Unit 7

The decimal number 0.345345345\ldots has a repeating block of 3 digits. What is the 50th digit after the decimal point?

Express the recurring decimal as a fraction in its simplest form. Show all your working.

Explain how to write and as fractions in their simplest form. Describe the differences in your working and the forms of the answers.

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.

A company models the cost, $C, in dollars, of producing x batches of items by the equation below. \[ C = \frac{1800}{x} + 70x \] For what value of x is the cost C minimized (to the nearest whole number)?

The function is to be plotted for .

Complete the table below by calculating the value of y for each value of x.

Consider the algebraic form of a reciprocal equation.

A sector of a circle has a radius of 10 cm. The angle at the centre is 72°. Calculate the area of the sector. Give your answer to 3 significant figures.