A Level Maths: Indices 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:
- GCSE Maths Indices — a solid grasp of integer powers and the basic index laws from GCSE is assumed
- GCSE Maths Algebra — comfort manipulating algebraic expressions is needed before tackling fractional and negative indices
A Level Maths indices is the foundational algebra topic covering how powers, exponents, and roots work. A solid grasp of the index laws makes calculus, exponentials, and binomial expansion feel natural and much easier to handle, so it pays off many times over to master this early.
At A Level you handle all rational indices: positive integer powers ($x^3$, $x^5$), negative powers ($x^{-2}$ means $1/x^2$), and fractional powers ($x^{1/2}$ means the square root of $x$, $x^{2/3}$ means the cube root of $x$ squared). You apply the three core laws — $x^a \times x^b = x^{a+b}$, $x^a \div x^b = x^{a-b}$, and $(x^a)^b = x^{ab}$ — fluently and in combination, including rewriting different bases as powers of a common base. You also use indices to simplify expressions before differentiating or integrating, which is a high-leverage skill that turns intimidating calculus questions into routine ones.
Indices are part of the Pure Maths strand of A Level Maths and underpin algebraic work throughout the rest of the course. Essential A Level Maths revision content for all UK exam boards including AQA, Edexcel, OCR, and OCR MEI.
Watch out for…
A few things to be careful with: $x^{-1/2}$ is $\frac{1}{\sqrt{x}}$, not $-\sqrt{x}$; $x^a \times x^b$ is $x^{a+b}$, not $x^{ab}$ — addition, not multiplication of the indices; $x^0 = 1$ for any non-zero $x$; terms with different powers like $3x^2$ and $5x^3$ cannot be combined; and $(xy)^a = x^a y^a$, but $(x+y)^a$ is NOT $x^a + y^a$. With negative bases and fractional exponents, $(-8)^{1/3}$ is defined and equals $-2$, but $(-4)^{1/2}$ is not a real number at A Level.