Topical Revision Paper 1 Unit 1 Advanced Algebraic Manipulations

Topical Revision Paper 1 Term 1 Unit 1 Advanced Algebraic Manipulation Question 1: Given that 22 44x x y y   and that xy , find the value of 3 xy . [3] Solution: 22 4 4 ( )( ) 4( )x x y y x y x y x y        Since xy , 04x y x y     Hence 3 3 4xy 6 Question 2: Simplify into a single fraction 3 3 2 3 2 2 2 8 16 4 4 (4 2 ) x y xy x x y y x    . [4] Solution: 3 3 2 3 2 2 2 22 2 8 16 4 4 (4 2 ) ( 2 )( 2 4 ) 4 (2 )(2 ) ( 2 )( 2 ) 4(2 ) x y xy x x y y x x y x xy y x y x y x x y x y yx           2 2 22 4 2 22 x xy y xy x x y y x     2224 2 xy xy   Question 3: (a) Factorise completely 3 2 2 32 6 8 24a a b ab b . [3] (b) Make q the subject of the formula 2249pq q p . [3] Solution: a) 3 2 2 32 6 8 24a a b ab b

222 ( 3 ) 8 ( 3 )a a b b a b    22(2 8 )( 3 )a b a b   2( 2 )( 2 )( 3 )a b a b a b    (b) 2249pq q p 2 2 2 2 49p q q p   2 2 2(4 ) 9q p p   2 2 2 93 or 4 4 ppq p p      Question 4: (a) It is given that 2 2 1 1 R v c   . (i) Find the value of R when 5v and 3c . [1] (ii) Express v in terms of R and c . [3] (b) Factorise completely 4 2 2 14 49x x xy y   . [3] Solution: (a) 1 51 9 1= 2 3 3= 2 R  

(b) 2 2 2 2 22 2 22 2 2 2 2 2 2 22 2 1 1 or or 1 R v c c cv ccv R c R c cv c v RR cvR R           (c)        4 2 2 4 2 2 24 22 14 49 14 49 7 7 7 x x xy y x x xy y x x y x x y x x y                Question 5: (a) Given that 4 3 2a b a b   , find the value of 22 2 2 ab ab . [3] (b) Solve for x and y if 333 1 2 5 3 0x y x y      . [4] Solution: (a) 222 2 4 3 2 35 3 a 5 322 30 5 2 43 32 5 a b a b ab b aaab ab aa         (b)

3 3 3 3 3 1 2 6 2 (1) 2 5 3 (2) (1) (2) : 1 1 sub into (1) 31 4 16 xy xy xy y y x x x               