ࡱ>  (   G .www.mathsmadeeasy.co.uk>http://www.mathsmadeeasy.co.uk/LASTLASTLASTLASTLAST&Example 2&&Example 3&,Example 4&2Example 5&8Example 5: FIRSTG.www.mathsmadeeasy.co.uk>http://www.mathsmadeeasy.co.uk// 0LDArialԖ0Ԗ0ll`0ׯ0@ .  @n?" dd@  @@`` X/$  01./, / 0AA f3f@3fʚ;ʚ;g4CdCd= ׯ0ppp@ <4dddd8vS0l<0 <4BdBd8T0l0___PPT10 pp^___PPT9@ G?  %4Rearranging algebraic Formulae for GCSE Mathematics> David Weeks Free GCSE maths papers: www.mathsmadeeasy.co.uk H?"" 0& $ 0&=Example1 3f Example 2 3f Example 3 3f  Example 4 3f  Example 5 3f Answers3f   0` 33` Sf3f` 33g` f` www3PP` ZXdbmo` \ғ3y`Ӣ` 3f3ff` 3f3FKf` hk]wwwfܹ` ff>>\`Y{ff` R>&- {p_/̴>?" dd@$|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>>N0 <(    68y I'ga  T Click to edit Master title style! !  0{ M'gp  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S  0̂ ^ `  >*  0p ^   @*  0  ^ `  @*`B  s *D3fo"f  03f"lH  0޽h ? 33___PPT10i.y+D=' x= @B + Default Design0XN0  P(  f  03f"lr  S L\6 6 r  S \6 `   6   <- W J6Slides self animate - Use mouse click after each slideV  0޽h ?"` 33___PPT10i.y+D=' x= @B += 0N0 vn0 / 0 (   x  c $ّ'g     <8ۑi8,$ 0 _/H=8e + 2, Make e the subject of the formulae00  < /[O,$ 0 W'Lets see how we got H. . . in H=8e + 2 ((  0% E ,$ 0 V&Do the exact opposite to get e . . ''  Bff!V,$D 0 ; We get H  l .2 $ ,$D 0   B̙.2 ? Start with e   B33 ,̙l %2  % ! ,$D 0   B|%2  FMultiply all by 8 x8   B33   ,̙l  3] & " ],$D 0   BD6 3 :Add 2 +2     B(633M] ,̙  B6̙  ,$D  0 :We get e  &l  ^  )   ,$D  0   B ^  Divide all by 8 80"   B BP633 k  ,̙l    (   ,$D  0   B6   ? Subtract 2 -2  B B633 v  ,̙l    '   ,$D  0   B46ff0   ? Start with H  B B633w (Z  ,̙l  8 < - 8 <,$D  0 !  B6 8 X So e=(H-2)8 or e= (H-2) . "  `B "  0Do# I I #  B*6~ ] < 18 , < 6,T_L,$0 h4Your turn: Make a the subject of the formula F=6a +5553f . 0Yl$D000" / <26R:3 & David Weeks, www.mathsmadeeasy.co.uk''" &   G0&H  0޽h ? 33%%___PPT10%.y$+5vDN$' = @B D $' = @BA?%,( < +O%,( < +D@#' =%(%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%( DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%((#D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*$ %(D' =-s6Bwipe(left)*<3<*$ D' =%(,D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*% %(D' =-s6Bwipe(left)*<3<*% D' =%(2D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*& %(D' =-s6Bwipe(left)*<3<*& D' =%(8D@' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bbox(out)*<3<* D' =%(>DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(8JD9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*' %(D' =-u6Bwipe(right)*<3<*' D' =%( ND9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*( %(D' =-u6Bwipe(right)*<3<*( D' =%(SD9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*) %(D' =-u6Bwipe(right)*<3<*) D' =%(YD@' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bbox(out)*<3<* D' =%(_D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*- %(D' =-s6Bwipe(left)*<3<*- Du' =%(ToD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*, %(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*. %(+P+0+ 0 ++0+ 0 ++0+ 0 ++0+ 0 ++0+ 0 ++0+, 0 +. 