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