MATHEMATICS
Algebra
AQA 8300 | Premium Learning Edition
What this pack does
Algebra is one of the six broad AQA GCSE Mathematics areas. This pack teaches the methods that sit inside
algebra, shows how to recognise each question type and then builds from short practice to mixed exam-style
problems.
LEARN SEE IT
Plain-English teaching in short sections. Worked questions with every step explained.
TRY IT FIX IT
Questions immediately after each lesson. Answer sheet explains the method, not just the
result.
Independent resource
Original revision material aligned to the current AQA topic structure. ClearGrade is not affiliated with or
endorsed by AQA. Questions are independently written and are not reproduced past-paper questions.
ClearGrade GCSE | Premium Learning Edition Mathematics | 1
, Before you start
Algebra is one of the six broad AQA GCSE Mathematics areas. This pack teaches the methods that sit inside
algebra, shows how to recognise each question type and then builds from short practice to mixed exam-style
problems.
By the end of this pack, you should be able to:
• explain and apply algebra basics and substitution
• explain and apply expanding and factorising
• explain and apply linear equations
• explain and apply inequalities
• explain and apply sequences
• explain and apply straight-line graphs
• explain and apply simultaneous equations
• explain and apply quadratics
• explain and apply rearranging formulae and functions
• explain and apply algebraic proof
How to use the pack
1. Read one lesson. 2. Cover the page and explain it from memory. 3. Study the worked example. 4. Attempt
the three “Your turn” questions without looking back. 5. Mark them using the explained answers at the back. 6.
Re-do every question you got wrong.
ClearGrade GCSE | Premium Learning Edition Mathematics | 2
, LESSON 1
Algebra basics and substitution
The idea in plain English
Algebra uses letters to represent numbers. Like terms can be collected; substitution replaces letters with given
values.
What you need to know
• Only collect terms with the same variable and power.
• Use brackets when substituting negative numbers.
• Know the difference between expression, equation, identity and formula.
WORKED EXAMPLE
Question: Evaluate 2x^2+5x-1 when x=-3.
Step 1: Substitute using brackets: 2(-3)^2+5(-3)-1.
Step 2: Square first: (-3)^2=9, so 18-15-1.
Step 3: Answer=2. The brackets stop you accidentally treating -3^2 as +9 without thinking.
EXAM TIP COMMON MISTAKE
Write enough working that another student could Do not jump straight to a remembered shortcut if
follow your method. Calculator answers without a you cannot explain why it applies. Write the rule
setup can lose method marks. first.
YOUR TURN
1. Simplify 8a+3b-5a+7b. [1-2 marks]
2. Evaluate 3x-4 for x=-2. [2-3 marks]
3. If a=4,b=-3, find 2a+b. [3-4 marks]
LESSON 2
Expanding and factorising
The idea in plain English
Expanding removes brackets by multiplying every term. Factorising reverses this by taking out common factors
or forming brackets.
What you need to know
• Every term in a bracket must be multiplied.
• Factor out the highest common factor where possible.
• For x^2+bx+c, look for two numbers multiplying to c and adding to b.
ClearGrade GCSE | Premium Learning Edition Mathematics | 3
Algebra
AQA 8300 | Premium Learning Edition
What this pack does
Algebra is one of the six broad AQA GCSE Mathematics areas. This pack teaches the methods that sit inside
algebra, shows how to recognise each question type and then builds from short practice to mixed exam-style
problems.
LEARN SEE IT
Plain-English teaching in short sections. Worked questions with every step explained.
TRY IT FIX IT
Questions immediately after each lesson. Answer sheet explains the method, not just the
result.
Independent resource
Original revision material aligned to the current AQA topic structure. ClearGrade is not affiliated with or
endorsed by AQA. Questions are independently written and are not reproduced past-paper questions.
ClearGrade GCSE | Premium Learning Edition Mathematics | 1
, Before you start
Algebra is one of the six broad AQA GCSE Mathematics areas. This pack teaches the methods that sit inside
algebra, shows how to recognise each question type and then builds from short practice to mixed exam-style
problems.
By the end of this pack, you should be able to:
• explain and apply algebra basics and substitution
• explain and apply expanding and factorising
• explain and apply linear equations
• explain and apply inequalities
• explain and apply sequences
• explain and apply straight-line graphs
• explain and apply simultaneous equations
• explain and apply quadratics
• explain and apply rearranging formulae and functions
• explain and apply algebraic proof
How to use the pack
1. Read one lesson. 2. Cover the page and explain it from memory. 3. Study the worked example. 4. Attempt
the three “Your turn” questions without looking back. 5. Mark them using the explained answers at the back. 6.
Re-do every question you got wrong.
ClearGrade GCSE | Premium Learning Edition Mathematics | 2
, LESSON 1
Algebra basics and substitution
The idea in plain English
Algebra uses letters to represent numbers. Like terms can be collected; substitution replaces letters with given
values.
What you need to know
• Only collect terms with the same variable and power.
• Use brackets when substituting negative numbers.
• Know the difference between expression, equation, identity and formula.
WORKED EXAMPLE
Question: Evaluate 2x^2+5x-1 when x=-3.
Step 1: Substitute using brackets: 2(-3)^2+5(-3)-1.
Step 2: Square first: (-3)^2=9, so 18-15-1.
Step 3: Answer=2. The brackets stop you accidentally treating -3^2 as +9 without thinking.
EXAM TIP COMMON MISTAKE
Write enough working that another student could Do not jump straight to a remembered shortcut if
follow your method. Calculator answers without a you cannot explain why it applies. Write the rule
setup can lose method marks. first.
YOUR TURN
1. Simplify 8a+3b-5a+7b. [1-2 marks]
2. Evaluate 3x-4 for x=-2. [2-3 marks]
3. If a=4,b=-3, find 2a+b. [3-4 marks]
LESSON 2
Expanding and factorising
The idea in plain English
Expanding removes brackets by multiplying every term. Factorising reverses this by taking out common factors
or forming brackets.
What you need to know
• Every term in a bracket must be multiplied.
• Factor out the highest common factor where possible.
• For x^2+bx+c, look for two numbers multiplying to c and adding to b.
ClearGrade GCSE | Premium Learning Edition Mathematics | 3
