Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 690 · 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 straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 110° (b) 70° (c) 140° (d) 71°
2. 2.What is the sum of the roots of x² − 6x + 8 = 0? (a) 7 (b) 5 (c) 8 (d) 6
3. 3.In a class of 22 children, 15 like tea, 7 like coffee and 2 like both. How many like at least one of the two? (a) 22 (b) 18 (c) 20 (d) 21
4. 4.How many prime numbers are there between 20 and 50? (a) 6 (b) 7 (c) 8 (d) 9
5. 5.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
6. 6.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
7. 7.A bag has 10 red balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 12 (c) 20 (d) 11
8. 8.There are 3 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 24 (b) 15 (c) 7 (d) 12
9. 9.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
10. 10.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 1/3 (c) 2/3 (d) 1/2
11. 11.What is the sum of all the whole numbers from 1 to 26? (a) 702 (b) 338 (c) 351 (d) 325
12. 12.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 324 (b) 162 (c) 171 (d) 26
13. 13.If a + b = 13 and ab = 36, what is (a − b)²? (a) 97 (b) 169 (c) 5 (d) 25
14. 14.In which quadrant does the point (−1, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
15. 15.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 546 (c) 556 (d) 555
16. 16.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 1/3 (c) 3/4 (d) 1/4
17. 17.What is the distance between the points (2, 16) and (10, 1)? (a) 18 (b) 289 (c) 23 (d) 17
18. 18.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 50° (c) 40° (d) 100°
19. 19.A bag has 8 blue, 2 yellow and 3 green balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 11/13 (b) 2/11 (c) 1/3 (d) 2/13
20. 20.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 96 cu cm (d) 64 cu cm
21. 21.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/8 (b) 7/8 (c) 1/4 (d) 3/8
22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 56? (a) 7 (b) 6 (c) 5 (d) 4
23. 23.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
24. 24.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 12 (c) 30 (d) 15
25. 25.In a class of 21 children, 12 like tea, 9 like coffee and 2 like both. How many like neither? (a) 2 (b) 0 (c) 3 (d) 4
26. 26.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 12 (b) 13 (c) 25 (d) 24
27. 27.What is the midpoint of the line joining (6, 0) and (16, 8)? (a) (11, 4) (b) (4, 11) (c) (5, 4) (d) (22, 8)
28. 28.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 1/3 (b) 5/6 (c) 2/3 (d) 1/4
29. 29.What is the mean of 15, 6, 19 and 20? (a) 12 (b) 16 (c) 15 (d) 20
30. 30.In a class of 41 children, 19 like mangoes, 20 like bananas and 7 like both. How many like at least one of the two? (a) 25 (b) 39 (c) 41 (d) 32
31. 31.The mean of 9 numbers is 37. When the number 27 is added to them, what is the new mean? (a) 36 (b) 32 (c) 35 (d) 37
32. 32.Using (a + b)² = a² + 2ab + b², what is 102²? (a) 10004 (b) 10404 (c) 9604 (d) 10414
33. 33.How many factors does 25 have? (a) 3 (b) 2 (c) 1 (d) 4
34. 34.Two angles of a triangle are 35° and 100°. What is the third angle? (a) 80° (b) 145° (c) 135° (d) 45°
35. 35.Using (a − b)² = a² − 2ab + b², what is 86²? (a) 8084 (b) 7406 (c) 8836 (d) 7396
36. 36.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 135° (b) 46° (c) 45° (d) 90°
37. 37.In a class of 43 children, 20 like mangoes, 22 like bananas and 9 like both. How many like only mangoes? (a) 21 (b) 13 (c) 20 (d) 11
38. 38.What is the product of the roots of x² − 11x + 24 = 0? (a) 11 (b) 25 (c) 24 (d) 23
39. 39.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/11 (b) 3/11 (c) 1/9 (d) 1/12
40. 40.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/36 (c) 1/12 (d) 1/18

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