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National Curriculum: Geometry and measures - KS3 - Exemplification


Created on 24 October 2013 by ncetm_administrator
Updated on 04 June 2014 by ncetm_administrator

Exemplification

Example A

Write down the names of three quadrilaterals whose diagonals cross at right angles.

For which of these quadrilaterals do the diagonals also bisect each other?

Example B

quadrilateral

ABCD is a quadrilateral.

Work out the size of the largest angle in the quadrilateral.

Example C

The size of each exterior angle of a regular polygon is 24°.

Work out the number of sides the polygon has.

Example D

semi-circle

N.B. The diagram is not drawn accurately

A semicircle has a diameter of 20 cm.

Work out the perimeter of the semicircle.

Take the value of 𝜋 to be 3.14

Example E

The perimeter of this triangle is 22 cm.

All lengths on the diagram are in centimetres.

triangle

N.B. The diagram is not drawn accurately

  1. Work out the value of t
  2. What is the length of the longest side?

Example F

cuboid

N.B. The diagram is not drawn accurately

The diagram represents a large tank in the shape of a cuboid.
The tank has a base.
It does not have a top.
The width of the tank is 2.6 metres.
The length of the tank is 3.5 metres.
The height of the tank is 4.2 metres.

The outside of the tank is going to be painted.

1 litre of paint will cover 2.5 m2 of the tank.
The cost of paint is £5.99 per litre.

Calculate the cost of the paint needed to paint the outside of the tank.

Example G

triangle

N.B. The diagram is not drawn accurately

PQ is a straight line.

  1. Work out the size of the angle marked x°.

    Give a reason for your answer.
  2. Work out the size of the angle marked y°.

    Explain how you worked out your answer.

Example H

parallelograms

N.B. The diagrams are not drawn accurately

Parallelogram B is an enlargement of parallelogram A.
The scale factor of the enlargement is 3.

  1. Calculate the length of the side marked x.
  2. Work out the length of side y.
  3. Work out the size of angle z.

Example I

Here is a solid cube of side 2 cm.

cuboid

N.B. The diagram is not drawn accurately

  1. Write down

    the number of faces of the cube,

    the number of vertices of the cube,

    the number of edges of the cube.

  2. Draw an accurate net of this cube.

Example J

The diagrams show the circular top of a cylinder and a piece of plastic in the shape of a right-angled triangle. The two shorter sides of the triangle have lengths 76 cm and 77 cm.

Can the triangular piece of plastic fit on the top of the cylinder without overlapping?

circle and triangle

N.B. The diagrams are not drawn to scale

Example K

irregular shaped car park illustration

N.B. The diagrams is not drawn accurately

The diagram shows a car park.

Mrs Roberts is selling the car park. She will accept any offer that is more than £30 per square metre.

  1. Mr Brown offers £239 900 for the car park.

    Will Mrs Roberts accept Mr Brown’s offer for the car park? You must show how you reached your decision.
  2. When the car park is sold the new owner intends to put a fence around the entire perimeter.

    What is the length of fencing required?

Fencing is sold in 5m lengths and costs £38.95 per 5m section. Sections can only be bought in 5 metres (no parts)

What is the total cost of the perimeter fence?

 


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