Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 190 · 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.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 50° (c) 40° (d) 140°
2. 2.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
3. 3.A drawer has lots of red, blue, black 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) 5 (c) 4 (d) 8
4. 4.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 7/8 (b) 1/8 (c) 1/4 (d) 1/7
5. 5.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 165° (b) 110° (c) 85° (d) 15°
6. 6.What is the smallest prime factor of 133? (a) 7 (b) 1 (c) 2 (d) 19
7. 7.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 21 (c) 42 (d) 11
8. 8.What is the midpoint of the line joining (3, 22) and (9, 10)? (a) (12, 32) (b) (6, 16) (c) (3, 6) (d) (16, 6)
9. 9.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 150° (c) 30° (d) 60°
10. 10.A bag has 8 green balls and 5 yellow 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) 6 (c) 13 (d) 9
11. 11.A bag has 5 black balls and 6 red 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) 7 (c) 11 (d) 6
12. 12.How many factors does 16 have? (a) 4 (b) 6 (c) 3 (d) 5
13. 13.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 35 (b) 10 (c) 60 (d) 30
14. 14.A bag has 4 blue, 6 red and 9 yellow balls. One ball is taken out without looking. What is the probability that it is not red? (a) 6/19 (b) 1/3 (c) 13/19 (d) 14/19
15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/12 (c) 1/11 (d) 3/11
16. 16.3 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) 7 (b) 15 (c) 24 (d) 12
17. 17.Which is the correct factorisation of x² + 11x + 24? (a) (x + 1)(x + 24) (b) (x + 1)(x + 10) (c) (x + 3)(x + 8) (d) (x − 3)(x − 8)
18. 18.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 150° (b) 60° (c) 31° (d) 30°
19. 19.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 120° (b) 155° (c) 145° (d) 60°
20. 20.What is the mean of 14, 12, 6 and 16? (a) 16 (b) 11 (c) 13 (d) 12
21. 21.A cuboid is 10 cm long, 9 cm wide and 3 cm high. What is its total surface area? (a) 588 sq cm (b) 270 sq cm (c) 294 sq cm (d) 147 sq cm
22. 22.What is the midpoint of the line joining (1, 18) and (13, 6)? (a) (14, 24) (b) (7, 12) (c) (12, 7) (d) (6, 6)
23. 23.What is the sum of the first 7 terms of the AP 6, 8, 10, …? (a) 18 (b) 91 (c) 168 (d) 84
24. 24.If a + b = 19 and ab = 90, what is (a − b)²? (a) 361 (b) 271 (c) 181 (d) 1
25. 25.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 150 sq cm (c) 125 sq cm (d) 25 sq cm
26. 26.What are the roots of x² − 7x + 10 = 0? (a) 2 and 5 (b) 3 and 4 (c) 1 and 6 (d) 1 and 10
27. 27.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 12 (c) 8 (d) 6
28. 28.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
29. 29.In a class of 32 children, 17 like maths, 17 like science and 8 like both. How many like at least one of the two? (a) 34 (b) 32 (c) 18 (d) 26
30. 30.What is the median of 31, 3, 18, 24, 36, 40 and 27? (a) 24 (b) 27 (c) 31 (d) 28
31. 31.In a class of 48 children, 27 like cricket, 28 like football and 8 like both. How many like at least one of the two? (a) 48 (b) 47 (c) 55 (d) 39
32. 32.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
33. 33.What is the prime factorisation of 15? (a) 3³ × 5 (b) 3 × 5² (c) 3 × 5 (d) 3² × 5
34. 34.A bag has 11 blue balls and 12 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) 23 (c) 12 (d) 13
35. 35.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 130° (b) 110° (c) 160° (d) 70°
36. 36.Two angles of a triangle are 35° and 65°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 115° (d) 145°
37. 37.The mean of 3 numbers is 12. When the number 8 is added to them, what is the new mean? (a) 13 (b) 10 (c) 12 (d) 11
38. 38.In a class of 44 children, 29 like maths, 16 like science and 11 like both. How many like only maths? (a) 29 (b) 28 (c) 5 (d) 18
39. 39.The mean of 7 numbers is 15. When the number 47 is added to them, what is the new mean? (a) 20 (b) 15 (c) 19 (d) 31
40. 40.How many factors does 76 have? (a) 7 (b) 6 (c) 5 (d) 4

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