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Basic algebraic equations for OCR GCSE Maths

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

State which of the given are terms and which are factors of an expression 21z + 9 โˆ’ 4y.

โˆ’4,
9,
21z,
y

21z and 9 are terms.
Factors are parts of a term; therefore, โˆ’4 and y are factors.

terms: 21z, 9
factors: โˆ’4, y

State which of the given are terms and which are factors of an expression 21z + 9 โˆ’ 4y. 

โˆ’4, 
9, 
21z, 
y

2

Which of the given expressions equals to 21?

A) 5 ร— 8 โˆ’ 5ยฒ + (6 โˆ’ 1)
B) 6ยฒ + (3 ร— 3) โˆ’ (20 + 5)
C) (9 ร— 7) รท (5 โˆ’ (2 ร— 2) + 2)

for expression A:
5 ร— 8 โˆ’ 5ยฒ + (6 โˆ’ 1) =
= 5 ร— 8 โˆ’ 5ยฒ + 5 =
= 5 ร— 8 โˆ’ 25 + 5 =
= 40 โˆ’ 25 + 5 = 20

for expression B:
6ยฒ + (3 ร— 3) โˆ’ (20 + 5) =
= 6ยฒ + 9 โˆ’ 25 =
= 36 + 9 โˆ’ 25 = 20

for expression C:
(9 ร— 7) รท (5 โˆ’ (2 ร— 2) + 2) =
= 63 รท (5 โˆ’ 4 + 2) =
= 63 รท 3 = 21

Thus, expression C is the one that equates to 21.

C

Which of the given expressions equals to 21? 

A) 5 ร— 8 โˆ’ 5ยฒ + (6 โˆ’ 1) 
B) 6ยฒ + (3 ร— 3) โˆ’ (20 + 5) 
C) (9 ร— 7) รท (5 โˆ’ (2 ร— 2) + 2)

3

Write the expression provided in algebraic notation.

โ€œa is multiplied by b, added to 4 and then cubed.โ€

The expression in algebraic notation is (ab + 4)ยณ.

(ab + 4)ยณ

Write the expression provided in algebraic notation. 

โ€œa is multiplied by b, added to 4 and then cubed.โ€

4

What is the difference between a mathematical expression and an equation?

An expression is a set of terms combined using mathematical operations, whereas an equation is a statement which shows two expressions which are equal.

set of terms versus several expressions

What is the difference between a mathematical expression and an equation?

5

Find the result of 11 ร— (4 + 2)ยฒ.

Using BIDMAS, 11 ร— (4 + 2)ยฒ = 11 ร— 6ยฒ = 11 ร— 36 = 396.

396

Find the result of 11 ร— (4 + 2)ยฒ.

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