Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 985 · 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.Two angles of a triangle are 65° and 45°. What is the exterior angle at the third corner? (a) 70° (b) 135° (c) 110° (d) 115°
2. 2.What is the distance between the points (5, 5) and (10, 17)? (a) 17 (b) 13 (c) 169 (d) 14
3. 3.A bag has 7 red balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 12 (c) 8 (d) 9
4. 4.A drawer has lots of white, blue 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) 3 (b) 2 (c) 4 (d) 6
5. 5.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 379 (b) 378 (c) 369 (d) 324
6. 6.What is the sum of the roots of x² − 12x + 27 = 0? (a) 11 (b) 12 (c) 13 (d) 27
7. 7.What is the midpoint of the line joining (2, 1) and (12, 3)? (a) (14, 4) (b) (2, 7) (c) (7, 2) (d) (5, 1)
8. 8.A drawer has lots of red, black, white, blue and yellow 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) 2 (c) 5 (d) 6
9. 9.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 11 (d) 10
10. 10.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 20° (c) 10° (d) 11°
11. 11.Using (a − b)² = a² − 2ab + b², what is 96²? (a) 9984 (b) 9216 (c) 9226 (d) 10816
12. 12.There are 7 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) 84 (b) 13 (c) 49 (d) 42
13. 13.What is the 22nd term of the AP 15, 24, 33, 42, …? (a) 204 (b) 189 (c) 198 (d) 213
14. 14.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 35° (c) 125° (d) 70°
15. 15.The mean of 6 numbers is 13. When the number 6 is added to them, what is the new mean? (a) 12 (b) 13 (c) 14 (d) 11
16. 16.A bag has 5 black balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 14 (b) 6 (c) 2 (d) 7
17. 17.What is the mean of 16, 9, 3, 3, 9 and 8? (a) 9 (b) 10 (c) 7 (d) 8
18. 18.What is the mean of 3, 16, 10, 4, 3 and 12? (a) 10 (b) 7 (c) 9 (d) 8
19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 65? (a) 6 (b) 17 (c) 16 (d) 18
20. 20.A drawer has lots of blue 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) 4 (b) 5 (c) 3 (d) 2
21. 21.In which quadrant does the point (8, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
22. 22.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 12 (c) 8 (d) 6
23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/18 (c) 1/12 (d) 1/11
24. 24.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 45 (c) 90 (d) 100
25. 25.A bag has 8 blue, 4 red and 7 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/3 (b) 7/12 (c) 12/19 (d) 7/19
26. 26.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 66 (d) 121
27. 27.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 46 (b) 572 (c) 286 (d) 308
28. 28.How many factors does 117 have? (a) 4 (b) 5 (c) 7 (d) 6
29. 29.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
30. 30.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 25° (b) 150° (c) 155° (d) 55°
31. 31.A bag has 8 black balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 9 (b) 11 (c) 2 (d) 10
32. 32.A drawer has lots of blue, red, yellow, 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) 5 (b) 6 (c) 2 (d) 10
33. 33.If a + b = 13 and ab = 40, what is a² + b²? (a) 249 (b) 129 (c) 89 (d) 169
34. 34.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
35. 35.In which quadrant does the point (5, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
36. 36.In a class of 32 children, 16 like mangoes, 22 like bananas and 7 like both. How many like neither? (a) 1 (b) 2 (c) 8 (d) 7
37. 37.In a class of 42 children, 21 like tea, 27 like coffee and 5 like neither. How many like both? (a) 37 (b) 6 (c) 11 (d) 5
38. 38.In a class of 18 children, 13 like dance, 10 like music and 7 like both. How many like only dance? (a) 3 (b) 8 (c) 6 (d) 13
39. 39.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 160° (b) 20° (c) 200° (d) 21°
40. 40.In a class of 14 children, 8 like cricket, 6 like football and 2 like neither. How many like both? (a) 1 (b) 3 (c) 2 (d) 12

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