Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 584 · 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 drawer has lots of red and blue 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) 2 (c) 3 (d) 5
2. 2.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 1/8 (c) 1/4 (d) 7/8
3. 3.If a + b = 14 and ab = 48, what is (a − b)²? (a) 196 (b) 2 (c) 100 (d) 4
4. 4.What is the median of 36, 29, 14, 22, 3, 11 and 13? (a) 22 (b) 13 (c) 15 (d) 14
5. 5.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 65° (c) 40° (d) 50°
6. 6.In a class of 35 children, 20 like dance, 22 like music and 8 like both. How many like neither? (a) 2 (b) 1 (c) 9 (d) 8
7. 7.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 155° (c) 65° (d) 25°
8. 8.A drawer has lots of red, black, blue, green 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) 2 (b) 6 (c) 10 (d) 5
9. 9.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 49 (c) 21 (d) 42
10. 10.A bag has 8 green, 5 yellow and 3 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/3 (b) 1/2 (c) 9/16 (d) 1/16
11. 11.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 30 cu cm (c) 400 cu cm (d) 600 cu cm
12. 12.What is the midpoint of the line joining (1, 7) and (3, 11)? (a) (9, 2) (b) (1, 2) (c) (2, 9) (d) (4, 18)
13. 13.7 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 56 (b) 98 (c) 49 (d) 14
14. 14.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) 13 (b) 12 (c) 25 (d) 24
15. 15.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 169 (c) 91 (d) 156
16. 16.What is the distance between the points (8, 11) and (32, 4)? (a) 25 (b) 625 (c) 31 (d) 26
17. 17.What is the distance between the points (1, 3) and (25, 10)? (a) 25 (b) 31 (c) 26 (d) 625
18. 18.What is the mean of 16, 6, 7, 15, 11 and 5? (a) 9 (b) 12 (c) 11 (d) 10
19. 19.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
20. 20.A drawer has lots of blue, black, red 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) 8 (c) 2 (d) 4
21. 21.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 302 (b) 297 (c) 594 (d) 52
22. 22.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 20 (c) 240 (d) 25
23. 23.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 20 (b) 150 (c) 84 (d) 75
24. 24.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 46° (c) 55° (d) 90°
25. 25.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 120° (b) 150° (c) 300° (d) 30°
26. 26.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 115° (c) 130° (d) 66°
27. 27.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 3/11 (c) 1/11 (d) 1/9
28. 28.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 51° (b) 130° (c) 50° (d) 230°
29. 29.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 440 cm (d) 110 cm
30. 30.In a class of 35 children, 19 like cricket, 15 like football and 5 like both. How many like at least one of the two? (a) 29 (b) 34 (c) 35 (d) 24
31. 31.If a + b = 15 and ab = 56, what is (a − b)²? (a) 113 (b) 169 (c) 225 (d) 1
32. 32.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 5/8 (c) 1/4 (d) 3/8
33. 33.In a class of 36 children, 10 like cricket, 20 like football and 10 like neither. How many like both? (a) 26 (b) 5 (c) 4 (d) 10
34. 34.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/36 (c) 1/11 (d) 1/18
35. 35.In which quadrant does the point (5, 3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
36. 36.A drawer has lots of red 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) 4 (b) 2 (c) 3 (d) 5
37. 37.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 1386 cm (d) 264 cm
38. 38.In a class of 25 children, 19 like tea, 14 like coffee and 11 like both. How many like only tea? (a) 11 (b) 19 (c) 3 (d) 8
39. 39.In which quadrant does the point (−2, −9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
40. 40.In a class of 31 children, 18 like maths, 15 like science and 10 like both. How many like neither? (a) 18 (b) 9 (c) 8 (d) 10

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