Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 163 · 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 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
2. 2.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 182 (c) 105 (d) 91
3. 3.What is the missing term in the AP 8, 16, ?, 32, 40? (a) 32 (b) 24 (c) 25 (d) 23
4. 4.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
5. 5.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 12 (c) 8 (d) 18
6. 6.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 105° (c) 100° (d) 80°
7. 7.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 20 (c) 10 (d) 21
8. 8.What is the distance between the points (1, 1) and (13, 6)? (a) 13 (b) 169 (c) 14 (d) 17
9. 9.A drawer has lots of green 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) 2 (b) 4 (c) 5 (d) 3
10. 10.What is the mode of 7, 19, 11, 19, 6, 7 and 19? (a) 7 (b) 11 (c) 6 (d) 19
11. 11.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3
12. 12.Which is the correct factorisation of x² + 10x + 24? (a) (x + 1)(x + 9) (b) (x + 1)(x + 24) (c) (x − 4)(x − 6) (d) (x + 4)(x + 6)
13. 13.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 15 (b) 14 (c) 8 (d) 7
14. 14.A bag has 3 black balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 5 (b) 4 (c) 2 (d) 6
15. 15.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
16. 16.In a class of 37 children, 22 like mangoes, 21 like bananas and 7 like both. How many like only mangoes? (a) 14 (b) 16 (c) 22 (d) 15
17. 17.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 410 (b) 508 (c) 507 (d) 498
18. 18.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
19. 19.What is the prime factorisation of 35? (a) 5² × 7 (b) 5 × 7² (c) 5³ × 7 (d) 5 × 7
20. 20.In a class of 38 children, 16 like dance, 29 like music and 11 like both. How many like neither? (a) 5 (b) 11 (c) 4 (d) 15
21. 21.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 73 (c) 74 (d) 82
22. 22.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
23. 23.In a class of 40 children, 27 like mangoes, 19 like bananas and 9 like both. How many like only mangoes? (a) 10 (b) 21 (c) 27 (d) 18
24. 24.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 136° (b) 45° (c) 135° (d) 315°
25. 25.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
26. 26.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 478 (c) 600 (d) 609
27. 27.A bag has 11 yellow balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 20 (b) 13 (c) 2 (d) 12
28. 28.In a class of 19 children, 12 like dance, 5 like music and 2 like both. How many like at least one of the two? (a) 13 (b) 17 (c) 19 (d) 15
29. 29.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 49 (b) 522 (c) 266 (d) 261
30. 30.A bag has 12 black balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 14 (b) 15 (c) 13 (d) 2
31. 31.What is the 32nd term of the AP 20, 25, 30, 35, …? (a) 180 (b) 175 (c) 155 (d) 160
32. 32.The mean of 5 numbers is 19. When the number 25 is added to them, what is the new mean? (a) 20 (b) 21 (c) 22 (d) 19
33. 33.A bag has 9 yellow, 2 red and 7 white balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/3 (b) 1/2 (c) 1/18 (d) 5/9
34. 34.What is the sum of all the whole numbers from 1 to 53? (a) 1432 (b) 2862 (c) 1431 (d) 1378
35. 35.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/4
36. 36.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
37. 37.What is the mode of 9, 9, 17, 15, 17, 8 and 17? (a) 17 (b) 9 (c) 8 (d) 15
38. 38.What is the 13th term of the AP 9, 13, 17, 21, …? (a) 61 (b) 57 (c) 48 (d) 52
39. 39.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 21 (b) 28 (c) 29 (d) 22
40. 40.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 35° (b) 145° (c) 215° (d) 36°

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