Unit 1
Mathematical Methods (Queensland)
Topic 0: Surds
Note: This topic is NOT part of the current Mathematical Methods syllabus. However, the manipulation of surds is widely considered a useful skill (both in methods and specialist). For this reason, I include a short course on surds here.

Surds: What they are and why we need them

Proof that the square root is equal to the power of 1/2

Simplifying surds

Adding and Subtracting surds by grouping like terms

Multiplying surds

Surds and the distributive law

Dividing Surds

Surds Rationalising denominators

Rationalising denominators using conjugates

Infinite nested radicals
Topic 1: Arithmetic Sequences and Series

Sequence Notation

Recurrence Relations

Using a recurrence relation

Defining a sequence in terms of n

Applications of recurrence relations

Applications of recurrence relations non arithmetic

Using a calculator with recurrence relations

Arithmetic sequence formula

Rearranging the arithmetic sequence formula

Arithmetic sequences using simultaneous equations

Arithmetic sequences and series

Simultaneous equations using arithmetic series and sequences

Application of the arithmetic sequence

Simple Interest using arithmetic sequences

The Middle Term as the arithmetic mean in an arithmetic sequence

Introduction to the Sum of an arithmetic series

Arithmetic Series Formula Where it comes from and how to use it

Arithmetic Series resulting in a quadratic

Arithmetic Series and Simultaneous equations

Finding the number of terms in an arithmetic sequence

Arithmetic series Finding the number of terms that sum to a given number

Application of arithmetic series
Topic 2: Functions and Graphs

Set Notation: Introduction

Interval Notation and Number Lines

Relations Domain and Range

Relations, Functions and the vertical line test

domain and range notation

Domain and Range of functions and relations

Graphing on calculator using restricted domains

What’s a function

Function notation

Function Notation: Better ways of representing functions

Piecewise Functions

Function Transformations intro

Functions Transformation fx+a

Function transformation f(x+a)

Function transformation afx

Functions transformations f(ax)

Anatomy of a quadratic graph

Solving Quadratics 3 ways

3 forms of the quadratic equation

Review of sketching quadratics two ways

The quadratic formula and the discriminant

Modelling and problem solving with quadratics

solving simultaneous equations using quadratic and linear graphs

Direct vs inverse proportion

Equations of hyperbola and sketching

Finding equation of reciprocal function from sketch

Sketching Hyperbolas and why there’s an asymptote

Sketching circles and finding equations of circles

The square root function

Intersecting Functions

Direct and Indirect Proportion

Factor Theorem Examples

Long Division: Learn this before polynomial division

Polynomial division

Finding a linear factor of a polynomial

Factorise solve and sketch a cubic

Cubics in “Turning Point” Form: (But it’s not a turning point)

Full quadratic review video

Fitting Indirect Proportion function to data using TI Nspire

Graphing and finding key points on the TI Nspire

Determining intersections of functions graphically on the TI Nspire

Sketching a graph on the TI Nspire

Solving simultaneous equations using LinSolve TI Nspire

Solving polynomials on the TI Nspire
Topic 3: Counting and Probability

The Language of Sets

Theoretical Probability with sets

All Probabilities sum to 1

Venn Diagrams the complement

Experimental probability

simplified tree diagram

The Addition rule of probability

Probability Tables intro

Conditional Probability formula

Conditional Probability Do you watch the bachelorette

Conditional probability rearranging the formula

Conditional Probability and Tree Diagrams

Independent events intro and tests

Independent events 2

Pascal’s Triangle and Selections

Binomial expansion using pascal’s triangle
Topic 4: Exponential Functions

Index Law 1 – multiplication of indices

Index Law 2 – dividing indices

Index Law 3 – raising to the power of zero

Index Law 4 – Raising a power to another power

Index Law 5 – worked examples using the fifth index law

Index Law 6 – expanding brackets around a fraction raised to a power

Index law 7 Negative Indices – converting Negative indices into positive indices using fractions

Index Laws Fractional indices

Index Laws Negative bases

Index Laws simplifying by decomposing

Scientific notation Converting to scientific notation

Scientific Notation Convert scientific notation to decimal

Scientific notation Multiplying and dividing
Topic 5: Geometric Sequences and Series

Geometric sequences and the recursive definition

Geometric Sequence formula

Geometric sequences finding the common ratio

Geometric Sequences finding the value of n

Geometric Sequences and simultaneous equations

Geometric Sequences Geometric mean

Compound interest as a geometric sequence

Geometric series formula proof and example

Geometric series find the value of n

Regular deposits as a geometric series

Geometric Series Sum to Infinity and Zeno’s Paradox

Geometric series sum to infinity application

Geometric Series Sum to infinity writing recurring decimals as fractions