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1. The curve C has equationy = (2x-3)5

The point P lies on C and has coordinates (w, - 32).Find(a) the value ofw,

(2)(b) the equation of the tangent to Cat the point P in the form y = mx+ c, where m andc are constants.

(5)

.J... w ' .~ ~ ; : . , . , . . ..boA-.... 2:: .. - z;.. . .. \=s (-2)A( X 2. = \bD

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a n ~ 2. g(x) = e x-l + x -6

(a) Show that the equation g(x) =0 can be written asX = n(6 - X) +1, X < 6 (2)

The root of g(x) =0 is a.The iterative formula

X II+ I = ln(6 - X II ) +1' Xo = 2is used to find an approximate value for a.(b) Calculate the values of x1 , x2 and x3 to 4 decimal places. (3)(c) By choosing a suitable interval, show that a= 2.307 correct to 3 decimal places.

(3)

___) _ X-\ \ ~ ( b - - x . - " ' L X : : \ ~ - x . ) : \__L \(\ (A ~ ~ ~ 0 b-JC..__ L O . X-_5_b_] _ __b) 'X.e> 2. - - - - ~ ) - f . ( _ 2 _ : _ 3 - Q b S - ODOC>18_____ t_, "; L _ 2 : > _ B _ 6 ~ -- f 1 - ( 2 - = - 3 0 1 - j ) ~ Q Q _ C Q . 4 1

= ~ i , < 6 ~ - - - - - - - - - - -___' X . ~ - : ; 13 \1.5_ _ _ ~ - " - '- . ' ) ~ k , . . . ~ e _ _ --------=---- ~ \ l - L . e _ , oc'\-- - ' , - A x . . ~ ~ 1 3 0 - b S S ~ b - . . ' l 3 0 ~ a-'cJ-'2 303:$---- -- : -. cJ.. ~ b ~ O T - { - ~ p ' ) - - - - - - - - - - - - - - - - - - - - - ~ ~ ~ ~

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3.

-

yy = f(x)

0 X

Figure 1Figure 1 shows part of the curve with equation y = f(x), x E IRLThe curve passes through the points Q(O,2) and P(-3, 0) as shown.(a) Find the value of ff(-3) .

(2)On separate diagrams, sketch the curve with equation

(2)(c) y=f(lxl) - 2, (2)(d) y =2f X ) . (3)Indicate clearly on each sketch the coordinates of the points at which the curve crosses ormeets the axes.

_ c.\)__f._(-3) = fJ_o_,J-__,.,2.____ _ _ _ _ _

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c )f { \ ~ \ ) - 2-

d.)

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4. (a) Express 6 cos()+ 8 sin() in the form R cos(() - a.), where R > 0 and 0 < a.