Mr. Valsa's Math Page
Home
AP Calculus AB
Course Intro
Unit 01: Limits & Continuity
>
1.1 Intro to Calculus
1.2 Defining Limits & Using Limit Notation
1.3 Estimating Limit Values from a Graph
1.4 Estimating Limit Values from a Table
1.5 Determining Limits Using Algebraic Properties
1.6 Determining Limits Using Algebraic Manipulation
1.7 Selecting Procedures for Determining Limits
1.8 Squeeze Theorem
1.9 Multiple Representations of Limits
1.10 Exploring Types of Discontinuities
1.11 Defining Continuity
1.12 Confirming Continuity over an Interval
1.13 Removing Discontinuity
1.14 Infinite Limits & Vertical Asymptotes
1.15 Connecting Limits at Infinity & Horizontal Asymptotes
1.16 Intermediate Values Theorem (IVT)
Unit 02: Intro to the Derivative
>
2.1 Defining Average & Instantaneous Rates of Change
2.2 Defining the Derivative of a Function
2.3 Estimating the Derivative at a Point
2.4 Determining When Derivatives Exist
2.5 Applying the Power Rule
2.6 Derivative Rules
2.7: Derivatives of sin, cos, e^x, ln(x)
2.8 Product Rule
2.9 Quotient Rule
2.10 Derivative of tan/cot/sec/csc
Unit 03: Advanced Differentiation
>
3.1 The Chain Rule
3.2 Implicit Differentiation
3.3 Inverse Function Derivatives
3.4 Inverse Trig Derivatives
3.5 Selecting Procedures for Calculating Derivatives
3.6 Higher Order Derivatives
Unit 04: Contextual Applications of Derivatives
>
4.1 The Meaning of the Derivative in Context
4.2 Straight Line Motion
4.3 Rates of Change in Applied Contexts
4.4 Introduction to Related Rates
4.5 Solving Related Rates Problems
4.6 Approximating Values using Linearization
4.7 L'Hospital's Rule
Unit 05: Analytical Applications
>
5.1 Using the Mean Values Theorem (MVT)
5.2 Extreme Values Theorem (EVT)
5.3 Determining where a function is increasing/decreasing
5.4 First derivative test for extrema
5.5 Candidates Test for Extreme Values
5.6 Determining Concavity of a Function
5.7 Second Derivative Test for Extrema
5.8 Sketching Functions & their Derivatives
5.9 Connecting a Function and it's 1st/2nd Derivative
5.10 Intro to Optimization Problems
5.11 Solving Optimization Problems
5.12 Exploring Implicit Relationships
Unit 06: Integration & Accumulation of Change
>
6.1 Exploring Accumulations of Change
6.2 Approximating Areas with Riemann Sums
6.3 Riemann Sums/Summation Notation/Definite Integrals Notation/
6.4 FTC (Fundamental Theorem of Calculus) & Accumulation
6.5 Interpreting the Behavior of Accumulation Functions
6.6 Applying Properties of Definite Integrals
6.7 FTC and Definite Integrals
6.8 Anti-Derivatives - Basic Rules & Notation
6.9 Integration Using Substitution
6.10 Integration by Long Division & Completing the Square
6.14 - Selecting Techniques of Anti-Differentiation
Unit 07: Differential Equations
>
7.1 Modeling Situations with Differential Equations
7.2 Verifying Solutions to Differential Equations
7.3 Sketching Slope Fields
7.4 Reasoning with Slope Fields
7.6 Finding General Solutions using Separation of Variables
7.7 Finding Particular Solutions using Initial Conditions
7.8 Exponential Models with Differential Equations
Unit 08: Applications of Integration
PreCalculus
Course Intro
Unit 01: Function Analysis
>
1.1 Set & Interval Notation
1.2 Function Review
1.3 Domain & Range
1.4 End Behavior & Extrema
1.5 Inc/Dec/Const
1.6 Symmetry
1.7 Function Transformations
1.8 Function Operations
1.9 Inverses
Unit 02: Polynomial & Rational Functions
>
