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Functions
MYP 4 & 5 - Unit Plans - Functions-Introduction
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 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
Using Technology for Functions
Finding Solutions of Equations
Finding solutions of equations
Test on Functions (Non-Calculator)
Test on Functions (Calculator)
Graphs of Functions
MYP 4 & 5 - Unit Plans - Functions-Graphs of Functions
Quadratic Functions Using Technology
Graphs of Quadratic Function
Cubic Functions Using Technology (Enrichment)
Graphs of Cubic Function
Graphs of Quartic Function
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
MYP 4 & 5 - Unit Plans - Functions-Composite Functions
Enrichment
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)
Reciprocal Functions
MYP 4 & 5 - Unit Plans - Functions-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
Parts of a reciprocal function
Parts of a Reciprocal Graph
Reciprocal Functions involving Simultaneous Equations
Functions involving Simultaneous Equations
Inverse Functions
MYP 4 & 5 - Unit Plans - Functions-Inverse Functions
Enrichment
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
MYP 4 & 5 - Unit Plans - Functions-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 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
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
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
MYP 4 & 5 - Unit Plans - Functions-Cubic Functions
Cubic Functions - Concept
Expansions to form cubic functions
Determining the x and y intercepts
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
MYP 4 & 5 - Unit Plans - 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
Parts of an Exponential Function
Solving Exponential Equations
Exponential Equations
Solving Exponential Functions Using Technology
Solving Exponential Equations using Technology
Problem Solving with Exponential Functions
Problem Solving with Exponential Functions
Logarithmic Function
MYP 4 & 5 - Unit Plans - Functions-Logarithmic Functions
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 (Enrichment)
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 Logarithmic Equations using Technology
Solving exponential equations using Logs
Solving Exponential Equations using Logs
Word Problems to solve Exponential Equations using Logs
Variation
MYP 4 & 5 - Unit Plans - Functions-Direct and Inverse 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
Trigonometry - Unit Circle
MYP 4 & 5 - Unit Plans - Functions-Trigonometry - Unit Circle
Enrichment
Concept of Unit Circle
Writing exact coordinates
Signs in quadrants
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
MYP 4 & 5 - Unit Plans - Functions-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
MYP 4 & 5 - Unit Plans - Functions-Transformations of Trigonometric Functions
Enrichment
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