GCSEMathsOCRHigherRevision Notes6. AlgebraIntroduction to AlgebraSubstitution

Substitution (OCR GCSE Maths): Revision Note

Exam code: J560

Mark Curtis

Written by: Mark Curtis

Reviewed by: Dan Finlay

Updated on

OCR Maths: HigherWJEC Maths & Numeracy (Double Award): FoundationWJEC Maths & Numeracy (Double Award): HigherWJEC Eduqas Maths: FoundationWJEC Eduqas Maths: HigherOCR Maths: FoundationAQA Maths: FoundationAQA Maths: HigherEdexcel Maths: FoundationEdexcel Maths: Higher

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 put brackets around any substituted negative numbers!

Be careful with negatives and powers. For example, if x equals negative 4 then x squared equals open parentheses negative 4 close parentheses squared equals 16.

Worked Example

(a) Given that x equals 2 and y equals negative 4, find the value of the expression:

(i)  2 x open parentheses x plus 3 y close parentheses

(ii) y squared plus y cubed

Answer:

(i)

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

-40  

(ii)

Substitute the numbers given
Use brackets () around negative numbers

open parentheses negative 4 close parentheses squared plus open parentheses negative 4 close parentheses cubed

Work out the powers remembering to include the brackets

16 plus open parentheses negative 64 close parentheses

Complete the calculation

16 minus 64

-48

(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.

Answer:

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

l equals 6 space cm 

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Author
Reviewer
Mark Curtis

Author: Mark Curtis

Expertise: Maths Content Creator

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

Reviewer: Dan Finlay

Expertise: Maths Subject 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.