 9.In a class of 29 children, 10 like maths, 23 like science and 1 like neither. How many like both? (a) 28 (b) 5 (c) 1 (d) 4
10. 10.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 140° (b) 80° (c) 120° (d) 100°
11. 11.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 60° (c) 150° (d) 75°
12. 12.In a class of 33 children, 17 like cricket, 16 like football and 10 like both. How many like neither? (a) 20 (b) 11 (c) 0 (d) 10
13. 13.How many factors does 106 have? (a) 5 (b) 3 (c) 2 (d) 4
14. 14.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 110° (c) 70° (d) 130°
15. 15.What is the distance between the points (8, 7) and (12, 4)? (a) 6 (b) 25 (c) 7 (d) 5
16. 16.A drawer has lots of blue, green 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) 2 (b) 6 (c) 3 (d) 4
17. 17.A bag has 5 white, 4 blue and 4 yellow balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 4/9 (b) 4/13 (c) 1/3 (d) 9/13
18. 18.What is the mean of 6, 19, 20, 13 and 12? (a) 16 (b) 14 (c) 15 (d) 13
19. 19.Which is the correct factorisation of x² + 11x + 18? (a) (x + 1)(x + 10) (b) (x + 1)(x + 18) (c) (x − 2)(x − 9) (d) (x + 2)(x + 9)
20. 20.Which term of the AP 3, 9, 15, 21, … is 51? (a) 10th (b) 9th (c) 11th (d) 8th
21. 21.What is the distance between the points (1, 8) and (13, 3)? (a) 14 (b) 17 (c) 13 (d) 169
22. 22.A bag has 3 green balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 4 (c) 2 (d) 11
23. 23.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
24. 24.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/8 (c) 3/4 (d) 3/8
25. 25.A bag has 6 blue balls and 8 red 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) 7 (c) 2 (d) 9
26. 26.A drawer has lots of green, black, red, yellow and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 6 (c) 5 (d) 2
27. 27.What is the sum of all the whole numbers from 1 to 13? (a) 78 (b) 92 (c) 182 (d) 91
28. 28.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 21 (c) 18 (d) 6
29. 29.The mean of 8 numbers is 21. When the number 3 is added to them, what is the new mean? (a) 12 (b) 21 (c) 20 (d) 19
30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 67? (a) 16 (b) 14 (c) 6 (d) 15
31. 31.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
32. 32.Two angles of a triangle are 60° and 35°. What is the third angle? (a) 95° (b) 85° (c) 145° (d) 120°
33. 33.Two angles of a triangle are 40° and 75°. What is the third angle? (a) 115° (b) 140° (c) 65° (d) 105°
34. 34.A drawer has lots of white and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 3 (c) 4 (d) 2
35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 21 (b) 9 (c) 19 (d) 20
36. 36.A bag has 3 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) 2 (b) 11 (c) 4 (d) 9
37. 37.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 1/11 (c) 7/36 (d) 1/6
38. 38.What is the distance between the points (0, 5) and (5, 17)? (a) 13 (b) 169 (c) 14 (d) 17
39. 39.How many prime numbers are there between 50 and 60? (a) 2 (b) 4 (c) 1 (d) 3
40. 40.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 5/6 (c) 1/3 (d) 2/3

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