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.

Changing the subject to suit the context

Maths

In this unit, pupils use the distributive law to find the product of two binomials. In algebraic manipulation, pupils use apply this knowledge in order to factorise quadratics.

In the prior unit, pupils learnt how to rearrange an equation to find a specific value that satisfied the equation. In expressions and formulae, pupils use their understanding of rearrangement to change the subject of a formula.

Expressions and formulae

You can divide both sides of the formula $$s\times{t}=d$$ by $$t$$ to make $$s$$ the __________.

$$s={d\over{t}}$$ can be rearranged as $$s\times{t}=d$$ and $$t={d\over{s}}$$. Which arrangement is the most useful if you know time and speed and wish to calculate distance?

Which of these arrangements of the formula for area of a circle is most useful if you know the area and wish to find the radius?

Which rearrangement of the linear equation $$6x+7y=126$$ should you use if you know the $$x$$ coordinate and wish to find the $$y$$ coordinate?

What is the gradient of the straight line with the linear equation $$5y-2x=30$$ ?

The gradient of a straight line is $$-{5\over3}$$ and the $$y$$-intercept is $$(0,20)$$. Give the equation of the line in the form $$ax+by=c.$$

For the linear equation $$y=5x-7$$, you can call $$y$$ the __________ of the equation.

Which of the below are correct rearrangements of the formula $$V=a\times{l}$$ ?

Make $$y$$ the subject of the equation $$8y-3x=24.$$

Make $$e$$ the subject of $${{c+d}\over{e}}=f.$$ 

Make $$d$$ the subject of $${{c-d}\over{e}}=f.$$

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

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