Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 396 · 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 team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 20 (c) 25 (d) 11
2. 2.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 120° (c) 80° (d) 100°
3. 3.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 45 (c) 20 (d) 90
4. 4.What is the median of 12, 32, 1, 26, 6, 36 and 10? (a) 10 (b) 12 (c) 26 (d) 13
5. 5.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 2 times (c) 4 times (d) 6 times
6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 5/36 (b) 1/9 (c) 4/11 (d) 1/11
8. 8.What are the roots of x² − 17x + 72 = 0? (a) 1 and 72 (b) 2 and 36 (c) 1 and 16 (d) 8 and 9
9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/18 (b) 2/11 (c) 1/11 (d) 1/12
10. 10.What is the midpoint of the line joining (6, 8) and (16, 6)? (a) (11, 7) (b) (7, 11) (c) (22, 14) (d) (5, 1)
11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/11 (b) 5/36 (c) 1/11 (d) 1/6
12. 12.In a class of 31 children, 22 like mangoes, 14 like bananas and 1 like neither. How many like both? (a) 5 (b) 1 (c) 6 (d) 30
13. 13.A bag has 4 blue balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 2 (c) 12 (d) 5
14. 14.In a class of 23 children, 14 like maths, 12 like science and 4 like neither. How many like both? (a) 3 (b) 19 (c) 7 (d) 4
15. 15.In a class of 26 children, 20 like maths, 13 like science and 10 like both. How many like neither? (a) 3 (b) 13 (c) 4 (d) 10
16. 16.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 7 (d) 8
17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 3 (b) 4 (c) 2 (d) 1
18. 18.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 104 sq cm (b) 24 sq cm (c) 26 sq cm (d) 52 sq cm
19. 19.In which quadrant does the point (6, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
20. 20.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 36 (c) 18 (d) 81
21. 21.The mean of 8 numbers is 31. When the number 40 is added to them, what is the new mean? (a) 32 (b) 31 (c) 33 (d) 34
22. 22.Two angles of a triangle are 20° and 55°. What is the third angle? (a) 125° (b) 160° (c) 105° (d) 75°
23. 23.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 1/4 (c) 5/8 (d) 3/5
24. 24.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 36 (c) 30 (d) 15
25. 25.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
26. 26.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
27. 27.Which is the correct factorisation of x² + 10x + 21? (a) (x + 1)(x + 9) (b) (x + 1)(x + 21) (c) (x + 3)(x + 7) (d) (x − 3)(x − 7)
28. 28.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)
29. 29.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
30. 30.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 332 (c) 391 (d) 390
31. 31.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 55° (c) 125° (d) 70°
32. 32.In a class of 24 children, 11 like mangoes, 12 like bananas and 8 like both. How many like neither? (a) 9 (b) 8 (c) 17 (d) 1
33. 33.The mean of 6 numbers is 19. When the number 12 is added to them, what is the new mean? (a) 17 (b) 20 (c) 19 (d) 18
34. 34.A bag has 6 yellow, 7 red and 8 green balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 2/7 (b) 1/3 (c) 5/7 (d) 16/21
35. 35.What is the mode of 1, 7, 5, 4, 1, 5 and 5? (a) 5 (b) 1 (c) 4 (d) 7
36. 36.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
37. 37.There are 7 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 35 (b) 70 (c) 42 (d) 12
38. 38.A bag has 9 black balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 16 (c) 8 (d) 10
39. 39.What is the smallest prime factor of 77? (a) 2 (b) 7 (c) 1 (d) 11
40. 40.In a class of 23 children, 13 like mangoes, 11 like bananas and 7 like both. How many like at least one of the two? (a) 17 (b) 10 (c) 23 (d) 24

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