All Exercise Answers

UEB Maths Advanced Module - Exercise 1.1

#a4 a"6b "7 ;c

#b4 x"6y "7 ;z

#c4 #bx "7 ;y

#d4 am"-an

#e4 ;x-axis

#f4 ;,x-axis

#g4 ,! product ( a & ;b1 "<;ab">1 gives ! >ea4

#h4 ,! ratio p;3q

#i4 ;,ab "7 ,xb"6,yb

#aj4 #dr"/#br "7

UEB Maths Advanced Module - Exercise 1.2

#a4 ,exp& "<a"6#b">"<a"6#d">

#b4 ,exp& & simplify "<#c;a"6#e">"<a"6#a">

#c4 "<q"6#d">"<q"-#b">

#d4 #bx"<#cx"-#a">"6#c"<#cx"-#a">

#e4 ab"6cd "7 ;gd

#f4 "<m"6#c">"<m"6#c"> "7 m"<m"6#c">"6#c"<m"6#c">

#g4 #ba;a"/#g;a "7 #c

#h4 mn"6yz "7

#i4 #g;b"6#e;b "7

#aj4 "<t"-#d">"<t"-#g">

UEB Maths Advanced Module - Exercise 2.1

#a4 ,evaluate ;(mn./#c)"/(m./n)

#b4 ;;(,,pqr./,,xz)

#c4 ;;(,pq,r./xz)

#d4 ;y "7 ;(x./#b)

#d4 ;;;y "7 (x./#b);'

#e4 ;(#c;a./#e)"6(a./#e)

#f4 ;(#b#a/b./x"6y)

#g4 ;(#hx"-#bdy./#h)

#h4 ;(#dm"6#ab./#c)"8(#fm./m"6#c)

#i4 ;(#f"<h"6#e">./h"6#i)

#aj4 ,simplify ;(#ew"6#aj./#e)

UEB Maths Advanced Module - Exercise 2.2

#a4 ;(#d"6#c"6#b./#f"-#c"6#h)

#b4 ;(#b_/#c./#e)

#c4 ,a "7 ;(h./#b)"<a"6b">

#d4 ;(#c"<h"6#e">./h"6#i)

#e4 #e4c/d1bjj

#f4 ;(@s#ee./#e)

#g4 ;(#bdm./#c;cm)

#h4 #c/aj"jjj

#i4 #d1jjj/aj

#aj4 ;;((x./#b)"6(y./#c)./x"6y)

#aj4 ;(;(x./#b)"6(y./#c)./x"6y)

UEB Maths Advanced Module - Exercise 3.1

#a4 #af"-#e _@> #aj

#b4 #c"6#c _@< #c"8#c

#c4 #ae @< #ag

#d4 #bi @> #bc

#e4 a"6b "7@: ;c

#f4 #aexy"/#cx "7 ;(#aexy./#cx)

#g4 #c"<#d"-#bx"> _@> #ah

#h4 #b4e"8#g4g ^9 #ai

#i4 ;x "7 _6#ae

#aj4 #c;a"6#b;b "7 #e;c

UEB Maths Advanced Module - Exercise 3.2

#a4 #e"6"-#b "7

#b4 #i"6"-#f "7 "6#c

#c4 #4fgb

#d4 #a"gde"gaa/f"ebg

#e4 ;(@s#ee4ej./#e)

#f4 ;(#bjm./#d;cm)

#g4 ;;(a./b"6c)

#g4 ;(a./b"6c;)

#h4 ;(x./#d1jjj)

#i4 ,exp& "<#bx"-#e">"<#cx"6#g">

#aj4 ;;((p./#e)"6(q./#aj)./p"6q)

#aj4 ;(;(p./#e)"6(q./#aj)./p"6q)

UEB Maths Advanced Module - Exercise 4.1

#a4 #aj9#b

#b4 ;;x9<b"6#a>

#b4 x;9;<b"6#a>

#c4 x;9#a/b

#d4 ;;x9<#a_/#b>

#d4 x;9;<#a_/#b>

#e4 x;5#d

#f4 ;;x5<#b"6>

#f4 x;5;<#b"6>

#g4 x;9#b

#h4 ,p;5x

#i4 ;;;a9<"-n> "7 (#a./a9n);'

#i4 a;9;<"-n;> "7 ;(#a./a9n)

#i4 ;;a9<"-n> "7 ;(#a./a9n)

#aj4 ;;;a9na9m "7 a9<n"6m>;'

#aj4 a;9na;9m "7 a;9;<n"6m;>

#aj4 ;;a9na9m "7 ;;a9<n"6m>

UEB Maths Advanced Module - Exercise 4.2

#a4 #j4jjbe "7 #b4e"8#aj9<"-#c>

#b4 ;;x5<a"6b>

#b4 x;5;<a"6b;>

#c4 a;5#b"6b5#c

#d4 x;9yz

#e4 ;;(x9<"-#i>./#d)

#e4 ;(x;9;<"-#i>./#d)

#f4 ;;(x9y./z)

#f4 ;(x;9y./z;)

#g4 ;;(x9#a4b./#d)

#g4 ;(x;9#a4b./#d)

#h4 ;;(x9<"-#c/d>./#d)

#h4 ;(x;9;<"-#c/d>./#d)

#i4 #g;e5<#bx>

#aj4 ;;e9<x9#c>y

#aj4 e;9;<x;9#c>y

UEB Maths Advanced Module - Exercise 5.1

#a4 ;%#be+ "7 #e

#b4 ;%#c9#b+"6#d

#c4 #c%#bh+"-#b%#g+

#d4 ;%#bt+"8%#h+ "7 #d%#c+

#e4 ;%#aft+ "7 #d%#c+

#f4 ;(#f./#b%#c+)

