Equations, Inequalities & Graphs (Cambridge (CIE) O Level Additional Maths): Exam Questions

Solve the inequality $\left|4x-1\right|>9$.

On the axes below, sketch the graph of $y=\left|(x-2)(x+1)(x+2)\right|$showing the coordinates of the points where the curve meets the axes.

The diagram shows the graph of $y=\mathrm{f}\left(x\right)$, where $\mathrm{f}\left(x\right)$ is a cubic polynomial.

Find $\mathrm{f}\left(x\right)$.

Write down the values of $x$ such that $\mathrm{f}\left(x\right)<0$.

On the axes below, sketch the graph of $y=(x-2)(x+1)(3-x)$, stating the intercepts on the coordinate axes.

Hence write down the values of $x$ such that $(x-2)(x+1)(3-x)>0$.

Solve $\left|3x-2\right|=4+x$ .

The diagram shows the graph of $y=\left|\mathrm{f}\right(x\left)\right|$, where $\mathrm{f}\left(x\right)$ is a cubic function.

Find the possible expressions for $\mathrm{f}\left(x\right)$ in factorised form.

The diagram shows the graph of a cubic curve .

Find an expression for $\mathrm{f}\left(x\right)$.

Solve $\mathrm{f}\left(x\right)\le 0$.

Write $2x^2+3x-4$ in the form $a{(x+b)}^2+c$, where $a,b$ and $c$ are constants.

Hence write down the coordinates of the stationary point on the curve $y=2x^2+3x-4$.

On the axes below, sketch the graph of $y=\left|2x^2+3x-4\right|$, showing the exact values of the intercepts of the curve with the coordinate axes.

Find the value of $k$ for which $\left|2x^2+3x-4\right|=k$ has exactly 3 values of $x$.

The diagram shows the graph of $y=\left|\mathrm{p}\left(x\right)\right|$ , where $\mathrm{p}\left(x\right)$ is a cubic function. Find the two possible expressions for $\mathrm{p}\left(x\right)$.

Solve the inequality $\left|3x+2\right|>8+x$.