Preview Functions

Coordinate Geometry

Distance between 2 points

Distances involving using unknowns or variables

Distance between 2 points – Using Variables

Using Unknowns

Equidistant Points

Equidistant points

Equidistant points from x/y axes

Identifying geometrical shapes

Proving Geometrical Shapes

Finding the Midpoint

Finding the midpoint when points are given

Finding the midpoint when points are in terms of variables

Finding the midpoint from the given diagram

Finding points from midpoint

Finding points when the midpoint is given

Application in parallelogram

Application - Parallelogram

Application in triangle

Application – Miscellaneous

Application for Centroid

Centroid

Test on Co-Ordinate Geometry (Non-Calculator)

Straight Lines

Gradient

Finding gradient from two points

Gradients - Finding the value of an unknown

Gradient from a Diagram

Finding the gradient of a line

Parallel and Perpendicular Gradients

Gradients of parallel and perpendicular lines

Involving Unknowns in the gradients of parallel and perpendicular lines

Collinear Points

Checking for Collinear Points

Determining Unknowns in Collinear points

Determining the Gradient and y-intercept

Determining the gradient and y-intercept

Determining the form

Determining the form – General or gradient-intercept

Determining the equation with gradient and y-intercept

Determining the equation of a line when the gradient and y-intercept are given

Determining the equation with gradient and x-intercept

Determining the equation of a line when the gradient and x-intercept/point are given

Determining the equation when two points are given

Determining the equation of a line when two points are given or a point and x/y-intercept are given

Determining x and y intercepts

Determining x & y intercepts

Finding the values of coordinates

Finding values of coordinates

Determining the equation from graphgiven points

Equation of a line – From a graph

Equation of a line from diagram (when the points are given)

Determining unknowns in parallel and perpendicular gradients

Parallel Gradients

Perpendicular Gradients

Combination of Parallel and Perpendicular Lines

Horizontal and Vertical Lines

Determining the equation of lines parallel/perpendicular to the axes

Equation of a Line with a point and determination of gradient

Drawing Graphs

Test on Straight Lines - I (Non-Calculator)

Test on Straight Lines - II (Non-Calculator)

Equations of Perpendicular Bisectors

Finding midpoint and slope of perpendicular

Finding the equation of the perpendicular bisector

Functions

Functions - An Introduction

Mapping Functions

Mapping functions

Types of Mapping Relations

Classification of mapping relationships

Concept of Domain and Range

Determining the Range

Determining the range

Using Graphs to Determine Domain and Range

Using Graphs to describe domain and range

Using Sets to Determine Domain and Range

Using Sets to determine domain and range

Classification of Functions

Classification of Functions – using sets

Classification of functions using vertical line test

Function Notation Using Constants and Variables

Function Notation using constants

Function Notation using Variables (Non GDC)

Finding the Range for a Given Domain

Finding the range for a particular domain of a function

Finding the Value of x for a given function

Finding the value of x for a given value of the function

Functions Involving Simultaneous Equations - 2 variables

Functions involving Simultaneous Equations – 2 variables

Functions Involving Simultaneous Equations - 3 variables

Functions involving Simultaneous Equations – 3 variables

Reading Values from a Graph

Reading values from a graph

Using Technology for Functions

Finding Solutions of Equations

Finding solutions of equations

Test on Functions (Non-Calculator)

Test on Functions (Calculator)

Graphs of Functions

Quadratic Functions Using Technology

Graphs of Quadratic Function

Cubic Functions Using Technology

Graphs of Cubic Function

Graphs of Quartic Function

Root Functions Using Technology

Graphs of Root Functions

Reciprocal Functions Using Technology

Graphs of Reciprocal Functions

Exponential Functions Using Technology

Graphs of Exponential Functions

Solving Equations Using Technology

Solving Graphs Using Technology

Application - Word Problems

Application – Word Problems

Composite Functions

Composite Functions - Using Constants and Variables

Composite Functions with constants (Non GDC)

Composite functions with Variables (Non GDC)

Composite Functions - Involving 3 Functions

Composite functions involving 3 functions – With Constants

Composite functions involving 3 functions – With Variables

Composite Functions - Choosing Appropriate Functions

Choosing appropriate functions

Test on Composite Functions (Non Calculator)

Absolute Value Functions

Concept of Absolute Value Functions

Absolute Value with Constants

Absolute Value with Constant and Variables

Absolute value with variables (Non GDC)

Solving Equations with Absolute Value

Solving equations with absolute value (Non GDC)

Graphs of Absolute Value Functions

Drawing Graphs of Absolute Value Functions

Drawing Graph of Absolute Value Functions

Determining Equation & Line of Symmetry

Determining the equation of the function

Determining line of symmetry

Test on Absolute Value Functions (Non Calculator)

Reciprocal Functions

Concept of reciprocal functions

Function Notation using constants & Variables

Function Notation using constants

Function Notation using Variables (Non GDC)

