Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 247 · 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 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) 2 (b) 10 (c) 5 (d) 6
2. 2.A drawer has lots of red, blue, 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) 4 (b) 2 (c) 8 (d) 5
3. 3.In which quadrant does the point (1, 5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
4. 4.Two angles of a triangle are 25° and 100°. What is the exterior angle at the third corner? (a) 55° (b) 80° (c) 155° (d) 125°
5. 5.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 56 (c) 36 (d) 28
6. 6.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
7. 7.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
8. 8.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 58? (a) 7 (b) 6 (c) 5 (d) 4
10. 10.5 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 60 (b) 11 (c) 30 (d) 35
11. 11.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/5 (b) 5/6 (c) 1/6 (d) 1/3
12. 12.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/4 (c) 2/3 (d) 1/3
13. 13.The mean of 5 numbers is 14. When the number 8 is added to them, what is the new mean? (a) 13 (b) 11 (c) 12 (d) 14
14. 14.In a class of 45 children, 18 like cricket, 28 like football and 11 like both. How many like at least one of the two? (a) 35 (b) 46 (c) 24 (d) 45
15. 15.If a + b = 5 and ab = 4, what is (a − b)²? (a) 3 (b) 17 (c) 9 (d) 25
16. 16.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 253 (c) 231 (d) 506
17. 17.A bag has 12 blue balls and 9 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 14 (b) 21 (c) 2 (d) 13
18. 18.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 28 (c) 64 (d) 56
19. 19.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 260° (b) 80° (c) 100° (d) 160°
20. 20.A bag has 8 blue, 8 green and 8 yellow balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/2 (b) 3/8 (c) 2/3 (d) 1/3
21. 21.How many prime numbers are there between 50 and 60? (a) 1 (b) 3 (c) 2 (d) 4
22. 22.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 49 (c) 28 (d) 42
23. 23.Using (a − b)² = a² − 2ab + b², what is 19²? (a) 399 (b) 371 (c) 361 (d) 441
24. 24.In a class of 28 children, 17 like maths, 7 like science and 4 like both. How many like neither? (a) 4 (b) 9 (c) 8 (d) 12
25. 25.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
26. 26.A drawer has lots of red, yellow, green, white and blue 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) 10 (c) 5 (d) 6
27. 27.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 37 (b) 24 (c) 25 (d) 36
28. 28.What is the distance between the points (7, 4) and (13, 12)? (a) 100 (b) 14 (c) 11 (d) 10
29. 29.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
30. 30.What is the median of 8, 33, 20, 10 and 31? (a) 31 (b) 10 (c) 21 (d) 20
31. 31.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
32. 32.What is the midpoint of the line joining (5, 3) and (17, 15)? (a) (9, 11) (b) (11, 9) (c) (6, 6) (d) (22, 18)
33. 33.A bag has 4 red, 5 white and 2 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 10/11 (b) 2/11 (c) 1/3 (d) 9/11
34. 34.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 81 (c) 18 (d) 36
35. 35.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 9 (d) 11
36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 64? (a) 6 (b) 16 (c) 17 (d) 18
37. 37.If a + b = 15 and ab = 56, what is a² + b²? (a) 225 (b) 169 (c) 337 (d) 113
38. 38.If a + b = 9 and ab = 8, what is (a − b)²? (a) 65 (b) 81 (c) 49 (d) 7
39. 39.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 7 (c) 15 (d) 14
40. 40.What is the sum of the first 9 terms of the AP 4, 6, 8, …? (a) 117 (b) 216 (c) 108 (d) 20

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad