CAIE Mathematics (9709)

tion of a curve is such that forx>3. The curve passes through the point 4, 5. Find the equation of the curve.

in the expansion ofx+a in the expansion of ax+3 isq. It is given thatp+q=276. Find the possible values of the constant a.

3 (a)Express 4 +c, whereaandbare integers andcis to be given in terms of the constant p. [2] pfor which the equation 4x real roots.

4Solve the equation 8 +215x

y= 10x The diagram shows the curve with equation y=10x 2forx>0. The curve meets thex-axis at the points 0, 0and4, 0. Find the area of the shaded region.

1rad The diagram shows a sector OABof a circle with centreO. AngleAOB=1radians andOP=AP=x. (a)Show that the arc length ABis 2x1cos1. [2] (b)Find the area of the shaded region APBin terms ofxand1.

cos1+sin1 cos1+sin1 for 0 (ii)Hence verify that the only solutions of the equation cos 0 and π.

(b)Prove the identitysin cos1+sin1 (c)Using the results of(a)(ii)and(b), solve the equationsin cos1+sin1

π π π 2π The diagram shows the graph of x=3+2 sin (a)On the diagram above, sketch the graph ofy=f x. [2] (b)Find an expression for f x.

(c)π π π 2π The diagram above shows part of the graph of the function g x=3+2 sin Complete the sketch of the graph of g xon the diagram above and hence explain whether the function g has an inverse. [2] (d)Describe fully a sequence of three transformations which can be combined to transform the graph of πto the graph ofy=fx, making clear the order in which the transformations are applied.

(b)Show that the nth term of one of the two possible geometric progressions is equal to multiplied by thenth term of the other geometric progression.

10The equation of a circle is =20. The liney= x+6 is a tangent to the circle at the point (a)Show that one possible value of

(b)For (c)For found in(b).

11The equation of a curve isy=k

where kis a positive constant. (a)Find (b)Find the x-coordinate of the stationary point in terms ofk.

(c)Given that to the curve makes an angle of tan 2with the positivex-axis.

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