IB Maths AA 1.9 Notes

This page contains our IB Maths AA notes for 1.9. By reading each one of these notes, you will fully cover the content for IB Maths AA 'Partial fractions'.

All Topic 1 Sub-topics 1.1: Scientific Notation 1.2: Arithmetic Sequences 1.3: Geometric Sequences 1.4: Interest 1.5: Exponents & Logs 1.6: Deductive Proofs 1.7: Binomial Theorem (HL)1.8: Counting principles (HL)1.9: Partial fractions (HL)1.10: Complex numbers (HL)1.11: Additional proofs (HL)1.12: Systems of equations

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Chapters

1. Partial fractions

2. General form and method

3. Substitution method

4. Comparing coefficients method

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Partial fractions

Partial fractions are used to rewrite a rational expression as a sum of simpler fractions. In this topic, the denominator will factor into at most two distinct linear factors, and the degree of the numerator will be less than the degree of the denominator.

This is useful because simpler fractions are easier to manipulate and later become easier to integrate.

A rational expression can be decomposed into partial fractions when:

the denominator can be factorised
and the degree of the numerator is less than the degree of the denominator

For example, $\frac{2x+1}{x^2+x-2}$ is suitable because the denominator factors as $x^2+x-2=(x-1)(x+2)$ and the numerator has lower degree than the denominator.

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