Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 789 · 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.How many times is the digit 5 written when you write all the numbers from 1 to 80? (a) 17 (b) 19 (c) 8 (d) 18
2. 2.In a class of 44 children, 19 like mangoes, 25 like bananas and 9 like neither. How many like both? (a) 9 (b) 35 (c) 8 (d) 10
3. 3.What is the median of 6, 8, 26, 7, 4, 36 and 3? (a) 9 (b) 6 (c) 7 (d) 8
4. 4.Using (a + b)² = a² + 2ab + b², what is 54²? (a) 2516 (b) 2926 (c) 2116 (d) 2916
5. 5.A bag has 10 black balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 11 (b) 20 (c) 12 (d) 2
6. 6.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 56 sq cm (b) 60 sq cm (c) 224 sq cm (d) 112 sq cm
7. 7.What is the missing term in the AP 1, 7, ?, 19, 25? (a) 12 (b) 19 (c) 13 (d) 14
8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 89? (a) 19 (b) 8 (c) 20 (d) 18
9. 9.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 10 (c) 15 (d) 25
10. 10.How many factors does 100 have? (a) 8 (b) 10 (c) 7 (d) 9
11. 11.In a class of 31 children, 10 like tea, 21 like coffee and 5 like neither. How many like both? (a) 5 (b) 26 (c) 6 (d) 4
12. 12.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 2/3 (c) 5/6 (d) 1/4
13. 13.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 160° (b) 70° (c) 340° (d) 20°
14. 14.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
15. 15.What is the product of the roots of x² − 14x + 48 = 0? (a) 14 (b) 47 (c) 48 (d) 49
16. 16.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
17. 17.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 132 (c) 144 (d) 24
18. 18.What are the roots of x² − 16x + 63 = 0? (a) 3 and 21 (b) 7 and 9 (c) 1 and 15 (d) 1 and 63
19. 19.How many prime numbers are there between 50 and 60? (a) 2 (b) 4 (c) 3 (d) 1
20. 20.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/2 (c) 1/3 (d) 1/4
21. 21.There are 7 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 98 (b) 56 (c) 49 (d) 14
22. 22.What is the distance between the points (4, 13) and (7, 9)? (a) 5 (b) 7 (c) 6 (d) 25
23. 23.A bag has 3 black balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 4 (c) 13 (d) 2
24. 24.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
25. 25.What is the median of 21, 37, 28, 24, 32, 25 and 10? (a) 24 (b) 26 (c) 25 (d) 28
26. 26.A bag has 8 yellow, 4 green and 6 white balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 5/9 (c) 4/5 (d) 4/9
27. 27.In a class of 29 children, 21 like maths, 17 like science and 10 like both. How many like only maths? (a) 7 (b) 12 (c) 21 (d) 11
28. 28.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 276 (c) 552 (d) 45
29. 29.How many prime numbers are there between 60 and 70? (a) 1 (b) 3 (c) 4 (d) 2
30. 30.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 25 (b) 24 (c) 37 (d) 36
31. 31.Which term of the AP 19, 25, 31, 37, … is 133? (a) 20th (b) 22nd (c) 21st (d) 19th
32. 32.What is the smallest prime factor of 203? (a) 1 (b) 7 (c) 29 (d) 2
33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 5 (b) 3 (c) 4 (d) 2
34. 34.In a class of 29 children, 16 like cricket, 21 like football and 11 like both. How many like at least one of the two? (a) 37 (b) 15 (c) 26 (d) 29
35. 35.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
36. 36.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 25 (c) 20 (d) 15
37. 37.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 302 (b) 52 (c) 594 (d) 297
38. 38.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/6 (b) 1/3 (c) 1/5 (d) 5/6
39. 39.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 440 cm (d) 220 cm
40. 40.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 7/36 (b) 1/6 (c) 6/11 (d) 1/11

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