Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 177 · 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 bag has 9 red balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 18 (b) 10 (c) 11 (d) 2
2. 2.What is the prime factorisation of 72? (a) 2⁴ × 3² (b) 2² × 3² (c) 2³ × 3² (d) 2² × 3³
3. 3.Using (a − b)² = a² − 2ab + b², what is 16²? (a) 384 (b) 266 (c) 576 (d) 256
4. 4.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) 2 (b) 5 (c) 3 (d) 4
5. 5.In a class of 40 children, 30 like tea, 16 like coffee and 11 like both. How many like only tea? (a) 19 (b) 5 (c) 24 (d) 30
6. 6.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 132 cm (d) 1386 cm
7. 7.In a class of 32 children, 18 like maths, 10 like science and 3 like both. How many like at least one of the two? (a) 28 (b) 25 (c) 22 (d) 32
8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 4 (b) 13 (c) 15 (d) 14
9. 9.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 220° (b) 40° (c) 140° (d) 41°
10. 10.What is the 16th term of the AP 18, 27, 36, 45, …? (a) 135 (b) 144 (c) 153 (d) 162
11. 11.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 120° (c) 30° (d) 60°
12. 12.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 140° (b) 85° (c) 95° (d) 135°
13. 13.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
14. 14.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 80° (c) 100° (d) 40°
15. 15.A bag has 4 red, 6 blue and 2 yellow balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 1/2 (c) 7/12 (d) 1/12
16. 16.How many factors does 33 have? (a) 2 (b) 5 (c) 4 (d) 3
17. 17.A drawer has lots of black and white 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) 2 (c) 5 (d) 4
18. 18.What is the smallest prime factor of 77? (a) 7 (b) 1 (c) 11 (d) 2
19. 19.Two angles of a triangle are 75° and 70°. What is the exterior angle at the third corner? (a) 105° (b) 145° (c) 35° (d) 110°
20. 20.In a class of 29 children, 13 like mangoes, 20 like bananas and 7 like both. How many like neither? (a) 10 (b) 3 (c) 4 (d) 7
21. 21.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 20 (c) 120 (d) 25
22. 22.What is the median of 19, 34, 39, 5, 3, 30 and 22? (a) 30 (b) 19 (c) 5 (d) 22
23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 18 (b) 17 (c) 6 (d) 16
24. 24.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 120° (c) 60° (d) 130°
25. 25.What is the 21st term of the AP 13, 15, 17, 19, …? (a) 42 (b) 53 (c) 40 (d) 55
26. 26.If a + b = 16 and ab = 48, what is (a − b)²? (a) 8 (b) 256 (c) 160 (d) 64
27. 27.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
28. 28.In a class of 40 children, 24 like tea, 13 like coffee and 5 like both. How many like neither? (a) 3 (b) 13 (c) 8 (d) 5
29. 29.A bag has 3 red, 8 blue and 4 white balls. One ball is taken out without looking. What is the probability that it is red? (a) 4/5 (b) 1/5 (c) 1/4 (d) 1/3
30. 30.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 146 (c) 154 (d) 145
31. 31.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 14 (b) 60 (c) 54 (d) 108
32. 32.A bag has 3 blue balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 2 (c) 4 (d) 5
33. 33.What is the smallest prime factor of 35? (a) 2 (b) 1 (c) 7 (d) 5
34. 34.What is the product of the roots of x² − 11x + 30 = 0? (a) 29 (b) 31 (c) 30 (d) 11
35. 35.What is the 16th term of the AP 18, 22, 26, 30, …? (a) 64 (b) 60 (c) 82 (d) 78
36. 36.What is the 11th term of the AP 9, 16, 23, 30, …? (a) 79 (b) 70 (c) 77 (d) 86
37. 37.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
38. 38.What is the mean of 17, 17, 2, 11, 8 and 11? (a) 13 (b) 10 (c) 11 (d) 12
39. 39.In a class of 37 children, 15 like dance, 18 like music and 2 like both. How many like at least one of the two? (a) 37 (b) 33 (c) 29 (d) 31
40. 40.Which is the correct factorisation of x² + 11x + 30? (a) (x + 1)(x + 30) (b) (x + 5)(x + 6) (c) (x + 1)(x + 10) (d) (x − 5)(x − 6)

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