Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 250 · 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 37 children, 24 like cricket, 21 like football and 3 like neither. How many like both? (a) 11 (b) 34 (c) 8 (d) 3
2. 2.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
3. 3.In a class of 51 children, 31 like mangoes, 31 like bananas and 12 like both. How many like at least one of the two? (a) 50 (b) 38 (c) 51 (d) 62
4. 4.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 25 (c) 10 (d) 20
5. 5.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 85° (b) 10° (c) 105° (d) 170°
6. 6.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 12 (c) 24 (d) 16
7. 7.What is the distance between the points (7, 9) and (14, 33)? (a) 26 (b) 625 (c) 31 (d) 25
8. 8.Two angles of a triangle are 75° and 55°. What is the third angle? (a) 130° (b) 50° (c) 105° (d) 125°
9. 9.What is the prime factorisation of 240? (a) 2⁵ × 3 × 5 (b) 2⁴ × 3 × 5 (c) 2 × 3 × 5⁴ (d) 2³ × 3 × 5
10. 10.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 25° (c) 130° (d) 35°
11. 11.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 534 (b) 525 (c) 428 (d) 535
12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 30? (a) 2 (b) 4 (c) 3 (d) 1
13. 13.A bag has 10 green balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 17 (b) 11 (c) 12 (d) 2
14. 14.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 16) (b) (x + 8)(x + 9) (c) (x + 1)(x + 72) (d) (x − 8)(x − 9)
15. 15.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) 24 (b) 25 (c) 12 (d) 13
16. 16.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 40° (c) 65° (d) 50°
17. 17.A drawer has lots of green, blue 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) 6 (b) 4 (c) 3 (d) 2
18. 18.How many prime numbers are there between 20 and 50? (a) 9 (b) 6 (c) 7 (d) 8
19. 19.What is the prime factorisation of 360? (a) 2 × 3² × 5³ (b) 2⁴ × 3² × 5 (c) 2³ × 3² × 5 (d) 2² × 3² × 5
20. 20.A drawer has lots of green, black, yellow, white and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 2 (c) 5 (d) 10
21. 21.What is the smallest prime factor of 319? (a) 1 (b) 11 (c) 29 (d) 2
22. 22.A drawer has lots of yellow, white, 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) 8 (b) 5 (c) 2 (d) 4
23. 23.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 30 (c) 15 (d) 9
24. 24.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 42) (b) (x + 6)(x + 7) (c) (x + 1)(x + 12) (d) (x − 6)(x − 7)
25. 25.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 41 (b) 42 (c) 32 (d) 50
26. 26.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 276 (c) 286 (d) 285
27. 27.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 160° (b) 20° (c) 40° (d) 21°
28. 28.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 225 (c) 105 (d) 210
29. 29.What is the mean of 15, 9, 5, 4, 18 and 15? (a) 10 (b) 13 (c) 12 (d) 11
30. 30.A bag has 5 green, 5 yellow and 4 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 9/14 (b) 5/14 (c) 1/3 (d) 5/9
31. 31.What is the 36th term of the AP 2, 10, 18, 26, …? (a) 280 (b) 282 (c) 288 (d) 290
32. 32.What is the smallest prime factor of 155? (a) 1 (b) 5 (c) 2 (d) 31
33. 33.What is the sum of the first 11 terms of the AP 9, 14, 19, …? (a) 374 (b) 379 (c) 748 (d) 59
34. 34.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 121 (c) 66 (d) 55
35. 35.Two angles of a triangle are 50° and 55°. What is the exterior angle at the third corner? (a) 130° (b) 75° (c) 125° (d) 105°
36. 36.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 91 (c) 169 (d) 25
37. 37.A bag has 6 red balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 10 (c) 8 (d) 7
38. 38.Which is the correct factorisation of x² + 12x + 35? (a) (x + 1)(x + 11) (b) (x + 1)(x + 35) (c) (x − 5)(x − 7) (d) (x + 5)(x + 7)
39. 39.The mean of 4 numbers is 18. When the number 3 is added to them, what is the new mean? (a) 14 (b) 16 (c) 18 (d) 15
40. 40.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 69 (b) 19 (c) 78 (d) 138

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