#g4 #e"<#b%#c+"6#c">

#h4 ;;%a9#b"6b9#b+

#h4 ;%a;9#b"6b9#b+

#i4 ;;;,e "7 %#a"-(b9#b./a9#b)+;'

#i4 ;,e "7 ;%#a"-(b9#b./a9#b)+

#aj4 ;;;,v "7 %#b;g,r+;'

#aj4 ;,v "7 ;%#b;g,r+

UEB Maths Advanced Module - Exercise 5.2

#a4 ;;;x "7 %x9#b+;'

#a4 ;x "7 ;%x;9#b+

#a4 ;x "7 ;;%x9#b+

#b4 ;x "7 ;(#e"6%#de+./#b)

#b4 ;;;x "7 (#e"6%#de+./#b);'

#c4 "<a"-#d">9#b

#d4 "<b"-#d"> "7 _6;%#c+

#e4 "-"<#ex"-#c"> _@> #b

#f4 ;;;,f "7 (mv9#b./r);'

#f4 ;,f "7 ;(mv;9#b./r)

#f4 ;,f "7 ;;(mv9#b./r)

#g4 ;;;m "7 (y5#b"-y5#a./x5#b"-x5#a);'

#g4 ;m "7 ;(y;5#b"-y5#a./x5#b"-x5#a)

#g4 ;m "7 ;;(y5#b"-y5#a./x5#b"-x5#a)

#h4 #aj9<"-#d>

#i4 "<#br">9#a/b

#aj4 ,t;5n "7 a"6"<n"-#a">d

UEB Maths Advanced Module - Exercise 6.1

#a4 #j4ce<#abc>^4

#a4 #j4ce<#a>^4#b<#c>^4

#b4 _[,,efg is adjac5t to _[,,gfh

#c4 ;;;$#c:,,abc _= $#c:,,def;'

#c4 ;$#c:,,abc _= ;$#c:,,def

#d4 _[,,oca "7@: _[,,ocb

#e4 #c"<#h"6#e"> "7 #c"8$#d:"6#c"8$#d

#f4 ,,ef #l ,,gh

#g4 ;,* ,,pq #- ,,rs

#h4 _<,craig1 ,fr.es1 ,t>na_>

#i4 _[,,abc "7 _[,,def

#aj4 ;;;$#c:,,edf #_l $#c:,,fdg;'

#aj4 ;$#c:,,edf #_l ;$#c:,,fdg

UEB Maths Advanced Module - Exercise 6.2

#a4 "<x"6#e">9#b "7 x;9#b"6$#d:x"6#be

#b4 ,p"<x"> "7 #e"-#cx"6x9#b

#c4 "<#iy"6#a">"<#gy"6#b"> "7 #j

#d4 ;;;v "7 %(g./k)+;'

#d4 ;v "7 ;%;(g./k;);+

#d4 ;v "7 ;;%(g./k)+

#e4 ,a "7 #a/b;h"<a"6b">

#f4 ;;;,s "7 (n./#b)"<a"6l">;'

#f4 ;,s "7 ;(n./#b)"<a"6l">

#g4 ;(#by./#e) "7 #aa"-(y./#c)

#h4 ;;;,t5n "7 ar9<n"-#a>;'

#h4 ,t;5n "7 ar;9;<n"-#a>

#h4 ,t;5n "7 ;;ar9<n"-#a>

#i4 ;%#h4da"8#aj9<"-#h>+

#aj4 "<xy">;9#c

UEB Maths Advanced Module - Exercise 7.1

#a4 ,s9,a

#b4 ,log"<x"6y">

#c4 #ftan#ij^j

#d4 ,s9#cj

#e4 #e,sin#de

#f4 #g;cos#ex

#g4 log a"6log ;b "7 log ;ab

#h4 log;5#d "7 "-#b

#i4 ;(s9,c./c;) "7 ;(s9,a./a;)

#i4 ;;;(sin,c./c) "7 (sin,a./a);'

#i4 ;;(sin,c./c) "7 ;;(sin,a./a)

#aj4 ;;;(sin,z./#ce) "7 (sin#gj^j./#g);'

#aj4 ;(s9,z./#ce) "7 ;(s9#gj^j./#g)

UEB Maths Advanced Module - Exercise 7.2

#a4 ;(#e./$#d:) "7 #cj/cf

#b4 ,9 ;$#c:,,def1 _[,e "7 #ij^j

#c4 ;%#i;a9#h+

#d4 "<#be/di">9#a/b

#e4 ;;%m9#b+

#e4 ;%m;9#b+

#f4 ;(#ah;cos#ab^j./#actan#fh^j)

#g4 ;;%9#f#aja4i+

#g4 ;%;9#f#aja4i+

#h4 ,9 ;$#c:,,klm1 _[,m "7 #bg^j#ea7

#i4 s9,z "7 ;(#cesin#gj^j./#de)

#aj4 log;5e"<#b/c">

UEB Maths Advanced Module - Exercise 8.1

#a4 ,a "7 ;(.?./#cfj)"8#b.pr

#b4 ;,v "7 #a/c.pr9#b;h

#c4 ,a "7 #b.pr9#b"6#b.prh

#d4 ;,s "7 .?r"<r"6l">

#e4 ;,* ,.sx "7 #aie

#f4 ;,v "7 #a/c.p

#g4 ;,c "7 #b.pr

#h4 ,/&>d devia;n "<.s;5n">

#i4 ,m1n "7 ;;(,.sfx./,.sf)

