Changing the subject to suit the context | Maths | Quizalize & Oak National Academy

Starter quiz

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

gradient

solution

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

$V=l\times{a}$ ✓

$l=a\times{V}$

${V\over{l}}=a$ ✓

${V\over{a}}=l$ ✓

${l\over{V}}=a$
Make $y$ the subject of the equation $8y-3x=24.$

$8y=3x+24$

$y={3\over8}x+24$

$y={3\over8}x+3$ ✓

$y=3x+24-7y$

$y={{3x+24}\over8}$ ✓
Make $e$ the subject of ${{c+d}\over{e}}=f.$

${{c+d}\over{f}}=e$ ✓

$f(c+d)=e$

${{f}\over{c+d}}=e$

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

${{c-f}\over{e}}=d$

$c-ef=d$ ✓

$ef-c=d$

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

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

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

${5c-{b}}=a$

${5\over{c}}-b=a$ ✓

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

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

divisor

equation

subject ✓

substitution
$s={d\over{t}}$ 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?

$s={d\over{t}}$

$s\times{t}=d$ ✓

$t={d\over{s}}$
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?

$A={\pi}r^2$

${A\over{\pi}}=r^2$

$\sqrt{{A\over{\pi}}}=r$ ✓

${A\over{r^2}}=\pi$
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?

$6x+7y=126$

$x={{126-7y}\over6}$

$y={{126-6x}\over7}$ ✓

$7y=126-6x$
What is the gradient of the straight line with the linear equation $5y-2x=30$ ?

$-2$

$2\over5$ ✓

$2$

$5\over2$

$5$
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 $ax+by=c.$

$5x+3y=20$

$3x+5y=20$

$5x+3y=60$ ✓

$5x-3y=60$

$3x+5y=60$

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Formulae are used in a variety of places, such as the science lab but also in factories.
Rearranging the formula may be beneficial when what you wish to calculate is not the subject.
You can compare rearranging the formula to solving for one unknown.

That the gradient of a line given the equation of the line is always just the coefficient of the x term.

Using graphing software to explore this could help.

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.