Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 555 · 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. 1.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 56 (c) 64 (d) 36
2. 2.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 42) (b) (x + 6)(x + 7) (c) (x − 6)(x − 7) (d) (x + 1)(x + 12)
3. 3.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
4. 4.In which quadrant does the point (1, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
5. 5.If a + b = 20 and ab = 99, what is (a − b)²? (a) 202 (b) 400 (c) 4 (d) 2
6. 6.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 16) (b) (x + 8)(x + 9) (c) (x − 8)(x − 9) (d) (x + 1)(x + 72)
7. 7.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 25 times (c) 125 times (d) 10 times
8. 8.In a class of 42 children, 18 like tea, 23 like coffee and 6 like both. How many like at least one of the two? (a) 42 (b) 29 (c) 41 (d) 35
9. 9.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 10° (c) 5° (d) 95°
10. 10.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
11. 11.A cuboid is 12 cm long, 10 cm wide and 7 cm high. What is its total surface area? (a) 840 sq cm (b) 1096 sq cm (c) 548 sq cm (d) 274 sq cm
12. 12.In which quadrant does the point (−7, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
13. 13.In a class of 23 children, 14 like mangoes, 12 like bananas and 7 like both. How many like at least one of the two? (a) 23 (b) 26 (c) 12 (d) 19
14. 14.In a class of 43 children, 23 like dance, 25 like music and 11 like both. How many like at least one of the two? (a) 26 (b) 37 (c) 48 (d) 43
15. 15.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 30 (c) 15 (d) 36
16. 16.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 391 (b) 390 (c) 381 (d) 332
17. 17.What is the midpoint of the line joining (3, 10) and (13, 16)? (a) (5, 3) (b) (16, 26) (c) (13, 8) (d) (8, 13)
18. 18.In a class of 14 children, 8 like mangoes, 7 like bananas and 3 like neither. How many like both? (a) 3 (b) 11 (c) 4 (d) 1
19. 19.Using (a − b)² = a² − 2ab + b², what is 99²? (a) 9801 (b) 9999 (c) 9811 (d) 10201
20. 20.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 37 (b) 28 (c) 38 (d) 46
21. 21.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
22. 22.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) 28 (c) 22 (d) 21
23. 23.The mean of 4 numbers is 40. When the number 55 is added to them, what is the new mean? (a) 40 (b) 44 (c) 43 (d) 42
24. 24.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 306 (b) 171 (c) 33 (d) 153
25. 25.In a class of 44 children, 21 like tea, 22 like coffee and 6 like both. How many like neither? (a) 7 (b) 13 (c) 6 (d) 1
26. 26.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 110° (b) 55° (c) 235° (d) 125°
27. 27.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/2 (c) 1/4 (d) 1/3
28. 28.In a class of 28 children, 19 like cricket, 9 like football and 5 like both. How many like neither? (a) 0 (b) 5 (c) 6 (d) 10
29. 29.What is the midpoint of the line joining (2, 8) and (10, 0)? (a) (4, 6) (b) (6, 4) (c) (4, 4) (d) (12, 8)
30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/12 (b) 1/11 (c) 2/11 (d) 1/18
31. 31.Two angles of a triangle are 40° and 105°. What is the exterior angle at the third corner? (a) 35° (b) 140° (c) 75° (d) 145°
32. 32.A bag has 11 white balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 12 (b) 2 (c) 15 (d) 13
33. 33.What is the median of 24, 3, 12, 36 and 4? (a) 24 (b) 4 (c) 13 (d) 12
34. 34.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 235° (b) 55° (c) 125° (d) 110°
35. 35.What is the 16th term of the AP 1, 4, 7, 10, …? (a) 45 (b) 49 (c) 46 (d) 48
36. 36.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 270° (b) 130° (c) 90° (d) 140°
37. 37.A bag has 6 yellow, 4 green and 6 blue balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 13/16 (c) 3/4 (d) 1/4
38. 38.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 65 (b) 120 (c) 60 (d) 16
39. 39.A drawer has lots of green 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) 5 (b) 2 (c) 3 (d) 4
40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 3 (b) 4 (c) 2 (d) 1

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