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An improper algebraic fraction has a numerator of equal or higher degree than its denominator. This topic converts one into a polynomial plus a proper fraction by algebraic division — the key first step before partial fractions. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive course teaches the method with worked examples and gives instant-feedback practice questions to lock it in.
How you do it
When the top degree is at least the bottom degree, divide first to get a polynomial plus a proper fraction. Only then split the remaining proper part into partial fractions. Skipping the division is why the standard form fails.
Before you start
Best tackled after algebraic division and algebraic fractions. You meet it in Pure 3. It carries straight through to partial fractions. Filed under Algebra.
What you learn
A fraction is improper when the degree of the numerator is greater than or equal to the degree of the denominator. The course works through algebraic long division, the coefficient-matching identity, dividing by a quadratic, finding unknown coefficients and asymptotes from the quotient. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Improper Algebraic Fractions is part of the Algebra strand of our free A-level maths courses, studied in the AS year. It runs to 5 concepts, each followed by a check, with 5 worked examples along the way. Students often pair it with Indices and Surds, Inequalities, Modulus Function, Partial Fractions and Quadratic Functions & Discriminant. For unlimited practice, the Algebra revision engine builds new questions on demand and records your accuracy.
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