Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 31 · 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.What is the smallest prime factor of 33? (a) 2 (b) 3 (c) 1 (d) 11
2. 2.What is the distance between the points (9, 1) and (21, 17)? (a) 21 (b) 20 (c) 400 (d) 28
3. 3.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 48 (c) 12 (d) 24
4. 4.What is the mean of 5, 13, 17, 15 and 15? (a) 14 (b) 13 (c) 12 (d) 15
5. 5.What is the 28th term of the AP 3, 11, 19, 27, …? (a) 227 (b) 216 (c) 224 (d) 219
6. 6.A bag has 2 red, 5 green and 4 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 4/11 (c) 7/11 (d) 4/7
7. 7.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 66 (c) 132 (d) 24
8. 8.A drawer has lots of red 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) 5 (c) 3 (d) 4
9. 9.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 70 (b) 40 (c) 12 (d) 35
10. 10.What is the mean of 5, 8, 7, 18, 17 and 11? (a) 10 (b) 12 (c) 11 (d) 13
11. 11.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 24 (c) 16 (d) 12
12. 12.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) 29 (b) 21 (c) 22 (d) 28
13. 13.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
14. 14.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
15. 15.In a class of 39 children, 13 like cricket, 24 like football and 6 like both. How many like only cricket? (a) 13 (b) 18 (c) 15 (d) 7
16. 16.What is the sum of all the whole numbers from 1 to 87? (a) 3741 (b) 7656 (c) 3828 (d) 3829
17. 17.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 125 times (c) 25 times (d) 5 times
18. 18.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
19. 19.A bag has 6 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) 2 (b) 7 (c) 9 (d) 4
20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 4 (b) 7 (c) 5 (d) 6
21. 21.What is the mode of 19, 18, 11, 11, 11, 15 and 15? (a) 11 (b) 19 (c) 18 (d) 15
22. 22.If a + b = 16 and ab = 60, what is a² + b²? (a) 256 (b) 376 (c) 136 (d) 196
23. 23.What is the 21st term of the AP 1, 3, 5, 7, …? (a) 40 (b) 43 (c) 42 (d) 41
24. 24.The mean of 3 numbers is 32. When the number 16 is added to them, what is the new mean? (a) 29 (b) 32 (c) 24 (d) 28
25. 25.What is the 31st term of the AP 8, 11, 14, 17, …? (a) 90 (b) 98 (c) 93 (d) 101
26. 26.What is the mode of 9, 9, 9, 5, 16, 19 and 5? (a) 5 (b) 9 (c) 19 (d) 16
27. 27.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 9 (d) 10
28. 28.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
29. 29.What is the 37th term of the AP 13, 20, 27, 34, …? (a) 272 (b) 259 (c) 265 (d) 252
30. 30.What is the mode of 2, 2, 8, 2, 13, 6 and 13? (a) 13 (b) 2 (c) 6 (d) 8
31. 31.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 56 (c) 64 (d) 16
32. 32.A bag has 7 red balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 9 (c) 8 (d) 13
33. 33.In which quadrant does the point (8, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
34. 34.What is the distance between the points (7, 3) and (22, 11)? (a) 17 (b) 289 (c) 23 (d) 18
35. 35.Which is the correct factorisation of x² + 14x + 48? (a) (x + 1)(x + 13) (b) (x + 6)(x + 8) (c) (x − 6)(x − 8) (d) (x + 1)(x + 48)
36. 36.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
37. 37.A bag has 12 red balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 13 (b) 14 (c) 2 (d) 20
38. 38.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 25 (b) 12 (c) 13 (d) 24
39. 39.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
40. 40.Which is the correct factorisation of x² + 15x + 54? (a) (x + 1)(x + 14) (b) (x − 6)(x − 9) (c) (x + 6)(x + 9) (d) (x + 1)(x + 54)

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