Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 91 · 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 190°. What is each of the other two angles? (a) 170° (b) 95° (c) 86° (d) 85°
2. 2.In which quadrant does the point (3, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
3. 3.In a class of 45 children, 18 like mangoes, 20 like bananas and 2 like both. How many like at least one of the two? (a) 34 (b) 38 (c) 36 (d) 45
4. 4.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
5. 5.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 105° (b) 140° (c) 145° (d) 75°
6. 6.What is the prime factorisation of 28? (a) 2 × 7 (b) 2² × 7 (c) 2 × 7² (d) 2³ × 7
7. 7.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) 25 (b) 24 (c) 13 (d) 12
8. 8.What is the distance between the points (0, 9) and (4, 12)? (a) 7 (b) 5 (c) 6 (d) 25
9. 9.In a class of 32 children, 19 like maths, 16 like science and 4 like both. How many like only maths? (a) 19 (b) 15 (c) 16 (d) 12
10. 10.What is the distance between the points (6, 2) and (13, 26)? (a) 625 (b) 26 (c) 25 (d) 31
11. 11.A bag has 11 yellow balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 23 (b) 12 (c) 2 (d) 13
12. 12.A bag has 10 red balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 11 (c) 20 (d) 12
13. 13.A cuboid is 8 cm long, 4 cm wide and 6 cm high. What is its volume? (a) 32 cu cm (b) 18 cu cm (c) 208 cu cm (d) 192 cu cm
14. 14.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
15. 15.What is the mean of 18, 2, 5 and 11? (a) 12 (b) 8 (c) 10 (d) 9
16. 16.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
17. 17.In which quadrant does the point (−7, 8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
18. 18.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/4 (c) 1/2 (d) 1/3
19. 19.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 5/6 (b) 1/4 (c) 1/3 (d) 2/3
20. 20.What is the product of the roots of x² − 6x + 8 = 0? (a) 9 (b) 8 (c) 6 (d) 7
21. 21.A drawer has lots of blue, black, yellow and red 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) 8 (c) 4 (d) 5
22. 22.If a + b = 18 and ab = 80, what is (a − b)²? (a) 4 (b) 324 (c) 2 (d) 164
23. 23.What is the distance between the points (6, 3) and (30, 10)? (a) 26 (b) 25 (c) 625 (d) 31
24. 24.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 160° (b) 135° (c) 155° (d) 45°
25. 25.How many factors does 118 have? (a) 2 (b) 4 (c) 3 (d) 5
26. 26.A drawer has lots of red, blue 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) 6 (b) 2 (c) 3 (d) 4
27. 27.What is the distance between the points (7, 21) and (15, 6)? (a) 23 (b) 289 (c) 18 (d) 17
28. 28.What is the midpoint of the line joining (1, 8) and (5, 12)? (a) (10, 3) (b) (2, 2) (c) (3, 10) (d) (6, 20)
29. 29.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
30. 30.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 343 cu cm (c) 21 cu cm (d) 294 cu cm
31. 31.In a class of 38 children, 17 like maths, 26 like science and 11 like both. How many like only maths? (a) 17 (b) 12 (c) 15 (d) 6
32. 32.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) 15 (b) 14 (c) 8 (d) 7
33. 33.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
34. 34.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 36 (c) 21 (d) 15
35. 35.What is the midpoint of the line joining (6, 9) and (16, 13)? (a) (5, 2) (b) (11, 11) (c) (22, 22) (d) (12, 11)
36. 36.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 265° (c) 85° (d) 86°
37. 37.4 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 8 (b) 20 (c) 32 (d) 16
38. 38.Which is the correct factorisation of x² + 14x + 48? (a) (x + 1)(x + 13) (b) (x + 6)(x + 8) (c) (x − 6)(x − 8) (d) (x + 1)(x + 48)
39. 39.If a + b = 15 and ab = 36, what is (a − b)²? (a) 225 (b) 153 (c) 9 (d) 81
40. 40.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3

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