Composite reciprocal functions

Composite Functions

Determining the equation of the reciprocal function

Determine the equation of the reciprocal function

Concept of coming close to zero and infinity

Asymptotes with linear functions in the denominator

Determine the equations of the asymptotes – Linear function in denominator

Asymptotes with Quadratic functions in the denominator

Determine the equations of the asymptotes – Quadratic function in denominator

Asymptotes with linear/Quadratic functions in the numerator & denominator

Determine the equations of the asymptotes – Linear/Quadratic function in numerator and denominator

Finding Asymptotes with constant term added to the reciprocal function

Determine the equations of the asymptotes – Adding constant to the reciprocal function

Concept of oblique asymptote

Oblique Asymptote

Determining the domain and range of reciprocal functions

Determining domain and range of reciprocal functions

Finding the range for a restricted domain of a reciprocal function

Finding the range for a particular domain of a function

Parts of a reciprocal function

Parts of a Reciprocal Graph

Reciprocal Functions involving Simultaneous Equations

Functions involving Simultaneous Equations

Root Functions

Root functions - using constants & variables

Function Notation using constants

Function Notation using Variables (Non GDC)

Finding the value of 'x' for a root function

Finding the value of x for a given value of the function

Composite Root Functions

Composite Functions

Determining domain and range for a root function (using graphs)

Using Graphs to describe domain and range

Finding range of a root funciton for a restricted domain

Finding the range for a particular domain of a function

Root function involving simultaneous equations with 2 variables

Functions involving Simultaneous Equations – 2 variables

Root function involving simultaneous equations with 3 variables

Functions involving Simultaneous Equations – 3 variables

Using technology for root functions

Using Technology for Functions

Inverse Functions

Concept of inverse functions

Finding the coordinates of the inverse function

Determining the possibility of having an inverse function

Determining the possibility of an inverse function

Identifying the inverse graph

Domain and range of an inverse function

Domain and Range of inverse

Reading values from a graph for an inverse function

Reading values from a graph

Finding the inverse of a Function algebraically

Finding the inverse algebraically

Finding the inverse algebraically for a root function

Finding the inverse algebraically (Root Functions)

Test on Inverse Functions (Non Calculator)

Quadratic Functions

Concept of Quadratic Functions

Checking for quadratic functions (Non- GDC)

Finding the value of y when x is given

Finding the value of y, when x is given

Plotting a Quadratic Function

Finding the value of x when y is given

Finding the value(s) of x, Finding the value(s) of x, when y is given

Determining whether a point lies on a lie & finding missing points

Determining whether a point lies on the function

Finding Missing points/ Unknowns

Determining the x and y intercepts

Determine the y-intercept

Determine the x-intercept

Determining the real roots

Determining the real roots (zeros)

Predicting the shape of a quadratic function

Predicting the shape (Non GDC)

Axis of Symmetry using x-intercepts

Axis of Symmetry (using x – intercepts)

Determining x-intercept when axis of symmetry is given

Determining Axis of Symmetry from equation

Axis of Symmetry – From Equation

Finding Variables from Axis of Symmetry

Determining the Coordinates of the Vertex

Vertex

Changing from General Form to Vertex Form

Changing from general form to vertex form

Parts of a Quadratic Function

Determination of Equation of a Quadratic Function

Determining the Equation of the Function – x –intercepts and another point

Determination of Equation of a Quadratic Function when Coordinates are given

Determining the Equation of the Function when Coordinates are given

Determination of Equation of a Quadratic Function when Vertex and point are given

Determining the Equation of the Function when Vertex and a Point are given

Determination of Equation of a Quadratic Function from Graph

Determining the Equation of the Function from the Graph

Finding Points of Intersection Using Technology

Finding Points of Intersection – Using Technology

Word Problems on Quadratic Functions

Word Problems - Quadratic Functions

Cubic Functions

Cubic Functions - Concept

Expansions to form cubic functions

Determining the x and y intercepts

Determining Cubic Function from Graph

Determining the cubic function from graph

Determine the graph for the given cubic function

Determining the Equation of the Cubic Function

Determining the equation of the cubic function

Using Unknowns in Cubic Functions

Finding unknowns

Using Technology in Cubic Functions

Using Technology - Parts of a Cubic Function

Word Problems in Cubic Functions

Word Problems - Cubic Functions

Exponential Functions

Fractional Powers with Constants and Variables

Fractional Powers with Constants

Fractional Power with Variables

Exponential Functions - Concept and Finding the Value

Checking for Exponential Functions

Finding the value of the Exponential Functions

Finding x for a particular value of a function

Finding the value of x for a given value of the function

Graphs of Exponential Functions

Graphs of Exponential Functions (y = ax)

Graphs Involving Vertical Translation

Graphs of Exponential Functions Involving Vertical Translation

Exponential Functions Involving Scale Factors

Involving Scale Factors

Graphs Involving Horizontal Translation

Horizontal Translation

Exponential Functions Involving Reflections

Involving Reflections

Finding Unknowns in Exponential Functions

Finding unknowns in exponential functions

Parts of an Exponential Function

Solving Exponential Equations

Exponential Equations

Solving Exponential Functions Using Technology

Solving Exponential Equations using Technology

Inverse of an Exponential Function

Inverse of Exponential Functions

Domain and Range of Exponential Functions

Problem Solving with Exponential Functions

Finding the Power of a Model

Determine the Equation of the Model (Power Models)

