Edexcel Pure Paper 2 2024 Question 1 Solution

Edexcel Pure Paper 2 2024 Question 1 – Differentiation and Second Derivatives

❓ The Question

🧠 Before you start

There isn’t really anything hidden in this one.

It’s the kind of question you’d expect right at the start of the paper — just straightforward differentiation. The difficulty isn’t the maths itself, it’s whether you stay switched on.

A lot of marks go missing here for no real reason. Not because people don’t know what to do, but because they move too quickly and don’t check anything.

So the mindset is simple: take it steady, keep it clean.

✏️ Working

Part (a)(i)

Differentiate each term separately. No shortcuts needed.

Start with
$4x^3$ → $12x^2$

Then
$-7x^2$ → $-14x$

Next
$5x$ → $5$

And the constant just drops out.

So you end up with:

$\frac{dy}{dx} = 12x^2 – 14x + 5$

That’s it. Nothing clever going on — just applying the rule properly.

Part (a)(ii)

Now go again.

$12x^2$ becomes $24x$
$-14x$ becomes $-14$

The +5 disappears this time.

So:

$\frac{d^2y}{dx^2} = 24x – 14$

You’ll probably feel like you’re just repeating yourself here — and you are. That’s all this part is.

Part (b)

Now we actually use what we’ve found.

That word “hence” is doing a lot of work. It’s basically saying: don’t go back to the start — use the second derivative you’ve just got.

Set it equal to zero:

$24x - 14 = 0$

Then solve it:

$24x = 14$

So:

$x = \frac{14}{24}$

And if you tidy it up:

$x = \frac{7}{12}$

Done.

🎯 Where the Marks Are

This is one of those questions where the marks follow a very clear path.

Get the first derivative right — you’re fine.
Get the second derivative right — still fine.
Solve the equation properly — finished.

There’s no recovery if the first step goes wrong, though. Everything builds from that.

⚠️ What Went Wrong

This question wasn’t meant to be difficult, and most people did okay with it.

But the same small mistakes kept showing up.

Some answers had powers reduced incorrectly — writing things like $12x$ instead of $12x^2$ . That’s just a lapse in concentration.

Another one was the second derivative being changed to something like $12x - 7$ . That usually comes from trying to “simplify” when there’s nothing to simplify.

And then right at the end, a few people left $\frac{14}{24}$ as it is. Not a big error, but still unnecessary.

None of these are hard mistakes — they’re just avoidable ones.

💡 One Small Tip

If a question feels easy, slow down slightly.

That sounds backwards, but it works. These are the marks you lock in early, so it’s worth being a bit more careful than you think you need to be.

🚀 If This Felt Difficult

If this didn’t feel as straightforward as it should, it’s usually just a consistency issue.

Working through more questions like this with proper support with maths revision tends to sort that out quite quickly.

And if you’re aiming to feel confident across full papers, not just isolated questions, an A level maths exam preparation course helps bring that together so these become automatic.

🔗 Next Steps

← Back to Paper Overview
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👨‍🏫Author Bio

S Mahandru is an experienced A Level Maths teacher focused on clear methods and exam performance. The aim is to make problems manageable and help students avoid the small mistakes that cost marks.

❓ Frequently Asked Questions

📌 Why is the constant removed?

Because the derivative of a constant is always zero.

📌 What does “hence” really mean?

Use what you’ve already found — don’t start again.

📌Do I always need to simplify?

Yes, unless the question says otherwise.

📌Is this typical of the exam?

Very. Questions like this come up regularly and are usually early marks.