Mathematics 0580 · IGCSE · Differentiation

Differentiation — practice question

The graph of $y = 10 - 8x^2$ for $-1.5 \leq x \leq 1.5$ is plotted on the grid.
(a)[1]

Write down the equation for the graph’s line of symmetry.

(b)[3]

On the grid opposite, draw the tangent to the curve at the point where $x = 0.5$. Find the gradient of this tangent.

(c(i))[3]

Complete the table.

(c(ii))[4]

On the grid opposite, draw the graph of $y = x^3 + 3x + 4$ for $-1.5 \leq x \leq 1.5$.

(d)[1]

Show that the values of $x$ where the two curves intersect are the solutions to the equation $x^3 + 8x^2 + 3x - 6 = 0$.

(e)[3]

By drawing an appropriate straight line, solve the equation $x^3 + 5x + 2 = 0$ for $-1.5 \leq x \leq 1.5$.

Worked solution & mark scheme

This 15-mark question has a full step-by-step worked solution and mark scheme. One marking point: The equation is $x=0$.

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