Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 176 · 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 11 blue balls and 3 red 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) 14 (c) 2 (d) 4
2. 2.What is the missing term in the AP 12, 21, 30, ?, 48? (a) 39 (b) 38 (c) 40 (d) 48
3. 3.The mean of 5 numbers is 23. When the number 5 is added to them, what is the new mean? (a) 23 (b) 21 (c) 20 (d) 14
4. 4.A drawer has lots of green, yellow 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) 6 (b) 2 (c) 4 (d) 3
5. 5.In a class of 34 children, 16 like cricket, 19 like football and 10 like both. How many like only cricket? (a) 9 (b) 16 (c) 6 (d) 15
6. 6.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
7. 7.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 13 (c) 117 (d) 39
8. 8.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
9. 9.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 1/4 (b) 5/6 (c) 2/3 (d) 1/3
10. 10.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
11. 11.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 6 (c) 21 (d) 18
12. 12.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 60 (c) 20 (d) 63
13. 13.What is the mean of 4, 7, 11, 5, 3 and 18? (a) 8 (b) 9 (c) 7 (d) 10
14. 14.A drawer has lots of black, blue and red 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) 2 (c) 6 (d) 3
15. 15.Using (a + b)² = a² + 2ab + b², what is 91²? (a) 7921 (b) 8291 (c) 8281 (d) 8101
16. 16.Which is the correct factorisation of x² + 14x + 48? (a) (x + 1)(x + 13) (b) (x + 6)(x + 8) (c) (x + 1)(x + 48) (d) (x − 6)(x − 8)
17. 17.What is the smallest prime factor of 299? (a) 23 (b) 13 (c) 1 (d) 2
18. 18.What is the distance between the points (4, 5) and (16, 10)? (a) 13 (b) 17 (c) 169 (d) 14
19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 74? (a) 7 (b) 18 (c) 19 (d) 17
20. 20.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 3/4 (c) 3/8 (d) 1/8
21. 21.In a class of 30 children, 15 like mangoes, 11 like bananas and 2 like both. How many like neither? (a) 6 (b) 4 (c) 2 (d) 8
22. 22.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 140° (d) 40°
23. 23.A cuboid is 10 cm long, 9 cm wide and 3 cm high. What is its total surface area? (a) 588 sq cm (b) 294 sq cm (c) 147 sq cm (d) 270 sq cm
24. 24.A bag has 8 yellow balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 9 (b) 12 (c) 10 (d) 2
25. 25.What is the mode of 17, 5, 19, 9, 5, 17 and 17? (a) 9 (b) 5 (c) 19 (d) 17
26. 26.What is the 31st term of the AP 17, 20, 23, 26, …? (a) 93 (b) 107 (c) 90 (d) 110
27. 27.What are the roots of x² − 14x + 45 = 0? (a) 3 and 15 (b) 5 and 9 (c) 1 and 45 (d) 1 and 13
28. 28.A drawer has lots of blue, white, green and red 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) 8 (c) 4 (d) 5
29. 29.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 110° (c) 250° (d) 70°
30. 30.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
31. 31.What is the mode of 2, 14, 16, 2, 12, 12 and 12? (a) 16 (b) 14 (c) 12 (d) 2
32. 32.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 160° (b) 85° (c) 95° (d) 105°
33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 3/11 (b) 1/12 (c) 1/11 (d) 1/9
34. 34.In which quadrant does the point (2, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
35. 35.What is the product of the roots of x² − 11x + 24 = 0? (a) 25 (b) 23 (c) 11 (d) 24
36. 36.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 70 (b) 140 (c) 80 (d) 22
37. 37.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
38. 38.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 144 (c) 24 (d) 66
39. 39.What is the median of 37, 4, 27, 15, 29, 17 and 33? (a) 27 (b) 29 (c) 15 (d) 17
40. 40.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2

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