Mathematics 9709 · AS & A Level · Coordinate geometry

Coordinate geometry — practice question

The curve, which goes through $(0, 3)$, is described by $y = f(x)$. Also given is $f'(x) = 1 - \frac{2}{(x-1)^3}$.

(a)[4]

Determine the equation of the curve.

(b)[4]

Show that the $x$-coordinate of $P$ satisfies the equation $(2x + 1)(x - 1)^2 - 1 = 0$.

(c)[2]

Check that $x = \frac{3}{2}$ satisfies this equation and therefore determine the $y$-coordinate of $P$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Obtain $y=x+(x-1)^{-2}+c$ by integration” …