Algebra (Linear and Quadratic) Revision1. Simplify the following epressions.a)!x " #y $ x " !y !x " #y $ x " !y b)%a $ &b " 'a $ !b %a $ &b " 'a $ !bc)!xy " #yz $ !zy " &xy $ %xz !xy " #yz $ !zy " &xy $ %xz d)!x!" #x $ 'x! !x!" #x $ 'x! e)a!$ #b#" !b!$ &a! a!$ #b#" !b!$ &a! f)&x . %y &x . %yg)!a . #b . &c !a . #b . &c h)x! . &x# x! . &x# i)!ab! . %a!c . bc !ab! . %a!c . bc ()(!x)& (!x)& ))(#a!b#c)! (#a!b#c)! l)b* b* m)&a+a &a+a n)!,a!b&-a%b !,a!b&-a%b

o)b!' b#! b!' b#! p)x!&$ x!% x!&$ x!%

!. .valuate the following by using substitution.a) !p/ if p 0 & and / 0 1# b) #)(!) " 1) if ) 0 1&c)V 0 u!" !ad find 2 if u 0 #.,3 a0 &.% and d0%.' V 0 u!" !ad find 2 if u 0 #.,3 a0 &.% and d0%.'

#. .pand and then simplify if possible.a)#(a " %) #(a " %) b)$ !b(&a $ #b) $ !b(&a $ #b)c)&q " #(!q $ +) &q " #(!q $ +) d),(!p $ #) " &(p $ !) ,(!p $ #) " &(p $ !)e)(m " &)(m $ ,) (m " &)(m $ ,) f)(x $ #)(x $ &) (x $ #)(x $ &)g)(t $ +)(t " 1!) (t $ +)(t " 1!) h)(p " &)! (p " &)! &. 4actorise the following epressiona)!x " + !x " + b)$ %x " 1*xy $ %x " 1*xyc)abc " ab " ac abc " ab " ac d)#x!$ 'x# #x!$ 'x# e),p!q!" 1&p!q ,p!q!" 1&p!q f)x!" -x " !* x!" -x " !* g)x!$ -x " 1+ x!$ -x " 1+ h)x!$ x $ 1! x!$ x $ 1! i)x!$ !x " 1 x!$ !x " 1 ()x!$ - x!$ - ()&x!$ #' &x!$ #' %. Solve the following linear e/uationsa)x " , 0 !& x " , 0 !& b)$ !x " 1! 0 #+ $ !x " 1! 0 #+c)#(x " &) 0 $ 1% #(x " &) 0 $ 1% d)!(m $ &) " &m 0 $ !* !(m $ &) " &m 0 $ !*e)+q $ 1! 0 $ &q " 1% +q $ 1! 0 $ &q " 1% f)$ !(x $ %) 0 &(x " -) $ !(x $ %) 0 &(x " -)g)m%" ' 0 1# m%" ' 0 1# h)%q " ,'0 $ + %q " ,'0 $ + '. Solve the following /uadratic e/uationsa)(x " #)(x $ !) 0 * (x " #)(x $ !) 0 * b)(x $ ')!0 * (x $ ')!0 * c)x!" +x " 1! 0 * x!" +x " 1! 0 * d)x!$ 1#x " &* 0 * x!$ 1#x " &* 0 * e) x!$ &- 0 * x!$ &- 0 * f)x!" ,x 0 $ 1! x!" ,x 0 $ 1! g)x!0 -x " !! x!0 -x " !! h)x!0 !*x x!0 !*x ,a) 5a)e y the sub(ect of #x " y 0 1! #x " y 0 1!b) 5a)ethe sub(ect of$ !x $ %y 0 # $ !x $ %y 0 #c) 5a)e r the sub(ect ofV 0 r!h V 0 r!h +. A printer3 /uoting to offset print a single sided leaflet for a local sports club3 charges 6!%* for the paper and an hourly rate of 6&!.a) 7f h e/uals the number of hours of labour re/uired to print the leaflets3 complete the e/uation89ost of leaflets 0 ::::. h " ::::..b) ;he sports club has only 61#** budgeted for the printing (ob.hat is the cost of a single leaflet if the club spends all of its proposed budget=-. ;hree children in a family are related as follows8?en is three years older than 9arolAbe is half 9arol@s age;he sum of all their ages is ##a) 7f 9arol@s age is represented by the letter c3 then write an epression for the sum of the three children@s ages in terms of 9arol.b) 9alculate the age of each of the children by solving the last epression you have written.1*. A piece of wire is attached and hung between twopoles.A ball is threaded onto the wire and releasedfrom point A and travels through to the other side.;he height (metres) the ball is above the ground at anytime (t seconds) is given by the formulah 0 t!$ 't " - h 0 t!$ 't " - a) hat is the cost of the proposed etension.A1!. ;he table below gives the length of a spring when different weights are attached from it.>eight ()g) Spring length(cm)1 1#! 1'# 1-& !!% !%a) 7s this se/uence of spring lengths a linear or /uadratic relationship= .plain.b) 4ind the rule that relates the spring length (L) to the weight attached to it (>).c)