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OCR GCSE Maths Basic algebraic equations

Basic algebraic equations

This page covers the following topics:

1. Order of operations
2. Vocabulary of equations
3. Terms and factors
4. Algebraic notation
5. Substituting values

For equations with multiple steps, operations must be performed in the following order: brackets, indices, division and multiplication, addition and subtraction. An acronym to remember this is BIDMAS. For the operations that rank equally, operations are performed from left to right.

Order of operations

An expression is a set of terms combined using mathematical operations. An equation is a mathematical statement which shows that two expressions are equal. A formula is a rule written in mathematical symbols, which is given as an equation made up of physical quantities. An identity is an equation which is true for any values chosen for the variables.

Vocabulary of equations

An algebraic term is either a single number or variable, or numbers and variables multiplied together. An algebraic factor is one part of a term which can be multiplied to give the term.

Terms and factors

When writing algebraic equations or expressions, letters are used to represent unknown values, these are known as variables. The rules of algebraic notation given in the table can be used to write and interpret algebraic expressions and equations.

Algebraic notation

The value of an expression can be calculated by putting known values into it in the place of variables and carrying out the operations using BIDMAS. This replacement of letters into values is called substitution.

Substituting values

1

Give the definition of an equation.

Give the definition of an equation.

2

Perimeter is a sum of lengths of all sides of a shape. Give an algebraic expression for the square of the perimeter of the shape shown in the image.

Perimeter is a sum of lengths of all sides of a shape. Give an algebraic expression for the square of the perimeter of the shape shown in the image.

3

State which of the given expressions does not equal to 13.

(1) 7 Γ— 4 + 5 βˆ’ 5 Γ— 4
(2) 21 Γ· 3 + 5 Γ— 2 βˆ’ 2Β²
(3) 5 + (7 βˆ’ 3) βˆ’ 2Β³

State which of the given expressions does not equal to 13. 

(1) 7 Γ— 4 + 5 βˆ’ 5 Γ— 4 
(2) 21 Γ· 3 + 5 Γ— 2 βˆ’ 2Β² 
(3) 5 + (7 βˆ’ 3) βˆ’ 2Β³

4

A stationary shop has a back to school offer. For every notebook sold, a buyer gets 5 pencils. Write an equation relating the number of notebooks (n) with the number of pencils (p).

A stationary shop has a back to school offer. For every notebook sold, a buyer gets 5 pencils. Write an equation relating the number of notebooks (n) with the number of pencils (p).

5

The expression 10a + cb βˆ’ 4e is given. State which of the given are terms or factors in this expression:

10a,
βˆ’4,
c,
b.

The expression 10a + cb βˆ’ 4e is given. State which of the given are terms or factors in this expression: 

10a, 
βˆ’4, 
c, 
b.

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