0N0 P 0@6(  x  c $X6'g  6   <6TV,$ 0 c3V=7(c+9)+ 10, Make c the subject of the formulae44  <6 ",$ 0 \,Lets see how we got V. . . In V=7(c+9)+10 --  0L6 ,$ 0 V&Do the exact opposite to get c . . ''l C( )T,$D 0  B6̙C(E ? Start with c  B62- :Add 9 +9     B 6j2  FMultiply all by 7 x7   B6ff 2 ; We get V     B 633 ,̙   BP633Zj ,̙   BT633 p ,̙  B6S2 < Add 10 +10    B633 p ,̙,l  kz  *? /| ,$D 0  B6̙ p  ; We get c    B6 z  < Minus 9 -9    Bp6  % p  Divide all by 7 70"    B6ff kp  ? Start with V !B B6333   ,̙ "B B6333   ,̙ #B B633)   ,̙ $ B p  > Minus 10 -10   %B B33@  P  ,̙l  [ - [,$D 0  B [  &So c=(V-10)7 -9 or c= (V-10) - 9 .' "  `B ' 0Do3 S  ( B  17  , <,TL,$0 m9Your turn: Make z the subject of the formula F=6(z+9) + 8::3f / 0jl$D 000 0 <R\3 S David Weeks"   H  0޽h ? 33___PPT10.y$+ B1D' = @B Di' = @BA?%,( < +O%,( < +D' =%(%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%((#D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*)%(D' =-s6Bwipe(left)*<3<*)D' =%(:DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D'  =-s6Bwipe(left)*<3<*D' =%( ND9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<**%(D' =-u6Bwipe(right)*<3<**D' =%(gD7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*-%(D'  =-s6Bwipe(left)*<3<*-Du' =%( {D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*/%(++0+0 ++0+0 ++0+0 ++0+,0 +- 0N0 h``-0 (  ~  s *P*'g     <+`J,$ 0 x2T=(s+4)2+ 3, Make s the subject of the formulae*3 +  <1&F,$  0 r,Lets see how we got T. . . In T=(s+4)2+3 *-&   0h8 < ,$ 0 V&Do the exact opposite to get s . . ''l C( X,$D 0  <<̙C(E ? Start with s  <|A2- :Add 4 +4     <\Ej2  PSquared all ( )2"    <@@ff 2 ; We get T     <G33 ,̙   <Q33Zj ,̙   <8U33 p ,̙  <WS2 :Add 3 +3    <\33 p ,̙l  kz    3` ,$D 0  <_̙ p  ; We get s    <0b z  < Minus 4 -4    <Dg  % p  b"Square root all "$"  <lff kp  ? Start with T B <p333   ,̙ B <,u333   ,̙ B <y33)   ,̙  <h{ p  < Minus 3 -3   B <<33@  P  ,̙+ ! <h,TL,$0 9Your turn: Make p the subject of the formula F=(p+9)2 + 86:43f3f3fl  XY ) XY,$D 0(  B9 XY JSo s=(T-3)" -4 or s= "(T-3) - 4 H& "  "  ( C BC[DEFAA[-D-[@    9  , 0jl$D 000 - <PR\3 S David Weeks"   H  0޽h ? 33___PPT10.y$+= D' = @B Di' = @BA?%,( < +O%,( < +D' =%(%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(DD' =A@BBBB0B%( D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(%D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(<DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D'  =-s6Bwipe(left)*<3<*D' =%(PD9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-u6Bwipe(right)*<3<* D' =%(xiD7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*)%(D'  =-s6Bwipe(left)*<3<*)Du' =%(0uD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*!%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(++0+0 ++0+0 ++0+0 ++0+!0 +r/ 0N0 p#.6(  x  c $'g     <ȦJ,$ 0 KLets see how we got X. . .   