Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 512 · 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 a + b = 11 and ab = 30, what is (a − b)²? (a) 91 (b) 61 (c) 121 (d) 1
2. 2.The mean of 6 numbers is 27. When the number 55 is added to them, what is the new mean? (a) 27 (b) 31 (c) 41 (d) 32
3. 3.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 88 cm (d) 352 cm
4. 4.In a class of 30 children, 20 like dance, 10 like music and 2 like both. How many like at least one of the two? (a) 30 (b) 28 (c) 26 (d) 29
5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 5/36 (b) 1/9 (c) 4/11 (d) 1/11
6. 6.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
7. 7.A bag has 5 white balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 6 (c) 7 (d) 2
8. 8.What is the mean of 19, 12, 20 and 5? (a) 16 (b) 13 (c) 15 (d) 14
9. 9.A drawer has lots of yellow 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) 5 (d) 3
10. 10.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 198 (c) 208 (d) 207
11. 11.How many factors does 43 have? (a) 1 (b) 3 (c) 4 (d) 2
12. 12.A bag has 7 black balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 9 (b) 8 (c) 2 (d) 15
13. 13.In a class of 35 children, 21 like maths, 16 like science and 8 like neither. How many like both? (a) 8 (b) 2 (c) 10 (d) 27
14. 14.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 125 sq cm (c) 25 sq cm (d) 150 sq cm
15. 15.Using (a − b)² = a² − 2ab + b², what is 28²? (a) 1024 (b) 896 (c) 784 (d) 794
16. 16.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 105° (b) 76° (c) 150° (d) 75°
17. 17.A bag has 3 white balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 6 (c) 5 (d) 4
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 product of the roots of x² − 17x + 72 = 0? (a) 71 (b) 73 (c) 72 (d) 17
20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 85? (a) 19 (b) 20 (c) 18 (d) 8
21. 21.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/3 (c) 1/4 (d) 2/3
22. 22.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
23. 23.A bag has 3 green, 2 yellow and 9 red balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/6 (b) 1/3 (c) 1/7 (d) 6/7
24. 24.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 210 (c) 105 (d) 225
25. 25.How many factors does 36 have? (a) 10 (b) 8 (c) 9 (d) 7
26. 26.What is the sum of all the whole numbers from 1 to 23? (a) 277 (b) 276 (c) 253 (d) 552
27. 27.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 5 times (d) 2 times
28. 28.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 621 (b) 630 (c) 492 (d) 631
29. 29.If a + b = 9 and ab = 20, what is a² + b²? (a) 121 (b) 61 (c) 41 (d) 81
30. 30.Which term of the AP 17, 26, 35, 44, … is 179? (a) 21st (b) 19th (c) 18th (d) 20th
31. 31.A bag has 7 red balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 8 (c) 14 (d) 9
32. 32.Using (a + b)² = a² + 2ab + b², what is 92²? (a) 8474 (b) 8464 (c) 8104 (d) 7744
33. 33.In a class of 48 children, 27 like mangoes, 21 like bananas and 8 like both. How many like only mangoes? (a) 13 (b) 19 (c) 27 (d) 8
34. 34.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
35. 35.A bag has 6 black balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 13 (b) 8 (c) 7 (d) 2
36. 36.The mean of 6 numbers is 35. When the number 7 is added to them, what is the new mean? (a) 32 (b) 21 (c) 31 (d) 35
37. 37.A drawer has lots of black, 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) 3 (b) 4 (c) 2 (d) 6
38. 38.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/4 (c) 1/2 (d) 1/3
39. 39.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
40. 40.Two angles of a triangle are 65° and 45°. What is the exterior angle at the third corner? (a) 70° (b) 135° (c) 115° (d) 110°

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