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.

Evaluating expressions with and without changing the subject

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

$$a=\sqrt{{c^2}-b^2}$$ is a __________ of $$a^2+b^2=c^2$$.

Which arrangement of the formula for area of a triangle makes it quickest for you to find $$b$$ if you know $$A$$ and $$h$$?

The formula for the area of a triangle is $$A={1\over2}bh$$.  The base $$b$$ of a triangle with area 24 m² and height 8 m is {{}}m.

$$r={2\pi\over{{C}}}={2\pi\over{{42}}}={\pi\over{21}}$$

$$r={2C\over{{\pi}}}={2\times 42\over{{\pi}}}={84\over{\pi}}$$

$$r={C\over{2{\pi}}}={42\over{2{\pi}}}={21\over{\pi}}$$

Rearrange the formula $$C=2{\pi}{r}$$ to find the radius of a circle with circumference 42 cm. Leave your answer in terms of $$\pi$$.

Which rearrangement makes it easiest to find length $$b$$ if you know lengths $$a$$ and $$c$$?

Yes, $$b$$ must be the subject before you can substitute.

Yes, because $$b=\sqrt{{10^2}-6^2}$$ is the fastest way to find $$b$$.

No, you can substitute $$a$$ and $$c$$ into $$a^2+b^2=c^2$$ before evaluating.

Jun says "You have to rearrange the formula $$a^2+b^2=c^2$$ into the form $$b=\sqrt{{c^2}-a^2}$$ with $$b$$ as the subject if you want to find $$b$$ given that $$a=6$$ and $$c=10$$." Is Jun right?

Substitute means to put in place of another. In algebra, substitution can be used to replace __________ with values.

$$A={1\over2}(a+b)h$$ is the formula for area of a trapezium. It can be rearranged to $${2A\over{h}}-a=b$$ in order to make $$b$$ the {{}} of the formula.

The formula for area of a triangle is $$A={1\over2}bh$$. The area of a triangle with base 7.5 cm and height 6 cm is {{}}cm²

The formula $$s={d\over{t}}$$ can be rearranged to $$t={d\over{s}}$$ or $$d=s\times {t}$$. If $$d=12$$ and $$s=3$$, find $$t$$.

$$A={1\over2}(3.2+4.8)+7=11$$ square units

$$A={1\over2}(3.2+4.8)\times7=28$$ square units

$$A={1\over2}(3.2\times4.8)\times7=53.76$$ square units

Find the area of a trapezium with $$h=7$$, $$a=3.2$$, $$b=4.8$$.

$$A={1\over2}(a+b)h$$ is the formula for area of a trapezium. Select all the correct rearrangements of this formula.

This lesson will be removed by end of Summer Term 2025.

Evaluating expressions with and without changing the subject

Lesson outcome

This lesson will be removed by end of Summer Term 2025.