Chapter 2: Graphs
IB Significant Figures and Scientific Notation
Rules for Significant Figures
Scientific Notation
2-2 Distance in the Plane
Distance Formula
Midpoint Formula
2-3 Equation of a Line
Equation of a Line Using Two Points
Standard Form of a Line
Finding Parallel Lines
Finding Perpendicular Lines
10-1 Systems of Linear Equations
Substitution
Elimination
Graphing
PlySmlt2
Chapter 3: Functions
3-1 Functions
12 Basic Functions (corny music video)
10 Basic Functions
3-2 Graphing Functions
Finding Domain and Range from Graphs
Increasing / Decreasing and Local Max / Min
Asymptotes
3-3 Transformations of Functions
Translations (Shifts)
Reflections
Vertical Dilations
Horizontal Dilations
3-4 Quadratic Functions
Graphing Quadratic Functions by Hand
Factoring Quadratic Equations
Using the Quadratic Formula
Using the Discriminant: Ex 1 Ex 2 Ex 3
Vertex Form and Completing the Square
3-5 Composition of Functions
Composing
Decomposing
3-6 Inverse Functions
The Basics
Finding the Inverse of a Function
Graphing Inverse Functions as Reflections
Chapter 4: Polynomial and Rational Functions
4-4 Rational Functions and Asymptotes
Vertical Asymptotes: Example 1 Example 2
Horizontal Asymptotes: Basics Further Detail
Graphing Rational Functions: Example 1 Example 2
Example 3 Example 4
IB Solving Rational Equations: GDC Word Problems
IB Solving Rational Equations: Analytical Methods
Example 1 Example 2 Example 3 Example 4
Chapter 5: Exponential and Logarithmic Functions
R-2 Exponents and Radicals
Applying the Rules of Exponents: Ex1 Ex2 Ex3
Roots and Fractional Exponents
Intro to Negative and Fractional Exponents
Examples with Negative Exponents: Ex1 Ex2 Ex3
Examples with Fractional Exponents: Ex1 Ex2 Ex3
5-1 Exponential Functions and Transformations
Features of exponential functions
Transformations of exponential functions: Part 1 Part 2
5-1 The Mathematics of Finance
Compound Interest - Annual
Compound Interest - Other Time Periods: Part 1 Part 2
Finding the Initial Principal
Finding an Interest Rate: Part 1 Part 2
Compound Interest - Continuous
5-2 Exponential Models
Exponential Growth Applications
Exponential Decay Applications
5-3a Logarithmic Functions
5-3b Logarithmic Properties
5-5a Equation Solving and Modeling: Inverses
5-5b Equation Solving and Modeling: Properties
Chapter 6: Trigonometric Functions
6-1 Angles and Their Measures
Unit Circle: Degrees
Unit Circle: Radians
Coterminal angles
Reference angles in degrees
Reference angles in radians
Radians and Degrees
IB Central Angles, Arcs, and Sector Area
Tutorial Examples
6-3 Solving Right Triangles [Special Right Triangles]
Basic Trigonometry: SohCahToa
Basic Trigonometry: 30-60-90
Basic Trigonometry: 45-45-90
Worked Examples
Worked Examples, including 30-60-90
Worked Examples, including 45-45-90
6-4 Properties of Trigonometric Functions
Signs of Trig Functions
Quadrant I Quadrant III
Quadrant II Quadrant IV
Trig Ratios of Special Triangles: Part 1 Part 2
Trig Values of 0 - 90 - 180 - 270
6-4 Graphs of Sine and Cosine
Graphing the Sine Function
Graphing the Cosine Function
Sine and Cosine from the Unit Circle
Properties of Periodic Functions
6-5 Transformations of Sine and Cosine Graphs
Intro to Trig Transformations
Amplitude and Vertical Shift
Period and Phase Shift
Writing equations of transformations #1
Writing equations of transformations #2
6-5 Graphing Sine and Cosine Transformations
Trig Transformations: Amplitude/Period [skip tangent]
Trig Transformations: Midline/Phase Shift 1 [skip tangent]
Trig Transformations: Midline/Phase Shift 2 [skip tangent]
IB Applications: Navigation
Intro to Bearings
Example 1 Example 2 Example 3
Example 4 Example 5
Off-course Captain Part 1 Part 2
IB Applications: Harmonic Motion
Intro to Harmonic Motion
Alien Meets Trig Step-by-Step Example
Sunrise/Sunset Example
Chapter 7: Trigonometric Identities
7-1 Basic Identities
Reciprocal and Pythagorean Identities
Basic: Fractions: Factoring:
Example 1 Example 1 Example 1
Example 2 Example 2 Example 2
Example 3
7-1 Verifying Trigonometric Identities
Cool example using manipulatives!
