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BRIDGE THE GAP ASSIGNMENT CLASS VIII SUBJECT – MATHEMATICS Instructions:1. The following assignment has to be done on A4 size ruled sheets. 2. You have to submit the assignment to your respective teacher. 3. It will be discussed in the class. ALGEBRA 1. Solve(i) 𝒙𝒙 𝟑𝟑 𝟓𝟓 + =𝟐𝟐 2. Find the solution 𝟐𝟐 𝟑𝟑𝟑𝟑+𝟓𝟓 𝟐𝟐𝟐𝟐+𝟏𝟏 3. Find the solution of 4. 𝟑𝟑 (ii) = 𝐱𝐱+𝟔𝟔 𝟒𝟒 𝟏𝟏 𝟑𝟑 + 𝐱𝐱 − 𝟑𝟑 𝟓𝟓 = 𝟏𝟏𝟏𝟏 𝟒𝟒 - 7x = 9 (iii) x 4 + x 6 =x-7 𝟓𝟓𝟓𝟓−𝟒𝟒 𝟖𝟖 Which value of b would make 𝑦𝑦 2 + 𝑏𝑏𝑏𝑏 − 24 factorable? 81 6. For what value of c are the factors of 𝑥𝑥 2 − 𝑐𝑐𝑐𝑐 + 16 the same? 7. polynomials is exactly divisible by (𝑥𝑥 2 + 3𝑥𝑥 + 2). 5. What must be subtracted from (𝑥𝑥 4 + 6𝑥𝑥 3 + 13𝑥𝑥 2 + 13𝑥𝑥 + 8) so that the resulting Three numbers are in ratio 3:4:5. The sum of their cubes is 27000. Find the numbers. 8. The present age of Sahil’s mother is three times the present age of Sahil. After 5 years their ages will add to 66 years. Find the present age of Sahil. 9. 10. 3 The perimeter of a rectangle is 13 cm and its width is 2 cm. Find its length in cm. 4 Bansi has 3 times as many two-rupee coins as he has five-rupee coins. If he has in all a sum of Rs 77, how many coins of each denomination does he have? 11. The sum of three consecutive multiples of 11 is 363. Find these multiples. 12. The difference between two whole numbers is 66. The ratio of the two numbers is 2 : 5. What are the two numbers? 13. Sum of two numbers is 95. If one exceeds the other by 15, find the numbers. 14. Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers? 15. Three consecutive integers add up to 51. What are these integers? 16. The sum of three consecutive multiples of 8 is 888. Find the multiples. 17. 18. If m= 5 and n = − 2, then the value of m2- 2mn+n2 is . The algebraic language of ‘ Twice cube of a number x subtract from five times the sum of Y and 2 ’ is .................... Factorise: 𝑥𝑥 2 + 𝑥𝑥𝑥𝑥 − 𝑥𝑥 − 𝑦𝑦. Factorise : 𝑎𝑎3 + 𝑎𝑎𝑎𝑎(1 − 2𝑎𝑎) − 2𝑏𝑏 2 19. 20. EXPONENTS & POWERS 1. 2. 3. 4. 5. 𝑥𝑥 𝑎𝑎 𝑐𝑐 𝑥𝑥 𝑏𝑏 𝑎𝑎 𝑥𝑥 𝑐𝑐 𝑏𝑏 Find the value of �𝑥𝑥 𝑏𝑏 � × �𝑥𝑥 𝑐𝑐 � × �𝑥𝑥 𝑎𝑎 � −2 2𝑥𝑥 Find x: � 7 � 12 4 −7 −1 ×�2� 13 −8 Find x : �13 � × �12 � Solve for 𝑥𝑥: = −8 343 12 2𝑥𝑥 = �13 � 81−2 ÷ 7291−𝑥𝑥 = 92𝑥𝑥 2 −1 Simplify: {2−1 + 30 + 51 + 72 + 93 } ÷ �3� Square and Square Roots/Cube and cube roots 1. Find the square root of 0.7 to two decimal places. 2. Find the square root of 2116 and 1764 and hence find the value of 3. Three numbers are in the ratio 1:2:3.The sum of their cubes is 7776.Find the √0.2116 +√0.1764 . √0.2116 −√0.1764 numbers. 4. Find the smallest number by which 192 should be multiplied to make it a perfect cube. 5. Find the smallest number that should be subtracted from 300 to make it perfect square.