#i4 ,m1n "7 ;(,.sfx./,.sf;)

#aj4 surface >ea "7 .prs"6.pr;9#b

UEB Maths Advanced Module - Exercise 8.2

#a4 #j _@< ;x _@< #b.p

#b4 ;(#be.p./#h)m9#b

#c4 ;;"<log5ex">9#d

#c4 "<log;5ex">;9#d

#d4 s9.? "7 ;(#ad4fsin#dh^j./#ab4f)

#e4 _[,,dac "7 _[,,acb

#f4 ;;;,* $#c:,,abc _= $#c:,,abd;'

#f4 ;,* ;$#c:,,abc _= ;$#c:,,abd

#g4 ;;%9#c#hu9#ah+

#g4 ;%;9#c#hu9#ah+

#h4 #be;gh"/$#d "7 #e;g

#i4 ;y "7 "-#a/b"<x"6#d">"<#b"-x">

#aj4 ,,de #l ;,,ac & ,,ce;3,,eb "7 #b3#c

#aj4 ,,de #l ;,,ac & ,,ce3,,eb "7 #b3#c

UEB Maths Advanced Module - Exercise 9.1

#a4 ,a "7 .pr;9#b

#b4 ;(#d%#c+"8%#ah+./%#ab+)

#c4 "t "7 ;(4t.e./spe$;)

#c4 "t "7 ;(di/.e./spe$;)

#c4 "t "7 ;;(distance./speed)

#d4 #dr9#d"/#br

#e4 x;9#g4i

#f4 ,a "7 ,p"<#a"6r">9n

#g4 #c%#h+

#h4 ;;x9<"-#b>

#h4 x;9;<"-#b>

#i4 x;9#cy

#aj4 "<#bx"6#i">9#b

#aa4 ;;(x9#a/d./#d)

#aa4 ;(x;9#a/d./#d)

#ab4 ;;%9#c#b+x

#ab4 ;%;9#c#b+x

#ac4 _<#b1 #d1 "-#f_>

#ad4 ,p"<,e"> "7 ;;(n"<,e">./n"<,s">)

#ad4 ,p"<,e"> "7 ;(n"<,e">./n"<,s">;)

#ae4 ;%#if+"/%#ab+

#af4 ;y "7 "-#a/b"<x"-#a">9#e

#ag4 ;,,ab #l ,,pq

#ah4 ;;;,* $#c:,,mno _= $#c:,,pqr;'

#ah4 ;,* ;$#c:,,mno _= ;$#c:,,pqr

#ai4 #c6 "7 #c"4#b"4#a

#bj4 ;(#cx9#b"-#fx./x9#b"6x"-#f)

UEB Maths Advanced Module - Exercise 10.1

#a4 ;;%a9#b"6b9#b+

#a4 ;%a;9#b"6b9#b+

#b4 ;;%9#c4d#h+

#b4 ;%;9#c4d#h+

#c4 ,! m1n "7 ;;(,.sfx./,.sf)

#c4 ,! m1n "7 ;(,.sfx./,.sf;)

#d4 ;y "7 x;9#d"-x9#c"-#ajx9#b"-#hx

#e4 log;(#a"6x./x)

#f4 ;(a./s9#bj^j) "7 ;(#ab./sin#fj^j)

#f4 ;;;(a./sin#bj^j) "7 (#ab./sin#fj^j);'

#f4 ;;(a./sin#bj^j) "7 ;(#ab./sin#fj^j)

#g4 ;;;y "7 log5af"<x">;'

#g4 ;y "7 log;5af"<x">

#h4 f"<,l"> "7 #b.p%(,l./g)+

#i4 f"<x"> "7 #b;cos"<x"6(.p./#b)">"6#a

#aj4 log"<x;9#b"-x"-#b">"-log"<x"6#a">

#aa4 log;%x;9#b"-#dx"6#d+

#aa4 ;;log%x9#b"-#dx"6#d+

#ab4 ;;log5a(x./%y+)

#ab4 log;5a;(x./;%y;+;)

#ac4 s9#abj^j "7 #j4hg

#ad4 tan.? "7 ;;(sin.?./cos.?)

#ad4 tan.? "7 ;(s9.?./cos.?;)

#ae4 cos;(.p./#e) "7 ;(#a"6%#e+./#d)

#af4 log;5ex

#ag4 ;;;m "7 (y5#b"-y5#a./x5#b"-x5#a);'

#ag4 ;m "7 ;(y;5#b"-y5#a./x5#b"-x5#a)

#ag4 ;m "7 ;;(y5#b"-y5#a./x5#b"-x5#a)

#ah4 ;(#a./k"<k"6#a">"<k"6#b">)

#ai4 ;(#d4a"8%#dh4ab+./#bf4bc)

#bj4 ;;("-b_6%b9#b"-#d;ac+./#b;a)

#bj4 ;("-b_6;%b;9#b"-#d;ac+./#b;a)

UEB Maths Extension Module - Exercise 1.1

#a4 ;(r"-#c./#b) _@< "-#f

#b4 ,simplify #b/c"-(x"-#a./#d)

#c4 ;;;,* x "7 (#e"6%#de+./#b);'

#c4 ;,* ;x "7 ;(#e"6%#de+./#b)

#d4 ;;;q "7 %9#cx9#c"6y9#c"6z9#c+;'

#d4 ;q "7 ;%;9#cx9#c"6y9#c"6z9#c+

#d4 ;q "7 ;;%9#cx9#c"6y9#c"6z9#c+

#e4 ;;(m9#b"-#h./m"6#a) _@> #d

#e4 ;(m;9#b"-#h./m"6#a) _@> #d

#f4 "<#i/be">9<k"6#c> "7 ;%#c/e+

#g4 ;;;(y./w) @> (#a"6%#e+./#b);'