Logarithmic Function

Introduction

Convert Exponential Statements to log statements

Converting Exponential statements to logarithmic expressions (using constant values) (Non GDC)

Converting Exponential statements to logarithmic expressions (using variable values) (Non GDC)

Convert Log Statements to Exponential statements

Converting logarithmic expressions to exponential statement (using constant values) (Non GDC)

Converting logarithmic expressions to exponential statement (using variable values) (Non GDC)

Finding values of log statements

Finding logarithmic values without a calculator (whole numbers) (Non GDC)

Finding logarithmic values without a calculator (surds/decimals/fractions) (Non GDC)

Changing subject of formula in log statements

Making x the subject of formula in logarithmic or exponential expressions (Non GDC)

Solving for the unknown value in log statements

Solving for the unknown value (Non GDC)

Finding Approximate values

Finding Values and Approx Values (Non GDC)

Using the Calculator for Log Statements

Using GDC for different expressions (GDC)

Logarithmic Functions

Concept of Inverse of a log function

Inverse of a log function

Inverse of Logarithmic Function

Domain & Range of a Logarithmic Function

Domain and Range of Logarithmic Functions

Parts of a logarithmic Function

Parts of Logarithmic Functions

Laws of Logarithms

Product Law

Laws of Logarithms – Product Law

Quotient Law

Laws of Logarithms – Quotient Law

Power Law

Laws of Logarithms – Power Law

Combination of Logarithmic Law

Laws of Logarithms – Combined

Writing statements without logs

Laws of Logs involving equations

Laws of Logarithms – Involving Equations

Laws of logs involving change of subject

Laws of Logarithms – Making y the subject

Laws of logs involving variables

Laws of Logarithms – Writing in terms of Variables

Simplification of logarithmic expressions

Simplification

Exponential statement to log statement & vice-versa

Writing an Exponential Statement as a Logarithmic Equation

Writing an Logarithmic Statements as an Exponential Equation

Logarithms involving substitutions

Involving Substitutions

Solving Logarithmic Equations using Technology

Solving exponential equations using Logs

Solving Exponential Equations using Logs

Word Problems to solve Exponential Equations using Logs

Variation

Variation - Concept

Concept

Word Problems on Variation

Direct Variation

Inverse Variation

Powers in direct variation

Powers in Direct Variation

Powers in Direct Variation – Word Problems

Powers in Inverse variation

Powers in Indirect Variation

Powers in Indirect Variation – Word Problems

Powers in Direct & Inverse variation involving Changes

Powers in Direct and Inverse Variation

Percentage changes in direct & inverse variation

Powers in Direct and Inverse Variation involving Percentage Change

Power Model in Variation

Power Model

Trigonometry - Unit Circle

Concept of Unit Circle

Writing exact coordinates

Signs in quadrants

Missing values involving sin x

Finding missing value – involving sin θ

Missing values involving Cos x

Finding missing value - involving cos θ

Finding missing angle – involving negative values of cos θ

Missing values involving Tan x

Finding missing value - involving tan θ

Values of Standard Angles

Finding value of standard angles

Remembering Values of Standard Angles

Operations on Values of Standard Angles

Operations on values of standard angles

Relation between sin and cos

Relation between sin θ and cos θ

Value of Standard Angles Using Unit Circle

Finding value of standard angles using a unit circle

Values of Standard angles involving squares

Finding values of standard angles (involving squares)

Missing value of x

Finding missing value of x (from 90° to 360°)

Exact value of non-standard angles

Finding the exact value (Non-standard angles)

Values of other angles

Find the value of other angles using the unit circle (sin)

Find the value of other angles using the unit circle (cos)

Find the value of other angles using the unit circle (tan)

Graphs of Trigonometric Functions

Sine Curve

Graph of Sine Curve – Maximum, Minimum and zero

Using trigonometric equation of sin x to find other values of x (Non GDC, using graph)

Using trigonometric equation of sin x to find other values of x (With GDC)

Cosine Curve

Graph of Cosine Curve – Maximum, Minimum and zero (Non GDC)

Using trigonometric equation of cos x to find other values of x (Non GDC)

Using trigonometric equation of cos x to find other values of x (With GDC)

Tan Curve

Graph of Tan Curve - Maximum, Minimum and zero (Non GDC)

Using trigonometric equation of tan x to find other values of x (Non GDC)

Using trigonometric equation of tan x to find other values of x (With GDC)

Combination

Combination of trigonometric curves (With GDC)

Combination of trigonometric functions and other functions

Inequalities in trigonometric curves

Transformation of Trigonometric Functions

Identify the value of the amplitude from graph/equation

Identify the period from the equation

Identify the period from the graph

Determine the value of the principal axis from the equation

Determine the value of the principal axis from the graph

Identify the unknowns a, b, d from the graph (With form given)

Identify the type of graph and the unknowns a, b, d

Using Technology to find the value of x (screenshot needed)

Using Technology to find the value of x

Preview - Functions