Evaluating expressions with and without changing the subject | Maths

Starter quiz

Substitute means to put in place of another. In algebra, substitution can be used to replace __________ with values.
- constants
- equations
- solutions
- variables ✓
$A={1\over2}(a+b)h$ 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.
- 'subject' ✓
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
- '22.5' ✓
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 $t$ .
- $36$
- $4$ ✓
- ${1\over{4}}$
Find the area of a trapezium with $h=7$ , $a=3.2$ , $b=4.8$ .
- $A={1\over2}(3.2+4.8)+7=11$ square units
- $A={1\over2}(3.2+4.8)\times7=28$ square units ✓
- $A=2(3.2+4.8)\times7=112$ square units
- $A={1\over2}(3.2\times4.8)\times7=53.76$ square units
$A={1\over2}(a+b)h$ is the formula for area of a trapezium. Select all the correct rearrangements of this formula.
- ${2A\over{h}}-b=a$ ✓
- ${Ah\over{2}}-a=b$
- ${A\over{2h}}-a=b$
- ${2h\over{A}}-a=b$
- ${2A\over{a+b}}=h$ ✓

Exit quiz

$a=\sqrt{{c^2}-b^2}$ is a __________ of $a^2+b^2=c^2$ .
- expression
- rearrangement ✓
- solution
- substitution
- variable
Which arrangement of the formula for area of a triangle makes it quickest for you to find $b$ if you know $A$ and $h$ ?
- $A={1\over2}bh$
- ${2A\over{b}}=h$
- ${2A\over{h}}=b$ ✓
- ${h\over{2A}}=b$
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.
- '6' ✓
Rearrange the formula $C=2{\pi}{r}$ to find the radius of a circle with circumference 42 cm. Leave your answer in terms of $\pi$ .
- $r=2C\pi=2\times 42\times \pi=84\pi$
- $r={2\pi\over{{C}}}={2\pi\over{{42}}}={\pi\over{21}}$
- $r={2C\over{{\pi}}}={2\times 42\over{{\pi}}}={84\over{\pi}}$
- $r={C\over{2{\pi}}}={42\over{2{\pi}}}={21\over{\pi}}$ ✓
Which rearrangement makes it easiest to find length $b$ if you know lengths $a$ and $c$ ?
- $a=\sqrt{{c^2}-b^2}$
- $b=\sqrt{{c^2}-a^2}$ ✓
- $b^2=c^2-a^2$
- $b=\sqrt{{a^2}-c^2}$
- $b=\sqrt{{c^2}+a^2}$
$Jun says "You have to rearrange the formula <Math>a^2+b^2=c^2</Math> into the form <Math>b=\sqrt{{c^2}-a^2}</Math> with <Math>b</Math> as the subject if you want to find <Math>b</Math> given that <Math>a=6</Math> and <Math>c=10</Math>." Is Jun right?$

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?
- 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. ✓

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Lesson Details

Key learning points

Changing the subject can make it easier to evaluate a formula.
It is possible to evaluate a formula without changing the subject.
Both forms of the formula give the same result.

Common misconception

Changing the subject of an equation or formula is only done when you are told to.

Having students practise rearranging before substituting and vice versa allows them to decide when the skill could be useful.

Keywords

Subject of an equation/formula - 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.