Example 1 Example 2 Example 3
Example 4 Example 5 Example 6
7-3 Double Angle Identities
Example 1 Example 2
Example 3 Example 4
7-5 Solving Trigonometric Equations by Hand
Example 1 Example 2
Example 3 Example 4
7-5 Solving Trigonometric Equations by Calculator
Chapter 8: Applications of Trigonometry
8-1 The Law of Sines
Proof of the Sine Rule
Finding Sides Finding Angles
Ambiguous Case Applications
8-2 The Law of Cosines
Finding a side Finding an angle
Word Problems: Example 1 Example 2 Example 3
IB Syllabus: The Area of Triangles
Example 1 Example 2
IB Applications: Navigation
Intro to Bearings
Example 1 Example 2 Example 3
Example 4 Example 5
Off-course Captain Part 1 Part 2
Fantastic review of all trig formulas
Chapter 11: Sequences and Series
11.1 Sequences and Series, Sigma Notation
Part 1
Part 2
Sigma Notation
11.3 Arithmetic Sequences and Series
Geometric Sequences and Series
Infinite Series
11.6 The Binomial Theorem
Part 1
Part 2
Part 3
Chapter P: Probability
P.1 What is Probability?
Introduction to Probability
Using lattice diagrams
Using Venn diagrams
Using tree diagrams
P.2 Independent and Dependent Events
Independent events
Dependent events
Examples of both
P.3 Basic Set Theory
Shading 2 sets: Example
Shading 3 sets: Example 1 Example 2
Word problems
P.4 Combined and Mutually Exclusive Events
A video on combined events
Addition Rule Example 1 Examples 2
P.5 Conditional Probability
Intro to conditional probability
Basic example Complicated example
P.6 Probability Distributions and Expected Value
Probability distributions and expected value
P.7 Binomial Probability
What is binomial probability?
Working with the binomial probability formula
Example 1 Example 2
Chapter S: Statistics
S.1 Frequency Tables and Histograms
How to create a histogram
S.2 Measures of Central Tendency: Mean, Median, and Mode
Central tendency: raw data
Raw data entry on the TI-84
Central tendency: grouped data
Mean of grouped data
Grouped data entry on the TI-84 - single values
Grouped data entry on the TI-84 - range of values
S.3 Measures of Dispersion:
Percentiles and quartiles
Box & whisker plots
Drawing a cumulative frequency diagram
Interpreting a cumulative frequency diagram
Example 1 Example 2
S.4 Measures of Variation: Variance and St. Deviation
What is the standard deviation?
Finding variance and standard deviation on the TI-84
Interpreting the standard deviation
S.5 The standard normal distribution
Random events lead to the normal distribution
Z-scores and the normal distribution: Part 1 Part 2
Calculating z-scores
S.6 Z-Scores and the Standard Normal Distrubution
Z-scores and Standard Normal
S.7 Probability and the Normal Distribution
Using the GDC Probability and Normal Distribution
S.8 Linear Correlation and Linear Regression
What is correlation?
