AQA GCSE Mathematics Paper 2 (Foundation), June 2025: Question 4

Simplifying Basic Algebraic Expressions

📋 What this question tests

Core algebraic notation and manipulation skills: writing products without multiplication signs, collecting like terms through repeated addition, representing repeated multiplication using index notation (powers), and dividing a term by itself.

Question 4 (a) • 1 Mark

Simplify: a × b

Writing products of variables in standard algebraic form

✅ Correct Answer

ab (or ba )

Mark allocation: [1 mark] for ab or ba (B1). Upper case A and/or B are accepted.

💡 Key Knowledge

In algebra, we omit the multiplication symbol ( × ) between letters.
Writing letters side-by-side means they are multiplied together.
Conventionally, letters are written in alphabetical order: ab .

❌ Common Errors

Leaving the multiplication sign: a × b (scores 0).
Writing indices: aᵇ or bᵃ (confusing multiplication of different letters with powers).

🧠 Exam Technique

When an exam question says "Simplify" on an expression with a multiplication symbol between letters, the task is simply to remove the × sign and write the letters adjacent to each other.

Question 4 (b) • 1 Mark

Simplify fully: c + c + c

Collecting identical like terms via repeated addition

✅ Correct Answer

Mark allocation: [1 mark] for 3c (B1).

💡 Key Knowledge

Adding identical terms means multiplying by how many there are: 1c + 1c + 1c = 3c .
The number in front is the coefficient.
In standard algebraic notation, the coefficient always goes before the variable.

❌ Common Errors

Writing the number after the letter: c3 (not accepted).
Writing multiplication explicitly: 3 × c or c × 3 (not fully simplified).
Confusing addition with powers: writing c³ instead of 3c .

🧠 Exam Technique

Think of c as an object: 1 cat + 1 cat + 1 cat = 3 cats ( 3c ). Addition changes the coefficient, never the power!

Question 4 (c) • 1 Mark

Simplify fully: p × p × p

Expressing repeated multiplication using index notation (powers)

✅ Correct Answer

p³

Mark allocation: [1 mark] for p³ (B1).

💡 Key Knowledge

Repeated multiplication of the same base number or variable is written as a power (index).
Since p is multiplied by itself 3 times: p¹ × p¹ × p¹ = p¹⁺¹⁺¹ = p³ .

❌ Common Errors

Writing the power as a standard-sized number next to the letter: p3 (scores 0).
Confusing multiplication with addition: writing 3p instead of p³ .

🧠 Exam Technique

Make sure your superscript is clearly smaller and raised above the baseline. Writing p3 looks like an algebraic term or variable label, which examiners cannot award.

Question 4 (d) • 1 Mark

Simplify: d ÷ d

Dividing any non-zero algebraic term by itself

✅ Correct Answer

Mark allocation: [1 mark] for 1 (B1).

💡 Key Knowledge

Any value (except zero) divided by itself equals 1 .
As a fraction: d / d = 1 .
Using index laws: d¹ ÷ d¹ = d¹⁻¹ = d⁰ = 1 .

❌ Common Errors

Thinking terms completely cancel out to leave nothing: writing 0 .
Leaving the answer as an unsimplified fraction: 1/1 or d/d .
Writing d .

🧠 Exam Technique

Test with a real number whenever you are unsure: 5 ÷ 5 = 1 , 12 ÷ 12 = 1 . Therefore, d ÷ d must also equal 1 .

AQA GCSE Mathematics Paper 2 (Foundation), June 2025: Question 4

Question

Mark scheme

How to answer it

Simplifying Basic Algebraic Expressions

📋 What this question tests

Simplify: a × b

Writing products of variables in standard algebraic form

✅ Correct Answer

💡 Key Knowledge

❌ Common Errors

🧠 Exam Technique

Simplify fully: c + c + c

Collecting identical like terms via repeated addition

✅ Correct Answer

💡 Key Knowledge

❌ Common Errors

🧠 Exam Technique

Simplify fully: p × p × p

Expressing repeated multiplication using index notation (powers)

✅ Correct Answer

💡 Key Knowledge

❌ Common Errors

🧠 Exam Technique

Simplify: d ÷ d

Dividing any non-zero algebraic term by itself

✅ Correct Answer

💡 Key Knowledge

❌ Common Errors

🧠 Exam Technique

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