Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 351 · 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 dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/36 (b) 5/11 (c) 1/6 (d) 1/11
2. 2.In a class of 48 children, 24 like dance, 25 like music and 9 like both. How many like only dance? (a) 16 (b) 24 (c) 23 (d) 15
3. 3.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 40° (b) 20° (c) 21° (d) 160°
4. 4.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 121 (c) 110 (d) 55
5. 5.A bag has 9 white balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 20 (b) 10 (c) 11 (d) 2
6. 6.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 40° (b) 130° (c) 50° (d) 310°
7. 7.In a class of 32 children, 24 like tea, 10 like coffee and 4 like both. How many like at least one of the two? (a) 34 (b) 26 (c) 32 (d) 30
8. 8.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 12 (c) 48 (d) 24
9. 9.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 4 (d) 2
10. 10.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
11. 11.What is the median of 31, 20, 22, 26, 35, 9 and 39? (a) 27 (b) 31 (c) 22 (d) 26
12. 12.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
13. 13.In a class of 36 children, 21 like cricket, 12 like football and 4 like both. How many like at least one of the two? (a) 29 (b) 33 (c) 25 (d) 36
14. 14.A bag has 9 white balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 10 (c) 19 (d) 11
15. 15.What is the distance between the points (9, 4) and (21, 20)? (a) 21 (b) 20 (c) 28 (d) 400
16. 16.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 6 (d) 7
17. 17.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 1/4 (c) 2/3 (d) 1/2
18. 18.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 171 (c) 380 (d) 190
19. 19.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
20. 20.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 1/4 (c) 7/8 (d) 1/8
21. 21.How many factors does 30 have? (a) 9 (b) 6 (c) 7 (d) 8
22. 22.A drawer has lots of yellow, white, green 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) 2 (b) 4 (c) 8 (d) 5
23. 23.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 60° (b) 30° (c) 120° (d) 70°
24. 24.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 240 (c) 25 (d) 120
25. 25.A drawer has lots of blue, red, green, yellow 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) 2 (b) 5 (c) 6 (d) 10
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) 24 (b) 13 (c) 25 (d) 12
27. 27.A bag has 9 yellow, 3 white and 3 green balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 13/15 (c) 1/5 (d) 4/5
28. 28.Two angles of a triangle are 50° and 20°. What is the third angle? (a) 160° (b) 70° (c) 110° (d) 130°
29. 29.If a + b = 14 and ab = 48, what is (a − b)²? (a) 2 (b) 196 (c) 4 (d) 100
30. 30.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
31. 31.What are the roots of x² − 7x + 10 = 0? (a) 1 and 6 (b) 2 and 5 (c) 3 and 4 (d) 1 and 10
32. 32.4 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 48 (b) 10 (c) 24 (d) 28
33. 33.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
34. 34.What is the mean of 4, 2, 7, 7, 17 and 5? (a) 7 (b) 6 (c) 8 (d) 9
35. 35.What is the mean of 7, 2, 17, 20 and 9? (a) 13 (b) 11 (c) 12 (d) 10
36. 36.In a class of 28 children, 21 like maths, 15 like science and 9 like both. How many like at least one of the two? (a) 36 (b) 18 (c) 28 (d) 27
37. 37.What is the sum of the roots of x² − 15x + 54 = 0? (a) 15 (b) 14 (c) 16 (d) 54
38. 38.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/3 (b) 1/4 (c) 1/2 (d) 3/4
39. 39.A cuboid is 5 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 87 sq cm (b) 348 sq cm (c) 135 sq cm (d) 174 sq cm
40. 40.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm

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