Algebra & Functions — A-Level Mathematics Revision
Revise Algebra & Functions for A-Level Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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- Algebra & Functions in A-Level Mathematics: explanation, examples, and practice links on this page.
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Go to Coordinate GeometryWhat 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 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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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
Exam-style questions for Algebra & Functions with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel and OCR specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Algebra & Functions
Core concept
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, an…
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.