Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 941 · 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 cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 64 sq cm (c) 97 sq cm (d) 16 sq cm
2. 2.Two angles of a triangle are 25° and 75°. What is the exterior angle at the third corner? (a) 100° (b) 105° (c) 155° (d) 80°
3. 3.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 517 (b) 507 (c) 516 (d) 416
4. 4.How many factors does 33 have? (a) 5 (b) 2 (c) 3 (d) 4
5. 5.In a class of 36 children, 20 like maths, 22 like science and 5 like neither. How many like both? (a) 31 (b) 6 (c) 11 (d) 5
6. 6.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 24 sq cm (c) 8 sq cm (d) 16 sq cm
7. 7.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
8. 8.What is the mean of 10, 19, 10, 19, 14 and 6? (a) 15 (b) 12 (c) 14 (d) 13
9. 9.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 130° (c) 25° (d) 155°
10. 10.What is the 13th term of the AP 20, 28, 36, 44, …? (a) 116 (b) 104 (c) 124 (d) 96
11. 11.In a class of 49 children, 21 like maths, 25 like science and 6 like both. How many like at least one of the two? (a) 46 (b) 49 (c) 34 (d) 40
12. 12.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 121 (c) 240 (d) 120
13. 13.Two angles of a triangle are 25° and 100°. What is the third angle? (a) 155° (b) 125° (c) 80° (d) 55°
14. 14.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 130° (c) 25° (d) 35°
15. 15.In a class of 32 children, 13 like cricket, 21 like football and 3 like both. How many like neither? (a) 4 (b) 2 (c) 1 (d) 3
16. 16.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 5/6 (b) 1/6 (c) 1/5 (d) 1/3
17. 17.What is the mode of 11, 3, 11, 11, 16, 9 and 9? (a) 3 (b) 9 (c) 11 (d) 16
18. 18.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 40° (b) 50° (c) 140° (d) 320°
19. 19.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 2/11 (c) 1/18 (d) 1/12
20. 20.Two angles of a triangle are 35° and 80°. What is the third angle? (a) 65° (b) 100° (c) 145° (d) 115°
21. 21.What is the 25th term of the AP 16, 20, 24, 28, …? (a) 116 (b) 100 (c) 112 (d) 96
22. 22.What is the mode of 17, 13, 17, 8, 18, 17 and 18? (a) 18 (b) 17 (c) 13 (d) 8
23. 23.What is the prime factorisation of 70? (a) 2³ × 5 × 7 (b) 2² × 5 × 7 (c) 2 × 5 × 7² (d) 2 × 5 × 7
24. 24.A bag has 3 blue balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 5 (b) 4 (c) 8 (d) 2
25. 25.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
26. 26.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 16 (c) 144 (d) 48
27. 27.What is the mode of 3, 20, 7, 3, 20, 2 and 20? (a) 2 (b) 7 (c) 20 (d) 3
28. 28.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
29. 29.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 22 cm (d) 44 cm
30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/11 (b) 5/36 (c) 1/6 (d) 5/11
31. 31.What is the median of 10, 35, 38, 26, 40, 16 and 21? (a) 35 (b) 27 (c) 26 (d) 21
32. 32.If a + b = 13 and ab = 12, what is (a − b)²? (a) 169 (b) 11 (c) 145 (d) 121
33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 84? (a) 19 (b) 18 (c) 17 (d) 8
34. 34.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 20 (c) 25 (d) 240
35. 35.A bag has 8 green balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 16 (c) 9 (d) 10
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) 145° (d) 115°
37. 37.A drawer has lots of white, green 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) 6 (b) 3 (c) 4 (d) 2
38. 38.A bag has 6 white balls and 7 green 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) 13 (d) 8
39. 39.3 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 5 (b) 12 (c) 6 (d) 9
40. 40.In a class of 31 children, 20 like tea, 12 like coffee and 2 like both. How many like only tea? (a) 19 (b) 18 (c) 10 (d) 20

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