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Understand and Use Algebraic Terms 1

In this worksheet, students will learn the difference between key algebraic concepts: term, expression, equation and formula, plus touch on the concept of identity.

'Understand and Use Algebraic Terms 1' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Algebra

Curriculum subtopic:   Notation, Vocabulary and Manipulation, Algebraic Formulae

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Algebra is a universal mathematical language, so it uses specific vocabulary to help us communicate different ideas.

 

Here are some of the key words we use in algebra:

 

Term is part of an expression. It consists of letters and/or numbers.

Variable is a part of a term and is represented by letters, usually x, or symbols. Variables can take any value.

Coefficient is the number that stands in front of the variable.

 

Let's see these in action now.

 

e.g. 10x

The term is 10x as a whole, the coefficient is 10 and the variable is x

 

 

Expressions are made up of algebraic terms which are connected by mathematical operator (+  , -, x, /). 

They do not include an equals sign.

 

Here's an example of an expression with three terms: 3x2 - 4x + 5

The terms are: 3x2, 4x, 5

 

 

3x24y+2

Equations are the same as expression but they do contain an equals sign.

As a result of this, we can solve them for some, but not all, values of x (or another variable).

 

This is an equation: 5x + 9 = 24

And so is this: x2 + 3x - 12 = 0

 

 

Formula is related to an equation.

Formulae will also have an equals sign, but they will be true for many values of the variable.

Therefore, we cannot solve a formula, unless we know the values of some of the variables

 

You might have seen some formulae in maths or science already.

Some well-known examples include:

Formula for speed: s = d ÷ t

Formula for area of a circle: A = πr2

To use these formulae, you need to know the value of one (or more of the variables). 

 

 

 

In this activity, we will identify where these definitions apply and, therefore, which calculations we can and cannot perform in each situation. 

Does the algebra below represent a term, an expression, an equation or a formula?

 

3x + 5 = 20

Term

Expression

Equation

Formula

Match each piece of terminology below to an appropriate example of it in action.

Column A

Column B

5ab
Formula
2x + 8
Equation
A = (a + b)h ÷ 8
Term
9y
Expression
4 = 3x - 8
Term

What are the variables in the expression below?

 

3x2 + 4x -2y + 7 + 2xy

x


y

xy

7

Match the key words below to their definitions.

Column A

Column B

Equation
Has an equals sign, but cannot be solved unless so...
Expression
Made of terms connected by mathematical operators,...
Formula
A combination of letters and numbers without any m...
Term
A mathematical statement that shows that two expre...

How many terms do each of the expressions below have?

 Number of terms
6a + 7b - c
5x + 4y - 2z + 5
-6s - 4t - 2u

Match each example below to the algebraic definition it represents. 

Column A

Column B

x + x + x + x
Formula
4x - 7 = 5
Identity
A = 1/2bh
Term
2x + 5 = 5 + 2x
Equation
x
Expression

Which word best describes the mathematical object highlighted?

 

3a + 5b = 32

Equation

Expression

Term

Identity

Which word best describes the mathematical object highlighted below?

 

5a - 2b = 3a + b

Expression

Term

Equation

Formula

Pick all the identities from the mathematical objects below.

-5x + 2x ≡ -3

4r ≡ r + r + 2r

b + b = 5

t - 3 = s + 4

What is the best way to describe the highlighted mathematical object?

 

3a + 7 = 4(a + 1)

Expression

Equation

Identity

Term

  • Question 1

Does the algebra below represent a term, an expression, an equation or a formula?

 

3x + 5 = 20

CORRECT ANSWER
Equation
EDDIE SAYS
This is an equation. How do we know this? It has an equals sign and could be solved to reveal the value of x.
  • Question 2

Match each piece of terminology below to an appropriate example of it in action.

