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

Checking and securing understanding of the distributive law with algebraic terms

Checking and securing solving linear equations

The product of two binomials

Difference of two squares

More complex binomial products

Additive relationships

Multiplicative relationships between terms

Changing the subject with simple formula

Changing the subject with more complex formula

Evaluating expressions with and without changing the subject

Problem solving with expressions and formulae

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.

This unit develops pupil understanding of formulae and how to rearrange them. Pupils will learn how to recognise and manipulate binomials and learn to recognise the difference of two squares.

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 $${5\over{a+b}}=c.$$

Starter Quiz

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