Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 609 · 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. 1.4 T-shirts and 3 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) 24 (c) 16 (d) 12
2. 2.What is the smallest prime factor of 39? (a) 3 (b) 2 (c) 13 (d) 1
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
4. 4.In a class of 26 children, 9 like dance, 12 like music and 2 like both. How many like neither? (a) 7 (b) 2 (c) 5 (d) 9
5. 5.What is the midpoint of the line joining (10, 5) and (14, 17)? (a) (12, 11) (b) (11, 12) (c) (2, 6) (d) (24, 22)
6. 6.What is the mode of 6, 6, 6, 15, 14, 3 and 3? (a) 3 (b) 6 (c) 15 (d) 14
7. 7.Two angles of a triangle are 40° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 100° (c) 280° (d) 80°
8. 8.A cuboid is 10 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 512 sq cm (b) 180 sq cm (c) 128 sq cm (d) 256 sq cm
9. 9.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 11° (c) 160° (d) 10°
10. 10.In a class of 34 children, 20 like maths, 18 like science and 9 like both. How many like neither? (a) 6 (b) 5 (c) 14 (d) 9
11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/18 (b) 1/11 (c) 1/12 (d) 1/36
12. 12.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
13. 13.In a class of 41 children, 18 like tea, 27 like coffee and 9 like both. How many like only tea? (a) 18 (b) 9 (c) 10 (d) 14
14. 14.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
15. 15.What is the sum of the roots of x² − 9x + 14 = 0? (a) 8 (b) 14 (c) 9 (d) 10
16. 16.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 100° (c) 80° (d) 50°
17. 17.A bag has 4 black balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 5 (c) 16 (d) 2
18. 18.Which is the correct factorisation of x² + 11x + 18? (a) (x + 2)(x + 9) (b) (x − 2)(x − 9) (c) (x + 1)(x + 10) (d) (x + 1)(x + 18)
19. 19.A cube has edges of 8 cm. What is its volume? (a) 512 cu cm (b) 384 cu cm (c) 256 cu cm (d) 24 cu cm
20. 20.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
21. 21.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 216 (c) 75 (d) 24
22. 22.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 50° (c) 70° (d) 40°
23. 23.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 506 (c) 253 (d) 43
24. 24.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
25. 25.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 14) (b) (x + 1)(x + 56) (c) (x + 7)(x + 8) (d) (x − 7)(x − 8)
26. 26.Two angles of a triangle are 35° and 80°. What is the third angle? (a) 145° (b) 100° (c) 115° (d) 65°
27. 27.A drawer has lots of red, blue, 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) 10 (b) 6 (c) 5 (d) 2
28. 28.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 70° (c) 60° (d) 30°
29. 29.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 171 (c) 19 (d) 60
30. 30.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
31. 31.In a class of 22 children, 13 like maths, 10 like science and 3 like neither. How many like both? (a) 3 (b) 1 (c) 4 (d) 19
32. 32.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm
33. 33.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 11 (c) 10 (d) 25
34. 34.3 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) 36 (b) 18 (c) 9 (d) 21
35. 35.If a + b = 12 and ab = 35, what is (a − b)²? (a) 2 (b) 74 (c) 144 (d) 4
36. 36.A bag has 3 yellow, 2 white and 9 green balls. One ball is taken out without looking. What is the probability that it is not white? (a) 6/7 (b) 1/3 (c) 13/14 (d) 1/7
37. 37.There are 8 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 40 (b) 64 (c) 32 (d) 12
38. 38.In a class of 27 children, 16 like tea, 15 like coffee and 12 like both. How many like neither? (a) 12 (b) 9 (c) 8 (d) 20
39. 39.In a class of 24 children, 10 like mangoes, 14 like bananas and 7 like both. How many like only mangoes? (a) 3 (b) 10 (c) 4 (d) 7
40. 40.A cuboid is 7 cm long, 2 cm wide and 6 cm high. What is its volume? (a) 84 cu cm (b) 14 cu cm (c) 136 cu cm (d) 15 cu cm

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