### Functions and Relations

What Is The Maximal Domain Of A Function?

How to find the Domain & Range of a Parabola

How to find f(2a) in a Quadratic function & f(a+3) in a Piecewise Function

How to determine if the Composite Functions fog and gof exist

How To Sketch A Hybrid Function

How To Sketch An Absolute Value Function

How To Sketch Another Absolute Value Function

How To Find The Domain and Range of a Quadratic Function with a Restricted Domain

How To Find The Domain and Range of a Linear Function with a Restricted Domain

How To Find The Domain and Range of a Hybrid Function

### Linear Relations

How to find the gradient and y-intercept of a straight line parallel to another line passing through a point.

Find the equation of a line passing through a point and parallel to another line & when perpendicular to the other line.

### Families of Functions

How To Sketch A Truncus

How to sketch an absolute value graph of a Hyperbola

Example 1: How to find a b and c in a Hyperbola in one example. Example 2: how to find a and b when given two points that belong to the Hyperbola.

### Polynomials

How to find the Factors of a Polynomial without using Long Division.

3 examples on how to apply the Factor & Remainder Theorems

How To Sketch The Graphs Of 2 Different Types Of Cubic Functions That Have Stationary Points Of Inflection.

How To Sketch The Graphs Of 2 Cubic Functions – Each With A Restricted Domain.

How To Sketch The Graph Of A Cubic Function With A Restricted Domain – Without Using A Calculator.

How To Sketch The Graph Of The Cubic Function

y = (x -1)(x – 2)(x + 3).

How To Sketch The Graph Of The Cubic Function

y = x(x + 1)(x – 1).

How To Sketch The Graph Of The Cubic Function

y = 3x^{3}-5x^{2}-4x+4 without using your calculator.

How to solve a Cubic Equation for x when given one of the Factors of the Cubic.

How To Find The Value Of *k* When A Pair Of Quadratic Graphs Intersect At 2 Points.

### Logs and Exponentials

How To Find The Domain Of A Log Function So It’s Inverse Function Will Exist

How To Find The Value Of ‘a’ In The Domain So The Log Function Has An Inverse

How to find the Inverse of an Exponential function

How To Solve Four Log Equations & Two Exponential Equations Without A Calculator

How to solve a Log equation and an Exponential equation without the use of a calculator.

### Differentiation Basics

How to Differentiate an Algebraic Fraction with a Square Root in it

How to differentiate an Algebraic Fraction without using the Quotient Rule.

2 examples showing how to use the Chain Rule to find the derivative of a Trig function and a Quadratic function raised to a fractional power.

How to use the Product Rule

How to differentiate a Log Function and an Exponential Function using the Product Rule

### Applications of Differentiation

Applications of Differentiation – Max & Min Values.

How To Find The Maximum Area Of A Rectangle In A Parabola.

How To Find The Minimum Surface Area Of A Triangular Prism.

Find the rate at which the height of a cone is increasing as water fills it at a constant rate.

Find the rate of decrease of the height of water in a cone as water is draining from the cone at a certain rate.

How To Find The Nature Of The Stationary Points Of A Quartic Function Using Differentiation.

How To Find The Correct Statement About The Turning Points Of A Function That Has Had 3 Transformation Applied To It

How To Find a,b and c In A Cubic Equation That Has A Stationary Point At (2,15) And Is Also Passing Through A Given Point

How to find the value of ‘k’ in the equation of a Tangent to a Log Graph

#### Frankston High School SAC

Part 1: Find POI of 2 curves, find the Equation of the 2 Tangents at the POI & find the Acute Angle between the curves at the POI.

Part 2: Find an expression for the Area of the Quadrilateral, find the length of AB which is one side of the Quadrilateral which has an Area of 7 sq. units.

### Integration

How To Find The Area Under A Curve Using Rectangles.

### Exam Solutions