IB Maths AA 1.9 Definitions

This page contains our IB Maths AA definitions for 1.9. By learning each one of these definitions, 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

constants

Fixed numbers (not depending on '

x

') introduced in a partial fraction form, such as '

A

' and '

B

', which are determined to make two expressions identical.

decomposed

Written in an equivalent form as a sum of simpler fractional terms, typically by introducing constants such as '

A

' and '

B

' and determining their values.

degree

The highest power of

x

with a non-zero coefficient in a polynomial.

denominator

The polynomial or expression written below the fraction bar in a rational expression; its factorisation determines the form of the decomposition.

expand

To rewrite a product such as

A(x+2)

as a sum by distributing multiplication, for example

A(x+2)=Ax+2A

factorise

To rewrite an expression as a product of simpler factors, for example '

x^2+x-2=\left(x-1\right)\left(x+2\right)

integration by substitution

Replacing one expression with another to simplify a differential equation, such as using '

y=vx

' so that '

\frac{dy}{dx}=v+x\frac{dv}{dx}

numerator

The expression written above the fraction bar; in this topic its degree is lower than the degree of the expression below the fraction bar.

Partial fractions

A method for rewriting a rational expression as a sum of simpler fractions, which are usually easier to manipulate and integrate.

rational

Expressible as a ratio of integers, written as $n=\frac{p}{q}$ with integers $p,q$ and $q\neq0$ , allowing the series form of $(1+x)^n$ to be used.

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