Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 524 · 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 canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 35 (c) 40 (d) 70
2. 2.A bag has 4 yellow balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 5 (b) 15 (c) 2 (d) 6
3. 3.What is the smallest prime factor of 77? (a) 1 (b) 7 (c) 11 (d) 2
4. 4.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 60° (b) 100° (c) 120° (d) 140°
5. 5.What is the distance between the points (7, 1) and (14, 25)? (a) 31 (b) 625 (c) 26 (d) 25
6. 6.How many prime numbers are there between 50 and 70? (a) 3 (b) 5 (c) 6 (d) 4
7. 7.What is the mean of 15, 3, 9 and 17? (a) 12 (b) 13 (c) 11 (d) 10
8. 8.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 45° (c) 136° (d) 135°
9. 9.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 6 times (c) 27 times (d) 3 times
10. 10.In which quadrant does the point (5, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
11. 11.In a class of 38 children, 17 like tea, 30 like coffee and 1 like neither. How many like both? (a) 37 (b) 1 (c) 10 (d) 9
12. 12.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 7 (b) 15 (c) 8 (d) 14
13. 13.In a class of 53 children, 28 like tea, 26 like coffee and 8 like both. How many like neither? (a) 6 (b) 8 (c) 7 (d) 15
14. 14.A bag has 11 black balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 13 (b) 15 (c) 2 (d) 12
15. 15.What is the 22nd term of the AP 6, 10, 14, 18, …? (a) 90 (b) 94 (c) 84 (d) 88
16. 16.What is the prime factorisation of 112? (a) 2⁴ × 7 (b) 2³ × 7 (c) 2 × 7⁴ (d) 2⁵ × 7
17. 17.Two angles of a triangle are 35° and 25°. What is the third angle? (a) 60° (b) 155° (c) 145° (d) 120°
18. 18.In a class of 34 children, 14 like maths, 28 like science and 9 like both. How many like at least one of the two? (a) 24 (b) 34 (c) 33 (d) 42
19. 19.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 12 (c) 3 (d) 9
20. 20.How many factors does 52 have? (a) 7 (b) 4 (c) 5 (d) 6
21. 21.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
22. 22.6 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
23. 23.In a class of 39 children, 13 like cricket, 23 like football and 4 like both. How many like at least one of the two? (a) 39 (b) 36 (c) 28 (d) 32
24. 24.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/3 (b) 1/6 (c) 5/6 (d) 1/5
25. 25.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 28 (c) 49 (d) 21
26. 26.What is the mode of 13, 5, 5, 15, 16, 16 and 5? (a) 5 (b) 15 (c) 13 (d) 16
27. 27.In a class of 51 children, 26 like tea, 24 like coffee and 8 like both. How many like at least one of the two? (a) 50 (b) 42 (c) 34 (d) 51
28. 28.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) 25 (c) 13 (d) 24
29. 29.How many prime numbers are there between 90 and 120? (a) 5 (b) 7 (c) 6 (d) 8
30. 30.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 54 sq cm (c) 9 sq cm (d) 36 sq cm
31. 31.Which is the correct factorisation of x² + 10x + 16? (a) (x + 2)(x + 8) (b) (x + 1)(x + 9) (c) (x − 2)(x − 8) (d) (x + 1)(x + 16)
32. 32.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 2/3 (c) 1/4 (d) 1/3
33. 33.What is the median of 2, 29, 13, 14, 4, 31 and 24? (a) 24 (b) 15 (c) 13 (d) 14
34. 34.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
35. 35.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 230° (b) 65° (c) 50° (d) 115°
36. 36.Two angles of a triangle are 55° and 75°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 105° (d) 125°
37. 37.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) 25 (b) 36 (c) 24 (d) 37
38. 38.A drawer has lots of green, blue, white, 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) 2 (b) 6 (c) 10 (d) 5
39. 39.In a class of 34 children, 19 like maths, 16 like science and 8 like both. How many like only maths? (a) 8 (b) 19 (c) 11 (d) 18
40. 40.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 135° (b) 90° (c) 45° (d) 46°

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