2.1 Solving Polynomials
2.2 Classifying Polynomials
2.3 Complex Numbers
2.4 End Behavior
2.5 Writing Equations of Polynomials
2.6 Solving Rational Equations
2.7 Rational Inequalities
2.8 Types of Discontinuity
2.9 Graphing Rational Functions
Unit 03: Conic Sections
>
3.1 Intro to Conic Sections
3.2 Circles
3.3 Ellipses
3.4 Hyperbolas
3.5 Parabolas
Unit 04: Exponents & Logarithms
>
4.1 Exponents & Logarithms
4.2 Evaluating Logarithms
4.3 Solving Exponential & Log Equations
4.4 Growth & Decay Models
4.5 Properties of Logarithms
4.6 Graphing Exponentials
UNIT 05: Sequences & Series
>
5.1 Arithmetic & Geometric Sequences
5.2 Arithmetic Series
5.3 Finite Geometric Series
5.4 Infinite Geometric Series
5.6 Sigma Notation
5.7 Limits
Unit 06: Right Triangle Trigonometry
>
6.1 Right Angle Trigonometry
6.2 Applications of Trigonometry
6.3 Standard Position, Degrees, Radians
6.4 Coterminal & Reference Angles
6.5 Evaluating Trig Functions
6.6 The Unit Circle
6.7 Inverse Trig
6.8 Law of Sines/Cosines
Unit 06 Review Material
Unit 07: Graphing Trigonometric Functions
>
7.1 Graphing Basic Trig
7.2 Graphing Trig Functions
7.3 Trig Graphs w/ Phase Shifts
7.4 Writing Equations of Sine/Cosine Graphs
7.5 Modeling with Trig
Unit 07 Review Material
Unit 08: Trigonometric Identities
>
8.1 Complex Fractions
8.2 Simplifying Trig Expressionss
8.3 Verifying Identities
8.4 Sum & Difference Identities
8.5 Half & Double Angle Identities
8.6 Trigonometric Equations
Unit 08 Review Material
Unit 09: Polar Coordinates
Unit 10: Vectors
Unit 11: Intro to Calculus
Integrated Math 3
Course Intro
Unit 01: Analytic Geometry
>
1.1 Graphing Lines
1.2 Parallel & Perpendicular
1.3 Distance & Pythagorean Theorem
1.4 Classifying Quadrilaterals
Unit 02: Geometric Proofs & Modeling
>
2.1 Surface Area & Volume
2.2 Cross Sections
Unit 03: Circles & Parabolas
>
3.1 Circles Review
3.2 Arc Length & Sector Area
3.3 Writing & Graphing Circles
3.4 Completing the Square
3.5 Parabolas
Unit 04: Representing Functions
>
4.1 - Key Features
4-2 Even & Odd Symmetry
4.3 Graphing Review
4.4 Absolute Value Equations
4.5 Absolute Value Functions Cont.
4.6 Piecewise Functions
Unit 05: Trigonometry
>
5.0 Intro to Trig
5.1 Trig Applications
5.2 Degrees & Radians
5.3 Special Right Triangles
5.4 Evaluating Trig Functions
5.5 Reference Triangles
Unit 06: Graphing Trig
>
6.0 Intro to Trig Graphs
6.1 Vertical Shifts
6.2 Phase Shifts
6.3 Writing Trig Equations
Unit 07: Polynomial Functions
>
7.0 Operations & Classifying Polynomials
7.1 Factoring
7.2 Solving by Factoring
7.3 Solving Simultaneous Functions
7.4 Exploring Changes in Graphs
7.5 Key Features
7.6 End Behavior
7.7 Graphing Polynomials
7.8 Factor Theorem
Unit 07 Review Material
Unit 08: Rational Functions
>
8.0 Simplifying Rational Expressions
8.1 Adding/Subtracting Rational Expressions
8.2 Solving Rational Equations
8.3 Key Features
Unit 08 Review Material
Unit 09: Log & Exponential Functions
>
9.0 Exponent Rules
9.1 Common Bases
9.2 Uncommon Bases
9.3 Evaluating & Rewriting
9.4 Natural Logarithms
9.5 Inverses
9.6 Exponential Graphs
9.7 Transformations of Exponentials
9.8 Graphing Logarithms
9.9 Applications
Unit 09 Review Material
Unit 10: Inferential Statistics
>
10.0 Types of Studies
10.1 Sampling Methods
10.2 Sampling Technique Summary
10.3 Measures of Center
10.4 Histograms & Shape
10.5 Precision vs. Accuracy
10.6 Empirical Rule & Z-Scores
Unit 10 Review Material
Math Team
