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ej Cnr*1. (a) Show that

(b) Hence find, for

sin20 = tan9l+cos20

180'< I < 180'.all thesolutionsf(2)

2sin201+cos2d

Giveyouranswen o 1decimal lace.

t ) =\ /O=f^^-t

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2. A curveC hasequation35l=- ' ^ , x+- (s-3x) ' 3 g= (s-3f

ThepointP on C has r-coordinate. Findan equation fthe normal o C atP in the ormax+by + c = 0, wherea, b andc are ntegers. (7)

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-t . f(r) = 4.ot"" t - 4x+l , where is in radians.Show hat here s a roota of f(x)=Q inthe nterval 1.2,1.31.

Show hat he equation("r) = g "unbewritten n the form(2)

11x=-+-sinx 4(c) Use he terativeormula

' , , ,=I+1 ' xo- I '25 'sln , 4to calculatehe valuesof xr, x, and x,, givingyour answerso 4 decimal laces.(3)

(d) By consideringhechange f signof f(:r) in a suitablenterval, eri$ thata:I.29I correcto 3 decimal laces. (2\

taJ

(b)

(2)

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4. The unction is defined yf : . r r+12; r -5 jxeR

(a) Sketchhegraph ithequation = 11y;,showinghecoordinatesfthepointswherethegraph utsor meetsheaxes. (2)

(b ) So lve(x )=154t . (3)The functiong is defined y

g :x t -> ' -4x+ I , - rR, 0 ( - r (5Findfg(2).

Find herangeof g.

(c)

(d)(2)

(3)t(-)(z.sro)

lzr-s\= tS+r 2:--S=tS+lL

d- =ZO- (zr-s)=s+

' lO=$t-,c=

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3.

Figure 1Figure1 shows sketch f thecurveCwith theequation=(2x2 -5x+2)e-'.(a) Find he coordinatesf thepointwhereC crosseshey-axis. \=L . )v(b) Show hat C crosseshe.r-axisat x=2 and ind thex-coordinate f the otherpointwhereC crosseshex-axis. (3),'^ \ tr.i-i Y

OI

(d) Hencefind the exactcoordinatesof the furning points ofC.(3)

(s)

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6.

Figure 2Figure 2 showsa sketchof the curve with theequation v= f(t), r R.Thecurvehasa tumingpointaI A(3 , - 4) andalsopasseshroughhepoint (0, 5)(a) Write downthe coordinates f thepoint to which I is transformedonthe curvewithequatlon

11;=lr(x)1,gr+)( i i ) :2r()x). (61-S) (4)

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c tu\aqnJ/Jr(&-3f-q-) f(r) ts uof ono\oono=; sr> tC a^^ "otqr_ue-ou+_t^\^efsR-Crt C^rUUa,re. r \nverse-e -tt.e-bna,rr\stestrr-cfieal )L? 3 * rcs -s )

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8. (a) Simplify u1ly2x'+ 9x- 5x2+2x-15

Given hatln(2x2 9x- 5)= 1+ln(x2 2x -15), x + -5,

(b) find"r n termsof e.

(3)

-5n l2:L'+1x-5 =t a lnl2Lt

2_-Z