#g4 ;;(y./w) @> ;(#a"6%#e+./#b)

#g4 ;(y./w;) @> ;(#a"6%#e+./#b)

#h4 ;(#db;g9#c;h9#d./#g;h9#b) "7

#i4 ;;;,s "7 %(#c,v./h)+;'

#i4 ;,s "7 ;;%(#c,v./h)+

#i4 ;,s "7 ;%;(#c,v./h)+

#aj4 ,a "7 ;(h./#c)"<d5f"6#d;d5m"6d5l">

UEB Maths Extension Module - Exercise 1.2

#a4 "<#a/bg">9<#cn"6#a> "7 ;;(%#c+./#ha)

#a4 "<#a/bg">9<#cn"6#a> "7 ;(;%#c+./#ha)

#b4 ,a "7 ;(#b"-sin.?./#b;cos.?)

#c4 ,t;5n "7 #e9n"-#a

#d4 ;;;x "7 t%#di"-t9#b+;'

#d4 ;x "7 t;%#di"-t9#b+

#e4 ;;log"<(x9#b./y)"> "7 log#b

#e4 log"<;(x;9#b./y)"> "7 log#b

#f4 "<x"-h">;9#b "7 _6#d;a"<y"-k">

#g4 ,let ;;;r "7 %(#dp./#c)+;'

#g4 ,let ;r "7 ;;%(#dp./#c)+

#g4 ,let ;r "7 ;%;(#dp./#c)+

#h4 ;(#b;b./#e)"-#a/b _@> #f

#i4 ;(q"-#b./#c) @< #b"6(#cq./#d)

#aj4 "<x"6;(#a./x)">9#b

UEB Maths Extension Module - Exercise 2.1

#a4 ,log;(y./#d)

#b4 "-#a/dsec9#dx

#c4 ,log;5#b(%#b+./#d)

#d4 .? "7 ;;cos9<"-#a>"<#e4h/g4c">

#d4 .? "7 cos;9;<"-#a>"<#e4h/g4c">

#e4 ln#i4h"6log5#aj#ag

#f4 ;;log5a"<(x./y)">

#f4 log;5a"<;(x./y;)">

#g4 .? "7 ;;n.p"6tan9<"-#a>a

#g4 .? "7 n.p"6tan;9;<"-#a>a

#h4 ;;;log5ax "7 (log5bx./log5ba);'

#h4 log;5ax "7 ;;(log5bx./log5ba)

#h4 log;5ax "7 ;(log;5bx./log;5ba;)

#i4 cot,a "7 ;;(cos,a./sin,a)

#i4 cot,a "7 ;(cos,a./s9,a;)

#aj4 sec,a "7 ;(#a./cos,a)

UEB Maths Extension Module - Exercise 2.2

#a4 ;;a9<#cy"-#e> "7 ;(#a./a9#b)

#a4 a;9;<#cy"-#e> "7 ;(#a./a9#b)

#b4 ln"<#dx"6#e">

#c4 ;;;y"-y5#a "7 m"<x"-x5#a">;'

#c4 y"-y;5#a "7 m"<x"-x;5#a">

#d4 ;;sin9<"-#a>(x./a)"6,c

#d4 s9n;9;<"-#a>(x./a)"6,c

#e4 ;;;log5ax9n "7 n log5ax;'

#e4 ;;log5ax9n "7 ;n log;5ax

#e4 log;5ax;9n "7 ;n log;5ax

#f4 ;;;,k "7 n%(a./p)+;'

#f4 ;,k "7 ;;n%(a./p)+

#f4 ;,k "7 n;%;(a./p;);+

#g4 ;;log5a%xy+

#g4 log;5a;%xy;+

#h4 f"<x"> "7 #cx9#d"6#dx9#c"-#abx9#b

#i4 ;;log%x9#b"-#dx"6#d+"-log"<x"-#b">

#i4 log;%x;9#b"-#dx"6#d+"-log"<x"-#b">

#aj4 ;("-#e_6%#ba+./#b)

UEB Maths Extension Module - Exercise 3.1

#a4 ;;;z "7 (x"-x:./s);'

#a4 ;z "7 ;;(x"-x:./s)

#a4 ;z "7 ;(x"-x;:./s;)

#b4 x;: "7 ;(sum ( scores" ./numb] ( scores;)

#b4 x;: "7 ;(sum ( scores ./numb] ( scores;)

#b4 x;: "7 ;(sum ( scores./numb] ( scores;)

#c4 y;9#b "7 "-iy;:

#c4 ;;;y9#b "7 "-iy:;'

#d4 ;;;x: "7 (#be"6#ce"6#de./#e);'

#d4 x;: "7 ;(#be"6#ce"6#de./#e)

#e4 ;;<,,pq>,:

#e4 ;<,,pq;>;,:

#f4 ;;<m"6n>,:

#f4 ;<m"6n;>;,:

#g4 #d4a<#e>^4#b<#e>^4

#g4 #d4a<#ebe>^4

#h4 x^4 "7 ;;(t./t9#b"6#c)ms9<"-#a>

#h4 x^4 "7 ;(t./t;9#b"6#c)ms9<"-#a>

#i4 ;;x.9<44> "7 g"-kv

#i4 x.9;<44;> "7 g"-kv

#aj4 ;;x.9<44> "7 #be;e9<#et>ms9<"-#b>

#aj4 x.9;<44;> "7 #be;e9<#et>ms9<"-#b>

UEB Maths Extension Module - Exercise 3.2

#a4 log;5x"<#a/c"> "7 "-#a

#b4 ;,* .? "7 #cg^j#bc7

#c4 ;;(n9#b"-n"-#f./n9#b"6#en"6#f)

