MARKS Page four 8. ABCD is a rectangle with sides of lengths x centimetres and (x − 2) centimetres, as shown. If the area of ABCD is less than 15 cm2, determine the range of possible values of x. 9. A, B and C are points such that AB is parallel to the line with equation y + 3 = 0 x and BC makes an angle of 150º with the positive direction of the x-axis. Are the points A, B and C collinear? 10. Given that 3 π tan2 = , 0 < < 4 4 x x , find the exact value of (a) cos 2x (b) cos x. 11. T(−2, −5) lies on the circumference of the circle with equation (x + 8)2 + (y + 2)2 = 45. (a) Find the equation of the tangent to the circle passing through T. (b) This tangent is also a tangent to a parabola with equation y = −2x2 + px + 1 − p, where p > 3. Determine the value of p. 4 3 1 2 4 6 x cm A D C B (x – 2) cm