Unit 7

Solve the inequality .

A rectangular field has a perimeter of 38 m. The length is 4 m less than twice the width. Form a quadratic equation for the width, , and solve the equation to find the width. Show your reasoning.

A rectangular garden has an area of 96 m². The length of the garden is 4 metres longer than its width. Find the width of the garden.

A rectangular plot has an area of 77 m². The length of the plot is 6 metres shorter than twice its width. Let the width of the plot be metres.

Write down a quadratic equation in for this situation and solve the equation to find the width of the plot.

Solve the quadratic equation by completing the square. Give your answers in surd form.

A factory machines a rectangular sheet so that its length is 5 cm more than its width. The area of the sheet is 84 cm².

Let the width of the sheet be cm.

Form a quadratic equation for , solve it, and explain which solution is suitable for this context.

The equation of a cubic graph is .

Write down the value of when .

A reciprocal graph is given by .

Calculate the value of when .

The graph of is drawn for .

Explain what happens to the value of as gets larger and larger.

The equation models the volume, in cubic centimetres, of a container where is the length in centimetres.