#c4 ;(n;9#b"-n"-#f./n9#b"6#en"6#f)

#d4 ;;%("-#c;c./b"-a)+

#d4 ;%;("-#c;c./b"-a)+

#e4 ;;;log5ax "7 (log5bx./log5ba);'

#e4 log;5ax "7 ;;(log5bx./log5ba)

#e4 log;5ax "7 ;(log;5bx./log;5ba;)

#f4 log;5#g%9#d#g+

#g4 ;;;,* $#c:,,rst _= $#c:,,xyz;'

#g4 ;,* ;$#c:,,rst _= ;$#c:,,xyz

#h4 ;y "7 #b%x+ "7 #bx9#a/b

#i4 ;;;d "7 %"<x5#b"-x5#a">9#b+;'

#i4 ;d "7 ;;%"<x5#b"-x5#a">9#b+

#i4 ;d "7 ;%"<x;5#b"-x5#a">9#b+

#aj4 ;;(log5ex./e9<#bx>"6x)

#aj4 ;(log;5ex./e;9;<#bx>"6x)

UEB Maths Extension Module - Exercise 4.1

#a4 ,9put ;\o process ;\o \tput

#b4 ;;;x \o y;'

#b4 ;x ;\o ;y

#c4 ;;<,,ab>^:

#c4 ;<;,,ab;>;^:

#d4 ;;<,,ab>^:"6<,,cd>^:

#d4 ;<;,,ab;>;^:"6;<,,cd;>;^:

#e4 ;;lim.5<x\o#d>x9#b"6#e

#e4 lim.5;<x;\o#d>x9#b"6#e

#f4 ;;lim.5<x\o#=>(x./x9#b)

#f4 lim.5;<x;\o#=;>;(x./x;9#b)

#g4 ;;lim.5<g\o#a>(g9#b"-#a./g"-#a)

#g4 lim.5;<g;\o#a>(g9#b"-#a./g"-#a)

#h4 ;;lim.5<t\o#d>(t9#b"-#af./t"-#d)

#h4 lim.5;<t;\o#d>(t9#b"-#af./t"-#d)

#i4 ;;lim.5<x\o#=>(#cx9#b./x9#b"-#bx)

#i4 lim.5;<x;\o#=;>;(#cx9#b./x9#b"-#bx)

#aj4 ;;lim.5<h\o#j>(#b;h9#bx"6hx9#b./h)

#aj4 lim.5;<h;\o#j>(#b;h9#bx"6hx9#b./h)

UEB Maths Extension Module - Exercise 4.2

#a4 a ;\o ;y "7 ln"<x"6#a">

#b4 ;;(%#bx"6#a+./"<x"-#c">9#c)

#b4 ;(;%#bx"6#a+./"<x"-#c">9#c)

#c4 ;(#bx./"<x"6#e">9#a/b)

#d4 ,,oc "7 ;;%r9#b"-(x./#b)+

#d4 ,,oc "7 ;%r;9#b"-(x./#b)+

#e4 ;;;c9#b "7 a9#b"6b9#b"-#b;ab cos,c;'

#e4 c;9#b "7 a;9#b"6b9#b"-#b;ab cos,c

#f4 ;(#dhp9#bq9#d./#fpq9#c)

#g4 ,a "7 .p"<,r;9#b"-r9#b">

#h4 ;;;n "7 (#dbsin#aag^j./sin#ce^j);'

#h4 ;n "7 ;(#dbsin#aag^j./sin#ce^j)

#i4 cos,c "7 ;;(a9#b"6b9#b"-c9#b./#b;ab)

#i4 cos,c "7 ;(a;9#b"6b9#b"-c9#b./#b;ab)

#aj4 ;;lim.5<n\o#=>"<#a"6(#a./n)">9n

#aj4 lim.5;<n;\o#=;>"<#a"6(#a./n)">9n

UEB Maths Extension Module - Exercise 5.1

#a4 ,a "7 ;(.?./#cfj)"8.pr9#b

#b4 ;;;z "7 (x"-.m./.s);'

#b4 ;z "7 ;(x"-.m./.s;)

#b4 ;z "7 ;;(x"-.m./.s)

#c4 "<cos;(.p./#d)"-tan(.p./#d)">9#b

#d4 .? "7 #bn.p_6cos9<"-#a>a

#e4 tan"<.?"6.f">" "7 ;(tan.?"6.f./#a"-tan.?tan.f)

#e4 tan"<.?"6.f"> "7 ;(tan.?"6.f./#a"-tan.?tan.f)

#e4 tan"<.?"6.f"> "7 ;(tan.?"6.f./#a" "-tan.?tan.f)

#f4 n"<,v.6,c"> "7 n"<,v">"6n"<,c">

#g4 ,x.8,y "7 _<#a1 #aa1 #ab_>

#h4 n"<,d.6,f">" "7 n"<,c">"6n"<,f">"-n"<,d.8,f">

#h4 n"<,d.6,f"> "7 n"<,c">"6n"<,f">"-n"<,d.8,f">

#h4 n"<,d.6,f"> "7 n"<,c">"6n"<,f">" "-n"<,d.8,f">

#i4 ,p"<,a;: or ;,b"> "7 #a

#aj4 n"<,e.8,f"> "7 #j

UEB Maths Extension Module - Exercise 5.2

#a4 ;(pq./#e)"8(p./q)

