Algebraic Reasoning (Edexcel GCSE Maths)

Algebraic Reasoning

What are algebraic expressions, equations and identities?

• An algebraic expression is a set of terms involving constants (numbers) and variables (letters) that are combined using different operators

  • The following are all examples of algebraic expressions
    4x²
    2x  + y
    3(x  - 8)

• An equation is a mathematical statement where two expressions are equal to one another

  • An equation always contains an equals sign (=) 

  • It is true for certain values only

  • For example, 3x − 1 = 5 is an equation and is only true when x = 2

  • Or another example, x² = 9 is an equation and is true only when x = 3 or when x = −3

• An identity is a mathematical statement that is true for all values

  • For example, 2(3x) ≡ 6x is an identity because it is true for all values of x

    • Note that the symbol for an identity, ≡, is 3 horizontal lines (like an equals sign but with an extra line)

What notation do I need to be able to recognise?

• You may come across 'show that' questions that involve some of the following notation

• n is “any integer” (or m or k or…)

• n + 1 is the consecutive integer after n

  • the integer immediately after n

• 2n is an even integer

  • 2n + 2 is the next even integer

• 2m is a different even integer

  • not necessarily consecutive, but any other even integer

• 2n + 1 is an odd integer

  • it is the next consecutive integer after an even number

• a², b² are square numbers

• means 'not equal to'

What type of questions do I need to be able to solve?

• You may be given two different pieces of information about the same thing and asked to show that a particular mathematical statement is true

  • For example, you may be told that the volumes of two objects are same and asked to show that one of the lengths is equal to a particular expression

• To solve a question of this type

  • Find an expression for each item

  • Put an equals sign between the two expressions

  • Rearrange and simplify to find the statement that you are asked to find