In a "show that" question you are given two different pieces of information about the same quantity. What is the key step that turns them into an equation?

Write an expression for each piece of information, then put an equals sign between the two expressions, because they describe the same quantity. Rearranging and simplifying that equation gives the statement you were asked to show.

GCSEMathsEdexcelFoundationFlashcardsAlgebraAlgebraic Reasoning

Algebraic Reasoning (Edexcel GCSE Maths: Foundation): Flashcards

Exam code: 1MA1

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FrontAlgebraic Reasoning
Define an identity.

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Cards in this collection (5)

Define an identity.
An identity is a statement that is true for every value of the letters in it, and it is written with the sign $\equiv$ rather than $=$ .
For example, $2 (3 x) \equiv 6 x$ is true whatever value $x$ takes.
Is $x^{2} = 9$ an equation or an identity, and how can you tell?
$x^{2} = 9$ is an equation.
Substituting values shows why: it holds when $x = 3$ and when $x = - 3$ , but $x = 1$ gives $1 = 9$ , which is false, so it does not hold for every value.
Complete the sentences by filling in the missing expressions, where $n$ is any integer:
The integer immediately after $n$ is written as $______$ .
An even integer is written as $______$ .
The completed sentences are:
The integer immediately after $n$ is written as $n + 1$ .
An even integer is written as $2 n$ .
Every even integer is a multiple of $2$ , which is exactly what $2 n$ says.
In a "show that" question, one even integer has already been written using the letter $n$ . Why must a second, unrelated even integer use a different letter such as $m$ ?
Because the letter $n$ has already been fixed to the first even integer, so using it again would force the two to be the same number.
A different letter leaves the second even integer free to be any even integer.
In a "show that" question you are given two different pieces of information about the same quantity. What is the key step that turns them into an equation?
Write an expression for each piece of information, then put an equals sign between the two expressions, because they describe the same quantity.
Rearranging and simplifying that equation gives the statement you were asked to show.

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