What is A1: Algebraic notation?

Algebraic notation records operations compactly. Adjacent letters mean multiplication, so ab=a× b, while 3y means three lots of y.

How many marks are A1 questions worth?

In verified past-paper appearances, A1 questions on Edexcel GCSE Maths 1MA1 have been worth 1–4 marks.

Which past exam papers has A1 appeared in?

A1 has appeared in 9 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

Use and interpret algebraic manipulation: ab for a × b, 3y for y + y + y and 3 × y, a² for a × a, a³ for a × a × a, a²b for a × a × b, a/b for a ÷ b, coefficients as fractions, brackets

Algebraic notation

Worked answers, methods and verified real exam appearances for A1 on Edexcel GCSE Maths 1MA1.

Explanation

Algebraic notation records operations compactly. Adjacent letters mean multiplication, so $ab=a\times b$ , while $3y$ means three lots of $y$ .
An index records repeated factors: $a^2=a\times a$ and $a^2b=a\times a\times b$ .
A fraction bar represents division and also groups its numerator and denominator.
Write numerical coefficients before variables, usually as exact fractions rather than decimals, and use brackets when an operation acts on a complete expression.
Examiners expect conventional notation and the operations to remain unambiguous when translating words or repeated products.

Worked example

A rectangle has length $\dfrac{3x}{2}$ and width $y$ . Write its area and perimeter in conventional algebraic notation.

1.Area $=\dfrac{3x}{2}\times y=\dfrac{3xy}{2}$ .
2.Perimeter $=2\left(\dfrac{3x}{2}\right)+2y$ .
3.Simplify to $3x+2y$ .

Answer: Area $=\dfrac{3xy}{2}$ and perimeter $=3x+2y$ .

Common mistakes

Don't read $a^2$ as $2a$ instead of $a\times a$ .
Don't interpret $3y$ as $3+y$ rather than $3\times y$ .
Don't drop brackets when a multiplier must act on a whole expression.

Exam tip

Translate one operation at a time and use brackets before simplifying the notation.

Worked practice

Tier 1 · Easy

Write

m\times m\times n\times n\times n

using indices.

(1)

(Total for Question 1 is 1 mark)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	$m^2n^3$	1	There are two factors of $m$ and three factors of $n$ , so $m\times m=m^2$ and $n\times n\times n=n^3$ . Therefore the product is $m^2n^3$ .

Tier 2 · Standard

Write

p\times p\times p\times q\div5

in conventional algebraic notation, and state its coefficient.

(2)

(Total for Question 2 is 2 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	$\frac{p^3q}{5}$ Coefficient: $\frac15$	2	The three factors of $p$ give $p^3$ , and division by $5$ is shown by a fraction bar. Hence the expression is $p^3q/5=\frac15p^3q$ , so its coefficient is $\frac15$ .

Tier 3 · Hard

A rectangle has length

\frac{3x}{2}

and width

y

. Write its area and its perimeter in conventional algebraic notation.

(3)

(Total for Question 3 is 3 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	Area: $\frac{3xy}{2}$ Perimeter: $3x+2y$	3	Area is length multiplied by width, so $A=(3x/2)y=3xy/2$ . Perimeter is twice the length plus twice the width: $P=2(3x/2)+2y=3x+2y$ .

Tier 1 · Easy

Write

7

multiplied by

p

, then add

q

, in algebraic notation.

(1)

(Total for Question 4 is 1 mark)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$7p+q$	1	Multiplication is written without a multiplication sign, so $7$ multiplied by $p$ is $7p$ . Adding $q$ gives $7p+q$ .

Tier 2 · Standard

Write

2r^3s

as a product without using indices. Write down the coefficient of

r^3s

(2)

(Total for Question 5 is 2 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$2\times r\times r\times r\times s$ (accept factors in any order) Coefficient $2$	2	The index $3$ means that $r$ is a factor three times, so the product is $2\times r\times r\times r\times s$ . The number multiplying $r^3s$ is $2$ , so the coefficient is $2$ .

Tier 3 · Hard

A cuboid has length

\dfrac{x}{3}

, width

2y

and height

y

. Write its volume in conventional algebraic notation and write down its coefficient.

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	Volume $=\dfrac{2xy^2}{3}$ (or $\tfrac{2}{3}xy^2$ ) Coefficient $\dfrac{2}{3}$	3	Multiply the three dimensions: $\dfrac{x}{3}\times2y\times y=\dfrac{2xy^2}{3}$ . Written as $\dfrac{2}{3}xy^2$ , the numerical coefficient is $\dfrac{2}{3}$ .

Tier 2 · Standard

Write the product of

z

and the result of dividing

x

(y+4)

in conventional algebraic notation.

(2)

(Total for Question 7 is 2 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	$\dfrac{xz}{y+4}$ (or $\dfrac{zx}{y+4}$ )	2	Dividing $x$ by the whole expression $y+4$ gives $\dfrac{x}{y+4}$ . Multiplying this result by $z$ gives $\dfrac{xz}{y+4}$ .

Tier 3 · Hard

Write these in conventional algebraic notation: (i) the square of the sum of

p

and

3

; (ii) the sum of the square of

p

and

3

; (iii) half of the expression in (i).

(3)

(Total for Question 8 is 3 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	(i) $(p+3)^2$ (ii) $p^2+3$ (iii) $\dfrac{(p+3)^2}{2}$ (or $\tfrac12(p+3)^2$ )	3	In (i), the brackets show that the whole sum is squared. In (ii), only $p$ is squared before $3$ is added. Half of the first expression is found by dividing the complete square by $2$ , giving $\dfrac{(p+3)^2}{2}$ .

Tier 3 · Hard

A rule says: subtract

q

from

p

, square the result, then divide by the product of

6

and

r

. Write the rule in conventional algebraic notation. Explain why brackets are needed.

(3)

(Total for Question 9 is 3 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	$\dfrac{(p-q)^2}{6r}$ The brackets show that the whole difference $p-q$ is squared before it is divided by $6r$ .	3	Subtracting $q$ from $p$ gives $p-q$ . Brackets are needed before squaring, giving $(p-q)^2$ . The product of $6$ and $r$ is $6r$ , so the complete rule is $\dfrac{(p-q)^2}{6r}$ .

Q10

Tier 3 · Hard

Mara wants to write one third of the product of twice

x

and the square of

y

. She writes

\dfrac{2x+y^2}{3}

. Explain Mara's error and write the correct expression in conventional algebraic notation.

(3)

(Total for Question 10 is 3 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	Mara has added $2x$ and $y^2$ instead of multiplying them $\dfrac{2xy^2}{3}$ (or $\tfrac23xy^2$ )	3	Twice $x$ is $2x$ and the square of $y$ is $y^2$ . Their product is $2xy^2$ , not $2x+y^2$ . Taking one third gives $\dfrac{2xy^2}{3}=\tfrac23xy^2$ .

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2024-06	2F	Q5	1	Allowed	Foundation	QP MS
2022-06	3F	Q4	1	Allowed	Foundation	QP MS
2024-11	2F	Q11	3	Allowed	Foundation	QP MS
2021-11	3F	Q6	3	Allowed	Foundation	QP MS
2019-11	1F	Q13	3	Non-calculator	Foundation	QP MS
2019-06	2F	Q8	4	Allowed	Foundation	QP MS
2022-06	1F	Q2	1	Non-calculator	Foundation	QP MS
2021-11	2F	Q4	2	Allowed	Foundation	QP MS
2022-11	1F	Q5	1	Non-calculator	Foundation	QP MS

Other points in A Algebra · notation and manipulation

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