Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 383 · 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 43 children, 17 like mangoes, 25 like bananas and 9 like both. How many like at least one of the two? (a) 43 (b) 24 (c) 33 (d) 42
2. 2.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
3. 3.Two angles of a triangle are 30° and 90°. What is the third angle? (a) 90° (b) 120° (c) 60° (d) 150°
4. 4.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
5. 5.What is the missing term in the AP 2, 4, 6, ?, 10? (a) 7 (b) 10 (c) 9 (d) 8
6. 6.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 140° (b) 60° (c) 100° (d) 120°
7. 7.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/5 (b) 5/6 (c) 1/3 (d) 1/6
8. 8.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 1/4 (c) 3/4 (d) 1/3
9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 52? (a) 6 (b) 5 (c) 3 (d) 4
10. 10.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 35° (c) 55° (d) 110°
11. 11.A bag has 3 red balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 14 (c) 2 (d) 4
12. 12.What is the mean of 3, 6, 14 and 21? (a) 11 (b) 12 (c) 13 (d) 10
13. 13.If a + b = 20 and ab = 99, what is (a − b)²? (a) 2 (b) 4 (c) 400 (d) 202
14. 14.There are 6 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 84 (b) 48 (c) 13 (d) 42
15. 15.A canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 28 (b) 10 (c) 21 (d) 42
16. 16.What is the mean of 6, 13, 2 and 7? (a) 8 (b) 7 (c) 6 (d) 9
17. 17.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 100° (b) 120° (c) 140° (d) 60°
18. 18.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 104 (c) 96 (d) 95
19. 19.A bag has 11 red balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 12 (b) 16 (c) 2 (d) 13
20. 20.How many prime numbers are there between 60 and 70? (a) 2 (b) 1 (c) 4 (d) 3
21. 21.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 22 (c) 66 (d) 198
22. 22.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 25 (c) 20 (d) 15
23. 23.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 20 (c) 100 (d) 45
24. 24.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 1/3 (c) 5/6 (d) 1/4
25. 25.In a class of 42 children, 16 like maths, 22 like science and 8 like neither. How many like both? (a) 8 (b) 34 (c) 4 (d) 5
26. 26.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 121 (c) 110 (d) 55
27. 27.In a class of 28 children, 15 like tea, 13 like coffee and 9 like both. How many like only tea? (a) 4 (b) 6 (c) 9 (d) 15
28. 28.A bag has 11 red balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 7 (c) 17 (d) 2
29. 29.Two angles of a triangle are 55° and 60°. What is the third angle? (a) 65° (b) 115° (c) 120° (d) 125°
30. 30.How many prime numbers are there between 60 and 80? (a) 5 (b) 4 (c) 7 (d) 6
31. 31.What is the sum of all the whole numbers from 1 to 69? (a) 4830 (b) 2416 (c) 2415 (d) 2346
32. 32.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 40° (b) 115° (c) 105° (d) 140°
33. 33.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
34. 34.Two angles of a triangle are 65° and 90°. What is the third angle? (a) 155° (b) 115° (c) 90° (d) 25°
35. 35.A drawer has lots of green, red, black 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) 8 (b) 2 (c) 4 (d) 5
36. 36.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 164 sq cm (b) 42 sq cm (c) 41 sq cm (d) 82 sq cm
37. 37.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
38. 38.A bag has 7 red, 3 blue and 3 white balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 6/13 (c) 6/7 (d) 7/13
39. 39.What is the midpoint of the line joining (1, 10) and (11, 2)? (a) (5, 4) (b) (7, 6) (c) (6, 6) (d) (12, 12)
40. 40.What is the sum of the roots of x² − 8x + 15 = 0? (a) 8 (b) 9 (c) 7 (d) 15

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