Symmetry & Shapes (Cambridge International IGCSE Mathematics): Exam Questions

Write down the order of rotational symmetry of this regular octagon.

Write down the mathematical name for this

i) quadrilateral,

ii) solid.

On each shape draw all the lines of symmetry.

Write down the order of rotational symmetry of this shape.

Write down the order of rotational symmetry of the diagram.

The diagram shows a regular polygon.

i) Write down the mathematical name for this shape.

ii) Write down the order of rotational symmetry of this shape.

i) Write down the mathematical name for this type of angle.

ii) Measure this angle.

Write down the order of rotational symmetry of this regular pentagon.

The diagram shows some quadrilaterals.

Complete the statements.

Quadrilateral ................. is a rhombus.

Quadrilateral $A$ is a ..........................................

The diagram shows the nets of two solids.

Write down, under each net, the mathematical name for the solid.

Three quadrilaterals are shown on a 1 cm² grid.

Write down the mathematical name of the shaded quadrilateral.

Complete the statement.

Angle ...................... is a reflex angle.

The diagram shows a regular pentagon and a kite.

Complete the following statements.

The regular pentagon has ................................... lines of symmetry.

The kite has rotational symmetry of order ................................... .

In the space below, draw a circle with diameter 7cm.

Extract:

In the space below, draw a circle with diameter 7cm.

On your diagram, draw a chord.

The diagram shows a rhombus

On the diagram, draw all the lines of symmetry

Write down the mathematical name of this type of angle.

i) Measure the size of angle $x$.

ii) Write down the mathematical name of this type of angle.

Name the 3D shape.

Complete the table below

Write down the mathematical name for an angle which is less than 90°.

Write down the mathematical name for a polygon with 5 sides.

Write down the mathematical name for a quadrilateral with exactly one pair of parallel sides.

Write down the order of rotational symmetry of a regular pentagon.

Measure the length of this line in millimetres.

........................................... mm

i) Measure the size of angle $x$.

ii) Write down the mathematical name of this type of angle.

Write down the order of rotational symmetry of each shape.

The grid shows a point $E$ and four quadrilaterals, $A,B,C$ and $D$.

Write down the mathematical name of shape $A$.

Write down the mathematical name for this type of angle.

$A$and $B$ lie on a circle, centre $O$.

i) .Write down the mathematical name for line $AB$.

ii) $OA=8\mathrm{cm}$

Write down the length of the diameter of this circle.

............................................ cm [1]

The diagram shows a cuboid.

On the 1 cm² grid, complete the net of the cuboid. One face has been drawn for you.

Write down the mathematical name of a quadrilateral that has

• rotational symmetry of order 1

and

• only one line of symmetry.

Measure the length of the line $AB$ in millimetres.

.......................................... mm

Extract:

Measure the length of the line ![A B] in millimetres.

.......................................... mm

$AB$ is the diameter of a circle.

Draw this circle.

Write down the order of rotational symmetry of the shape.

Draw all the lines of symmetry on the shape.

The diagram shows the net of a triangular prism on a 1cm² grid.

Write down the mathematical name for the type of triangle shown on the grid.

Complete the description of this pattern.

The pattern has ................ lines of symmetry

and order of rotational symmetry ................

On each shape, draw all the lines of symmetry.

i)

ii)

Write down the name of a quadrilateral that has

• rotational symmetry of order 2

and

• exactly two lines of symmetry.

Complete each statement.

A quadrilateral with only one pair of parallel sides is called a ...............................................

An angle greater than 90° but less than 180° is called ...............................................

On the 1cm² grid, complete the net of this box.

The diagram shows a net of a solid.

Write down the mathematical name of the solid.

The diagram shows a quadrilateral on a 1 cm² grid.

Write down the mathematical name of this quadrilateral.

The diagram above shows a circle, centre $O$.

$P$ lies on the circumference.

Write down the mathematical name for the line $OP$.

Draw a tangent to the circle at $P$.

The diagram shows the net of a cuboid.

(i) Find the volume of the cuboid.

......................................... cm³ [2]

(ii) Show that the total surface area of the cuboid is 122 cm².

(iii) Calculate the total length of the edges of the cuboid.

.......................................... cm [2]

In this part, all measurements are in centimetres.

This is the net of a cuboid with edges of length $x,y$ and $( x - 3 )$.

Find an expression, in terms of $x$ and $y$, for the perimeter of the net. Give your answer in its simplest form.

Points $A$ and $B$ lie on the circle. A region has been shaded between line $AB$ and the circumference of the circle.

Write down the mathematical name for the shaded region.

Extract:

Circle with three points on its circumference labelled A, B and Q. A line segment inside the circle joins points A and B. Another line segment, with endpoints V and W, touches the circle at Q. The part of the circle on one side of line AB is shaded in.

The line $VW$ touches the circle at the point $Q$.

Write down the mathematical name for the line $VW$.

Shade two squares so that the diagram has rotational symmetry of order 2.

A cuboid measures 6 cm by 3 cm by 1 cm.

i) On the 1 cm² grid, draw an accurate net of this cuboid. One face has been drawn for you.

ii) Calculate the surface area of the cuboid.

.......................................... cm² [2]

A cuboid has length 5 cm, width 4 cm and height 3 cm.

On the 1 cm² grid, complete the net of the cuboid. One face has been drawn for you.

Extract:

A cuboid has length 5 cm, width 4 cm and height 3 cm.

Find the volume of the cuboid.

.......................................... cm³

The diagram shows the net of a solid on a 1cm² grid.

i) Write down the mathematical name for the solid.

ii) Work out the volume of the solid.

.......................................... cm³ [2]

A cuboid has length 3 cm, width 2 cm and height 1cm.

On the 1 cm² grid, draw a net of the cuboid.

A cuboid measures 6cm by 3cm by 2 cm. On this 1cm² grid, draw a net of the cuboid.

Shade two more small squares to give a pattern with exactly one line of symmetry.

Write down the co-ordinates of point $B$.

The quadrilateral $ABCD$ has$x=4$ as a line of symmetry.

On the grid, plot point $D$.

Extract:

The quadrilateral ABCD has x = 4 as a line of symmetry.

Write down the mathematical name of quadrilateral $ABCD$.

Extract:

Write down the mathematical name of quadrilateral ![A B C D].

Write down the order of rotational symmetry of quadrilateral $ABCD$.

Shade two more squares so that this grid has rotational symmetry of order 4.

The diagram shows a net of a cube.

i) The square labelled $B$ is the base.

Write the letter $T$ in the square that is the top of the cube.

ii) On the grid, draw a different net of this cube.