Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 769 · 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.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
2. 2.What is the midpoint of the line joining (1, 9) and (7, 21)? (a) (8, 30) (b) (4, 15) (c) (15, 4) (d) (3, 6)
3. 3.What is the missing term in the AP 17, 21, ?, 29, 33? (a) 25 (b) 26 (c) 24 (d) 29
4. 4.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 30° (b) 150° (c) 60° (d) 31°
5. 5.What is the sum of all the whole numbers from 1 to 20? (a) 210 (b) 420 (c) 200 (d) 190
6. 6.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
7. 7.A bag has 7 yellow balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 2 (c) 8 (d) 13
8. 8.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 180 (c) 171 (d) 162
9. 9.There are 3 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 18 (b) 21 (c) 9 (d) 36
10. 10.What is the mean of 12, 8, 7, 20, 20 and 5? (a) 11 (b) 12 (c) 13 (d) 14
11. 11.How many factors does 38 have? (a) 3 (b) 4 (c) 2 (d) 5
12. 12.In a class of 37 children, 17 like dance, 25 like music and 7 like neither. How many like both? (a) 5 (b) 12 (c) 30 (d) 7
13. 13.What is the midpoint of the line joining (10, 6) and (20, 16)? (a) (15, 11) (b) (30, 22) (c) (5, 5) (d) (11, 15)
14. 14.In a class of 37 children, 18 like tea, 22 like coffee and 8 like neither. How many like both? (a) 8 (b) 29 (c) 3 (d) 11
15. 15.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
16. 16.There are 6 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) 13 (b) 84 (c) 48 (d) 42
17. 17.What is the smallest prime factor of 91? (a) 1 (b) 7 (c) 13 (d) 2
18. 18.In a class of 46 children, 18 like dance, 29 like music and 10 like both. How many like at least one of the two? (a) 37 (b) 47 (c) 46 (d) 27
19. 19.Using (a − b)² = a² − 2ab + b², what is 28²? (a) 794 (b) 896 (c) 784 (d) 1024
20. 20.What is the mean of 4, 4, 14, 20, 11 and 7? (a) 11 (b) 12 (c) 10 (d) 9
21. 21.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 66 (c) 63 (d) 189
22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 16 (b) 4 (c) 14 (d) 15
23. 23.Using (a − b)² = a² − 2ab + b², what is 19²? (a) 371 (b) 441 (c) 361 (d) 399
24. 24.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
25. 25.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 60 (b) 100 (c) 50 (d) 18
26. 26.What is the prime factorisation of 180? (a) 2 × 3² × 5² (b) 2 × 3² × 5 (c) 2³ × 3² × 5 (d) 2² × 3² × 5
27. 27.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 66 (c) 55 (d) 121
28. 28.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 36 (c) 21 (d) 30
29. 29.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
30. 30.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) 12 (b) 13 (c) 25 (d) 24
31. 31.A bag has 11 green balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 12 (c) 13 (d) 21
32. 32.A bag has 7 yellow balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 15 (c) 2 (d) 9
33. 33.What is the 39th term of the AP 10, 17, 24, 31, …? (a) 273 (b) 276 (c) 266 (d) 283
34. 34.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 10 (c) 30 (d) 90
35. 35.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/3 (c) 2/3 (d) 1/4
36. 36.Two angles of a triangle are 55° and 85°. What is the third angle? (a) 125° (b) 40° (c) 95° (d) 140°
37. 37.A bag has 4 yellow, 5 red and 7 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 5/16 (c) 3/4 (d) 1/4
38. 38.In a class of 42 children, 26 like maths, 24 like science and 4 like neither. How many like both? (a) 4 (b) 8 (c) 38 (d) 12
39. 39.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 27 (c) 81 (d) 9
40. 40.Using (a − b)² = a² − 2ab + b², what is 49²? (a) 2601 (b) 2401 (c) 2411 (d) 2499

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