OCR•A-Level•Mathematics
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Algebra and Functions
Indices, surds, quadratics, polynomials, partial fractions, functions, and graph transformations
Practice 46 subtopics in Algebra and Functions. All questions match the OCR A-Level specification.
About Algebra and Functions
Algebra and Functions is a key topic in the OCR A-Level Mathematicsspecification. This topic covers indices, surds, quadratics, polynomials, partial fractions, functions, and graph transformations.
Master all 46 subtopics below with unlimited AI-generated questions. Each subtopic page includes sample questions and the ability to generate unlimited practice questions with detailed solutions.
All Subtopics (46)
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Laws of indices (integer, fractional, negative)Simplifying expressions with indicesManipulating surdsRationalising denominators (simple)Rationalising denominators (compound)Quadratic functions and their graphsCompleting the squareSolving quadratic equations by factorisationSolving quadratic equations by completing the squareSolving quadratic equations using the formulaDiscriminant and nature of rootsConditions for real, equal, or no real rootsSolving simultaneous equations (two linear)Solving simultaneous equations (one linear, one quadratic)Solving linear inequalitiesSolving quadratic inequalitiesRepresenting inequalities graphicallySet notation for solutionsManipulating polynomials algebraicallyExpanding brackets and collecting termsFactorising polynomialsAlgebraic (polynomial) divisionFactor theoremRemainder theoremModulus function |x| and |f(x)|Graphs of y = |f(x)| and y = f(|x|)Solving equations involving modulusSolving inequalities involving modulusGraphs of linear, quadratic, cubic functionsGraphs of quartic and reciprocal functionsGraphs involving y = 1/x and y = 1/x²AsymptotesPoints of intersection of graphsTranslations: y = f(x) + a, y = f(x + a)Stretches: y = af(x), y = f(ax)Reflections: y = -f(x), y = f(-x)Combined transformationsFunction notation f(x)Domain and rangeComposite functions fg(x)Inverse functions f⁻¹(x)Relationship between f and f⁻¹ graphsPartial fractions with linear factorsPartial fractions with repeated linear factorsPartial fractions with improper fractionsUsing algebra in modelling contexts
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