Mathematics 0580 · IGCSE · Graphs of functions

Graphs of functions — practice question

The function can be written as $y = \frac{x^3}{8} - \frac{2}{x^2}, \; x \neq 0$.
(a)[2]

Fill in the values in the table.

(b)[4]

On the grid, draw the graph of $y = \frac{x^3}{8} - \frac{2}{x^2}$ for $0.5 \le x \le 3.5$.

(c)[1]

Use your graph to solve $\frac{x^3}{8} - \frac{2}{x^2} = 0$.

(d(i))[1]

Write down a value of $k$ for which the equation has one solution.

(d(ii))[1]

Write down a value of $k$ for which the equation has three solutions.

(e)[3]

By drawing an appropriate tangent, estimate the gradient of the curve at $x = -3$.

(f(i))[3]

By drawing a suitable line on the grid, find $x$ when $\frac{x^3}{8} - \frac{2}{x^2} = 6 - x$.

(f(ii))[4]

Find the values of $a$, $b$ and $c$.

Worked solution & mark scheme

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