Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 976 · 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.What is the distance between the points (2, 0) and (8, 8)? (a) 10 (b) 11 (c) 100 (d) 14
2. 2.In a class of 33 children, 15 like tea, 11 like coffee and 2 like both. How many like neither? (a) 11 (b) 9 (c) 7 (d) 2
3. 3.What is the 33rd term of the AP 13, 21, 29, 37, …? (a) 269 (b) 264 (c) 277 (d) 256
4. 4.Which is the correct factorisation of x² + 10x + 16? (a) (x + 2)(x + 8) (b) (x − 2)(x − 8) (c) (x + 1)(x + 9) (d) (x + 1)(x + 16)
5. 5.If a + b = 20 and ab = 99, what is a² + b²? (a) 598 (b) 202 (c) 400 (d) 301
6. 6.In which quadrant does the point (−2, 5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
7. 7.What is the sum of all the whole numbers from 1 to 44? (a) 990 (b) 968 (c) 1980 (d) 946
8. 8.In a class of 35 children, 10 like tea, 23 like coffee and 6 like neither. How many like both? (a) 6 (b) 29 (c) 5 (d) 4
9. 9.A bag has 9 yellow, 9 white and 6 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 7/24 (c) 1/4 (d) 3/4
10. 10.A bag has 5 green, 8 red and 8 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 8/21 (b) 13/21 (c) 1/3 (d) 2/3
11. 11.What is the 18th term of the AP 16, 20, 24, 28, …? (a) 68 (b) 72 (c) 84 (d) 88
12. 12.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 15 (c) 21 (d) 30
13. 13.A bag has 8 red, 5 yellow and 8 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 2/3 (b) 1/3 (c) 13/21 (d) 8/21
14. 14.A bag has 11 green balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 13 (b) 23 (c) 12 (d) 2
15. 15.What is the sum of the roots of x² − 14x + 48 = 0? (a) 13 (b) 48 (c) 14 (d) 15
16. 16.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 51° (b) 50° (c) 100° (d) 130°
17. 17.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
18. 18.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 9 (c) 3 (d) 12
19. 19.The mean of 5 numbers is 30. When the number 6 is added to them, what is the new mean? (a) 30 (b) 18 (c) 26 (d) 27
20. 20.If a + b = 13 and ab = 36, what is a² + b²? (a) 169 (b) 97 (c) 133 (d) 241
21. 21.What is the sum of all the whole numbers from 1 to 26? (a) 351 (b) 338 (c) 702 (d) 325
22. 22.What is the smallest prime factor of 77? (a) 11 (b) 2 (c) 1 (d) 7
23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 87? (a) 16 (b) 17 (c) 14 (d) 8
24. 24.A bag has 3 black balls and 4 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) 5 (c) 4 (d) 7
25. 25.What is the distance between the points (1, 9) and (9, 24)? (a) 289 (b) 23 (c) 17 (d) 18
26. 26.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 56 (c) 16 (d) 28
27. 27.Two angles of a triangle are 55° and 85°. What is the third angle? (a) 40° (b) 125° (c) 95° (d) 140°
28. 28.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 1/9 (c) 5/36 (d) 4/11
29. 29.In which quadrant does the point (−2, 4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
30. 30.A bag has 4 red balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 6 (b) 5 (c) 2 (d) 11
31. 31.The mean of 9 numbers is 20. When the number 30 is added to them, what is the new mean? (a) 25 (b) 20 (c) 22 (d) 21
32. 32.The mean of 7 numbers is 39. When the number 7 is added to them, what is the new mean? (a) 35 (b) 23 (c) 36 (d) 39
33. 33.In which quadrant does the point (8, −5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
34. 34.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
35. 35.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 49 (c) 42 (d) 21
36. 36.7 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 14 (b) 98 (c) 56 (d) 49
37. 37.What is the distance between the points (6, 6) and (10, 9)? (a) 7 (b) 5 (c) 6 (d) 25
38. 38.Using (a − b)² = a² − 2ab + b², what is 65²? (a) 5625 (b) 4875 (c) 4235 (d) 4225
39. 39.Two angles of a triangle are 50° and 100°. What is the exterior angle at the third corner? (a) 150° (b) 130° (c) 80° (d) 30°
40. 40.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 110 (c) 22 (d) 55

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