Substitution (Cambridge (CIE) IGCSE Maths)

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Written by: Mark Curtis

Reviewed by: Dan Finlay

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Substitution

What is substitution?

Substitution means replacing a letter (variable) in a formula with a given number

How do I substitute numbers into a formula?

Write down the formula
Replace (substitute) the letters in the formula with the given numbers
- If substituting in a negative number, it is important to put brackets around it
  - For example, (-3)
Simplify any numerical calculations
Calculate the final value
Sometimes the result is an equation which you can then solve

Examiner Tips and Tricks

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

Worked Example

(a )Find the value of the expression $2 x (x + 3 y)$ when $x = 2$ and $y = - 4$ .

Substitute the numbers given
Use brackets () around negative numbers

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

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

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

-40

(b) The formula $P = 2 l + 2 w$ 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.

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

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

Simplify

$20 = 2 l + 8$

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

$12 = 2 l$

Divide both sides by 2

$l = 6$ cm

Last updated: 17 October 2024

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