Contact
AP Review
Home
AP Calculus AB
Course Intro
Unit 01: Limits & Continuity
>
1.1 Intro to Calculus
1.2 Defining Limits & Using Limit Notation
1.3 Estimating Limit Values from a Graph
1.4 Estimating Limit Values from a Table
1.5 Determining Limits Using Algebraic Properties
1.6 Determining Limits Using Algebraic Manipulation
1.7 Selecting Procedures for Determining Limits
1.8 Squeeze Theorem
1.9 Multiple Representations of Limits
1.10 Exploring Types of Discontinuities
1.11 Defining Continuity
1.12 Confirming Continuity over an Interval
1.13 Removing Discontinuity
1.14 Infinite Limits & Vertical Asymptotes
1.15 Connecting Limits at Infinity & Horizontal Asymptotes
1.16 Intermediate Values Theorem (IVT)
Unit 02: Intro to the Derivative
>
2.1 Defining Average & Instantaneous Rates of Change
2.2 Defining the Derivative of a Function
2.3 Estimating the Derivative at a Point
2.4 Determining When Derivatives Exist
2.5 Applying the Power Rule
2.6 Derivative Rules
2.7: Derivatives of sin, cos, e^x, ln(x)
2.8 Product Rule
2.9 Quotient Rule
2.10 Derivative of tan/cot/sec/csc
Unit 03: Advanced Differentiation
>
3.1 The Chain Rule
3.2 Implicit Differentiation
3.3 Inverse Function Derivatives
3.4 Inverse Trig Derivatives
3.5 Selecting Procedures for Calculating Derivatives
3.6 Higher Order Derivatives
Unit 04: Contextual Applications of Derivatives
>
4.1 The Meaning of the Derivative in Context
4.2 Straight Line Motion
4.3 Rates of Change in Applied Contexts
4.4 Introduction to Related Rates
4.5 Solving Related Rates Problems
4.6 Approximating Values using Linearization
4.7 L'Hospital's Rule
Unit 05: Analytical Applications
>
5.1 Using the Mean Values Theorem (MVT)
5.2 Extreme Values Theorem (EVT)
5.3 Determining where a function is increasing/decreasing
5.4 First derivative test for extrema
5.5 Candidates Test for Extreme Values
5.6 Determining Concavity of a Function
5.7 Second Derivative Test for Extrema
5.8 Sketching Functions & their Derivatives
5.9 Connecting a Function and it's 1st/2nd Derivative
5.10 Intro to Optimization Problems
5.11 Solving Optimization Problems
5.12 Exploring Implicit Relationships
Unit 06: Integration & Accumulation of Change
>
6.1 Exploring Accumulations of Change
6.2 Approximating Areas with Riemann Sums
6.3 Riemann Sums/Summation Notation/Definite Integrals Notation/
6.4 FTC (Fundamental Theorem of Calculus) & Accumulation
6.5 Interpreting the Behavior of Accumulation Functions
6.6 Applying Properties of Definite Integrals
6.7 FTC and Definite Integrals
6.8 Anti-Derivatives - Basic Rules & Notation
6.9 Integration Using Substitution
6.10 Integration by Long Division & Completing the Square
6.14 - Selecting Techniques of Anti-Differentiation
Unit 07: Differential Equations
>
7.1 Modeling Situations with Differential Equations
7.2 Verifying Solutions to Differential Equations
7.3 Sketching Slope Fields
7.4 Reasoning with Slope Fields
7.6 Finding General Solutions using Separation of Variables
7.7 Finding Particular Solutions using Initial Conditions
7.8 Exponential Models with Differential Equations
Unit 08: Applications of Integration
PreCalculus
Course Intro
Unit 01: Function Analysis
>
1.1 Set & Interval Notation
1.2 Function Review
1.3 Domain & Range
1.4 End Behavior & Extrema
1.5 Inc/Dec/Const
1.6 Symmetry
1.7 Function Transformations
1.8 Function Operations
1.9 Inverses
Unit 02: Polynomial & Rational Functions
>
2.1 Solving Polynomials
