Mathematics 0580 · IGCSE · Sketching curves

Sketching curves — practice question

$y=1-\frac{2}{x^2},\ x\ne0$
(a)[3]

Fill in the table.

(b)[5]

On the grid, sketch $y = 1 - \frac{2}{x^2}$ for $-5\le x\le-0.5$ and $0.5\le x\le5$.

(c(i))[2]

On the grid, sketch the graph of $y=-x-1$ for $-3\le x\le5$.

(c(ii))[1]

Solve $1-\frac{2}{x^2}=-x-1$.

(c(iii))[3]

The equation $1-\frac{2}{x^2}=-x-1$ may be written in the form $x^3+px^2+q=0$. Find the value of $p$ and the value of $q$.

(d(i))[1]

State the co-ordinates of $A$.

(d(ii))[1]

On the grid, sketch the straight line joining $A$ and $B$.

(d(iii))[2]

Complete the statement. The straight line that passes through $A$ and $B$ is a [BLANK] at the point [BLANK].

Worked solution & mark scheme

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