Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 260 · 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.In a class of 38 children, 26 like cricket, 20 like football and 9 like both. How many like only cricket? (a) 11 (b) 26 (c) 18 (d) 17
2. 2.What is the mean of 10, 9, 7, 14, 15 and 5? (a) 11 (b) 10 (c) 12 (d) 9
3. 3.How many factors does 69 have? (a) 4 (b) 3 (c) 2 (d) 5
4. 4.Two angles of a triangle are 20° and 65°. What is the third angle? (a) 115° (b) 160° (c) 95° (d) 85°
5. 5.What is the prime factorisation of 40? (a) 2³ × 5 (b) 2² × 5 (c) 2⁴ × 5 (d) 2 × 5³
6. 6.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 30° (c) 60° (d) 120°
7. 7.A bag has 3 blue balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 11 (b) 5 (c) 4 (d) 2
8. 8.A bag has 8 black balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 15 (c) 9 (d) 10
9. 9.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) 14 (c) 15 (d) 7
10. 10.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 300° (b) 60° (c) 30° (d) 120°
11. 11.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 190 (c) 37 (d) 380
12. 12.What is the distance between the points (1, 9) and (5, 12)? (a) 5 (b) 6 (c) 25 (d) 7
13. 13.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
14. 14.A bag has 4 yellow balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 6 (b) 15 (c) 2 (d) 5
15. 15.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 135° (b) 155° (c) 160° (d) 45°
16. 16.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 220° (b) 41° (c) 40° (d) 140°
17. 17.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 22 (b) 28 (c) 29 (d) 21
18. 18.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 342 (c) 171 (d) 324
19. 19.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 18 (c) 81 (d) 36
20. 20.How many factors does 19 have? (a) 1 (b) 4 (c) 3 (d) 2
21. 21.A drawer has lots of 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) 3 (b) 5 (c) 4 (d) 2
22. 22.What is the distance between the points (0, 4) and (15, 12)? (a) 17 (b) 18 (c) 289 (d) 23
23. 23.Which is the correct factorisation of x² + 17x + 72? (a) (x + 8)(x + 9) (b) (x + 1)(x + 16) (c) (x − 8)(x − 9) (d) (x + 1)(x + 72)
24. 24.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
25. 25.What is the mode of 20, 9, 9, 9, 15, 5 and 15? (a) 20 (b) 15 (c) 9 (d) 5
26. 26.A bag has 3 red, 3 yellow and 7 green balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 11/13 (c) 10/13 (d) 3/13
27. 27.In a class of 38 children, 28 like dance, 16 like music and 12 like both. How many like neither? (a) 6 (b) 12 (c) 7 (d) 18
28. 28.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/11 (b) 7/36 (c) 1/6 (d) 6/11
29. 29.What is the distance between the points (5, 3) and (21, 15)? (a) 21 (b) 28 (c) 20 (d) 400
30. 30.A bag has 10 red balls and 8 yellow 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) 9 (c) 18 (d) 11
31. 31.What is the missing term in the AP 9, ?, 17, 21, 25? (a) 14 (b) 17 (c) 13 (d) 12
32. 32.Which term of the AP 5, 13, 21, 29, … is 301? (a) 37th (b) 38th (c) 39th (d) 40th
33. 33.Two angles of a triangle are 45° and 60°. What is the third angle? (a) 75° (b) 120° (c) 135° (d) 105°
34. 34.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
35. 35.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 25° (c) 130° (d) 50°
36. 36.In a class of 38 children, 25 like dance, 9 like music and 5 like both. How many like neither? (a) 4 (b) 9 (c) 14 (d) 5
37. 37.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/4
38. 38.A bag has 9 red, 9 green and 3 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/7 (b) 6/7 (c) 19/21 (d) 1/3
39. 39.What is the distance between the points (7, 4) and (13, 12)? (a) 100 (b) 14 (c) 10 (d) 11
40. 40.What is the prime factorisation of 140? (a) 2³ × 5 × 7 (b) 2 × 5 × 7 (c) 2 × 5 × 7² (d) 2² × 5 × 7

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