A-Level Mathematics Revision — Algebra & Functions
Revise Algebra & Functions for A-Level Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), Pearson Edexcel International, OxfordAQA International, SQA, IB, AP.
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- This topic
- Algebra & Functions in A-Level Mathematics: explanation, examples, and practice links on this page.
- Who it’s for
- Students revising A-Level Mathematics for UK exams.
- Exam boards
- Practice is aligned to major specifications (AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), Pearson Edexcel International, OxfordAQA International, SQA, IB, AP).
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- Syllabus-shaped practice and progress tracking—not generic AI answers.
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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 1: Core method
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.
Worked example 2: Exam variation
Now change one detail in the question and keep the same structure: name the Algebra & Functions idea being tested, show the method or evidence, then explain why it answers the command word. This helps A-Level Mathematics students avoid memorising one surface pattern.
Worked example 3: Mark-scheme check
Finish by checking the answer against marks: one point for the correct Algebra & Functions idea, one for accurate working or evidence, and one for a precise final statement. If any step is vague, rewrite it before moving to timed practice.
Mini lesson for Algebra & Functions
1. Understand the core idea
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.
Can you explain Algebra & Functions without copying the notes?
2. Turn it into marks
Solve the inequality |2x - 3| > 5. This gives two separate inequalities: 2x - 3 > 5 or 2x - 3 < -5.
Underline the method, evidence, or command-word move that would earn credit in A-Level Pure Mathematics.
3. Fix the likely mark leak
Watch for this mistake: Incorrectly applying the laws of indices and logarithms, especially with negative or fractional powers.
Write one correction rule before doing another practice question.
Practise this topic
Start with low-focus cards for Algebra & Functions, then move into full exam-style practice when you want the heavier session.
Mini quiz: Algebra & Functions
Three quick checks for revision practice. They are original StudyVector prompts, not official exam-board questions.
Question 1
In one A-Level sentence, explain what Algebra & Functions is testing.
Answer: 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.
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Algebra & Functions question but is not sure how to start. What should the first method line establish?
Answer: It should identify the rule, equation, diagram feature, or transformation before any calculation. That protects method marks and makes later checking easier.
Mark focus: Method selection and command-word control.
Question 3
A student makes this mistake: "Incorrectly applying the laws of indices and logarithms, especially with negative or fractional powers." What should their next repair task be?
Answer: Do one Algebra & Functions question and review the mistake type.
Mark focus: Error correction and next-step practice.
Algebra & Functions flashcards
Core idea
What is the main idea in 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 functio...
Common mistake
What mistake should you avoid in Algebra & Functions?
Incorrectly applying the laws of indices and logarithms, especially with negative or fractional powers.
Practice
What is one useful practice task for Algebra & Functions?
Answer one Algebra & Functions question and review the mistake type.
Exam board
How should you use board notes for Algebra & Functions?
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.
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, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), Pearson Edexcel International, OxfordAQA International, SQA, IB, AP 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.