2.2 Classifying Polynomials
2.3 Complex Numbers
2.4 End Behavior
2.5 Writing Equations of Polynomials
2.6 Solving Rational Equations
2.7 Rational Inequalities
2.8 Types of Discontinuity
2.9 Graphing Rational Functions
Unit 03: Conic Sections
>
3.1 Intro to Conic Sections
3.2 Circles
3.3 Ellipses
3.4 Hyperbolas
3.5 Parabolas
Unit 04: Exponents & Logarithms
>
4.1 Exponents & Logarithms
4.2 Evaluating Logarithms
4.3 Solving Exponential & Log Equations
4.4 Growth & Decay Models
4.5 Properties of Logarithms
4.6 Graphing Exponentials
UNIT 05: Sequences & Series
>
5.1 Arithmetic & Geometric Sequences
5.2 Arithmetic Series
5.3 Finite Geometric Series
5.4 Infinite Geometric Series
5.6 Sigma Notation
5.7 Limits
Unit 06: Right Triangle Trigonometry
>
6.1 Right Angle Trigonometry
6.2 Applications of Trigonometry
6.3 Standard Position, Degrees, Radians
6.4 Coterminal & Reference Angles
6.5 Evaluating Trig Functions
6.6 The Unit Circle
6.7 Inverse Trig
6.8 Law of Sines/Cosines
Unit 06 Review Material
Unit 07: Graphing Trigonometric Functions
>
7.1 Graphing Basic Trig
7.2 Graphing Trig Functions
7.3 Trig Graphs w/ Phase Shifts
7.4 Writing Equations of Sine/Cosine Graphs
7.5 Modeling with Trig
Unit 07 Review Material
Unit 08: Trigonometric Identities
>
8.1 Complex Fractions
8.2 Simplifying Trig Expressionss
8.3 Verifying Identities
8.4 Sum & Difference Identities
8.5 Half & Double Angle Identities
8.6 Trigonometric Equations
Unit 08 Review Material
Unit 09: Polar Coordinates
Unit 10: Vectors
Unit 11: Intro to Calculus
Integrated Math 3
Course Intro
Unit 01: Analytic Geometry
>
1.1 Graphing Lines
1.2 Parallel & Perpendicular
1.3 Distance & Pythagorean Theorem
1.4 Classifying Quadrilaterals
Unit 02: Geometric Proofs & Modeling
>
2.1 Surface Area & Volume
2.2 Cross Sections
Unit 03: Circles & Parabolas
>
3.1 Circles Review
3.2 Arc Length & Sector Area
3.3 Writing & Graphing Circles
3.4 Completing the Square
3.5 Parabolas
Unit 04: Representing Functions
>
4.1 - Key Features
4-2 Even & Odd Symmetry
4.3 Graphing Review
4.4 Absolute Value Equations
4.5 Absolute Value Functions Cont.
4.6 Piecewise Functions
Unit 05: Trigonometry
>
5.0 Intro to Trig
5.1 Trig Applications
5.2 Degrees & Radians
5.3 Special Right Triangles
5.4 Evaluating Trig Functions
5.5 Reference Triangles
Unit 06: Graphing Trig
>
6.0 Intro to Trig Graphs
6.1 Vertical Shifts
6.2 Phase Shifts
6.3 Writing Trig Equations
Unit 07: Polynomial Functions
>
7.0 Operations & Classifying Polynomials
7.1 Factoring
7.2 Solving by Factoring
7.3 Solving Simultaneous Functions
7.4 Exploring Changes in Graphs
7.5 Key Features
7.6 End Behavior
7.7 Graphing Polynomials
7.8 Factor Theorem
Unit 07 Review Material
Unit 08: Rational Functions
>
8.0 Simplifying Rational Expressions
8.1 Adding/Subtracting Rational Expressions
8.2 Solving Rational Equations
8.3 Key Features
Unit 08 Review Material
Unit 09: Log & Exponential Functions
>
9.0 Exponent Rules
9.1 Common Bases
9.2 Uncommon Bases
9.3 Evaluating & Rewriting
9.4 Natural Logarithms
9.5 Inverses
9.6 Exponential Graphs
9.7 Transformations of Exponentials
9.8 Graphing Logarithms
9.9 Applications
Unit 09 Review Material
Unit 10: Inferential Statistics
>
10.0 Types of Studies
10.1 Sampling Methods
10.2 Sampling Technique Summary
10.3 Measures of Center
10.4 Histograms & Shape
10.5 Precision vs. Accuracy
10.6 Empirical Rule & Z-Scores
Unit 10 Review Material
Math Team
Contact