Pearson's Correlation Coefficient
Intro to linear regression
Finding the regression equation and r on the GDC
S.9 Interpreting the Regression Equation
IB Significant Figures and Scientific Notation
Rules for Significant Figures
Scientific Notation
2-2 Distance in the Plane
Distance Formula
Midpoint Formula
2-3 Equation of a Line
Equation of a Line Using Two Points
Standard Form of a Line
Finding Parallel Lines
Finding Perpendicular Lines
10-1 Systems of Linear Equations
Substitution
Elimination
Graphing
PlySmlt2
Chapter 3: Functions
3-1 Functions
12 Basic Functions (corny music video)
10 Basic Functions
3-2 Graphing Functions
Finding Domain and Range from Graphs
Increasing / Decreasing and Local Max / Min
Asymptotes
3-3 Transformations of Functions
Translations (Shifts)
Reflections
Vertical Dilations
Horizontal Dilations
3-4 Quadratic Functions
Graphing Quadratic Functions by Hand
Factoring Quadratic Equations
Using the Quadratic Formula
Using the Discriminant: Ex 1 Ex 2 Ex 3
Vertex Form and Completing the Square
3-5 Composition of Functions
Composing
Decomposing
3-6 Inverse Functions
The Basics
Finding the Inverse of a Function
Graphing Inverse Functions as Reflections
Chapter 4: Polynomial and Rational Functions
4-4 Rational Functions and Asymptotes
Vertical Asymptotes: Example 1 Example 2
Horizontal Asymptotes: Basics Further Detail
Graphing Rational Functions: Example 1 Example 2
Example 3 Example 4
IB Solving Rational Equations: GDC Word Problems
IB Solving Rational Equations: Analytical Methods
Example 1 Example 2 Example 3 Example 4
Chapter 5: Exponential and Logarithmic Functions
R-2 Exponents and Radicals
Applying the Rules of Exponents: Ex1 Ex2 Ex3
Roots and Fractional Exponents
Intro to Negative and Fractional Exponents
Examples with Negative Exponents: Ex1 Ex2 Ex3
Examples with Fractional Exponents: Ex1 Ex2 Ex3
5-1 Exponential Functions and Transformations
Features of exponential functions
Transformations of exponential functions: Part 1 Part 2
5-1 The Mathematics of Finance
Compound Interest - Annual
Compound Interest - Other Time Periods: Part 1 Part 2
Finding the Initial Principal
Finding an Interest Rate: Part 1 Part 2
Compound Interest - Continuous
5-2 Exponential Models
Exponential Growth Applications
Exponential Decay Applications
5-3a Logarithmic Functions
5-3b Logarithmic Properties
5-5a Equation Solving and Modeling: Inverses
5-5b Equation Solving and Modeling: Properties
Chapter 6: Trigonometric Functions
6-1 Angles and Their Measures
Unit Circle: Degrees
Unit Circle: Radians
Coterminal angles
Reference angles in degrees
Reference angles in radians
Radians and Degrees
IB Central Angles, Arcs, and Sector Area
Tutorial Examples
6-3 Solving Right Triangles [Special Right Triangles]
Basic Trigonometry: SohCahToa
Basic Trigonometry: 30-60-90
Basic Trigonometry: 45-45-90
Worked Examples
Worked Examples, including 30-60-90
Worked Examples, including 45-45-90
6-4 Properties of Trigonometric Functions
Signs of Trig Functions
Quadrant I Quadrant III
Quadrant II Quadrant IV
Trig Ratios of Special Triangles: Part 1 Part 2
Trig Values of 0 - 90 - 180 - 270
6-4 Graphs of Sine and Cosine
Graphing the Sine Function
Graphing the Cosine Function
Sine and Cosine from the Unit Circle
Properties of Periodic Functions
6-5 Transformations of Sine and Cosine Graphs
Intro to Trig Transformations
Amplitude and Vertical Shift
Period and Phase Shift
Writing equations of transformations #1
Writing equations of transformations #2
6-5 Graphing Sine and Cosine Transformations
Trig Transformations: Amplitude/Period [skip tangent]
Trig Transformations: Midline/Phase Shift 1 [skip tangent]
Trig Transformations: Midline/Phase Shift 2 [skip tangent]
IB Applications: Navigation
Intro to Bearings
Example 1 Example 2 Example 3
Example 4 Example 5
Off-course Captain Part 1 Part 2
IB Applications: Harmonic Motion
Intro to Harmonic Motion
Alien Meets Trig Step-by-Step Example
Sunrise/Sunset Example
Chapter 7: Trigonometric Identities
7-1 Basic Identities
Reciprocal and Pythagorean Identities
Basic: Fractions: Factoring:
Example 1 Example 1 Example 1
Example 2 Example 2 Example 2
Example 3
7-1 Verifying Trigonometric Identities
Cool example using manipulatives!
