Mathematics 4024 · O Level
Geometrical constructions
32 practice questions on Geometrical constructions, with worked solutions and instant marking.
The diagram illustrates the lines $AB$ and $BC$.
May/June 2015
Within triangle $ABC$, the lengths are $AB = 5$ cm and $AC = 6$ cm.
May/June 2015
The diagram depicts triangle $ABC$.
May/June 2016
The diagram shows the triangle labelled $ABC$.
May/June 2016
Triangle $ABC$ is drawn with sides $AB=8\text{ cm}$, $AC=7\text{ cm}$ and $BC=12\text{ cm}$.
May/June 2016
ABC forms a triangle. B and D lie on opposite sides of the line AC. DA = 9 cm and CD = 7 cm.
May/June 2017
The diagram indicates where point $A$ is positioned.
May/June 2017
The scale sketch represents a barn $ABCD$. Here, $AB = 7\text{ m}$ and $BC = 4\text{ m}$. The scale used is $1\text{ cm}$ to represent $1\text{ m}$. A horizontal rail is fixed to the outside wall of the barn from $A$ to $B$. Jasper is a dog on a $3\text{ m}$ rope. One end of the rope is fastened to the rail, and that end may move along the rail.
May/June 2018
On the diagram, construct the perpendicular bisector for $AB$.
May/June 2018
$ABC$ is a triangle with $AC=6\text{ cm}$ and $BC=9\text{ cm}$. $AB$ is shown below. Using only a ruler and a pair of compasses, construct triangle $ABC$.
May/June 2018
The diagram displays the layout of a garden, $ABCD$.
May/June 2019
For this question, use only a straight edge and a pair of compasses.
May/June 2019
$ABCD$ forms a parallelogram. $AD = 6\text{ cm}$, $AB = 8\text{ cm}$ and $BD = 11\text{ cm}$.
May/June 2019
Use only a ruler and compasses in this question.
May/June 2021
Construct the bisector of angle $PSR$ using only a straight edge and compasses.
May/June 2022
The diagram displays a field, $ABCD$, drawn at a scale of $1\text{ cm}$ to $50\text{ m}$.
May/June 2022
$ABC$ forms a triangle with $AC = 5\,\text{cm}$ and $BC = 10\,\text{cm}$. With a ruler and compasses only, construct triangle $ABC$. $AB$ has already been drawn for you.
May/June 2024
The scale diagram depicts a section of field $ABCD$. The drawing scale is $1\text{ cm}$ representing $50\text{ m}$.
May/June 2024
The diagram presents quadrilateral $ABCD$.
Oct/Nov 2016
The diagram represents triangle $ABC$.
Oct/Nov 2016
In the diagram, $PQ$ crosses $LM$ at $O$.
Oct/Nov 2018
The diagram depicts triangle $ABC$.
Oct/Nov 2019
Point $C$ lies above $AB$, with $AC = 5\text{ cm}$ and $BC = 7\text{ cm}$. Use a pair of compasses and a ruler only to construct triangle $ABC$.
Oct/Nov 2019
The diagram shows where boats $A$, $B$ and $C$ are positioned.
Oct/Nov 2020
In triangle $PQR$, the lengths are $PR = 7.5$ cm and $QR = 6$ cm.
Oct/Nov 2020
$ABC$ forms a triangle, with $AC = 5\,\text{cm}$ and $BC = 7\,\text{cm}$.
Oct/Nov 2021
The scale diagram depicts a garden with two trees $P$ and $Q$. The scale is $1$ centimetre represents $6$ metres.
Oct/Nov 2021
The scale diagram represents a plot of land, $PQRS$. The scale is $1\text{ cm}$ to $20\text{ m}$.
Oct/Nov 2022
The scale diagram indicates the locations of two boats $A$ and $B$. The scale used is $1 : 20000$.
Oct/Nov 2023
Determine angle $ABC$.
Oct/Nov 2023
The scale sketch shows field $ABCDE$. Inside the field is a stage, which is a sector of a circle with centre $C$. The scale used is $1\text{ cm}$ to $2.5\text{ m}$.
Oct/Nov 2024
Triangle ABC has AB = 8.5 cm, AC = 6 cm and BC = 7 cm.
Oct/Nov 2025