A-Level Mathematics Revision — Algebra & Functions
Revise Algebra & Functions for A-Level Mathematics with a topic explanation, worked example and common mistakes. Check the board notes for specification differences.
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- Algebra & Functions in A-Level Mathematics: explanation, examples, and practice links on this page.
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This page includes a topic explanation and a worked example. Check your course for current practice coverage.
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What is Algebra & Functions?
Algebra and functions at A-Level involve manipulating complex algebraic expressions and understanding the behaviour of various functions. This includes working with polynomials, rational functions, and modulus functions, as well as understanding transformations of graphs.
Board notes: The specific functions and transformations covered can vary slightly between exam boards. For example, some boards may place more emphasis on the modulus function than others. All boards (AQA, Edexcel, OCR) cover this topic in depth.
Step-by-step explanationWorked examples
Worked example
Solve the inequality |2x - 3| > 5. This gives two separate inequalities: 2x - 3 > 5 or 2x - 3 < -5. Solving the first gives 2x > 8, so x > 4. Solving the second gives 2x < -2, so x < -1. The solution is x < -1 or x > 4.
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Start with low-focus cards for Algebra & Functions, then move into full exam-style practice when you want the heavier session.
Common mistakes
- 1Incorrectly applying the laws of indices and logarithms, especially with negative or fractional powers.
- 2Errors in expanding brackets or factorising polynomials, particularly with cubic or quartic expressions.
- 3Misunderstanding the effect of transformations on a function's graph, such as the difference between f(x+a) and f(x)+a.
Algebra & Functions exam questions
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Frequently asked questions
How do I find the inverse of a function?
To find the inverse of a function f(x), you first write it as y = f(x). Then, you swap the x and y variables and solve the resulting equation for y. The new expression for y is the inverse function, f⁻¹(x).
What is the remainder theorem?
The remainder theorem states that if a polynomial f(x) is divided by (x-a), the remainder is f(a). This is a quick way to find the remainder without performing polynomial division.