Mathematics 4024 · O Level

Graphs of functions

20 practice questions on Graphs of functions, with worked solutions and instant marking.

The function is $f(x) = x^3$.

May/June 2015

Part B

May/June 2015

The table underneath gives several values of $x$ together with the matching values of $y$ for $y=\frac{1}{4}\times2^x$.

May/June 2016

From the figures shown, state which one could represent the graph of the equations given.

May/June 2018

The diagram represents a triangular prism, and every length is measured in centimetres.

May/June 2019

The graph of $y=\frac{x^3}{5}-3x+2$ has been plotted on the grid.

May/June 2022

Fill in the value table for $y = x^3 - 4x + 3$.

May/June 2022

A cuboid is given with side lengths of $x$ cm, $(5-x)$ cm and $15$ cm. The diagram depicts a pyramid whose square base has side length $9$ cm. The pyramid has height $x$ cm and volume $y$ cm$^3$.

May/June 2023

The diagram depicts the graph of $y = \dfrac{1}{x} + \dfrac{x}{2}$.

May/June 2024

$y = \frac{3}{5} \times 2^x$. The table gives some $x$-values together with the matching $y$-values, correct to one decimal place where needed.

Oct/Nov 2016

The function is $y=\dfrac{x}{20}(x^2-10)$.

Oct/Nov 2016

Zara encloses a plot of land beside a wall in order to create a vegetable garden. The garden is rectangular, with the wall forming one of its sides. The garden has an area of $18$ square metres. The width of the garden is $x$ metres.

Oct/Nov 2018

The rectangle $ABCD$ has an area of $80\,\text{cm}^2$. Triangle $PCQ$ is taken away from one corner of the rectangle. $BQ = DP = 4\,\text{cm}$. $AB = x\,\text{cm}$.

Oct/Nov 2019

Rectangle $ABCD$ has area $30\text{ cm}^2$. $AB=x$ cm. Rectangle $DEFG$ is cut away from one corner of rectangle $ABCD$. $AE = CG = 2$ cm.

Oct/Nov 2023

Complete the entries in the table for $y = \frac{4^x}{10}$.

Oct/Nov 2023

Complete the value table for $y = 4 + 2x - \frac{x^2}{2}$.

Oct/Nov 2024

Finish the table for $y = \frac{x}{4}(2x^2 - x - 10)$.

Oct/Nov 2024

This table lists some values of $y=x^3-3x+2$.

Oct/Nov 2025

Given $y=x^3-4x^2+12$.

Oct/Nov 2025

Sketch the graph of each function. Indicate the value where each graph crosses the y-axis.

Oct/Nov 2025