Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 823 · 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. 1.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 36 (c) 21 (d) 30
2. 2.What is the median of 10, 3, 19, 13, 7, 12 and 22? (a) 10 (b) 12 (c) 13 (d) 11
3. 3.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 5 times (d) 125 times
4. 4.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
5. 5.Using (a + b)² = a² + 2ab + b², what is 53²? (a) 2209 (b) 2809 (c) 2509 (d) 2819
6. 6.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
7. 7.In a class of 45 children, 26 like tea, 27 like coffee and 2 like neither. How many like both? (a) 2 (b) 10 (c) 43 (d) 8
8. 8.Using (a − b)² = a² − 2ab + b², what is 46²? (a) 2126 (b) 2484 (c) 2916 (d) 2116
9. 9.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
10. 10.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 1/12 (c) 1/18 (d) 2/11
11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/36 (b) 1/11 (c) 5/11 (d) 1/6
12. 12.A bag has 7 black balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 16 (b) 8 (c) 9 (d) 2
13. 13.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
14. 14.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 110° (b) 160° (c) 70° (d) 130°
15. 15.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 416 (b) 516 (c) 507 (d) 517
16. 16.In a class of 38 children, 13 like cricket, 21 like football and 2 like both. How many like at least one of the two? (a) 38 (b) 30 (c) 34 (d) 32
17. 17.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) 37 (c) 24 (d) 36
18. 18.A bag has 5 red balls and 6 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) 11 (c) 6 (d) 2
19. 19.A bag has 4 blue balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 5 (b) 12 (c) 2 (d) 6
20. 20.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 25 (c) 30 (d) 9
21. 21.What is the sum of the roots of x² − 17x + 72 = 0? (a) 18 (b) 16 (c) 72 (d) 17
22. 22.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/3 (c) 2/3 (d) 1/2
23. 23.What is the median of 13, 33, 26, 19 and 21? (a) 19 (b) 21 (c) 22 (d) 26
24. 24.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 15° (c) 30° (d) 150°
25. 25.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
26. 26.There are 5 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 60 (b) 30 (c) 11 (d) 35
27. 27.What is the midpoint of the line joining (8, 0) and (12, 4)? (a) (20, 4) (b) (2, 10) (c) (10, 2) (d) (2, 2)
28. 28.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
29. 29.What is the 12th term of the AP 17, 25, 33, 41, …? (a) 88 (b) 105 (c) 96 (d) 113
30. 30.What is the distance between the points (4, 0) and (12, 6)? (a) 14 (b) 10 (c) 100 (d) 11
31. 31.A bag has 6 white balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 12 (b) 2 (c) 7 (d) 8
32. 32.A canteen sells 8 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 56 (c) 64 (d) 112
33. 33.What is the midpoint of the line joining (0, 3) and (2, 9)? (a) (1, 6) (b) (6, 1) (c) (2, 12) (d) (1, 3)
34. 34.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
35. 35.Using (a − b)² = a² − 2ab + b², what is 99²? (a) 9811 (b) 9801 (c) 9999 (d) 10201
36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 3 (b) 2 (c) 5 (d) 4
37. 37.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
38. 38.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 282 (c) 306 (d) 316
39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 7 (b) 5 (c) 4 (d) 6
40. 40.In which quadrant does the point (−3, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant

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