IB Maths AA 1.8 Definitions

This page contains our IB Maths AA definitions for 1.8. By learning each one of these definitions, you will fully cover the content for IB Maths AA 'Counting principles'.

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

AND

Indicating that separate stages both occur, so the total number of outcomes is found by multiplying the numbers of ways for each stage, giving

m\times n

coefficient

The numerical factor multiplying a term in an expansion, for example the number multiplying

x^2

in a polynomial term.

combinations

The number of ways to pick

r

objects from

n

distinct objects when order does not matter, given by

{}^nC_r=\frac{n!}{r!\left(n-r\right)!}

factorials

Products of consecutive positive integers used in counting formulas, with

n!=n\times\left(n-1\right)\times\dots\times2\times1

and

0!=1

fractional

Describing an index

n

that is not an integer, so the expansion of

\left(1+x\right)^n

uses the general series

1+nx+\frac{n\left(n-1\right)}{2!}x^2+\frac{n\left(n-1\right)\left(n-2\right)}{3!}x^3+\dots

and does not terminate.

fundamental

Stating that if one task can be done in

m

ways and a second task can be done in

n

ways, then doing both tasks can be done in

m\times n

ways.

permutation

An arrangement of objects where order matters; the number of ways to arrange

r

objects chosen from

n

distinct objects is

{}^nP_r=\frac{n!}{\left(n-r\right)!}

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.

series

A sum of terms written in a continuing pattern, such as $1+nx+\frac{n(n-1)}{2!}x^2+\dots$ , which may be infinite when $n$ is not a positive integer.

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