Substitution (Edexcel IGCSE Maths B): Revision Note

On your calculator, don't forget to put brackets around any substituted negative numbers!

Be careful with negatives and powers. For example, if $x=-4$ then $x^2={\left(-4\right)}^2=16$.

(a) Given that $x=2$ and $y=-4$, find the value of the expression:

(i)  $2x\left(x+3y\right)$

(ii) $y^2+y^3$

Answer:

(i)

Substitute the numbers given
Use brackets () around negative numbers

$\begin{array}{cl}& 2\times 2\times \left(2+3\times \left(-4\right)\right)\end{array}$

Complete the calculation
Show every step of working, following the order of operations correctly

$\begin{array}{rcl}& =& 2\times 2\times \left(2-12\right)\\ & =& 2\times 2\times \left(-10\right)\\ & =& 4\times \left(-10\right)\end{array}$

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(ii)

Substitute the numbers given
Use brackets () around negative numbers

${\left(-4\right)}^2+{\left(-4\right)}^3$

Work out the powers remembering to include the brackets

$16+\left(-64\right)$

Complete the calculation

$16-64$

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(b) The formula $P=2l+2w$ is used to find the perimeter, $P$, of a rectangle of length $l$ and width $w$.

Given that the rectangle has a perimeter of 20 cm and a width of 4 cm, find its length.

Answer:

Substitute the values you are given for $P$ and $w$ into the formula

$20=2\times l+2\times 4$

Simplify

$20=2l+8$

Solve the resulting equation to find the value of $l$
Start by subtracting 8 from both sides

$12=2l$

Divide both sides by 2

$l=6\mathrm{cm}$