Topical Revision Paper 2 Unit 2 Surds Indices

Topical Revision Paper 2 Term 1 Unit 2 Surds and Indices Question 1: Without using a calculator, simplify     22 32 2 5 2 5   . [3] Solution:     22 32 2 5 2 5                22 2 3 2 5 2 2 5 2 5 2 5 3 9 4 5 2 9 4 5 1 9 20 5            Question 2: Solve for x 2432(27 ) 45(3 ) 3 xx x . [4] Solution: 2432(27 ) 45(3 ) 3 2(81 ) 45(9 ) 243 xx x xx   Let 9xy , equation becomes 2 2 2 45 243 2 45 243 0 (2 9)( 27) 0 4.5(n.a) or 27 yy yy yy yy          9 27 3 2 x x   Question 3:

The area of a rectangle ABCD is given by m2, and the length of side AB is m. Find, without using a calculator, the length of side BC in the form of m, where a and b are real numbers. [4] Solution: Length of the side BC 1 3 2 28 (1 3 2)(2 2 2) (2 8)(2 2 2) 2 2 2 6 2 12 4 10 4 2 4 5 2 m 2          Question 4: Without using a calculator, find the fractions, a and b, for which 6 7 5 4 5 7   can be expressed as 35ab . [3] Solution: 6 7 5 4 5 7   6 7 5 4 5 7 4 5 7 4 5 7           22 24 35 6 7 4 5 35 4 5 7     62 25 35 73  62 25 3573 73  62 73a  and 25 73b  Question 4:  1 3 2  28 ( 2)ab

(a) Without using a calculator, evaluate   0 11 4212 49 167     . [2] (b) Given that 21 1 24327 x  , find the value of x. [2] Solution: (a)   0 4 11 421 1 12 49 16 1 777 64 48 1 1 72 41 1 72 75 9 or -414 14               (b)   213533 6 3 5 68 4 3 x x x x        Question 5: Solve for x, 4 2 213 4(169 ) 2145xx  . [4] Solution: 4 2 213 4(169 ) 2145xx    4 2 413 13 4 13 2145xx       44169 13 4 13 2145xx    4165 13 2145x  413 13x  1 4x