Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 516 · 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 bag has 4 yellow balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 5 (c) 2 (d) 7
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/11 (b) 5/11 (c) 5/36 (d) 1/6
3. 3.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 28 (c) 56 (d) 64
4. 4.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 132 (c) 66 (d) 21
5. 5.A bag has 3 red, 4 yellow and 6 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 6/13 (b) 8/13 (c) 7/13 (d) 1/3
6. 6.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/11 (c) 1/18 (d) 1/36
8. 8.In a class of 54 children, 26 like dance, 30 like music and 9 like neither. How many like both? (a) 2 (b) 11 (c) 9 (d) 45
9. 9.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 70° (b) 71° (c) 250° (d) 110°
10. 10.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 1/4 (c) 5/8 (d) 3/8
11. 11.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 50° (c) 140° (d) 40°
12. 12.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 85° (c) 95° (d) 115°
13. 13.The mean of 4 numbers is 25. When the number 5 is added to them, what is the new mean? (a) 25 (b) 21 (c) 22 (d) 15
14. 14.If a + b = 14 and ab = 40, what is a² + b²? (a) 116 (b) 196 (c) 276 (d) 156
15. 15.What is the midpoint of the line joining (10, 6) and (14, 8)? (a) (12, 7) (b) (24, 14) (c) (7, 12) (d) (2, 1)
16. 16.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 30° (b) 150° (c) 115° (d) 95°
17. 17.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 196 (c) 105 (d) 91
18. 18.A bag has 3 black balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 5 (c) 13 (d) 4
19. 19.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 64 cu cm (c) 12 cu cm (d) 65 cu cm
20. 20.A bag has 12 blue balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 18 (b) 13 (c) 2 (d) 14
21. 21.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
22. 22.What is the missing term in the AP 18, 21, ?, 27, 30? (a) 23 (b) 27 (c) 25 (d) 24
23. 23.What is the sum of the roots of x² − 11x + 24 = 0? (a) 10 (b) 12 (c) 11 (d) 24
24. 24.The mean of 7 numbers is 15. When the number 7 is added to them, what is the new mean? (a) 14 (b) 11 (c) 15 (d) 13
25. 25.A bag has 6 black balls and 11 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) 2 (d) 17
26. 26.Using (a − b)² = a² − 2ab + b², what is 97²? (a) 9409 (b) 10609 (c) 9991 (d) 9419
27. 27.How many factors does 65 have? (a) 4 (b) 5 (c) 3 (d) 2
28. 28.Two angles of a triangle are 60° and 100°. What is the third angle? (a) 20° (b) 80° (c) 120° (d) 160°
29. 29.What is the distance between the points (1, 4) and (5, 7)? (a) 5 (b) 7 (c) 25 (d) 6
30. 30.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 30° (b) 150° (c) 135° (d) 75°
31. 31.What is the midpoint of the line joining (3, 11) and (5, 1)? (a) (1, 5) (b) (8, 12) (c) (6, 4) (d) (4, 6)
32. 32.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 135° (b) 130° (c) 85° (d) 95°
33. 33.What is the mean of 4, 18, 17 and 5? (a) 11 (b) 13 (c) 10 (d) 12
34. 34.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 100° (b) 160° (c) 80° (d) 81°
35. 35.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 3 times (d) 6 times
36. 36.A bag has 8 blue balls and 10 black 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) 11 (c) 18 (d) 9
37. 37.Using (a + b)² = a² + 2ab + b², what is 31²? (a) 841 (b) 971 (c) 901 (d) 961
38. 38.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 6 (b) 12 (c) 9 (d) 5
39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 56? (a) 6 (b) 3 (c) 4 (d) 5
40. 40.Two angles of a triangle are 35° and 80°. What is the third angle? (a) 115° (b) 100° (c) 65° (d) 145°

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