Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 170 · 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.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
2. 2.How many prime numbers are there between 70 and 90? (a) 7 (b) 4 (c) 5 (d) 6
3. 3.What is the median of 5, 32, 10, 15 and 29? (a) 16 (b) 29 (c) 10 (d) 15
4. 4.What is the 30th term of the AP 15, 18, 21, 24, …? (a) 105 (b) 102 (c) 90 (d) 87
5. 5.A drawer has lots of white, blue, green, 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) 10 (b) 6 (c) 5 (d) 2
6. 6.What is the 18th term of the AP 12, 18, 24, 30, …? (a) 102 (b) 114 (c) 108 (d) 120
7. 7.What is the 13th term of the AP 17, 19, 21, 23, …? (a) 26 (b) 24 (c) 43 (d) 41
8. 8.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 149 (c) 150 (d) 158
9. 9.A bag has 7 green, 7 yellow and 2 blue balls. One ball is taken out without looking. What is the probability that it is not green? (a) 5/8 (b) 1/3 (c) 9/16 (d) 7/16
10. 10.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 25 (c) 20 (d) 15
11. 11.What is the mean of 5, 18, 2, 8, 14 and 13? (a) 11 (b) 9 (c) 10 (d) 12
12. 12.Using (a − b)² = a² − 2ab + b², what is 28²? (a) 896 (b) 794 (c) 784 (d) 1024
13. 13.What is the smallest prime factor of 69? (a) 1 (b) 3 (c) 23 (d) 2
14. 14.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 249 (c) 240 (d) 238
15. 15.In a class of 38 children, 17 like mangoes, 30 like bananas and 11 like both. How many like neither? (a) 2 (b) 3 (c) 11 (d) 13
16. 16.In a class of 42 children, 22 like cricket, 18 like football and 8 like neither. How many like both? (a) 34 (b) 8 (c) 7 (d) 6
17. 17.Two angles of a triangle are 45° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 95° (c) 85° (d) 135°
18. 18.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 1/4 (c) 3/8 (d) 1/8
19. 19.What is the median of 34, 21, 14, 16, 15, 17 and 31? (a) 21 (b) 18 (c) 16 (d) 17
20. 20.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
21. 21.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
22. 22.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
23. 23.Two angles of a triangle are 40° and 95°. What is the third angle? (a) 85° (b) 135° (c) 45° (d) 140°
24. 24.What is the mean of 19, 13, 12 and 16? (a) 20 (b) 12 (c) 16 (d) 15
25. 25.Two angles of a triangle are 50° and 85°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 130° (d) 95°
26. 26.Using (a + b)² = a² + 2ab + b², what is 22²? (a) 494 (b) 404 (c) 484 (d) 324
27. 27.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 12 (c) 16 (d) 24
28. 28.In a class of 23 children, 11 like cricket, 8 like football and 5 like both. How many like neither? (a) 14 (b) 4 (c) 9 (d) 5
29. 29.In a class of 16 children, 12 like mangoes, 8 like bananas and 1 like neither. How many like both? (a) 15 (b) 5 (c) 4 (d) 1
30. 30.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 75° (c) 60° (d) 30°
31. 31.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 86° (c) 85° (d) 170°
32. 32.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 80° (b) 135° (c) 145° (d) 100°
33. 33.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7² (b) 2 × 3 × 5 × 7 (c) 2² × 3 × 5 × 7 (d) 2³ × 3 × 5 × 7
34. 34.In a class of 41 children, 28 like dance, 14 like music and 9 like neither. How many like both? (a) 32 (b) 9 (c) 10 (d) 1
35. 35.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 165° (b) 15° (c) 16° (d) 30°
36. 36.If a + b = 8 and ab = 12, what is a² + b²? (a) 40 (b) 52 (c) 88 (d) 64
37. 37.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
38. 38.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 9 (c) 12 (d) 3
39. 39.Two angles of a triangle are 75° and 80°. What is the third angle? (a) 155° (b) 100° (c) 25° (d) 105°
40. 40.What is the sum of the first 10 terms of the AP 10, 13, 16, …? (a) 470 (b) 37 (c) 250 (d) 235

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