IB Maths AA 1.7 Definitions

This page contains our IB Maths AA definitions for 1.7. By learning each one of these definitions, you will fully cover the content for IB Maths AA 'Binomial theorem'.

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

binomial coefficient

A number written as

{}^nC_r

\binom{n}{r}

, given by

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

, which counts combinations: the number of ways to choose

r

objects from

n

when order does not matter.

binomial theorem

A rule for expanding

(a+b)^n

for

n\in\mathbb{N}

by generating every term and coefficient systematically, rather than multiplying out repeatedly.

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)!}

factorial

A product written as

n!

meaning

n\times\left(n-1\right)\times\cdots\times2\times1

, with

0!=1

, used to define binomial coefficients.

general term

A single term in the binomial expansion written as

T_{r+1}={}^nC_r a^{n-r}b^r

, used to identify a specific term without expanding fully.

nCr

Combinatorial notation for the binomial coefficient, written as

{}^nC_r

, used as the coefficient of terms in binomial expansions and to count combinations.

Pascal's triangle

A triangular array of numbers where each interior entry is the sum of the two entries directly above it, and each row gives the coefficients for expanding

(a+b)^n

for a particular value of

n

probability

Measures how likely an event is to happen, taking a value between $0$ and $1$ , where $0$ means impossible and $1$ means certain.

sigma

A summation symbol used to write a series compactly, for example

(a+b)^n=\sum_{r=0}^{n}{}^nC_r a^{n-r}b^r

means add the terms for all integer values of

r

from

0

n

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