Edexcel Pure Paper 1 2024 Question 2

Edexcel Pure Paper 1 2024 Question 2 – Binomial Expansion & Validity

❓ The Question

You are asked to expand

$(1 – 9x)^{\frac{1}{2}}$

and then explain why $x = -\frac{2}{9}$ isn’t suitable to use in that expansion.

🧠 A Quick Thought Before Starting

This looks like a standard binomial question — and it is — but it’s one of those where the algebra can quietly go wrong if you rush.

Nothing complicated. Just easy to slip up.

✏️ Working Through It

Part (a)

We start from the usual expansion:

$(1 + x)^n = 1 + nx + \frac{n(n-1)}{2}x^2 + \frac{n(n-1)(n-2)}{6}x^3 + \dots$

Here’s the thing: the “x” in that formula isn’t just $x$ anymore. It’s $-9x$ . That matters.

First term is straightforward:

$1$

Next term:

$\frac{1}{2}(-9x)$

which gives

$-\frac{9}{2}x$

Now the next one — this is where people slow down, or make a sign error.

$\frac{\frac{1}{2}\left(\frac{1}{2}-1\right)}{2}(-9x)^2$

If you take it step by step (don’t rush it), this becomes:

$-\frac{81}{8}x^2$

One more term:

$\frac{\frac{1}{2}\left(\frac{1}{2}-1\right)\left(\frac{1}{2}-2\right)}{6}(-9x)^3$

Careful again with the signs — you end up with:

$-\frac{243}{16}x^3$

So putting it together:

$1 – \frac{9}{2}x – \frac{81}{8}x^2 – \frac{243}{16}x^3$

Part (b)

This part is where quite a few people lost the mark.

The expansion only works when the value you’re plugging in is small enough.

For the standard form, you need:

$|x| < 1$

But again — your $x$ isn’t just $x$ . It’s $-9x$ .

So the condition becomes:

$|-9x| < 1$

which simplifies to:

$|x| < \frac{1}{9}$

Now look at the value given:

$x = -\frac{2}{9}$

Its size is:

$\frac{2}{9}$

That’s bigger than $\frac{1}{9}$ , so it doesn’t fit the condition.

That’s really all you need to say — just clearly.

✅ Final Answer

Expansion:

$1 – \frac{9}{2}x – \frac{81}{8}x^2 – \frac{243}{16}x^3$

And the value $-\frac{2}{9}$ is outside the valid range, so the expansion can’t be used.

⚠️ A Few Things That Went Wrong

Nothing dramatic here — just small things:

losing the negative sign early on
rushing the fractions
or in part (b), not actually stating the inequality

Some answers just said “it’s too big”, which doesn’t really get you the mark.

💡 One Small Tip

If the expression inside the bracket isn’t just $x$ , pause.

Rewrite it mentally first.

Here it’s really a binomial in $-9x$ , not $x$ . That’s where most of the errors come from.

🚀 What To Do If This Didn’t Feel Smooth

If part (a) felt messy, it’s usually down to handling the fractions rather than the idea itself.

Working through a few of these with a maths tutor online can help tidy that up quite quickly — especially the structure of each term.

If it’s the second part that felt unclear, that’s more about understanding the condition than doing the maths. An A level maths course can help link those ideas properly so you’re not just following a process.

🔗 Next Steps

← Question 1
→ Question 3

👨‍🏫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 four terms?

Only if the question asks — don’t assume.

📌 Where do most mistakes happen?

Usually in the signs, or when simplifying the coefficients.

📌 Why check the condition at all?

Because the expansion only works in a certain range. Outside it, the result isn’t reliable.

📌 Best way to practise this?

Do a few, slowly. Focus on accuracy first — speed comes after.

Edexcel Pure Paper 1 2024 Question 2