## MA-F2 Graphing Techniques

Function Transformations intro

Functions Transformation fx+a

Function transformation f(x+a)

Function transformation afx

Functions transformations f(ax)

Equations of hyperbola and sketching

Finding equation of reciprocal function from sketch

Sketching Hyperbolas and why there's an asymptote

Exponential Functions Basic shape and Translations

Exponential Functions Dilations

Exponential functions 2 Sketching

Exponential functions sketching part 2

Exponential functions 3 Finding equation from a sketch

Exponential Model and Applications

Logarithmic functions Basic shape

Logarithmic functions Sketching

Finding equations of log functions

Exponential and logarithmic modelling

Absolute Value Functions

Sketch Absolute Value Functions with a vertical shift

Sketching an absolute value function worked example

Reflecting Functions in the y axis using absolute value functions

## MA-T3 Trigonometric Functions & Graphs

The unit circle solving unknown angles

Solving Simple Trig Equations Worksheet (worksheet in Description)

The unit circle solving unknowns in trig equations

Solving trig identity equations using quadratics

Solving trig identity equations using quadratics part 2

Sketching SinX and CosX

Sketching y = AsinX and AcosX

Sketching y = AsinX +D and AcosX + D

Sketching y = AsinBx + D or y = AcosBx +D

Sketching y = AsinB(x+C)+D

Finding the equation of a periodic function from a graph or sketch

Revision of radians and the unit circle

Solving Trig equations The Tricky 3 Quantum of Quadratics

Solving Trig equations The Tricky 3 Square or Die

Solving Trig equations The Tricky 3 Domain Domination

Sketching f(x) = tan(x) and why it looks like that.

## MA-C2 Differential Calculus

Derivatives of Exponential, Logarithmic and Trigonmetric functions

The chain rule revisited

The Product Rule Revisited

The quotient rule

## MA-C3 Applications of Differentiation

Finding Stationary points

Nature of Stationary points

Optimisation when the function is unknown

Introduction to Kinematics

Finding the equation of a tangent

Finding the equation of a normal

Equations of tangents and normals revisited

Rates of change application

Motion in a straight line An application of rates

Motion in a straight line acceleration recap

Concave up and Concave down Part 1: 2 useful definitions

Concave up and Concave Down Part 2 A more useful definition

Concavity and the second derivative

Points of Inflection and the 2nd derivative

The 2nd Derivative test

Sketching Functions with the second derivative and Points of Inflection

Introduction to Kinematics

Applications of Integration in motion questions

Optimisation when the function is unknown

## MA-C4 Integral Calculus

Intro to Integration and integrating polynomials

Integration a little bit of theory

Integration finding the c value

Integration the reverse chain rule

Integration resulting in a logarithm

Integrals of exponentials

Integration of trig functions

Integration by recognition updated

Applications of Integration in motion questions

The definite integral

The definite integral signed area

Area between two curves

The area under a derivative function

Trapezoidal Rule Fully explained

## MA-M1 Modelling Financial Situations

#### – M1.1:Modelling Investments & Loans

TVM mode on Graphics calculator

Compound interest Appreciation

The Time Value of Money

Home Loan Calculations with Graphics Calculator – Finding Repayments

Home Loan Calculations with Graphics Calculator – Finding unknowns

Compound interest different compounding periods

Compound interest introduction

Compound interest formula

Borrowing money intro

Home loans finding amount still owing

Home loans finding the payment and the total interest paid

Compound interest revision

Geometric Series

Geometric sequences

Present and future value intro

Present and future value problems

Linking annuities to geometric series

Finding the future value of an ordinary annuity

Finding the value of an ordinary annuity using graphics calculator

Present value of an ordinary annuity

Future value of annuity due

Present value of an annuity due

Finding repayments using annuities

Home loans finding the payment and the total interest paid

Home loans finding amount still owing

Calculating present value of a home loan

Solving annuities using your classpad

#### – M1.2 Arithmetic Sequences & 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

#### – M1.3 Geometric Sequences & 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

#### – M1.4 Financial Applications of Sequences & Series

Simple Interest using arithmetic sequences

Compound interest revision

Compound interest as a geometric sequence

Regular deposits as a geometric series

Linking annuities to geometric series

Present and future value intro

Finding the future value of an ordinary annuity

Present value of an ordinary annuity

Present and future value problems

Home loans finding the payment and the total interest paid

Home loans finding amount still owing

Calculating present value of a home loan

Finding repayments using annuities

## MA-S2 Descriptive Statistics & Bivariate Data Analysis

#### -S2.1 Data (grouped & ungrouped) & Summary Statistics

Statistics – Types of Data

Statistics column graph

Frequency histogram class intervals

Statistics Frequency Histogram

Statistics Frequency Polygon

Back to Back stem and Leaf plot

Measures of central tendency Mean, Median & Mode

Measures of spread Range and Interquartile range

Five Number Summary

preparing a boxplot

Comparing boxplots

#### S2.2 Bivariate Data Analysis

Scatterplots Displaying bivariate numerical data

Using two way tables to investigate associations between categorical variables

Introduction to Bivariate data and explanatory and response variables

Interpreting Scatterplots: Association, Strength & Outliers

Correlation Coefficient: Pearson's r

Calculating correlation coefficient Pearson's r using Casio Scientific Calculator

R Squared: Calculating and Interpreting The Coefficient of Determination

## MA-S3 Random Variables

#### – S3.1 Continuous Random Variables

Estimating probability of a continuous random variable using data

The probability Density Function

Mathematical proof that you do not exist

Calculating probability using a probability density function

Proving a function is a probability density function

unknowns in probability density functions

Unbounded Probability density functions

The mean of a continuous random variable

The Cumulative Probability Distribution Function

Calculating variance and standard deviation of a continuous random variable

Calculating percentiles from a probability density function

#### – S3.2 The Normal Distribution

The normal distribution Introduction

Determining normal probabilities on the casio fx cg50AU

The Inverse Normal Distribution on the Casio FX CG50AU

A tricky normal distribution question

The Normal Approximation to the binomial distribution

Using z scores to standardise and compare values