Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 541 · 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.Two angles of a triangle are 40° and 20°. What is the exterior angle at the third corner? (a) 140° (b) 60° (c) 160° (d) 120°
2. 2.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
3. 3.What is the mean of 13, 6, 4 and 21? (a) 13 (b) 11 (c) 12 (d) 10
4. 4.In which quadrant does the point (−9, 1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
5. 5.What is the prime factorisation of 28? (a) 2 × 7 (b) 2 × 7² (c) 2² × 7 (d) 2³ × 7
6. 6.What is the smallest prime factor of 119? (a) 1 (b) 2 (c) 17 (d) 7
7. 7.In a class of 30 children, 6 like dance, 23 like music and 3 like both. How many like only dance? (a) 6 (b) 3 (c) 7 (d) 20
8. 8.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 145° (c) 35° (d) 55°
9. 9.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 42) (b) (x + 6)(x + 7) (c) (x + 1)(x + 12) (d) (x − 6)(x − 7)
10. 10.What is the smallest prime factor of 35? (a) 1 (b) 5 (c) 7 (d) 2
11. 11.Two angles of a triangle are 75° and 55°. What is the exterior angle at the third corner? (a) 130° (b) 105° (c) 50° (d) 125°
12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/6 (b) 5/11 (c) 1/11 (d) 5/36
13. 13.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 7/8 (c) 1/8 (d) 3/8
14. 14.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
15. 15.A bag has 10 yellow balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 11 (b) 12 (c) 2 (d) 16
16. 16.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 1/3 (c) 2/3 (d) 5/6
17. 17.A drawer has lots of blue, yellow and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 6 (c) 2 (d) 4
18. 18.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 182 (c) 196 (d) 91
19. 19.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/11 (c) 1/12 (d) 1/18
20. 20.A drawer has lots of white and green 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) 4 (c) 3 (d) 5
21. 21.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 340° (b) 160° (c) 70° (d) 20°
22. 22.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 3/8 (c) 5/8 (d) 1/4
23. 23.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 15) (b) (x + 7)(x + 9) (c) (x − 7)(x − 9) (d) (x + 1)(x + 63)
24. 24.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
25. 25.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 21 (c) 14 (d) 42
26. 26.Which is the correct factorisation of x² + 14x + 45? (a) (x − 5)(x − 9) (b) (x + 1)(x + 13) (c) (x + 1)(x + 45) (d) (x + 5)(x + 9)
27. 27.A bag has 2 red, 8 white and 7 blue balls. One ball is taken out without looking. What is the probability that it is white? (a) 8/17 (b) 8/9 (c) 1/3 (d) 9/17
28. 28.Two angles of a triangle are 50° and 115°. What is the third angle? (a) 65° (b) 15° (c) 130° (d) 165°
29. 29.What is the distance between the points (9, 9) and (24, 17)? (a) 289 (b) 17 (c) 23 (d) 18
30. 30.What is the smallest prime factor of 57? (a) 2 (b) 1 (c) 19 (d) 3
31. 31.Two angles of a triangle are 50° and 65°. What is the third angle? (a) 65° (b) 130° (c) 115° (d) 245°
32. 32.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 7/8 (c) 1/8 (d) 1/7
33. 33.What is the 23rd term of the AP 20, 26, 32, 38, …? (a) 158 (b) 132 (c) 138 (d) 152
34. 34.A bag has 4 red balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 11 (c) 14 (d) 2
35. 35.In which quadrant does the point (4, 8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
36. 36.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 20° (c) 70° (d) 55°
37. 37.How many factors does 26 have? (a) 4 (b) 5 (c) 2 (d) 3
38. 38.What is the mode of 2, 10, 17, 2, 2, 3 and 10? (a) 10 (b) 3 (c) 17 (d) 2
39. 39.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
40. 40.Two angles of a triangle are 40° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 145° (c) 35° (d) 140°

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