Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 818 · 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 two equal angles are 35° each. What is the third angle? (a) 55° (b) 145° (c) 110° (d) 35°
2. 2.A bag has 2 blue, 9 red and 5 green balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 7/8 (c) 15/16 (d) 1/8
3. 3.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 27 sq cm (c) 36 sq cm (d) 9 sq cm
4. 4.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
5. 5.In a class of 46 children, 23 like maths, 27 like science and 5 like neither. How many like both? (a) 9 (b) 41 (c) 5 (d) 4
6. 6.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 25 (c) 7 (d) 6
7. 7.A bag has 11 yellow balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 17 (b) 2 (c) 12 (d) 13
8. 8.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/3 (c) 1/4 (d) 1/2
9. 9.Using (a + b)² = a² + 2ab + b², what is 105²? (a) 11025 (b) 11035 (c) 9025 (d) 10025
10. 10.In which quadrant does the point (1, 2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
11. 11.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 132 (c) 144 (d) 66
12. 12.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
13. 13.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
14. 14.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
15. 15.A bag has 6 yellow balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 2 (c) 7 (d) 14
16. 16.A drawer has lots of 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) 5 (b) 2 (c) 3 (d) 4
17. 17.What is the 39th term of the AP 6, 9, 12, 15, …? (a) 123 (b) 120 (c) 117 (d) 114
18. 18.Which is the correct factorisation of x² + 13x + 42? (a) (x − 6)(x − 7) (b) (x + 6)(x + 7) (c) (x + 1)(x + 42) (d) (x + 1)(x + 12)
19. 19.A bag has 6 red, 5 green and 2 white balls. One ball is taken out without looking. What is the probability that it is red? (a) 7/13 (b) 6/13 (c) 6/7 (d) 1/3
20. 20.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
21. 21.Using (a + b)² = a² + 2ab + b², what is 103²? (a) 9409 (b) 10619 (c) 10009 (d) 10609
22. 22.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 264 cm (d) 1386 cm
23. 23.What is the smallest prime factor of 341? (a) 31 (b) 1 (c) 11 (d) 2
24. 24.What is the mean of 3, 6, 17 and 18? (a) 13 (b) 12 (c) 11 (d) 10
25. 25.There are 7 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 84 (b) 42 (c) 13 (d) 49
26. 26.What is the mean of 17, 15, 17 and 19? (a) 17 (b) 19 (c) 16 (d) 18
27. 27.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 22 (c) 55 (d) 110
28. 28.If a + b = 12 and ab = 27, what is (a − b)²? (a) 144 (b) 6 (c) 90 (d) 36
29. 29.What is the mode of 9, 15, 7, 7, 9, 9 and 13? (a) 15 (b) 13 (c) 7 (d) 9
30. 30.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 528 (b) 430 (c) 537 (d) 538
31. 31.In a class of 16 children, 5 like mangoes, 12 like bananas and 2 like both. How many like only mangoes? (a) 10 (b) 4 (c) 5 (d) 3
32. 32.What is the sum of the roots of x² − 10x + 21 = 0? (a) 9 (b) 10 (c) 11 (d) 21
33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/11 (c) 3/11 (d) 1/12
34. 34.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 1/2 (c) 3/4 (d) 1/4
35. 35.Using (a + b)² = a² + 2ab + b², what is 21²? (a) 441 (b) 401 (c) 361 (d) 451
36. 36.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
37. 37.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 30° (b) 60° (c) 330° (d) 150°
38. 38.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 81 (c) 18 (d) 36
39. 39.A drawer has lots of black, 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) 4 (b) 8 (c) 2 (d) 5
40. 40.In which quadrant does the point (−4, 4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant

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