UNIT 1: Numbers and Algebra

Formulae (SL & HL)

Arithmetic Sequence

Increases or decreases by the addition of a numerical factor.

Arithmetic Sum

Geometric Sequence

Increases or decreases by the multiplication of a numerical factor.

Geometric Sum

Convergent Series

Keeps decreasing until it converges at one value e.g. geometric sequences.

Divergent Series

Keeps increasing till infinity e.g. arithmetic sequences.

Combinatorics

The number of way you choose r objects from n choices.

Permutations

Binomial Expansion

Binomial Expansion for Fractional Powers

Binomial Expansion for Negative Powers

Proof by Mathematical Induction

Zero and One Power Rules (Indices)

Product and Greater Exponent Rules (Indices)

Quotient and Negative Exponent Rules (Indices)

Fractional and Same Exponent Rules (Indices)

Inverse Function Rule (Logarithms)

Basic Logarithms

Addition Rule (Logarithms)

Subtraction Rule (Logarithms)

Power Rule (Logarithms)

Log of Base and 1 (Logarithms)

Quotient Rule (Logarithms)

Negative and Fractional Rules (Logarithms)

Natural Logs and Greater Exponent Rules (Logarithms)

Concept of ‘i’

Imaginary/Complex Numbers

Absolute Value (Complex Numbers)

Addition Rule (Complex Numbers)

Multiplication by a Scalar (Complex Numbers)

Complementary Imaginary Numbers

Magnitude of Complex Numbers

Polar Form (Complex Numbers)

Angle of a Complex Number

Angles in each Quadrant (Complex Numbers)

Euler’s Form (Complex Numbers)

Representation of Complex Numbers

Symmetry of Complex Numbers

Product Rule (Complex Numbers)

Quotient Rule (Complex Numbers)

De Moivre’s Theorem

Roots of Complex Numbers