What is A3: Expressions and identities?

An expression has no equality or inequality sign. An equation is true only for particular values, whereas an identity is true for every permitted value and is written with ≡.

How many marks are A3 questions worth?

In verified past-paper appearances, A3 questions on Edexcel GCSE Maths 1MA1 have been worth 4–4 marks.

Which past exam papers has A3 appeared in?

A3 has appeared in 1 verified past-paper question indexed on this page, with direct links to the official question paper and mark scheme for each.

Understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors

Draft — not yet indexed

Expressions and identities

Worked answers, methods and verified real exam appearances for A3 on Edexcel GCSE Maths 1MA1.

Explanation

An expression has no equality or inequality sign. An equation is true only for particular values, whereas an identity is true for every permitted value and is written with $\equiv$ .
A formula links quantities, and an inequality compares a range of possible values.
Terms are separated by addition or subtraction; factors are quantities multiplied together.
For example, $6x^2-15x$ has two terms and factorises as $3x(2x-5)$ , whose factors are $3x$ and $2x-5$ .
Examiners expect the correct vocabulary and a reason based on the statement's structure or truth.

Worked example

Classify $3(2x-1)=9$ , $3(2x-1)\equiv6x-3$ , and $3(2x-1)<9$ .

1. $3(2x-1)=9$ is true only for a particular value, so it is an equation.
2.Expanding $3(2x-1)$ always gives $6x-3$ , so the second statement is an identity.
3.The symbol $<$ compares possible values, so the third statement is an inequality.

Answer: Equation, identity, inequality, in that order.

Common mistakes

Don't call every statement containing an equals sign an identity.
Don't count factors as terms even though terms are separated by addition or subtraction.
Don't use $=$ instead of $\equiv$ for a relationship true for all permitted values.

Exam tip

When asked to classify a statement, justify whether it is always true, sometimes true or a comparison.

Worked practice

Tier 1 · Easy

State whether

5x+7

is an expression, equation or inequality.

(1)

(Total for Question 1 is 1 mark)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	Expression	1	The algebra has no equality or inequality sign, so it is an expression.

Tier 2 · Standard

For

8x^2-12x=4x(2x-3)

, state the number of terms on the left and name the two factors on the right.

(3)

(Total for Question 2 is 3 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	Two terms Factors $4x$ and $(2x-3)$	3	The addition or subtraction signs separate $8x^2$ and $-12x$ , so there are two terms. On the right, $4x$ is multiplied by the bracket $(2x-3)$ , so these are the two factors.

Tier 3 · Hard

Classify each statement as an equation, an identity or an inequality:

3(2x-1)=9

3(2x-1)\equiv6x-3

, and

3(2x-1)<9

(3)

(Total for Question 3 is 3 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	$3(2x-1)=9$ is an equation $3(2x-1)\equiv6x-3$ is an identity $3(2x-1)<9$ is an inequality	3	The first statement is true only for a particular value of $x$ , so it is an equation. Expanding the second gives $6x-3$ for every $x$ , so it is an identity. The final statement compares two quantities using $<$ , so it is an inequality.

Tier 1 · Easy

Write down the number of terms in

9a-2b+6

(1)

(Total for Question 4 is 1 mark)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$3$ terms	1	Terms are separated by addition or subtraction. The terms are $9a$ , $-2b$ and $6$ , so there are $3$ .

Tier 2 · Standard

Write down the two factors shown in

5p(q-2)

, then expand the expression.

(2)

(Total for Question 5 is 2 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	Factors $5p$ and $(q-2)$ $5pq-10p$	2	The multiplied quantities are $5p$ and $(q-2)$ , so these are the factors. Multiplying both terms in the bracket by $5p$ gives $5pq-10p$ .

Tier 3 · Hard

State whether each of these statements is an equation or an identity: (i)

6(x+2)=6x+12

(ii)

6(x+2)=30

. Give a reason for each answer.

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	(i) is an identity because $6(x+2)$ expands to $6x+12$ , so it is true for every value of $x$ (ii) is an equation because it is true only when $x=3$	3	Expanding gives $6(x+2)=6x+12$ , so statement (i) holds for every value of $x$ and is an identity. Statement (ii) gives $6x+12=30$ , so $x=3$ ; it is true only for that particular value, so it is an equation.

Tier 2 · Standard

For the expression

7x^2-5x+3

, write down (i) the coefficient of

x

, (ii) the constant term, and (iii) the number of terms.

(3)

(Total for Question 7 is 3 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	(i) $-5$ (ii) $3$ (iii) $3$ terms	3	The term containing $x$ to the first power is $-5x$ , so its coefficient is $-5$ . The term without a variable is $3$ . The terms $7x^2$ , $-5x$ and $3$ are separated by addition or subtraction, so there are $3$ terms.

Tier 3 · Hard

Sam says that

(2x+3)(x-4)

has four terms. Is Sam correct? Explain your answer using the words factor and term.

(3)

(Total for Question 8 is 3 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	No, $(2x+3)$ and $(x-4)$ are two factors; expanding gives $2x^2-5x-12$ , which has three terms (accept: as written the product is a single term made of two factors)	3	No. Before expansion, $(2x+3)$ and $(x-4)$ are the two factors in a product. Expanding gives $2x^2-8x+3x-12=2x^2-5x-12$ , and this simplified expression has three terms.

Tier 3 · Hard

A rectangle has length

l

, width

w

and area

A

. The statements

A=lw

and

A>48

are used. Name the mathematical type of each statement and explain the difference between them.

(3)

(Total for Question 9 is 3 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	$A=lw$ is a formula $A>48$ is an inequality; the formula links the area to the dimensions, whereas the inequality restricts the area to values greater than $48$ .	3	$A=lw$ gives a general relationship between the quantities $A$ , $l$ and $w$ , so it is a formula. The sign $>$ compares the possible values of $A$ with $48$ , so $A>48$ is an inequality rather than a formula or equation.

Q10

Tier 3 · Hard

Tariq says that

6x(x-2)+5

has three factors:

6

x

and

(x-2)

. Is Tariq correct? Explain your answer using the words term and factor.

(3)

(Total for Question 10 is 3 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	No, $6$ , $x$ and $(x-2)$ are factors of the first term only; the whole expression is a sum of two terms, $6x(x-2)$ and $5$ (or it expands to $6x^2-12x+5$ , which has three terms).	3	No. The addition sign separates the expression into the two terms $6x(x-2)$ and $5$ . Within the first term, $6$ , $x$ and $(x-2)$ are multiplied, so they are factors of that term, not factors of the complete expression. Expanding gives $6x^2-12x+5$ , which has three terms.

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2019-11	2F	Q18	4	Allowed	Foundation	QP MS

Other points in A Algebra · notation and manipulation

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