= 2 sin (x 60°) + 2 tan = 0 in the interval 180°. y x x − −180° ⩽ ⩽ (1) (Total 10 marks) ___________________________________________________________________________ A has equation = + 2. 11. C y x3 x2 x – – The point has 2. P x-coordinate (a) Find in terms of x. (2) (b) Find the equation of the tangent to the curve at the point C P. (4) The normal to at intersects the at C P x-axis A. (c) Find the coordinates of A. (4) (Total 10 marks) ___________________________________________________________________________ 12. f(x) = + + + where and are constants. x3 x2 px q, p q Given that f(5) = 0 and f(−3) = 8, (a) find the values of and p q, (7) (b) factorise f(x) completely. (5) (Total 12 marks) ___________________________________________________________________________ 13. is a parallelogram. and. OACB The points and divide and in the ratio 1 : 4 respectively. M, S, N T OB, BC, CA AO The lines and intersect at the point ST MN D. (a) Expressin terms of a and b.
y = 2 sin (x − 60°) + 2 tan x = 0 in the interval −180° ⩽ x ⩽ 180°. (1) (Total 10 marks) ___________________________________________________________________________ 11. A C has equation y = x3 – x2 – x + 2. The point P has x-coordinate 2. (a) Find in terms of x. (2) (b) Find the equation of the tangent to the curve C at the point P. (4) The normal to C at P intersects the x-axis at A. (c) Find the coordinates of A. (4) (Total 10 marks) ___________________________________________________________________________ 12. f(x) = x3 + x2 + px + q, where p and q are constants. Given that f(5) = 0 and f(−3) = 8, (a) find the values of p and q, (7) (b) factorise f(x) completely. (5) (Total 12 marks) ___________________________________________________________________________ 13. OACB is a parallelogram. and. The points M, S, N and T divide OB, BC, CA and AO in the ratio 1 : 4 respectively. The lines ST and MN intersect at the point D. (a) Expressin terms of a and b.
07_as_pure_mathematics_practice_paper_d.docx