0| ,$ 0 V&Do the exact opposite to get Y . . ''z C(  nM>,$D 0  <t̙C(E ? Start with Y  <2- :Add 5 +5     <䷍j2  Divide all by 7 70"    <tff 2 ; We get X     <33 ,̙   <33Zj ,̙   <ȍ33 p ,̙  <ˍS2 < minus 6 -6    <dЍ33 p ,̙z  kz    (u ,$D 0  <Ӎ̙ p  ; We get Y    <׍ z  < Minus 5 -5    <lۍ  % p  FMultiply all by 7 x7  <0ߍff kp  ? Start with X B <333   ,̙ B <\333   ,̙ B <33)   ,̙  <0 p  :Add 6 +6   B <x33@  P  ,̙9  B8  ,$ 0 %So Y=(X+6)x7 -5 or Y=7(X+6) - 5 .& "  bl XQ $XQ,$D 0  <DXQ c3X =(Y+5) - 6, Make Y the subject of the formulae44ZB ! s *DoO " <8 17z T ( T,$@ 0 ) <T n:Your turn: Make g the subject of the formula F= (g+9) - 7;;3fZB * s *D3fog + <@ 553f - 0vl$D 000 . <R\3 S David Weeks"   H  0޽h ? 33PH___PPT10(.y$+#xDT' = @B D' = @BA?%,( < +O%,( < +DF' =%(%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =-s6Bwipe(left)*<3<*$D' =%( DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(%D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(<DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D'  =-s6Bwipe(left)*<3<*D' =%(PD9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-u6Bwipe(right)*<3<*D' =%(xiDD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D'  =-s6Bwipe(left)*<3<*D' =%(yD7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =-s6Bwipe(left)*<3<*(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*-%(++0+0 ++0+0 ++0+0 +V0 0N0 QI!+ @(   ~  s *#=}     <8%#j,$ 0 v0T=4(u2+7), Make w the subject of the formulae*1 +  <+&JF,$ 0 q+Lets see how we got T. . . In T=4(u2+7) *,$   0,2 < ,$ 0 V&Do the exact opposite to get w . . ''l " % "*,$D 0   B6̙" ? Start with u   B8o"Z J Square it u2"      B4?"  FAdd 7 +7"     B|:ff, ; We get T     BI33_o ,̙   BG33y ,̙   BN33j ,̙   BR~ , FMultiply all by 4 x4   BW33  t ,̙>l 3 BV  (  3BV ,$D 0   B{̙3 V  ; We get u     B(*  V  < Minus 7 -7     B V  f&Square root All "$"   BHff BV  ? Start with T  B B(33   ,̙  B B(33  ,̙  B B䛔33   ,̙   B<0 V  lDivide by 4 4$ "    B Bh33   ,̙*  <̥,T[L,$ 0 8Your turn: Make p the subject of the formula F=5(p2 + 8)6923f3f3fl f i ' f i,$D 0^   B$f  BSo u=(T4 -7)" or u= T  7 b"" " " `B   0Do3 v v   B I i 14 #   BCtDEFAAo[t  @P  * 0)l$D 000 + <<R\3 S David Weeks"   H  0޽h ? 33___PPT10m.y$+%!Da' = @B D' = @BA?%,( < +O%,( < +DS' =%(%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%( DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(%D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*% %(D' =-s6Bwipe(left)*<3<*% D' =%(t@DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D'  =-s6Bwipe(left)*<3<* D' =%(SD9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*( %(D' =-u6Bwipe(right)*<3<*( D' =%(gD7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*' %(D'  =-s6Bwipe(left)*<3<*' D(' =%( {DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D'  =-s6Bwipe(left)*<3<* D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<** %(++0+ 0 ++0+ 0 ++0+ 0 ++0+ 0 + 0N0 .