A Level Maths: Transformations Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- Quadratic Equations — needed to sketch the parent quadratic graphs being transformed
- Straight Line Geometry — foundational graph-sketching skills
- GCSE Maths Graphs — recognising standard graph shapes is assumed
A Level Maths transformations is the topic that teaches you how to relate the graphs of related functions visually. Given the graph of $y = f(x)$, you learn to predict and sketch $y = af(x)$, $y = f(x) + a$, $y = f(x + a)$, and $y = f(ax)$, and to combine these transformations. This is hugely useful across the syllabus, especially when sketching trig curves, exponentials, and modulus functions in Functions and The Modulus Function.
You handle four basic transformations: vertical translations ($y = f(x) + a$ shifts up by $a$), horizontal translations ($y = f(x + a)$ shifts left by $a$ — note the sign inversion), vertical stretches ($y = af(x)$ stretches vertically by factor $a$, including reflection in the $x$-axis when $a$ is negative), and horizontal stretches ($y = f(ax)$ compresses horizontally by factor $a$, including reflection in the $y$-axis when $a$ is negative). You combine these to sketch graphs like $y = 3 + \sin(2x)$ or $y = -\cos(x/2 + \pi/4)$. You also identify the equation of a transformed graph from its sketch, which often appears in modelling and applied questions.
Transformations are part of the Pure Maths strand of A Level Maths and are essential revision content for all UK exam boards including AQA, Edexcel, OCR, and OCR MEI.
Watch out for…
A few things to be careful with: the sign in $y = f(x + a)$ is counter-intuitive — adding inside the bracket shifts the graph LEFT, not right; horizontal stretches by factor $a$ compress the graph by $1/a$ horizontally (so $y = f(2x)$ is COMPRESSED, not stretched, in the $x$ direction); when combining transformations, the order matters — inside-the-bracket changes happen in reverse of how you read them; and stretches keep the $x$-intercepts (for horizontal stretches) or $y$-intercepts (for vertical stretches) — translations move them.