Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 630 · 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.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
2. 2.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 182 (c) 196 (d) 91
3. 3.What is the 11th term of the AP 8, 15, 22, 29, …? (a) 78 (b) 70 (c) 85 (d) 77
4. 4.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 189 (c) 180 (d) 190
5. 5.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 115° (b) 120° (c) 125° (d) 55°
6. 6.In a class of 25 children, 14 like cricket, 18 like football and 10 like both. How many like at least one of the two? (a) 25 (b) 32 (c) 12 (d) 22
7. 7.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 616 cm (d) 44 cm
8. 8.In a class of 36 children, 14 like tea, 18 like coffee and 9 like neither. How many like both? (a) 9 (b) 5 (c) 27 (d) 6
9. 9.In a class of 33 children, 16 like tea, 22 like coffee and 9 like both. How many like at least one of the two? (a) 33 (b) 20 (c) 38 (d) 29
10. 10.If a + b = 8 and ab = 7, what is a² + b²? (a) 64 (b) 50 (c) 78 (d) 57
11. 11.The mean of 3 numbers is 10. When the number 6 is added to them, what is the new mean? (a) 11 (b) 10 (c) 9 (d) 8
12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/6 (b) 1/11 (c) 5/11 (d) 5/36
13. 13.Which is the correct factorisation of x² + 11x + 24? (a) (x + 1)(x + 24) (b) (x + 3)(x + 8) (c) (x − 3)(x − 8) (d) (x + 1)(x + 10)
14. 14.A bag has 9 yellow, 5 white and 5 red balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 5/19 (c) 15/19 (d) 14/19
15. 15.What is the mode of 16, 16, 16, 15, 8, 9 and 9? (a) 15 (b) 9 (c) 16 (d) 8
16. 16.What are the roots of x² − 8x + 15 = 0? (a) 1 and 7 (b) 3 and 5 (c) 1 and 15 (d) 2 and 6
17. 17.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 115° (b) 25° (c) 65° (d) 295°
18. 18.A drawer has lots of white 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) 3 (b) 5 (c) 4 (d) 2
19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 82? (a) 19 (b) 18 (c) 17 (d) 8
20. 20.A bag has 8 white, 2 red and 2 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 5/6 (c) 1/6 (d) 1/5
21. 21.Using (a + b)² = a² + 2ab + b², what is 35²? (a) 1235 (b) 625 (c) 1225 (d) 925
22. 22.Which is the correct factorisation of x² + 9x + 18? (a) (x − 3)(x − 6) (b) (x + 1)(x + 8) (c) (x + 1)(x + 18) (d) (x + 3)(x + 6)
23. 23.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 135° (b) 105° (c) 75° (d) 150°
24. 24.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 169 (c) 91 (d) 78
25. 25.In a class of 34 children, 19 like dance, 16 like music and 6 like both. How many like only dance? (a) 18 (b) 13 (c) 10 (d) 19
26. 26.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 90 (b) 48 (c) 10 (d) 45
27. 27.What is the 16th term of the AP 19, 21, 23, 25, …? (a) 32 (b) 51 (c) 30 (d) 49
28. 28.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 60° (c) 150° (d) 120°
29. 29.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 150° (b) 115° (c) 145° (d) 65°
30. 30.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 240 (c) 25 (d) 20
31. 31.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 3/8 (c) 7/8 (d) 1/8
32. 32.Which is the correct factorisation of x² + 8x + 12? (a) (x + 1)(x + 7) (b) (x + 2)(x + 6) (c) (x − 2)(x − 6) (d) (x + 1)(x + 12)
33. 33.What is the sum of the first 7 terms of the AP 5, 6, 7, …? (a) 56 (b) 112 (c) 57 (d) 11
34. 34.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 170° (c) 85° (d) 86°
35. 35.If a + b = 14 and ab = 40, what is a² + b²? (a) 156 (b) 116 (c) 276 (d) 196
36. 36.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 21 (c) 15 (d) 22
37. 37.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
38. 38.A drawer has lots of white, yellow, black and blue 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) 4 (c) 2 (d) 8
39. 39.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 226 (c) 216 (d) 225
40. 40.In a class of 23 children, 13 like cricket, 12 like football and 6 like neither. How many like both? (a) 6 (b) 2 (c) 8 (d) 17

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