CORRECT ANSWER

Column A

Column B

5ab
Term
2x + 8
Expression
A = (a + b)h ÷ 8
Formula
9y
Term
4 = 3x - 8
Equation
EDDIE SAYS
Take one of these at time here and consider which features each presents. Remember that terms and expressions do not have an equals sign, but equations and formulae do. Equations can be solved, but to work out the value of a formula you need to know what the letters stand for. An expression will have a mathematical sign (+, -, ×, ÷), but a term won't.
  • Question 3

What are the variables in the expression below?

 

3x2 + 4x -2y + 7 + 2xy

CORRECT ANSWER
x
y
EDDIE SAYS
This was tricky! Variables are just the letters, not including any coefficients or powers. This is why x² is not a variable, but x is. Similarly xy is not a variable, but x and y, which combine to make this, are. Remember this top tip moving forwards.
  • Question 4

Match the key words below to their definitions.

CORRECT ANSWER

Column A

Column B

Equation
A mathematical statement that sho...
Expression
Made of terms connected by mathem...
Formula
Has an equals sign, but cannot be...
Term
A combination of letters and numb...
EDDIE SAYS
Did you remember the information from the Introduction page? Flip back now if you need a reminder. Here are some examples from that page to help you match the definitions. Term: 10x Expression: 3x² - 4x + 5 Equation: 5x + 9 = 24 and x² + 3x - 12 = 0 Formula: s = d ÷ t and area= πr² Did you match those correctly?
  • Question 5

How many terms do each of the expressions below have?

CORRECT ANSWER
 Number of terms
6a + 7b - c
5x + 4y - 2z + 5
-6s - 4t - 2u
EDDIE SAYS
A term consists of a letter and/or a number without any mathematical operators (e.g. powers, +, -, etc.) 6a + 7b - c has 3 terms: 6a, 7b and c 5x + 4y - 2z + 5 has 4 terms: 5x, 4y, 2z and 5 -6s -4t - 2u has 3 terms: 6t, 4t, 2u Did you notice that even though '6t' has a minus before it, we ignore this when describing the value of the term?
  • Question 6

Match each example below to the algebraic definition it represents. 

CORRECT ANSWER

Column A

Column B

x + x + x + x
Expression
4x - 7 = 5
Equation
A = 1/2bh
Formula
2x + 5 = 5 + 2x
Identity
x
Term
EDDIE SAYS
A term is the smallest building block of mathematical language, represented by a number or letter (x). An expression is made from terms linked together by mathematical operators (x + x + x + x). If there is an equality sign and the value of the letter could be worked out, it is an equation (4x - 7 = 5). Otherwise it is a formula (A = 1/2bh). An identity is a type of equation where the right-hand side simplifies to exactly the same expression as the left-hand side. You can also think of an identity as a balanced equation.
  • Question 7

Which word best describes the mathematical object highlighted?

 

3a + 5b = 32

CORRECT ANSWER
Term
EDDIE SAYS
'3a' is best described as a term. In this case, it is a part of a formula without any mathematical operators.
  • Question 8

Which word best describes the mathematical object highlighted below?

 

5a - 2b = 3a + b

CORRECT ANSWER
Expression
EDDIE SAYS
This mathematical object is an expression as two terms and an operator have been highlighted. As a whole (including the highlighted and non-highlighted elements), this is an equation as it has an equals sign. However, the highlighted section does not include an equals sign, so it is not an equation without this.
  • Question 9

Pick all the identities from the mathematical objects below.

CORRECT ANSWER
-5x + 2x ≡ -3
4r ≡ r + r + 2r
EDDIE SAYS
Did you notice the symbol ≡? This is the identity symbol. It means that what is on the right of the sign is exactly the same as what is on the left side. If both sides of an equation are not identical, then we cannot use the identity sign.
  • Question 10

What is the best way to describe the highlighted mathematical object?

 

3a + 7 = 4(a + 1)

CORRECT ANSWER
Equation
EDDIE SAYS
This is an example of an equation. We know this because there is a = sign present and we could find out the value of x. Amazing work on this activity! Remember to keep these key terms in mind for all your work with algebra. Why not review the Introduction quickly so you can commit them to memory before you move on?
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