Example 1 Example 2 Example 3
Example 4 Example 5 Example 6
7-3 Double Angle Identities
Example 1 Example 2
Example 3 Example 4
7-5 Solving Trigonometric Equations by Hand
Example 1 Example 2
Example 3 Example 4
7-5 Solving Trigonometric Equations by Calculator
Chapter 8: Applications of Trigonometry
8-1 The Law of Sines
Proof of the Sine Rule
Finding Sides Finding Angles
Ambiguous Case Applications
8-2 The Law of Cosines
Finding a side Finding an angle
Word Problems: Example 1 Example 2 Example 3
IB Syllabus: The Area of Triangles
Example 1 Example 2
IB Applications: Navigation
Intro to Bearings
Example 1 Example 2 Example 3
Example 4 Example 5
Off-course Captain Part 1 Part 2
Fantastic review of all trig formulas
Chapter 11: Sequences and Series
11.1 Sequences and Series, Sigma Notation
Part 1
Part 2
Sigma Notation
11.3 Arithmetic Sequences and Series
Geometric Sequences and Series
Infinite Series
11.6 The Binomial Theorem
Part 1
Part 2
Part 3
Chapter P: Probability
P.1 What is Probability?
Introduction to Probability
Using lattice diagrams
Using Venn diagrams
Using tree diagrams
P.2 Independent and Dependent Events
Independent events
Dependent events
Examples of both
P.3 Basic Set Theory
Shading 2 sets: Example
Shading 3 sets: Example 1 Example 2
Word problems
P.4 Combined and Mutually Exclusive Events
A video on combined events
Addition Rule Example 1 Examples 2
P.5 Conditional Probability
Intro to conditional probability
Basic example Complicated example
P.6 Probability Distributions and Expected Value
Probability distributions and expected value
P.7 Binomial Probability
What is binomial probability?
Working with the binomial probability formula
Example 1 Example 2
Chapter S: Statistics
S.1 Frequency Tables and Histograms
How to create a histogram
S.2 Measures of Central Tendency: Mean, Median, and Mode
Central tendency: raw data
Raw data entry on the TI-84
Central tendency: grouped data
Mean of grouped data
Grouped data entry on the TI-84 - single values
Grouped data entry on the TI-84 - range of values
S.3 Measures of Dispersion:
Percentiles and quartiles
Box & whisker plots
Drawing a cumulative frequency diagram
Interpreting a cumulative frequency diagram
Example 1 Example 2
S.4 Measures of Variation: Variance and St. Deviation
What is the standard deviation?
Finding variance and standard deviation on the TI-84
Interpreting the standard deviation
S.5 The standard normal distribution
Random events lead to the normal distribution
Z-scores and the normal distribution: Part 1 Part 2
Calculating z-scores
S.6 Z-Scores and the Standard Normal Distrubution
Z-scores and Standard Normal
S.7 Probability and the Normal Distribution
Using the GDC Probability and Normal Distribution
S.8 Linear Correlation and Linear Regression
What is correlation?
Pearson's Correlation Coefficient
Intro to linear regression
Finding the regression equation and r on the GDC
S.9 Interpreting the Regression Equation