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Substitution (Cambridge (CIE) IGCSE International Maths)

Revision Note

Mark Curtis

Written by: Mark Curtis

Reviewed by: Dan Finlay

Cambridge (CIE) International Maths: ExtendedEdexcel Maths A (Modular): Higher Unit 1Cambridge (CIE) International Maths: CoreCambridge (CIE) Maths: CoreCambridge (CIE) Maths: ExtendedEdexcel Maths A: Higher

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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 open parentheses x plus 3 y close parentheses when x equals 2 and y equals negative 4.

Substitute the numbers given
Use brackets () around negative numbers

table row blank cell 2 cross times 2 cross times open parentheses 2 plus 3 cross times open parentheses negative 4 close parentheses close parentheses end cell end table

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

table row blank equals cell 2 cross times 2 cross times open parentheses 2 minus 12 close parentheses end cell row blank equals cell 2 cross times 2 cross times open parentheses negative 10 close parentheses space space end cell row blank equals cell 4 cross times open parentheses negative 10 close parentheses end cell end table

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(b) The formula P equals 2 l plus 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 equals 2 cross times l plus 2 cross times 4

Simplify

20 equals 2 l plus 8

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

12 equals 2 l

Divide both sides by 2

bold italic l bold equals bold 6 cm

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    Author
    Reviewer
    Mark Curtis

    Author: Mark Curtis

    Expertise: Maths

    Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.

    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.