Changing the subject with more complex formula | Maths

Starter quiz

The subject of a formula is a variable expressed in terms of the other __________.
- equations
- values
- variables ✓
- variants
$x^2$ is not the subject of the equation $x^2=9-y^2$ . Why not?
- Because the coefficient is not $1$ .
- Because the exponent of $x$ is not $1$ . ✓
- Because $y^2$ is the subject.
- That's incorrect. $x^2$ is the subject of the equation.
Which of these are rearrangements of the equation $5e-7=2d$ ?
- $7-5e=2d$
- $5e-2d=7$ ✓
- $5e=7+2d$ ✓
- $2d+7=5e$ ✓
- $2d+5e=7$
Which two inverse operations should you perform to both sides to solve the equation $6x+7=49$ ?
- $-49$
- $+7$
- $-7$ ✓
- $\times 6$
- $\div 6$ ✓
Select the expressions that are equivalent to ${1\over3}(y-5)$ .
- ${1\over3}y-5$
- ${y\over3}-5$
- ${y\over3}-{5\over3}$ ✓
- ${{y-5}\over3}$ ✓
- $y-{5\over3}$
Match each expression to its description.
- $5d+2$
  
  ⇔
  
  $d \text{ }$ multiplied by $5$ then add $2$ ✓
- ${d\over5}+2$
  
  ⇔
  
  $d\text{ }$ divided by $5$ then add $2$ ✓
- ${{d+5}\over2}$
  
  ⇔
  
  $d\text{ }$ add $5$ then divided by $2$ ✓
- $2d+5$
  
  ⇔
  
  $d\text{ }$ multiplied by $2$ then add $5$ ✓
- $5(d+2)$
  
  ⇔
  
  $d\text{ }$ add $2$ then multiplied by $5$ ✓
- ${1\over5}(d+2)$
  
  ⇔
  
  $d\text{ }$ add $2$ then divided by $5$ ✓

Performing the inverse operation $\div7$ would make $x$ the __________ of the equation $7x=y.$
- expression
- solution
- subject ✓
- value
Some Oak pupils are rearranging the equation $5e-f=14$ to make $e$ the subject. Who has a correct rearrangement?
- Laura: $5e=14+f$
- Andeep: $e={{1\over5}(14+f)}$ ✓
- Jun: $e=14-{f\over5}$
- Aisha: $e={14\over5}-{f\over5}$ ✓
- Alex: $e=5(14+f)$
Match each formula to the correct rearrangement with $d$ the subject.
- ${{d+6}\over8}=e$
  
  ⇔
  
  $d=8e-6$ ✓
- $8d+6=e$
  
  ⇔
  
  ${{e-6}\over8}=d$ ✓
- ${{d-6}\over8}=e$
  
  ⇔
  
  $d=8e+6$ ✓
- $8(d+6)=e$
  
  ⇔
  
  ${e\over8}-6=d$ ✓
- ${d\over8}-6=e$
  
  ⇔
  
  $d=8(e+6)$ ✓
Make $x$ the subject of the equation $y=7x^2$ .
- ${y\over7}=x^2$
- $({y\over7})^2=x$
- $\sqrt{{y\over7}}=x$ ✓
- ${\sqrt{y}\over7}=x$
Make $x$ the subject of the equation $y={7\over{x^2}}$ .
- $x^2={7\over{y}}$
- $x=\sqrt{7\over{y}}$ ✓
- $x={7\over\sqrt{y}}$
- $x={7\over{y^2}}$
- $x={7\times{y^2}}$
Match each formula to the correct rearrangement with $x$ the subject.
- $2x=\sqrt{y}$
  
  ⇔
  
  $x={\sqrt{y}\over2}$ ✓
- $2\sqrt{x}=y$
  
  ⇔
  
  $x=({y\over2})^2$ ✓
- $\sqrt{2x}=y$
  
  ⇔
  
  $x={y^2\over2}$ ✓
- $2x^2=y$
  
  ⇔
  
  $x=\sqrt{y\over2}$ ✓
- $(2x)^2=y$
  
  ⇔
  
  $x={{\sqrt{y}}\over2}$ ✓

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With more complex formula, it is important to apply the inverse operations in the right order.
The subject can be thought of as the unknown you are trying to find the value of.
Instead of finding a value though, you will find an expression that the unknown is equal to.

The subject of a formula is just the first term in the formula.

Draw attention to the variety of equations and formulae used in the lesson.

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.