11. Factorise completely. 12. Express. 13. Factorise 12x. 14. Factorise 6ac bd 2ad + 3bc. 15. Make p the subject of the equation x =.

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1 Algeraic Manipulation Questions Factorise 9 Factorise completely 8 6 Epress + + as a single fraction in its Factorise + + and hence deduce the factors of 0 55 Epress as a single fraction in its simplest form Factorise completely 6p 7pq 0q a a ac+ c Epand and simplify ( ) ( ) a a a + + 9a a 5 Factorise completely Given ( p + q) = (5p q), find the p q 7 Factorise completely: 9+ 9c + 0c+ 5 d 8 Given that = a a, epress in terms of a and 9 Epress as a fraction in its lowest term y 0 Given that =, find the value of y y+ 5 Factorise 6ac d ad + c c p 5 Make p the suject of the equation = q + p 6 Epress as a single fraction in its simplest form: Factorise completely n 9n p 8p Given that a =, epress in terms of a c and c 9 Epress the following as a single fraction, in its simplest form, k k k 0 Factorise fully a ac 9 + c Factorise and hence, find all the factors of 58 Given that v = u + as, make u the suject of the fomula 6 algeraic manipulation

2 56 Factorise the following completely + 0 a 9c + 8ac Factorise completely 6 y ac 7c 8a + 5 Epress as a single fraction + Epress as a single fraction in its simplest form a + a a + Simplify (7 ) + ( ) 5 Simplify Factorise completely y 9 9y Given that 5 k y = 6 + and y 7 Epress ( ), epress in terms of k as a single fraction in its + r 8 Given that p = q, epress t in terms of p, q t and r 9 Factorise completely 8y + y 6y 9 0 Epress as a single fraction in its 5+ ac Given that =, epress c in a terms of a, and a 5a+ (c) Simply the epression a + 5a Factorise completely () ( ) + Simplify m m mn + mn 7 Epress as a single fraction in its simplest form ( y + ) ( )( ) + y y+ y+ y 5 a ( a ) Simplify ( ) ( ) a 5a 9 Factorise 5a 6( a) completely 0 Simplify Epress as a single fraction in its simplest form p+ p 5 9p ( p + ) Simplify ( 7 ) + ( ) y Given that, = epress y in terms of y + + Simplify into a single epression Mathematics Drill Questions cosmic

3 5 Factorise completely 6 6 y + y Hence using answer from, epress 86 as the product of prime numers 56 Epress + as a fraction in its + 57 Factorise completely a( c) d( c ) 57 5y 6 Given that =, make y the suject of the 58 Factorise completely p pq pq + q y suject of the equation 59 Epress the following as a single fraction in its simplest form 5 9y+ t 7 It is given that y = c Find the value of t when c = and y = 7 Epress y in terms of t and c 60 Given that A = ( a + ) h, epress in terms of A, a and h 8 Factorise completely (9ap aq + 9 q ) q 6 Simplify the following epression as a single fraction 5 0y 9 Epress as a single fraction in its simplest form y 9y 8 6a 6q q a+ 8q+ aq+ q a q q a ( a+ q)(8 + q) 50y 8y 50 Simplify as a fraction in its simplest form 9 a ay + y Epress as a single fraction in its simplest form 5 Simplify the following epression as a single fraction a a( a) a a a Simplify y 7 y z 9 5 Simplify 5 y 8y 5 Factorise + 5+ Hence epress 506 as a product of prime numers 5 Factorise a+ 6a completely 6 Factorise completely 65 Epress as a single fraction + ( + ) 66 Factorise completely a a+ 6 a 55 Factorise the following (c) ac a 5c + 5 ( + y) Factorise completely aq p 8q + ap 6 algeraic manipulation

