Express $\dfrac{2\sqrt{3} - 1}{\sqrt{3} + 2}$ in the form $a + b\sqrt{3}$, where $a$ and $b$ are integers.
Free · Pure Mathematics · 9MA0 Paper 1 style
A Level Maths Predicted Paper 2027
A full 2-hour, 100-mark pure mathematics paper in the style of Edexcel 9MA0 Paper 1, with a step-by-step mark scheme. Sit it under timed conditions, mark it yourself, and see which topics to revise first. Free: we email you the link.
- 17 questions, 100 marks
- Full mark scheme
- Printable PDF
Our own prediction, not board material. This is A Level Math Revision's own practice paper, written by Pete Bromfield for 2027 revision. It is not an official Pearson Edexcel paper, it has not been seen or approved by Pearson, and it is not a leaked or 'real' paper. 'Predicted' means it covers topics that are examined on Paper 1 year after year; it does not forecast the actual questions.
17 questions across the pure content
The topics that come up on Paper 1 year after year, from surds to differential equations. Year 12 and Year 13 content, calculator allowed.
- Surds
- Small-angle approximations
- Binomial expansion
- Graph transformations and the modulus function
- Circles
- Functions and inverse functions
- Trigonometric identities and equations
- Geometric series
- Vectors
- Proof by contradiction
- Exponential models and logarithms
- Numerical methods
- Stationary points and concavity
- Connected rates of change
- Harmonic form R sin(x − α)
- Differential equations
- Tangents and area (problem solving)
The first two questions
Given that $\theta$ is small and measured in radians, use the small-angle approximations for $\cos\theta$ and $\tan\theta$ to show that
$\dfrac{1 - \cos 6\theta}{\theta\tan 2\theta} \approx 9$
Get the paper and the mark scheme
Enter your email and confirm it. We send you the link to the paper, the mark scheme and the PDFs.
Get the most from one paper
- Sit it in one go: 2 hours, a calculator and the formulae booklet, no notes.
- Mark it strictly against the mark scheme: a method mark needs the method, an accuracy mark needs the method mark first.
- List the questions where you lost marks, and revise those topics first on the A Level Maths topic pages.
- Then try a real paper: Edexcel 9MA0 past papers, or the timed mini-mocks that mark themselves.
Predicted Paper 2027: common questions
Is this the real 2027 exam paper?
No. It is our own practice paper, written by Pete Bromfield. It is not an official Pearson Edexcel paper, it has not been seen or approved by Pearson, and it is not a leaked paper. 'Predicted' means it covers topics that are examined on Paper 1 year after year; nobody outside the board knows the actual questions.
Which exam is it for?
It is written in the style of Pearson Edexcel A level Mathematics (9MA0) Paper 1: pure mathematics, 2 hours, 100 marks, calculator allowed. The content is the A Level Maths pure content that AQA and OCR examine too, so it is useful practice for any UK board.
What do I get?
A link to the paper online and as a printable PDF, plus the full mark scheme (method, accuracy and independent marks for every step). You also get the weekly Math Revision email (one short email a week), with a one-click unsubscribe.
Is it really free?
Yes. You only need to confirm your email address. Under 16? Give a parent's email and we will send it to them.