#b4 ,roots ( ,p"<z"> >e .a1 .a;:1 .b1 .b;:

#c4 s9.? "7 ;;(o./h)

#c4 s9.? "7 ;(o./h;)

#d4 ;;;x: "7 (,.sfx./,.sf);'

#d4 x;: "7 ;;(,.sfx./,.sf)

#d4 x;: "7 ;(,.sfx./,.sf;)

#e4 ;;lim.5<x\o#=>(#a./x) "7 #j

#e4 lim.5;<x;\o#=;>;(#a./x) "7 #j

#f4 ;;lim.5<.d\o#j>(.dy./.dx)

#f4 lim.5;<.d;\o#j>(.dy./.dx)

#g4 ;(y"6#a./y"-#a) @> #b

#h4 ,.s.5;<x"7#a>.9n"<#b9rx">

#h4 ;;,.s.5<x"7#a>.9n"<#b9rx">

#i4 s9"<.p"-;(.p./#f)">

#aj4 #a/b.<cos"<,a">"6cos"<,b">.>

UEB Maths Extension Module - Exercise 6.1

#a4 ;;(dy./dx) @> #j

#a4 ;(dy./dx;) @> #j

#b4 ;;(dy./dx)f7"<x">

#b4 ;(dy./dx;)f7"<x">

#c4 ;;(dy./dx)f7"<x">e9<f"<x">>

#c4 ;(dy./dx;)f7"<x">e;9;<f"<x">;>

#d4 ;;(d./dx)"<x9#b"-#bx">

#d4 ;(d./dx;)"<x;9#b"-#bx">

#e4 ;;;(dy./dx) "7 (#b./%#a"-x9#b+);'

#e4 ;;(dy./dx) "7 ;(#b./%#a"-x9#b+)

#e4 ;(dy./dx;) "7 ;(#b./%#a"-x9#b+)

#f4 ;;;(dy./dx)" "7 u(dv./dx)"6v(du./dx);'

#f4 ;;;(dy./dx) "7 u(dv./dx)"6v(du./dx);'

#f4 ;;(dy./dx)" "7 ;;u(dv./dx)"6v(du./dx)

#f4 ;;(dy./dx) "7 ;;u(dv./dx)"6v(du./dx)

#f4 ;(dy./dx;)" "7 u;(dv./dx;)"6v;(du./dx;)

#f4 ;(dy./dx;) "7 u;(dv./dx;)"6v;(du./dx;)

#g4 ;;;(d./dx)"<kx9n"> "7 knx9<n"-#a>;'

#g4 ;;(d./dx)"<kx9n"> "7 ;;knx9<n"-#a>

#g4 ;(d./dx;)"<kx;9n"> "7 knx;9;<n"-#a>

#h4 ;;(dy./dx) "7 #dx9#c"-#ix9#b"6#g

#h4 ;(dy./dx;) "7 #dx9#c"-#ix9#b"6#g

#i4 ;;(dy./dx) "7 f7"<x">cos f"<x">

#i4 ;(dy./dx;) "7 f7"<x">cos f"<x">

#aj4 ;;(d./dx).<f"<x">.>9#b "7

#aj4 ;(d./dx;).<f"<x">.>;9#b "7

UEB Maths Extension Module - Exercise 6.2

#a4 ;;;log5bx "7 (log5ax./log5ab);'

#a4 log;5bx "7 ;;(log5ax./log5ab)

#a4 log;5bx "7 ;(log;5ax./log;5ab;)

#b4 ;;;(.dy./.dx) "7 (.dy./.du)" "8(.du./.dx);'

#b4 ;;;(.dy./.dx)" "7 (.dy./.du)"8(.du./.dx);'

#b4 ;;(.dy./.dx) "7 ;;(.dy./.du)"8(.du./.dx)

#b4 ;;(.dy./.dx)" "7 ;;(.dy./.du)"8(.du./.dx)

#b4 ;(.dy./.dx;) "7 ;(.dy./.du;)" "8;(.du./.dx;)

#b4 ;(.dy./.dx;) "7 ;(.dy./.du;)"8;(.du./.dx;)

#c4 ;;;(dy./dx) "7 nx9<nx"-#a>;'

#c4 ;;(dy./dx) "7 ;;nx9<nx"-#a>

#c4 ;(dy./dx;) "7 nx;9;<nx"-#a>

#d4 ;;(ax5#a"6by5#a"6c./%a9#b"6b9#b+)

#d4 ;(ax;5#a"6by5#a"6c./%a9#b"6b9#b+)

#e4 ;;;(dy./dx) "7 (f7"<x">./f"<x">);'

#e4 ;;(dy./dx) "7 ;;(f7"<x">./f"<x">)

#e4 ;(dy./dx;) "7 ;(f7"<x">./f"<x">;)

#f4 ;;(dy./dx) "7 #ex9#d"-#i

#f4 ;(dy./dx;) "7 #ex9#d"-#i

#g4 ;;"<(de9#e;f./def9#d)">9#j

#g4 "<;(de;9#e;f./def9#d)">9#j

#h4 ;;lim.5<.?\o#j>(tan(.?./#c)./.?)

#h4 lim.5;<.?;\o#j>(tan(.?./#c)./.?)