4 58 68 Factorise completely 6a 69 Epress as a single fraction in its simplest form p p+ p 70 Factorise completely 5m+ ( m+ )( m ) + 9 5a a 9 7 Simplify a 9 9a 80 Given that a =, find the value of 8 Factorise completely y+ y 9 8 Factorise completely a 5 8 Epress as a fraction in its simplest 9 form 7 Given that a + = 7 and a =, calculate the 8 Epress as a single fraction in its value of (a ) ( a ) + lowest terms 7 Factorise completely ac c ad + d Given that c d, find the value of a when 85 Simplify ac c ad + d = 0 7 Epress as a single fraction in 86 Factorise completely ( y) ( y) + 7+ its simplest form 87 Given that y y+ 9= k, epress y interms 5 75 Epress as a fraction in its lowest of and k, where k > 0 6 terms 88 Simplify y 8 y 76 Factorise a + 0a+ 7 Hence, find factors of 007 other than and Factorise completely 5a + y 0ay 77 Given that + y= and y= 8, find the value of y + y 78 Simplify 6 79 Simplify + ( 5 p qr ) 90 Simplify the epression 0 ( ) answer in positive inde form p q r, leaving your 9t t 9 Epress + as a single fraction in its 9t tt simplest form 9 Make the suject of the formula a= + c y + y Mathematics Drill Questions cosmic

5 9 Epress as a single fraction in its simplest form Epress as a single fraction n n + Hence or otherwise, find Epress as a single fraction in its simplest form + a a a+ ( )( ) 5 96 If + y = y, and y k =, where k > 0 + y + y Hence, find k Epand ( ) 97 Factorise completely 6a + 5a 6 n 98 Factorise + n Hence, prove that if n is a positive integer, then the integer ( n + n) is always even 99 Factorise completely a 00 If k is a perfect square, state the value of k 6 algeraic manipulation

6 60 Answer keys: Questions (+ )( ) + 7 ( )( + ) (p 5 q)(p+ q) ( ac)(a ) or ( ca)( a) 8a 5 (+ 5)( ) p 6 = 6 q 7 ()( ) (c+ 5 + d)(c+ 5 d) =± a (9 + )(+ )( ) + + (+ )(+ ) 0 0 ( a+ )( c d) 5 6 ± cq ( + 5)( 7) 7 n ( n )( n+ ) ( p 5)( p ) 8 9 = a c k k+ 0 ( a )( a+ c) (5+ )( + ) 5 and are factors u=± v as ( )(+ ) ( a)( c)( + c) ( y)( + y) ( c6 )(a 7) = = 8 t = ( )( )( ) + k 6y 5y r p + q 9 (y + )(y ) 0 (c) 9( ) (m+ ) ( n+ ) + ( )(5+ ) c=a a a+ ( a )( a+ ) ( a+ )( a) ( 6)( + ) ( + y)( )( y )( y+ ) y a 9 (6 a)( a ) 0 59 (+ )()() ( p)( p) (p+ )(p) ( + )( 6) y = 5( + )( + ) 5 ( )( + )( y+ )( y ) (+)(+) 6 y = 0 86 = t = 89, y = 0 8 ( p q)( p+ q)( a+ ) a q (+ )(+ ) y 5 (+ )( + ), 5 ( + )( + a) 55 (a 5 )( c+ )( c ) (+ y+ 5)(+ y 5) (c) (+ )(5 ) ( + )( ) 57 ( a+ d)( c) ( p + q)( p q) ( )(+ ) 60 = A h a 5( + y)( + y) ( y) 6 6 y(5 y) ( a)( y) ( a )( a+ ) 8 y z + 66 ( a )(a ) 67 ( )( + 6) (a )( q+ p) 68 6( a)( + a) 69 p 9 p ( p )(p+ ) 70 (m+ )(m ) Mathematics Drill Questions cosmic

7 6 7 a 7 7 ( cd)(a ) 7 ( )( ) 96 k = ( y) y 97 (a+ )(a ) 98 nn+ ( ) The product of a odd and even numer is always even 99 ( + a )( a ) 75 + ( )( + ) 00 k = 5 76 (a+ 7)( a+ ) 07 and ( ) ( y+ )( y ) 8 ( + )( ) 8 ()( 5) 8 ( )( + ) ( y)( + y) y = 5 6( ) y ± k 89 ( y)(5a+ 7 ) p q r t(t+ ) = 6 ( ) y( c a+ )( c+ a) ( ac)( a + c) 9 nn+ ( ) a+ (a )( a+ ) 6 algeraic manipulation