Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 428 · 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 bag has 12 white balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 19 (b) 2 (c) 8 (d) 13
2. 2.Two angles of a triangle are 40° and 65°. What is the exterior angle at the third corner? (a) 75° (b) 115° (c) 140° (d) 105°
3. 3.A bag has 6 black balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 2 (c) 15 (d) 10
4. 4.In a class of 40 children, 20 like cricket, 27 like football and 12 like both. How many like neither? (a) 17 (b) 12 (c) 5 (d) 6
5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/11 (b) 1/12 (c) 1/18 (d) 1/36
6. 6.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 624 (c) 488 (d) 625
7. 7.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
8. 8.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 36 (c) 64 (d) 15
9. 9.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
10. 10.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 4 times (d) 5 times
11. 11.How many factors does 77 have? (a) 4 (b) 2 (c) 5 (d) 3
12. 12.A drawer has lots of white 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) 5 (c) 3 (d) 4
13. 13.In a class of 34 children, 10 like maths, 21 like science and 8 like neither. How many like both? (a) 5 (b) 26 (c) 6 (d) 8
14. 14.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 225 (c) 210 (d) 105
15. 15.If a + b = 7 and ab = 10, what is a² + b²? (a) 29 (b) 39 (c) 69 (d) 49
16. 16.What is the median of 1, 16, 4, 39 and 9? (a) 16 (b) 10 (c) 9 (d) 4
17. 17.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/8 (c) 7/8 (d) 1/7
18. 18.What is the median of 38, 21, 19, 27 and 7? (a) 19 (b) 27 (c) 21 (d) 22
19. 19.In a class of 36 children, 16 like cricket, 27 like football and 1 like neither. How many like both? (a) 1 (b) 35 (c) 7 (d) 8
20. 20.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 9856 sq cm
21. 21.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
22. 22.How many factors does 103 have? (a) 4 (b) 1 (c) 2 (d) 3
23. 23.In a class of 42 children, 17 like mangoes, 22 like bananas and 8 like neither. How many like both? (a) 6 (b) 34 (c) 8 (d) 5
24. 24.A bag has 3 red balls and 7 white 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) 8 (c) 4 (d) 10
25. 25.What is the midpoint of the line joining (1, 10) and (9, 22)? (a) (16, 5) (b) (10, 32) (c) (5, 16) (d) (4, 6)
26. 26.The mean of 6 numbers is 13. When the number 20 is added to them, what is the new mean? (a) 13 (b) 16 (c) 15 (d) 14
27. 27.What is the 16th term of the AP 5, 13, 21, 29, …? (a) 133 (b) 120 (c) 128 (d) 125
28. 28.In a class of 31 children, 18 like tea, 16 like coffee and 5 like neither. How many like both? (a) 3 (b) 26 (c) 5 (d) 8
29. 29.What is the mean of 15, 16, 6, 10 and 3? (a) 9 (b) 12 (c) 10 (d) 11
30. 30.What is the mean of 20, 11, 3 and 10? (a) 10 (b) 13 (c) 12 (d) 11
31. 31.In a class of 15 children, 9 like mangoes, 6 like bananas and 2 like neither. How many like both? (a) 3 (b) 13 (c) 1 (d) 2
32. 32.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 5 times (c) 8 times (d) 4 times
33. 33.In a class of 36 children, 28 like mangoes, 19 like bananas and 12 like both. How many like only mangoes? (a) 17 (b) 28 (c) 16 (d) 7
34. 34.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 56 (c) 36 (d) 64
35. 35.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 162 (c) 54 (d) 57
36. 36.Two angles of a triangle are 80° and 50°. What is the third angle? (a) 130° (b) 100° (c) 230° (d) 50°
37. 37.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 189 (c) 66 (d) 21
38. 38.Two angles of a triangle are 20° and 125°. What is the exterior angle at the third corner? (a) 35° (b) 145° (c) 55° (d) 160°
39. 39.A cuboid is 5 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 13 cu cm (b) 75 cu cm (c) 110 cu cm (d) 15 cu cm
40. 40.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 40° (c) 50° (d) 100°

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