Rearranging formulae (Edexcel GCSE Maths): Revision Notes

Worked Example: Finding Overtime Hours

Alicia's pay formula is $P = 8h + 12v$, where $h$ is normal hours and $v$ is overtime hours. If Alicia earned £328 working 32 normal hours, how many overtime hours did she work?

Solution:

• Substitute: $328 = 8 \times 32 + 12v$
• Simplify: $328 = 256 + 12v$
• Subtract 256: $72 = 12v$
• Divide by 12: $v = 6$

Alicia worked 6 hours of overtime.

Worked Example: Making p the subject

Make $p$ the subject of $N = 2p + 3q^2$

Solution:

• Start with: $N = 2p + 3q^2$
• Subtract $3q^2$ from both sides: $N - 3q^2 = 2p$
• Divide both sides by 2: $\frac{N - 3q^2}{2} = p$

Therefore: $p = \frac{N - 3q^2}{2}$

Worked Example: Positive term

Make $Q$ the subject of $R = 1 - 5Q$

Solution:

• Add $5Q$ to both sides: $R + 5Q = 1$
• Subtract $R$ from both sides: $5Q = 1 - R$
• Divide by 5: $Q = \frac{1 - R}{5}$

Worked Example: Fractions

Make $h$ the subject of $A = \frac{1}{2}bh$

Solution:

• Multiply both sides by 2: $2A = bh$
• Divide both sides by $b$: $h = \frac{2A}{b}$

Worked Example: Brackets

Make $n$ the subject of $p = 2(m - n)$

Solution:

• Expand the brackets: $p = 2m - 2n$
• Add $2n$ to both sides: $p + 2n = 2m$
• Subtract $p$ from both sides: $2n = 2m - p$
• Divide by 2: $n = \frac{2m - p}{2}$