Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 56 · 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.How many factors does 57 have? (a) 5 (b) 4 (c) 3 (d) 2
2. 2.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/2 (c) 1/3 (d) 3/4
3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 18 (d) 7
4. 4.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/11 (b) 5/11 (c) 1/6 (d) 5/36
5. 5.Two angles of a triangle are 55° and 115°. What is the third angle? (a) 65° (b) 125° (c) 170° (d) 10°
6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 88? (a) 20 (b) 18 (c) 19 (d) 8
7. 7.What is the mode of 3, 7, 7, 3, 14, 1 and 7? (a) 1 (b) 3 (c) 7 (d) 14
8. 8.In a class of 33 children, 20 like cricket, 12 like football and 10 like neither. How many like both? (a) 8 (b) 23 (c) 10 (d) 9
9. 9.What is the smallest prime factor of 33? (a) 3 (b) 11 (c) 1 (d) 2
10. 10.A bag has 12 blue balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 2 (c) 13 (d) 23
11. 11.A drawer has lots of red, yellow, green 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) 4 (b) 5 (c) 2 (d) 8
12. 12.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 24 (d) 48
13. 13.What is the 13th term of the AP 1, 8, 15, 22, …? (a) 91 (b) 92 (c) 84 (d) 85
14. 14.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 20 (b) 15 (c) 8 (d) 30
15. 15.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 70° (b) 45° (c) 155° (d) 135°
16. 16.If a + b = 5 and ab = 6, what is (a − b)²? (a) 1 (b) 25 (c) 19 (d) 13
17. 17.Using (a + b)² = a² + 2ab + b², what is 45²? (a) 1625 (b) 2025 (c) 2035 (d) 1225
18. 18.What is the mean of 10, 16, 13, 3 and 3? (a) 10 (b) 11 (c) 8 (d) 9
19. 19.What is the mode of 10, 10, 15, 6, 10, 15 and 11? (a) 11 (b) 6 (c) 10 (d) 15
20. 20.In which quadrant does the point (8, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
21. 21.In a class of 33 children, 16 like cricket, 9 like football and 10 like neither. How many like both? (a) 2 (b) 23 (c) 10 (d) 3
22. 22.Which is the correct factorisation of x² + 15x + 54? (a) (x − 6)(x − 9) (b) (x + 1)(x + 54) (c) (x + 1)(x + 14) (d) (x + 6)(x + 9)
23. 23.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
24. 24.What is the midpoint of the line joining (4, 5) and (14, 1)? (a) (18, 6) (b) (9, 3) (c) (3, 9) (d) (5, 2)
25. 25.A bag has 9 blue, 2 green and 3 white balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 5/14 (c) 9/14 (d) 5/9
26. 26.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 66 (c) 132 (d) 78
27. 27.Which is the correct factorisation of x² + 10x + 16? (a) (x + 1)(x + 9) (b) (x − 2)(x − 8) (c) (x + 1)(x + 16) (d) (x + 2)(x + 8)
28. 28.What is the mode of 6, 11, 3, 11, 11, 6 and 19? (a) 6 (b) 19 (c) 11 (d) 3
29. 29.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 100° (b) 145° (c) 115° (d) 35°
30. 30.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 80° (b) 20° (c) 160° (d) 70°
31. 31.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
32. 32.If a + b = 5 and ab = 6, what is a² + b²? (a) 37 (b) 19 (c) 25 (d) 13
33. 33.A cube has edges of 5 cm. What is its total surface area? (a) 125 sq cm (b) 100 sq cm (c) 150 sq cm (d) 25 sq cm
34. 34.What is the distance between the points (3, 24) and (10, 0)? (a) 26 (b) 31 (c) 625 (d) 25
35. 35.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 1/4 (c) 1/3 (d) 3/4
36. 36.If a + b = 8 and ab = 7, what is (a − b)²? (a) 36 (b) 64 (c) 50 (d) 6
37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 16 (b) 15 (c) 17 (d) 6
38. 38.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 176 sq cm
39. 39.What is the 28th term of the AP 16, 21, 26, 31, …? (a) 156 (b) 140 (c) 135 (d) 151
40. 40.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 50° (c) 40° (d) 130°

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