$@s(  $r $ S Ҕ'g    $ <֔/ `,1. Make a the subject of the formula F=6a +5--3f $ <Ք]x} e12. Make z the subject of the formula F=6(z+9) + 8223f $ <ݔ2jR 13. Make p the subject of the formula F=(p+9)2 + 862,3f3f3f  $ <f  05. Make p the subject of the formula F=5(p2 + 8)61*3f3f3f $ B ](  f24. Make g the subject of the formula F= (g+9) - 7333fXB $ 0D3fo p   $ B   553fe8  " '$  $ B ? a=(F-5)6 or a= (F-5) ." `B $ 0Do/Y/ $ BD" 16 $ B  ' z=(F-8)6 -9 or z= (F-8) - 9 .( "  XB $ 0Do2x2 $ B`s% 16 $ < r   LSo p=(F-8)" -9 or p= "(F-8) - 9 H' "  "  $ c BC[DEF[-D-[@    $ < 8   "g=(F+7)x5 -9 or g=5(F+7) - 9 .#" F f i $ ~& X $ < f  BSo p=(F5 -8)" or p= F  8 b"" " " ZB  $ s *Do3 v v !$ <P& I i 15 "$ # BCtDEFo[t  @P " $$ 6p,T@00 (" ($ 600mT#@&00 (" )$ 6T4CT@,00 (" *$ 6L7F T @200 (" +$ 6<vT,@800 (" -$ <AY@:00 7Restart .$ <DR\3 S David Weeks"   H $ 0޽h ? 33___PPT10i.y++D=' = @B +r8@ W v NR, 1Oh+'04& `h  Rearranging FormulaeDavidDavid7Microsoft Office PowerPoint@S @#y@PWQuG(%g  ..&RWMFC4L00l{ EMF0T 0F(GDICx!b $$=='% % V0xx x % % $$AA" FGDICF(GDICx( !b $$=='% % V0wk k % % $$AA: $$==_888 3f% % V,k k % % $$AA( : " FGDICF(GDIC 1FGDICRp@ArialxArialh`6lԞ*@Arial 0 DxO0lz0%0ԞLD0x 0txD\0t응dv%    T"B B!LRearranging algebraic Formulae  % ( Rp@ArialUArialh`6lԞ*@Arial 0 дDxO0lz0%0ԞLD0x0txD\0t응dv%    T(#x,B B(+Ltfor GCSE Mathematics % ( F(GDICCdFGDICRp@Arial'Arialb6lԞ*@Arial 0 D xO0lz0%0ԞLDx0txD\0tdv%    TT>EAJB B>JLP % ( Rp@Arial'@Arial 0 |)Q|Hm| n))LDx0tx%0Ԟ\0 tdvxK%h ht!Zdv%    TCEbJB BCJ LdDavid Weeks % ( Rp@Arialm.PmLh0@Arial  " & 0 8 : "!"!(m0-g0-\6eU0X0-%0ԞLeU0DDdK0~ 0*- 0DXN5 0r Ԟh0dv%    T LNPB B PL|Free GCSE maths papers:  % ( Rp@ArialmSv 0Ԟ( " & 0 8 : "!"!(m0-g0-ܗ|)Q|Hm|r ))LeU0DDdK00*- 0%0Ԟ쒑r h0dv~ 0*-pO%h ht!Zdv%    TOLPB BOPL|www.mathsmadeeasy.co.uk % ( &% OP6P% ( F(GDICbi( !b $$=='% % V0ai% % $$AA" FGDICRp@Arial_D0DhD5̙̙D$ R05PD%0ԞL  4 0e 5D0D5ԙtdv%    T cAgB B gLtSlides self animate  % ( Rp@Arial_̙D$ R05|)Q|Hm|r ))L  4 0e 5D%0Ԟ쒑 tdv54V%h ht!Zdv%    TTBcBgB BBgLP- % ( Rp@Arial_Q|Hm|r ))L  4 0e|)Q|Hm|r ))쒑 tdv54V%0Ԟ t!Zdv5X%h ht!Zdv%    T Dc|gB BDg LUse mouse click after each slide % (   x--$xx--'--$ww--3f-- $ww--'@Arialx??-. 62 !Rearranging algebraic Formulae ."System-@ArialU??-. %2 +(for GCSE Mathematics.-@Arial'??-.  2 J>.-@Arial'??-. 2 JC David Weeks.-@Arialm.??m???-. +2 P Free GCSE maths papers: .-@Arialm??????????-. *2 POwww.mathsmadeeasy.co.uk .--POP---$bhhbb--'@Arial_??-. %2 g Slides self animate .-@Arial_??-.  2 gB-.-@Arial_??-. 72 gD Use mouse click after each slide.-՜.+,D՜.+,l(    On-screen ShowM1 Creativity,'  ArialDefault Design5Rearranging algebraic Formulae for GCSE Mathematics Example1 Example 2 Example 3 Example 4 Example 5Answers  Fonts UsedDesign Template Slide Titles 8@ _PID_HLINKSAXN http://www.mathsmadeeasy.co.uk/ -1,-1,LAST -1,-1,LAST -1,-1,LAST -1,-1,LAST -1,-1,LAST258,3,Example 2259,4,Example 3260,5,Example 4261,6,Example 5261,6,Example 5 -1,-1,FIRST http://www.mathsmadeeasy.co.uk/_,DavidDavid  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root EntrydO)Current UserSummaryInformation(d&PowerPoint Document(,DocumentSummaryInformation8