Mathematics 0580 · IGCSE
Symmetry
60 practice questions on Symmetry, with worked solutions and instant marking.
Shade two additional squares so that this shape has rotational symmetry of order 2.
Feb/March 2017
The diagram displays a regular pentagon together with a kite.
Feb/March 2018
The diagram displays a regular pentagon together with a kite.
Feb/March 2018
The diagram shows two congruent triangles joined at a point, creating a bow-tie shape.
Feb/March 2021
The diagram consists of two congruent triangles joined at a single point, giving an hourglass-like shape.
Feb/March 2021
Draw a line through point $P$ so that it is perpendicular to line $l$.
Feb/March 2024
Draw every line of symmetry on the diagram.
Feb/March 2025
A quadrilateral has one line of symmetry. Its diagonals meet at right angles. Write down the mathematical name of the quadrilateral.
Feb/March 2025
A display of small square cells is shown, with some of the squares already shaded.
Feb/March 2025
Here are the shapes in the list: equilateral triangle, square, regular pentagon, parallelogram, regular hexagon, circle.
May/June 2015
The shape shown is symmetrical.
May/June 2015
The quadrilateral ABCD is a parallelogram.
May/June 2015
The diagram shows a shape.
May/June 2016
A quadrilateral has rotational symmetry of order 2 and no lines of symmetry. State the mathematical name of this quadrilateral.
May/June 2016
The shape shown above is a rhombus.
May/June 2017
The diagram has concentric circular rings, with four evenly spaced radial gaps in the outer ring and a central circle marked with an 'X'.
May/June 2018
Draw every line of symmetry on each shape.
May/June 2018
The diagram shows two figures: (i) a double-headed arrow, and (ii) a circle with a rotated square inside it.
May/June 2019
Shade an amount equal to five-eighths of the rectangle.
May/June 2019
The diagram shows a square grid, with several of the corner squares shaded.
May/June 2021
Draw the line of symmetry for this figure.
May/June 2021
A square grid is displayed, and several corner squares are shaded.
May/June 2021
Identify the mathematical name of a 4-sided shape with rotational symmetry of order $2$ and no lines of symmetry.
May/June 2023
A square grid diagram with a few squares already shaded.
May/June 2023
A $3 \times 3$ array of squares is shown. Three of the squares are shaded: the upper right square, the middle square, and the lower left square.
May/June 2023
A diagram displays a $3\times3$ array of equal squares. The grey-shaded squares are the top right square, the centre square, and the bottom left square.
May/June 2023
State the order of rotational symmetry for a rhombus.
May/June 2024
A figure in the form of a cross is shown.
May/June 2024
The diagram depicts a square.
May/June 2024
On the diagram, draw any lines of symmetry.
May/June 2024
Shade one additional small square so that the diagram has a single line of symmetry.
May/June 2025
The diagram depicts a pyramid ABCDE with a square base. M is at the centre of the square base, and E is directly above M. The diagram is not drawn to scale.
May/June 2025
A figure shaped like a jigsaw puzzle is shown.
May/June 2025
The diagram is a rectangular grid, and a few squares are shaded.
May/June 2025
This quadrilateral has the following features: • its diagonals are the only lines of symmetry • it has rotational symmetry of order 2
May/June 2025
The figures shown are a Parallelogram, a Trapezium and a Rhombus.
Oct/Nov 2015
The diagram shows a geometric figure with a shaded central region and three triangular parts arranged around it.
Oct/Nov 2015
The three shapes displayed are: Parallelogram, Trapezium and Rhombus.
Oct/Nov 2015
The diagram represents an equilateral triangle.
Oct/Nov 2016
A quadrilateral has a single line of symmetry and no rotational symmetry. Write down the name given to this quadrilateral.
Oct/Nov 2017
A regular pentagon is shown. $AB$ serves as the line of symmetry, and the top central angle is marked $d^{\circ}$. The diagram is not drawn to scale.
Oct/Nov 2017
A quadrilateral has one line of symmetry and no rotational symmetry. State the name of this quadrilateral.
Oct/Nov 2017
Draw the line of symmetry on the shape below.
Oct/Nov 2018
The diagram shows a shape in the form of a cross.
Oct/Nov 2018
The diagram depicts a regular pentagon.
Oct/Nov 2019
In part (a), a $4 \times 4$ array of small squares is shown, with some of them shaded. In part (b), a square is split by a diagonal into four triangular areas, with some of those shaded.
Oct/Nov 2019
Soraya makes rectangular flags.
Oct/Nov 2019
In the diagram, draw every line of symmetry.
Oct/Nov 2020
State the order of rotational symmetry of each shape.
Oct/Nov 2020
A six-sided figure is shown.
Oct/Nov 2021
State the order of rotational symmetry for a rectangle.
Oct/Nov 2021
Draw every line of symmetry on this shape.
Oct/Nov 2022
The diagram depicts a figure with four sides that are all the same length.
Oct/Nov 2022
The diagram depicts a rhombus.
Oct/Nov 2023
The grid shows one half of a shape, and $L$ is its line of symmetry.
Oct/Nov 2024
The diagram depicts a regular polygon.
Oct/Nov 2024
Shade one square so that the diagram has rotational symmetry of order 4.
Oct/Nov 2025
The diagram consists of equilateral triangles.
Oct/Nov 2025
A quadrilateral has rotational symmetry of order 2, and its only two lines of symmetry are the diagonals. State the geometrical name of this quadrilateral.
Oct/Nov 2025
State the order of rotational symmetry of a regular decagon.
Oct/Nov 2025