Edexcel Pure Paper 1 2024 Question 4

Edexcel Pure Paper 1 2024 Question 4 – Differentiation from First Principles

❓ The Question

A good way to think about first principles is that you are rebuilding differentiation from scratch. You are not using rules here — you are showing where they come from, step by step.

🧠 First Thoughts

This one always looks longer than it actually is.

There’s no trick. It’s just the definition… and a bit of algebra that needs to be handled properly.

If anything goes wrong here, it’s usually just a sign error somewhere in the middle.

✏️ Working

Start with first principles:

$f'(x) = \lim_{h \to 0} \frac{f(x+h) – f(x)}{h}$

Given $f(x) = 2x$

Find $f(x+h)$ :

$f(x+h) = 2(x+h) = 2x + 2h$

Now subtract $f(x)$ :

$f(x+h) - f(x) = (2x + 2h) - 2x = 2h$

Divide by $h$ :

$\frac{2h}{h} = 2$

Take the limit:

$\lim_{h \to 0} 2 = 2$

Final result

$f'(x) = 2$

🎯 Where the Marks Are

This is only 3 marks, so each step is doing a specific job.

M1
Correct use of first principles formula
(must show $\frac{f(x+h) – f(x)}{h}$ )

A1
Correct expansion and simplification
(including handling brackets and cancelling $h$ )

A1
Correct final derivative after taking the limit

⚠️ Where Things Go Wrong

Nothing unusual here, just small slips:

brackets not expanded properly
missing a negative sign when subtracting
cancelling $h$ too early

Also, some answers jumped steps. That makes it harder to pick up marks, even if the final line is right.

💡 A Quick Note

It’s tempting to try and speed this up.

Usually it doesn’t end well.

Writing it out clearly is quicker than fixing mistakes later.

🚀 If This Didn’t Feel Great

If this felt a bit clunky, it’s normally just the algebra.

Going through it with an A level maths tutor online can help tidy up the process so you’re not second-guessing each line.

If you’d rather work through it more steadily, an A level maths online course is useful for building this up step by step so it feels more routine.

🔗 Next Steps

← Question 3
→ Question 5

👨‍🏫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 need the full definition?

Yes — if the question says first principles, you need to show it.

📌 What usually causes mistakes?

The subtraction step. That’s where signs go wrong.

📌 Can I skip working if I know the answer?

Not here — the marks are in the process.

📌 Best way to get better at this?

Do a few slowly and properly. Speed comes after.

Edexcel Pure Paper 1 2024 Question 4