CAIE A-Level Further Math AS 1.2.1 Rational Graphs Questions

$x=-1, \quad x=2$
Vertical asymptotes.

y=1
Horizontal asymptote.

2

$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{\left(x^{2}-x-2\right)(2 x)-\left(x^{2}+2\right)(2 x-1)}{\left(x^{2}-x-2\right)^{2}}$

M1*

Finds $\frac{\mathrm{d} y}{\mathrm{~d} x}$.

$x^{2}+8 x-2=0$
Sets equal to 0 and forms equation.

(-8.2,0.9), (0.2, -0.9).
Condone
$$\left(-4-3 \sqrt{2}, \frac{2}{3} \sqrt{2}\right),\left(-4+3 \sqrt{2},-\frac{2}{3} \sqrt{2}\right) .$$

4

Axes and all three asymptotes.
Correct shape and position, crossing horizontal
asymptote.

States (0,-1) coordinates of intersection with axes,
may be seen on diagram.

3