The subject of an equation/a formula is a variable that is expressed in terms of other variables. It should have an exponent of 1 and a coefficient of 1

Checking and securing understanding of changing the subject with simple algebraic fractions

Maths

The functions unit requires pupils to write composite functions and pupils will need to draw on their understanding of how to manipulate various algebraic expressions and equations, including algebraic fractions.

In the prior unit, pupils explored various ways to manipulate and solve various equations and formulae. In this unit, pupils apply these skills to algebraic fractions in order to change the subject and manipulate the algebraic fraction.

Algebraic fractions

Make $$x$$ the subject of $$y = 2\pi x$$.

Make $$h$$ the subject of $$sin(\theta )={o\over h}$$.

Make $$a$$ the subject of $$b=\frac{5}{a+c}$$.

Make $$r$$ the subject of $$ p = \sqrt {q\over r}+1$$.

A formula for calculating the perimeter of a rectangle is shown. When $$P= 16$$ and $$b = 5$$, the value of $$a$$ is {{ }}.

The formula for the area of a sector is shown. When the area, $$A$$, is 110 cm² and the radius, $$r$$, is 10 cm, the value of $$\theta$$ is {{ }} to the nearest degree.

In which of these formulae is $$a$$ the subject?

Make $$x$$ the subject of $$3x = y + z$$.

The solution to the equation $${10\over x} = 2$$ is when $$x=$${{}}.

What is the solution to the equation $${5\over x}=7$$?

You are given the formula $$w=2xy+3x^2$$. When $$x=3$$ and $$y = 4$$, $$w=$${{}}.

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