Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 890 · 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 6 blue balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 2 (c) 8 (d) 13
2. 2.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 72 (b) 81 (c) 18 (d) 36
3. 3.A bag has 8 blue balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 10 (c) 12 (d) 9
4. 4.A bag has 12 green balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 14 (c) 13 (d) 23
5. 5.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 6 (b) 12 (c) 5 (d) 9
6. 6.In a class of 23 children, 12 like maths, 12 like science and 3 like both. How many like only maths? (a) 9 (b) 12 (c) 11 (d) 3
7. 7.The mean of 5 numbers is 19. When the number 1 is added to them, what is the new mean? (a) 10 (b) 19 (c) 17 (d) 16
8. 8.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
9. 9.Two angles of a triangle are 80° and 65°. What is the third angle? (a) 35° (b) 145° (c) 115° (d) 100°
10. 10.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) 7 (c) 15 (d) 14
11. 11.In a class of 22 children, 11 like maths, 9 like science and 6 like both. How many like only maths? (a) 11 (b) 5 (c) 13 (d) 3
12. 12.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 10 (d) 11
13. 13.What is the prime factorisation of 45? (a) 3 × 5 (b) 3² × 5 (c) 3 × 5² (d) 3³ × 5
14. 14.If a + b = 8 and ab = 12, what is (a − b)²? (a) 64 (b) 4 (c) 40 (d) 16
15. 15.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 50° (b) 130° (c) 40° (d) 310°
16. 16.What is the mean of 11, 17, 9 and 23? (a) 16 (b) 12 (c) 20 (d) 15
17. 17.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
18. 18.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 30 (c) 12 (d) 15
19. 19.What is the median of 26, 10, 38, 37 and 20? (a) 37 (b) 20 (c) 38 (d) 26
20. 20.A bag has 3 green, 8 red and 2 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 11/13 (b) 1/3 (c) 2/13 (d) 12/13
21. 21.What is the sum of all the whole numbers from 1 to 88? (a) 7832 (b) 3916 (c) 3828 (d) 3872
22. 22.How many prime numbers are there between 70 and 100? (a) 8 (b) 5 (c) 6 (d) 7
23. 23.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 57 (c) 162 (d) 18
24. 24.A bag has 11 white balls and 12 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) 23 (c) 12 (d) 13
25. 25.What is the distance between the points (2, 6) and (8, 14)? (a) 14 (b) 10 (c) 100 (d) 11
26. 26.How many factors does 115 have? (a) 3 (b) 5 (c) 2 (d) 4
27. 27.How many factors does 13 have? (a) 4 (b) 2 (c) 1 (d) 3
28. 28.In a class of 40 children, 25 like dance, 23 like music and 12 like both. How many like neither? (a) 16 (b) 4 (c) 12 (d) 5
29. 29.The mean of 7 numbers is 10. When the number 26 is added to them, what is the new mean? (a) 13 (b) 10 (c) 18 (d) 12
30. 30.What is the mean of 15, 4, 14, 7, 8 and 12? (a) 12 (b) 11 (c) 9 (d) 10
31. 31.How many factors does 106 have? (a) 3 (b) 2 (c) 4 (d) 5
32. 32.How many prime numbers are there between 30 and 40? (a) 3 (b) 4 (c) 1 (d) 2
33. 33.If a + b = 13 and ab = 40, what is (a − b)²? (a) 3 (b) 9 (c) 169 (d) 89
34. 34.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 15 (c) 22 (d) 21
35. 35.How many prime numbers are there between 90 and 100? (a) 1 (b) 2 (c) 3 (d) 0
36. 36.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
37. 37.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 9 (c) 15 (d) 30
38. 38.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/9 (b) 5/36 (c) 1/11 (d) 4/11
39. 39.What is the missing term in the AP 6, ?, 20, 27, 34? (a) 14 (b) 13 (c) 12 (d) 20
40. 40.A cuboid is 5 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 184 sq cm (b) 368 sq cm (c) 92 sq cm (d) 160 sq cm

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