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 = 3x3-5x2-4x+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
