CAIE Mathematics (9709)

Verify the identity

Prove the identitytan1+1tan

Using the results of

, solve the equationtan1+1tan =4 cos1, for 0 x=x+a where ais a positive constant.

Find an expression for f x.

(i)State the domain of the function f

State the range of the function f

Given that , solve the equation gf x=0. [3] y= 3x 2+ 12 y= 2x 2+ 13x The diagram shows curves with equations y=2x 2+13x 2andy=3x 2+12. The curves intersect at points AandB.

Find the coordinates of AandB. [4] 10The equation of a curve is

Find the x-coordinates of the stationary points of the curve and determine their nature.

State the set of values for which the function f is increasing. [1] 11The coordinates of points A,BandCare6, 4,p, 7and14, 18respectively, wherepis a constant. The line ABis perpendicular to the lineBC.

Given that A circle passes through the points A,BandC.

Find the equation of the circle.

Find the equation of the tangent to the circle at C, giving the answer in the formdx+ey+f=0, where d,eandfare integers. [3] Additional Page If you use the following lined page to complete the answer

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