GCSE Algebraic vocabulary Practice Questions

Look for an equals sign

Scan the statement: there is no $=$ sign anywhere.

Recall the definition

An expression is just a collection of terms with no equals sign.

State the answer

So $3x + 5$ is an expression.

Look for an equals sign

There is an $=$ sign.

Recall the definition

An equation has an equals sign and is true only for particular value(s) of the letter.

State the answer

So $5x - 2 = 8$ is an equation.

Recall equation versus identity

An equation has an equals sign and is true only for particular value(s) of the letter. An identity is true for every value of the letter and is written with the identity sign.

Ask whether it is true for all $x$

Check whether every value of $x$ works.

Test some values

True for $x = 3$ but not for $x = 2$.

Find the solutions

Only these two values make it true.

Decide equation or identity

Since it is not true for all $x$, it is not an identity.

State the answer

So $x^2 = 9$ is an equation.

Identify the terms

Split at each + sign.

Count the terms

There are $3$ terms.

Find the $x$ squared term

A lone $x^2$ means $1$ times $x^2$.

Coefficient of $x$ squared

The coefficient of $x^2$ is $1$.

Coefficient of $x$

The number multiplying $x$ is $9$.

Find the constant term

The term with no letter is $20$.

Expand the brackets

Multiply every term in the first bracket by each in the second.

Collect like terms

$5x + 4x$ combine to $9x$.

Compare both sides

The two sides match for all $x$, so it is an identity.

State all the answers

$3$ terms; coefficients $1$ and $9$; constant $20$; the factorisation is an identity.

Look at the whole statement

It has an equals sign and two letters.

Check for a formula

It gives a rule for cost from miles, so it is a formula.

Classify the whole statement

So $C = 3 + 2m$ is a formula.

Identify the subject

The subject is the letter on its own: $C$.

List the letters

The letters used are $C$ and $m$.

State the variables

The variables are $C$ and $m$.

Find the constant term

The fixed fee is the constant term $3$.

Interpret the constant

The $3$ is a fixed charge that does not depend on distance.

Find the term in $m$

The term containing $m$ is $2m$.

Read off the coefficient of $m$

The coefficient of $m$ is $2$.

Interpret the coefficient

The $2$ is the cost per mile travelled.

Look at $3 + 2m$ alone

On its own there is no equals sign.

Classify $3 + 2m$ alone

So $3 + 2m$ by itself is an expression.

Bring the parts together

Collect all answers.

State all the answers

It is a formula; subject $C$; variables $C$ and $m$; constant $3$; coefficient of $m$ is $2$ (cost per mile); and $3 + 2m$ alone is an expression.