Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 236 · 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.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 91 (c) 182 (d) 196
2. 2.What is the distance between the points (1, 3) and (7, 11)? (a) 11 (b) 100 (c) 10 (d) 14
3. 3.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 56 (b) 580 (c) 290 (d) 320
4. 4.How many factors does 82 have? (a) 5 (b) 2 (c) 3 (d) 4
5. 5.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
6. 6.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 72 (c) 36 (d) 81
7. 7.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 468 (c) 477 (d) 478
8. 8.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 378 (c) 53 (d) 729
9. 9.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
10. 10.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 35° (c) 145° (d) 115°
11. 11.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 3850 cm (d) 440 cm
12. 12.Using (a + b)² = a² + 2ab + b², what is 72²? (a) 5194 (b) 5184 (c) 4624 (d) 4904
13. 13.A bag has 3 red, 7 white and 8 green balls. One ball is taken out without looking. What is the probability that it is not red? (a) 8/9 (b) 1/3 (c) 1/6 (d) 5/6
14. 14.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
15. 15.A bag has 3 white balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 4 (b) 2 (c) 5 (d) 12
16. 16.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
17. 17.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
18. 18.Two angles of a triangle are 75° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 150° (c) 30° (d) 210°
19. 19.A canteen sells 5 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 50 (b) 10 (c) 30 (d) 25
20. 20.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 29 (b) 28 (c) 21 (d) 22
21. 21.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 80° (b) 81° (c) 160° (d) 100°
22. 22.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 155° (b) 130° (c) 310° (d) 25°
23. 23.How many factors does 64 have? (a) 6 (b) 7 (c) 5 (d) 8
24. 24.If a + b = 13 and ab = 42, what is (a − b)²? (a) 169 (b) 85 (c) 127 (d) 1
25. 25.4 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 7 (b) 16 (c) 24 (d) 12
26. 26.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 283 (c) 260 (d) 282
27. 27.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
28. 28.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 36 (c) 28 (d) 56
29. 29.A drawer has lots of yellow and green 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) 2 (c) 3 (d) 4
30. 30.What are the roots of x² − 10x + 24 = 0? (a) 4 and 6 (b) 1 and 24 (c) 1 and 9 (d) 2 and 12
31. 31.In a class of 30 children, 15 like maths, 22 like science and 2 like neither. How many like both? (a) 9 (b) 7 (c) 28 (d) 2
32. 32.A bag has 2 green, 2 red and 9 yellow balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 4/13 (b) 1/3 (c) 10/13 (d) 9/13
33. 33.Using (a + b)² = a² + 2ab + b², what is 52²? (a) 2704 (b) 2304 (c) 2714 (d) 2504
34. 34.What is the 27th term of the AP 13, 15, 17, 19, …? (a) 65 (b) 54 (c) 52 (d) 67
35. 35.How many factors does 120 have? (a) 17 (b) 15 (c) 16 (d) 14
36. 36.There are 4 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) 24 (b) 20 (c) 40 (d) 9
37. 37.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 90 (c) 100 (d) 45
38. 38.What is the distance between the points (1, 6) and (13, 11)? (a) 14 (b) 169 (c) 17 (d) 13
39. 39.In which quadrant does the point (6, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
40. 40.There are 5 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 40 (c) 70 (d) 35

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