#i4 ;;lim.5<x\o#=>(#c%x+./%x+"-#a)

#i4 lim.5;<x;\o#=;>;(#c%x+./%x+"-#a)

#aj4 ;;lim.5<x\o"-#a>" (x9#b"6#dx"6#a./x9#b"-#a)

#aj4 ;;lim.5<x\o"-#a>(x9#b"6#dx"6#a" ./x9#b"-#a)

#aj4 lim.5;<x;\o"-#a>" (x9#b"6#dx"6#a./x9#b"-#a)

#aj4 lim.5;<x;\o"-#a>(x9#b"6#dx"6#a>" ./x9#b"-#a)

UEB Maths Extension Module - Exercise 7.1

#a4 ;;!x9#b;dx

#a4 ;!x;9#b;dx

#b4 ;;!5#j9#b(#c./#d"6x9#b)dx

#b4 ;!;5#j9#b(#c./#d"6x9#b)dx

#c4 ;!#bx9#d;dx

#d4 ;;!5#c9.pcos"<(x./#b)"6.p">dx

#d4 ;!;5#c9.pcos"<(x./#b)"6.p">dx

#e4 ;;!5#j9#e(dx./x"6#c)

#e4 ;!;5#j9#e(dx./x"6#c)

#f4 ;;!5a9bf"<x">dx

#f4 ;!;5a;9bf"<x">dx

#g4 ;;!sin9#bxdx

#g4 ;!s9;9#bxdx

#h4 ;;!e9<ax"6b>dx

#h4 ;!e;9;<ax"6b;>dx

#i4 ;;;!tan xdx "7 ln cos x"6c;'

#i4 ;!tan xdx "7 ln cos x"6c

#aj4 ;;.p!5#j9(.p./#d)sec9#bxdx

#aj4 .p;!;5#j9(.p./#d)sec9#bxdx

UEB Maths Extension Module - Exercise 7.2

#a4 f77"<x"> "7 #fx"-#h

#b4 .a.b"6.a.g"6.b.g "7 ;;(c./a)

#b4 .a.b"6.a.g"6.b.g "7 ;(c./a;)

#c4 ;;(d9#bx./dt9#b)

#c4 ;(d;9#bx./dt9#b)

#d4 ,p"<,e7"> "7 #a"-p"<,e">

#e4 ;;;(dy./dx) "7 ,f7"<u">(du./dx);'

#e4 ;;(dy./dx) "7 ;;,f7"<u">(du./dx)

#e4 ;(dy./dx;) "7 ,f7"<u">;(du./dx;)

#f4 ;;!sec9#b"<ax"6b">dx

#f4 ;!sec;9#b"<ax"6b">dx

#g4 ;;,lim.5<.?\o#j>(sin.?./.?) "7 #a

#g4 ,lim.5;<.?;\o#j>(sin.?./.?) "7 #a

#h4 ;!cos"<ax"6b">dx

#i4 ;;!5#a9#b(x9#c"-x9#b"6#ex"6#c./x)dx

#i4 ;!;5#a9#b(x9#c"-x9#b"6#ex"6#c./x)dx

#aj4 ;;!"<ax"6b">9n

#aj4 ;!"<ax"6b">;9n

UEB Maths Extension Module - Exercise 8.1

#a4 _\y"-#d_\

#b4 ;;(_\x_\./x9#b) "7 #a

#b4 ;(_\x_\./x;9#b) "7 #a

#c4 _\x_\ _@> #j

#d4 ;;%a9#b+ "7 _\a_\

#d4 ;%a;9#b+ "7 _\a_\

#e4 ;(_\#cx"-#b_\./#cx"-#b) "7 #a

#f4 _\#cy"-#a_\"6_\#by"6#c_\ @> #e

#g4 y;9#b "7 #bsin_\x_\

#h4 _\z"-#b_\"6_\z"6#a_\ "7 #g

#i4 _\#cx"6#b_\ "7 #bx"-#c

#aj4 ;;_\<,o5#a,p>^:_\

#aj4 _\;<,o;5#a,p>^:_\

UEB Maths Extension Module - Exercise 8.2

#a4 ,a ^9 ;(h./#b)"<d5f"6d5l">

#b4 "<x"-h">;9#b "7 _6#d;a"<y"-k">

#c4 ;;;y "7 e9<f"<x">>;'

#c4 ;y "7 e;9;<f"<x">;>

#c4 ;y "7 ;;e9<f"<x">>

#d4 ;;(p9#a/b"8p9#a/b./p9#b)

#d4 ;(p;9#a/b"8p9#a/b./p9#b)

#e4 ;;;,s5n "7 (a"<r9n"-#a">./r"-#a);'

#e4 ,s;5n "7 ;;(a"<r9n"-#a">./r"-#a)

#e4 ,s;5n "7 ;(a"<r;9n"-#a">./r"-#a)

#f4 ;;;x9(#a./n) "7 %9nx+;'

#f4 x;9;(#a./n) "7 ;%;9nx;+

#f4 ;;x9(#a./n) "7 ;;%9nx+

#g4 ;(#a./%9#d"<#g"-x">9#b+)

#h4 ;;_\(m5#a"-m5#b./#a"6m5#am5#b)_\

#h4 _\;(m;5#a"-m5#b./#a"6m5#am5#b)_\

#i4 ;;f7"<x">n.<f"<x">.>9<n"-#a>

#i4 f7"<x">n.<f"<x">.>;9;<n"-#a>

#aj4 ;;lim.5<h\o#j>(#bxh"-h9#b"-#e;h./h)

#aj4 lim.5;<h;\o;>;(#bxh"-h9#b"-#e;h./h)

UEB Maths Extension Module - Exercise 9.1

#a4 #h4ged<#gei>^4

#a4 #h4ged<#g>^4#e<#i>^4

#b4 ,t;5n "7 a"6"<n"-#a">

#c4 y;: "7 "-#aj

#d4 ;;<,,ab>:

#d4 ;<,,ab;>;:

