Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 117 · 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 sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 378 (d) 729
2. 2.A bag has 4 red, 8 yellow and 2 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 2/7 (b) 5/7 (c) 11/14 (d) 1/3
3. 3.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 81 (c) 72 (d) 36
4. 4.Using (a − b)² = a² − 2ab + b², what is 99²? (a) 9801 (b) 9999 (c) 10201 (d) 9811
5. 5.A bag has 6 green balls and 5 red 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) 11 (c) 6 (d) 7
6. 6.A drawer has lots of yellow, blue, red and black 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) 8 (d) 4
7. 7.In a class of 43 children, 27 like cricket, 20 like football and 11 like both. How many like at least one of the two? (a) 36 (b) 25 (c) 43 (d) 47
8. 8.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 36 (c) 72 (d) 64
9. 9.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 3 (c) 9 (d) 6
10. 10.What is the midpoint of the line joining (0, 5) and (12, 3)? (a) (4, 6) (b) (12, 8) (c) (6, 4) (d) (6, 1)
11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 3/11 (c) 1/9 (d) 1/11
12. 12.What is the sum of all the whole numbers from 1 to 100? (a) 10100 (b) 4950 (c) 5050 (d) 5000
13. 13.Which is the correct factorisation of x² + 9x + 14? (a) (x + 1)(x + 14) (b) (x − 2)(x − 7) (c) (x + 1)(x + 8) (d) (x + 2)(x + 7)
14. 14.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 15 (c) 10 (d) 20
15. 15.A bag has 8 black balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 9 (b) 2 (c) 17 (d) 10
16. 16.A drawer has lots of blue, white 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) 4 (b) 2 (c) 3 (d) 6
17. 17.Two angles of a triangle are 45° and 115°. What is the third angle? (a) 135° (b) 65° (c) 160° (d) 20°
18. 18.Two angles of a triangle are 55° and 60°. What is the third angle? (a) 115° (b) 65° (c) 125° (d) 120°
19. 19.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) 15 (b) 8 (c) 14 (d) 7
20. 20.What is the smallest prime factor of 87? (a) 1 (b) 2 (c) 29 (d) 3
21. 21.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 145° (b) 35° (c) 215° (d) 70°
22. 22.Using (a + b)² = a² + 2ab + b², what is 32²? (a) 1034 (b) 1024 (c) 784 (d) 904
23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/18 (c) 1/11 (d) 1/12
24. 24.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 25 (c) 240 (d) 120
25. 25.In which quadrant does the point (7, −2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
26. 26.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 1331 cu cm (c) 726 cu cm (d) 484 cu cm
27. 27.What is the 13th term of the AP 6, 9, 12, 15, …? (a) 36 (b) 42 (c) 39 (d) 45
28. 28.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
29. 29.What is the median of 13, 15, 4, 27, 6, 3 and 25? (a) 27 (b) 6 (c) 15 (d) 13
30. 30.What is the mode of 16, 5, 7, 16, 7, 1 and 7? (a) 16 (b) 1 (c) 7 (d) 5
31. 31.Two angles of a triangle are 45° and 20°. What is the third angle? (a) 135° (b) 160° (c) 115° (d) 65°
32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 20 (b) 8 (c) 18 (d) 19
33. 33.What is the distance between the points (1, 12) and (25, 5)? (a) 25 (b) 26 (c) 31 (d) 625
34. 34.In a class of 42 children, 23 like dance, 19 like music and 3 like both. How many like neither? (a) 3 (b) 6 (c) 4 (d) 0
35. 35.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 490 (c) 398 (d) 489
36. 36.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
37. 37.A bag has 9 blue balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 16 (c) 10 (d) 11
38. 38.What is the midpoint of the line joining (9, 0) and (13, 6)? (a) (11, 3) (b) (2, 3) (c) (22, 6) (d) (3, 11)
39. 39.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 120 (c) 240 (d) 25
40. 40.A cuboid is 9 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 135 sq cm (b) 540 sq cm (c) 270 sq cm (d) 243 sq cm

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