Exact Values (OCR GCSE Maths: Foundation): Exam Questions

Triangle $ABC$ is a right-angled triangle.

$AB=4\mathrm{cm}$.
$AC=9\mathrm{cm}$.

Work out the length $BC$.
Give your answer as an exact value.

$BC=....................\mathrm{cm}$

$ABCD$ is a square.
All shapes within $ABCD$ are also squares.

What fraction of the square $ABCD$ is shaded?

A cylinder has a radius of 4 cm and a height of 7 cm.  

Find the volume of the cylinder.
Leave your answer in terms of $\pi$.

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

Here is a quarter circle of radius 6 cm

Work out the area of the quarter circle.
Give your answer in terms of $\mathrm{\pi }$.

............................cm²

A circular table top has radius 70 cm.

Calculate the area of the table top in cm², giving your answer as a multiple of$\pi$.

....................... cm² 

Triangle $ABC$ has perimeter $8+\sqrt{34}$ cm.

$AB=3\mathrm{cm}$.
$BC=5\mathrm{cm}$.

By calculation, deduce whether triangle $ABC$is a right-angled triangle.

The diagram shows two identical circles of diameter 4 cm inside another circle.

The two identical circles both touch the circumference of the larger circle and meet at its centre.

Frances says that exactly $\frac{1}{2}$ of the diagram is shaded. Is she correct?
You must show all your working.

The centimetre grid shows the plan and elevation of a cylinder.
1 square length on the grid represents 1 cm.

Work out the volume of the cylinder.
Give your answer in terms of $\pi$.

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

The diagram shows a circle drawn inside a square.

The circle has a radius of 6 cm.
The square has a side of length 12 cm.

Work out the shaded area.
Give your answer in terms of $\pi$.

The diagram shows a circle inside a square.

$ABCD$ is a square of side 10cm.
Each side of the square is a tangent to the circle.

Work out the total area of the shaded regions in terms of $\pi$.
Give your answer in its simplest form.

Here is a circle touching a square.

The area of the square is 64 cm²

Work out the area of the circle.

Give your answer in terms of $\pi$.

........................................ cm²