#e4 ln_\f"<x">_\"6c

#f4 ;;;x: "7 (,.sx./n);'

#f4 x;: "7 ;(,.sx./n;)

#f4 x;: "7 ;;(,.sx./n)

#g4 _\#ex"-#c_\ _@> #b

#h4 ;("<#bx9#g">9#cy9#b./x9#ajy)

#i4 .<#b"<x"6y">.>"/#d @< #aj

#aj4 _\"-#h_\ "7 _\#h_\ "7 #h

#aa4 cos,c "7 ;;(a9#b"6b9#b"-c9#b./#b;a)

#aa4 cos,c "7 ;(a;9#b"6b9#b"-c9#b./#b;a)

#ab4 ,a "7 ;;!5<"-#a>9#b"<#b"6x">dx

#ab4 ,a "7 ;!;5;<"-#a>9#b"<#b"6x">dx

#ac4 ;;!5b9cf"<x">dx

#ac4 ;!;5b;9cf"<x">dx

#ad4 s9"<.p"-;(.p./#h)">

#ae4 ;;(n6./r6"<n"-r">6)

#ae4 ;(n;6./r;6"<n"-r">;6;)

#af4 .? "7 n.p"6"<"-#a">9nsin9<"-#a>a

#ag4 ;;lim.5<x\o#j>f"<x">

#ag4 lim.5;<x;\o#j>f"<x">

#ah4 f;5#a"<x">"6f5#b"<x">

#ai4 ;;;,s5n "7 (n./#b).<#b;a"6"<a"-l">d.>;'

#ai4 ;;;,s5n" "7 (n./#b).<#b;a"6"<a"-l">d.>;'

#ai4 ;;;,s5n "7 (n./#b).<#b;a"6"<a" "-l">d.>;'

#ai4 ,s;5n "7 ;(n./#b).<#b;a"6"<a"-l">d.>

#ai4 ,s;5n" "7 ;(n./#b).<#b;a"6"<a"-l">d.>

#ai4 ,s;5n "7 ;(n./#b).<#b;a"6"<a" "-l">d.>

#bj4 f77"<x"> "7 k"<b;9#b"-x9#b">

UEB Maths Extension Module - Exercise 10.1

#a4 x;5#b "7 x;5#a"-(f"<x5#a">./f7"<x5#a">)

#a4 x;5#b" "7 x;5#a"-(f"<x5#a">./f7"<x5#a">)

#a4 ;;;x5#b" "7 x5#a"-(f"<x5#a">./f7"<x5#a">);'

#a4 ;;;x5#b "7 x5#a"-(f"<x5#a">./f7"<x5#a">);'

#b4 ;;!x9#b;dx

#b4 ;!x;9#b;dx

#c4 ;;;!(cos x./sin x)dx;'

#c4 ;!;(cos x./s9 x;)dx

#d4 ;;!5#b9#c(dx./x)

#d4 ;!;5#b9#c(dx./x)

#e4 ;;;d "7 %"<x5#b"-x5#a">+;'

#e4 ;d "7 ;%"<x;5#b"-x5#a">+

#f4 cosec,a "7 ;(#a./sin,a)1 s9,a "7@: #j

#g4 "<,re"<.a">">;9#b" "6"<,re"<.b">">9#b "7 #a

#g4 "<,re"<.a">">;9#b"6"<,re"<.b">">9#b "7 #a

#h4 ;;!(#fx9#b./x9#c)

#h4 ;!;(#fx9#b./x9#c)

#i4 ;;;d "7 (_\ax5#a_\./%a9#b+);'

#i4 ;d "7 ;;(_\ax5#a_\./%a9#b+)

#i4 ;d "7 ;(_\ax;5#a_\./%a9#b+)

#aj4 ;;(d./dx)"<(x9#b./x"-#a)">

#aj4 ;(d./dx;)"<;(x9#b./x"-#a)">

#aa4 ;;;x: "7 (,.sx./n);'

#aa4 x;: "7 ;(,.sx./n;)

#aa4 x;: "7 ;;(,.sx./n)

#ab4 ,.s.5#b.9#d_\#cp"-#b_\

#ac4 ;;;x.9<44> "7 "-n9#b"<x"-c">;'

#ac4 x.9;<44;> "7 "-n;9#b"<x"-c">

#ac4 ;;x.9<44> "7 "-n;9#b"<x"-c">

#ad4 ;;;y "7 tan9<"-#a>f"<x">;'

#ad4 ;y "7 tan;9;<"-#a>f"<x">

#ad4 ;y "7 ;;tan9<"-#a>f"<x">

#ae4 ,a;5n "7 ,p"<#a"6(r./#ajj)">9n

#af4 ;;;"<(mx5#b"6nx5#a./m"6n)1 (my5#b"6ny5#a./m"6n)">;'

#af4 ;;"<(mx5#b"6nx5#a./m"6n)1 ;;(my5#b"6ny5#a./m"6n)">

#af4 "<;(mx;5#b"6nx5#a./m"6n)1 ;(my;5#b"6ny5#a./m"6n)">

#ag4 ;;max.5<#j_@<x_@<#a>xe9<"-x9#b>

#ag4 max.5;<#j_@<x_@<#a>xe9<"-x9#b>

#ah4 ,.s.5;<i"7#a>.9nx5#ap5#a

#ai4 ;;lim.5<n\o#=>"<#a"6(#a./n)">9n

#ai4 lim.5;<n;\o#=;>"<#a"6(#a./n)">9n

#bj4 ;;!(f7"<x">./f"<x">)dx

#bj4 ;!;(f7"<x">./f"<x">;)dx