Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 732 · 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.What is the sum of the first 11 terms of the AP 7, 8, 9, …? (a) 17 (b) 132 (c) 264 (d) 133
2. 2.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 24 (b) 25 (c) 36 (d) 37
3. 3.If a + b = 16 and ab = 60, what is a² + b²? (a) 196 (b) 136 (c) 376 (d) 256
4. 4.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 20° (c) 160° (d) 10°
5. 5.A bag has 4 green balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 9 (b) 6 (c) 5 (d) 2
6. 6.Two angles of a triangle are 45° and 35°. What is the third angle? (a) 100° (b) 145° (c) 80° (d) 135°
7. 7.What is the 14th term of the AP 17, 25, 33, 41, …? (a) 112 (b) 121 (c) 129 (d) 104
8. 8.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 50° (c) 80° (d) 130°
9. 9.What is the distance between the points (1, 25) and (13, 9)? (a) 21 (b) 28 (c) 20 (d) 400
10. 10.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 56 (c) 36 (d) 28
11. 11.How many factors does 52 have? (a) 7 (b) 4 (c) 6 (d) 5
12. 12.How many factors does 87 have? (a) 3 (b) 4 (c) 2 (d) 5
13. 13.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 130° (c) 35° (d) 50°
14. 14.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 60° (b) 31° (c) 30° (d) 150°
15. 15.6 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) 84 (b) 42 (c) 13 (d) 48
16. 16.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 308 sq cm
17. 17.What is the median of 34, 30, 7, 5, 20, 1 and 8? (a) 8 (b) 15 (c) 20 (d) 5
18. 18.How many factors does 41 have? (a) 3 (b) 4 (c) 1 (d) 2
19. 19.A drawer has lots of red, 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) 5 (b) 4 (c) 8 (d) 2
20. 20.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
21. 21.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 2/3 (c) 1/2 (d) 1/3
22. 22.What is the distance between the points (1, 18) and (10, 6)? (a) 21 (b) 15 (c) 16 (d) 225
23. 23.A drawer has lots of blue, 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) 3 (b) 6 (c) 2 (d) 4
24. 24.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
25. 25.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 90° (b) 120° (c) 270° (d) 150°
26. 26.A drawer has lots of yellow, 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) 3 (c) 6 (d) 2
27. 27.What is the 25th term of the AP 9, 11, 13, 15, …? (a) 48 (b) 50 (c) 59 (d) 57
28. 28.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 152 sq cm (b) 40 sq cm (c) 38 sq cm (d) 76 sq cm
29. 29.How many factors does 20 have? (a) 4 (b) 7 (c) 5 (d) 6
30. 30.A canteen sells 8 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 96 (b) 56 (c) 14 (d) 48
31. 31.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 20 (c) 120 (d) 240
32. 32.In which quadrant does the point (5, −5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
33. 33.How many prime numbers are there between 70 and 80? (a) 2 (b) 5 (c) 3 (d) 4
34. 34.A drawer has lots of white, blue, green, red 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) 5 (b) 6 (c) 2 (d) 10
35. 35.How many prime numbers are there between 20 and 30? (a) 3 (b) 1 (c) 2 (d) 4
36. 36.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) 28 (b) 22 (c) 29 (d) 21
37. 37.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 120 (c) 225 (d) 105
38. 38.What is the 13th term of the AP 3, 6, 9, 12, …? (a) 39 (b) 40 (c) 36 (d) 42
39. 39.What is the median of 22, 11, 26, 8, 10, 7 and 38? (a) 10 (b) 8 (c) 11 (d) 22
40. 40.What is the smallest prime factor of 161? (a) 1 (b) 7 (c) 23 (d) 2

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