Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 637 · 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 12th term of the AP 5, 10, 15, 20, …? (a) 60 (b) 65 (c) 55 (d) 61
2. 2.What is the median of 12, 38, 8, 9 and 4? (a) 8 (b) 12 (c) 10 (d) 9
3. 3.Which term of the AP 2, 8, 14, 20, … is 164? (a) 30th (b) 29th (c) 28th (d) 27th
4. 4.A bag has 8 red balls and 9 green 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) 10 (c) 9 (d) 17
5. 5.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 21 (c) 42 (d) 14
6. 6.A drawer has lots of blue, yellow and red 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) 6 (c) 3 (d) 4
7. 7.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 72 (c) 81 (d) 36
8. 8.What is the 38th term of the AP 15, 20, 25, 30, …? (a) 205 (b) 185 (c) 190 (d) 200
9. 9.Two angles of a triangle are 50° and 75°. What is the exterior angle at the third corner? (a) 125° (b) 130° (c) 55° (d) 105°
10. 10.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 390 (c) 391 (d) 332
11. 11.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) 13 (c) 24 (d) 12
12. 12.A drawer has lots of red and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 5 (c) 3 (d) 2
13. 13.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 294 sq cm (c) 49 sq cm (d) 343 sq cm
14. 14.A bag has 12 blue balls and 6 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) 18 (c) 7 (d) 13
15. 15.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 85° (c) 265° (d) 95°
16. 16.In which quadrant does the point (−5, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
17. 17.A bag has 3 red, 8 green and 3 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 3/11 (b) 11/14 (c) 3/14 (d) 1/3
18. 18.If a + b = 15 and ab = 36, what is a² + b²? (a) 297 (b) 225 (c) 189 (d) 153
19. 19.3 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 30 (b) 18 (c) 8 (d) 15
20. 20.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 2 (d) 3
21. 21.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
22. 22.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 202 (b) 192 (c) 201 (d) 206
23. 23.Using (a + b)² = a² + 2ab + b², what is 105²? (a) 10025 (b) 11025 (c) 11035 (d) 9025
24. 24.In a class of 51 children, 27 like maths, 27 like science and 9 like both. How many like at least one of the two? (a) 36 (b) 45 (c) 54 (d) 51
25. 25.A bag has 4 blue balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 6 (b) 2 (c) 13 (d) 5
26. 26.In a class of 31 children, 16 like maths, 19 like science and 9 like both. How many like neither? (a) 6 (b) 5 (c) 9 (d) 14
27. 27.What is the midpoint of the line joining (10, 4) and (18, 14)? (a) (14, 9) (b) (4, 5) (c) (28, 18) (d) (9, 14)
28. 28.What is the mean of 10, 9, 14, 7, 20 and 12? (a) 13 (b) 14 (c) 11 (d) 12
29. 29.In a class of 32 children, 26 like cricket, 12 like football and 7 like both. How many like neither? (a) 8 (b) 2 (c) 1 (d) 7
30. 30.In a class of 34 children, 16 like tea, 22 like coffee and 8 like both. How many like at least one of the two? (a) 38 (b) 34 (c) 30 (d) 22
31. 31.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) 22 (c) 15 (d) 21
32. 32.A bag has 9 black balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 14 (b) 6 (c) 2 (d) 10
33. 33.What is the distance between the points (8, 18) and (20, 2)? (a) 21 (b) 20 (c) 400 (d) 28
34. 34.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 1/2 (c) 1/3 (d) 2/3
35. 35.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
36. 36.What is the smallest prime factor of 21? (a) 7 (b) 1 (c) 2 (d) 3
37. 37.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 378 (d) 729
38. 38.A bag has 9 blue balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 10 (b) 2 (c) 13 (d) 11
39. 39.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 170 (b) 320 (c) 25 (d) 160
40. 40.What is the missing term in the AP 10, 12, 14, ?, 18? (a) 17 (b) 15 (c) 16 (d) 18

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