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Edexcel Pure Paper 2 2024 Question 6
Edexcel Pure Paper 2 2024 Question 6 – Differentiation and Iteration
❓ The Question
🧠 Before you start
This one looks long when you first read it.
Not because any single part is difficult — it’s more that it switches direction a couple of times. You go from differentiation into an equation, and then into iteration. That change is what tends to slow people down.
If you just treat each part on its own, it’s actually quite manageable. It doesn’t need to be rushed.
✏️ Working
Part (a)
Start with the first function.
f(x) = e^{4x^2 – 1}
This is one of those where you have to remember the chain rule. It’s easy to forget if you’re moving quickly.
Differentiate the exponential as it is, then multiply by the derivative of what’s inside.
So:
f'(x) = e^{4x^2 – 1} \cdot 8x
Nothing unusual — just making sure that 8x appears. That’s the part that sometimes gets missed.
Now the second function.
g(x) = 8\ln x
This is more direct.
g'(x) = \frac{8}{x}
No chain rule this time, just standard differentiation.
Part (b)
Now we’re told the derivatives are equal.
So just set them equal and see where it goes:
8x e^{4x^2 – 1} = \frac{8}{x}
First thing I’d do here is simplify a bit — divide both sides by 8. It just makes things easier to look at.
x e^{4x^2 – 1} = \frac{1}{x}
Then multiply through by x:
x^2 e^{4x^2 – 1} = 1
At this point, it’s about rearranging into the form the question wants. Usually that means taking logs and tidying things carefully.
There isn’t a clever trick here. It’s more about not skipping steps, because that’s where mistakes creep in.
Eventually, you land on the required equation involving x.
Part (c)
Now the question switches again — this time to iteration.
You’re given a formula and a starting value:
x_1 = 0.6
From here, it’s just substitution.
Put 0.6 into the formula, calculate it properly, and that gives you x_2.
Then repeat the process to get the next value.
It’s quite mechanical, but this is exactly where small errors happen. Usually just rounding or pressing something slightly wrong on the calculator.
So it’s worth going a bit slower here than you think you need to.
Final answers:
(i)
x_2 = 0.7109
(ii)
a \approx 0.6687
🎯 Where the Marks Are
Part (a) is fairly standard — just correct differentiation.
Part (b) is where most of the marks sit. Not because it’s harder, but because there are more steps.
Part (c) is method-based. If your substitutions are clear, you’ll pick up marks even if the final value is slightly off.
⚠️ What Went Wrong
The chain rule caused a few issues in part (a). Some answers missed the 8x completely, which changes everything later.
In part (b), it was mostly algebra slips. Nothing major — just small rearranging mistakes.
Iteration in part (c) was generally okay, but rounding caused problems for some. Once one value is slightly off, the next one drifts further.
💡 One Small Tip
When a question moves into iteration, slow down rather than speed up.
It feels like the easy part, but that’s where careless mistakes happen.
🚀 If This Felt Difficult
If this felt a bit disjointed, that’s normal.
It’s not testing one idea — it’s testing whether you can move between a few without losing control of the maths.
Questions like this are useful for building that link between topics, which is what really helps you boost your maths confidence over time.
And if you want to make that process more consistent, working through a step-by-step maths revision course can help make these transitions feel less awkward.
🔗 Next Steps
👨🏫Author Bio
S Mahandru is an A Level Maths teacher focused on helping students stay accurate under exam pressure. The aim is to keep methods clear and build confidence through consistent exam-style practice.
❓ Frequently Asked Questions
📌Why is the chain rule needed?
Because the exponent isn’t just x — it’s a function of x.
📌Should I simplify early?
Usually yes. It keeps things clearer as you go.
📌How accurate should iteration be?
Follow whatever the question asks — usually a set number of decimal places.
📌Is this type of question common?
Yes, especially where exact solutions aren’t easy.