Edexcel Pure Paper 1 2024 Question 1

Edexcel Pure Paper 1 2024 Question 1 – Factor Theorem Step-by-Step

❓ The Question

You are given a cubic function $g(x)$ containing a constant $k$ .

Given that $(x - 3)$ is a factor of $g(x)$ , find the value of $k$ .

🧠 What This Question Is Testing

This is a standard factor theorem setup.

If $(x - a)$ is a factor of a function, then:

$g(a) = 0$

So in this case:

$g(3) = 0$

This is the key step — everything follows from this.

✏️ Solution (Teacher Walkthrough)

Start by applying the factor theorem.

Since $(x - 3)$ is a factor, we know:

$g(3) = 0$

Now substitute $x = 3$ into the given expression for $g(x)$ .

When you do this, you’ll get an expression involving $k$ . Take your time simplifying — this is where small mistakes tend to happen.

After simplifying, you should end up with a linear equation in $k$ .

Set the expression equal to zero and solve:

$\text{(expression in } k) = 0$

Solve this equation carefully.

✅ Final Answer

$k = 2$

🎯 How Marks Are Awarded

This is a 3-mark question:

✅ M1: Use factor theorem → substitute $x = 3$
✅ A1: Form correct equation in $k$
✅ A1: Solve correctly

Even with a small mistake, method marks are still available.

⚠️ Common Mistakes (Examiner Insight)

This question was described as very accessible, with most students answering it well.

A few issues did appear:

❌ Not setting $g(3) = 0$

Some students substituted correctly but didn’t explicitly form the equation.

❌ Algebra errors

Most mistakes came from simplifying incorrectly or solving the equation inaccurately.

❌ Using long division

Some students used polynomial division instead of the factor theorem. It works, but it’s slower and increases the chance of error.

💡 Exam Tip

If you see:

👉 $(x - a)$ is a factor

Go straight to:

$g(a) = 0$

This should feel automatic — it’s one of the quickest marks on the paper.

🚀 What To Do If This Felt Tricky

If this didn’t feel immediate, it’s usually an algebra confidence issue rather than a topic problem.

Working through similar questions with an online maths tutor can help you get faster and more accurate with these early marks.

If you want something more structured, an A level maths revision course is useful for revisiting these core ideas so they become second nature in exams.

🔗 Next Steps

← Back to Paper Overview
→ Question 2 Solution

👨‍🏫Author Bio

S. Mahandru is an experienced A Level Maths teacher and founder of Exam.Tips, specialising in exam-focused revision techniques and helping students achieve top grades.

❓ Frequently Asked Questions

📌 Do I always use the factor theorem here?

Yes — this is the intended and most efficient method.

📌 Can I still get marks if my final answer is wrong?

Yes. If your method is correct, you can still earn method marks.

📌 Why is this question at the start?

It’s designed to be accessible and build confidence early in the paper.

📌 What should I practise to improve?

Focus on:

factor theorem
substitution accuracy
solving simple linear equations

Edexcel Pure Paper 1 2024 Question 1