Math AP
912
Course Outline
Honors Algebra:
Course Overview:
High School Honors Algebra I prepares students for more advanced courses while they develop algebraic fluency; learn the skills needed to solve equations; and perform manipulations with numbers, variables, equations, and inequalities. They also learn concepts central to the abstraction and generalization that algebra makes possible. Students learn to use number properties to simplify expressions or justify statements; describe sets with set notation and find the union and intersection of sets; simplify and evaluate expressions involving variables, fractions, exponents, and radicals; work with integers, rational numbers, and irrational numbers; and graph and solve equations, inequalities, and systems of equations. They learn to determine whether a relation is a function and how to describe its domain and range; use factoring, formulas, and other techniques to solve quadratic and other polynomial equations; formulate and evaluate valid mathematical arguments using various types of reasoning; and translate word problems into mathematical equations and then use the equations to solve the original problems. The course is expanded with more challenging assessments, optional exercises, and threaded discussions that allow students to explore and connect algebraic concepts. There is also an independent honors project each semester.
Course Outline:
SEMESTER 1
Honors Algebra I A, Unit 1: Algebra Basics
The English word algebra and the Spanish word algebrista both come from the Arabic word aljabr, which means “restoration.” A barber in medieval times often called himself an algebrista. The algebrista also was a bonesetter who restored or fixed bones. Mathematicians today use algebra to solve problems.

Semester Introduction

Expressions

Variables

Translating Words into Variable Expressions

Equations

Translating Words into Equations

Replacement Sets

Problem Solving

Unit Review

Unit Test
Honors Algebra I A, Unit 2: Properties of Real Numbers
Every rainbow contains the colors red, orange, yellow, green, blue, indigo, and violet. These seven colors form a set with properties that scientists, engineers, and artists use every day. Numbers can also be grouped into sets, and these number sets have properties that can help solve problems.

Number Lines

Sets

Comparing Expressions

Number Properties

Distributive Property

Algebraic Proof

Opposites and Absolute Value

Unit Review

Unit Test
Honors Algebra I A, Unit 3: Operations with Real Numbers
There are many different types of numbers. Negative numbers, positive numbers, integers, fractions, and decimals are just a few of the many groups of numbers. What do these varieties of numbers have in common? They all obey the rules of arithmetic. They can be added, subtracted, multiplied, and divided.

Addition 1

Addition 2

Subtraction

Multiplication

Reciprocals and Division

Applications: Number Problems

Unit Review

Unit Test
Honors Algebra I A, Unit 4: Solving Equations
The Greek mathematician Diophantus is often called “the father of algebra.” His book Arithmetica described the solutions to 130 problems. He did not discover all these solutions himself, but he did collect many solutions that had been found by Greeks, Egyptians, and Babylonians before him. Some people of long ago obviously enjoyed doing algebra. It also helped them solve many realworld problems.

Addition and Subtraction Equations

Multiplication and Division Equations 1

Multiplication and Division Equations 2

Multiple Transformations

Variables on Both Sides of an Equation

Transforming Formulas

Estimating Solutions

Cost Problems

Unit Review

Unit Test
Honors Algebra I A, Unit 5: Solving Inequalities
Every mathematician knows that 5 is less than 7, but when is y < x? An inequality symbol can be used to describe how one number compares to another. It can also indicate a relationship between values.

Inequalities

Solving Inequalities

Combined Inequalities

Absolute Value Equations and Inequalities

Applications: Inequalities

Unit Review

Unit Test
Honors Algebra I A, Unit 6: Applying Fractions
What do a scale drawing, a bicycle’s gears, and a sale at the local store all have in common? They all present problems that can be solved using equations with fractions.

Ratios

Proportions

Percents

Applications: Percents

Applications: Mixture Problems

Unit Review

Unit Test
Honors Algebra I A, Unit 7: Linear Equations and Inequalities
You have probably heard the phrase, “That’s where I draw the line!” In algebra, this expression can be taken literally. Linear functions and their graphs play an important role in the neverending quest to model the real world.

Graphs

Equations in Two Variables

Lines and Intercepts

Slope

SlopeIntercept Form

PointSlope Form

Parallel and Perpendicular Lines

Equations from Graphs

Applications: Linear Models

Graphing Linear Inequalities

Inequalities from Graphs

Unit Review

Unit Test
Honors Algebra I A, Unit 8: Systems of Equations
When two people meet, they often shake hands or say “hello” to each other. Once they start talking to each other, they can find out what they have in common. What happens when two lines meet? Do they say anything? Probably not, but whenever two lines meet, they have at least one point in common. Finding the point at which they meet can help solve problems in the real world.

Systems of Equations

Substitution Method

Linear Combination

Linear Combination with Multiplication

Applications: Systems of Linear Equations

Systems of Linear Inequalities

Unit Review

Unit Test
Honors Algebra I A, Unit 9: Semester Review and Test

Semester Review

Semester Test
Honors Project: Profession Using Algebra

Project Proposal

Project Outline

Project Paper
SEMESTER 2
Honors Algebra I B, Unit 1: Relations and Functions
A solar cell is a little machine that takes in solar energy and puts out electricity. A mathematical function is a machine that takes in a number as an input and produces another number as an output. There are many kinds of functions. Some have graphs that look like lines, while others have graphs that curve like a parabola. Functions can take other forms as well. Not every function has a graph that looks like a line or a parabola. Not every function has an equation. The important thing to remember is that any valid input into a function, results in a single result out of it.

Semester Introduction

Relations

Functions

Function Equations 1

Function Equations 2

Absolute Value Functions

Direct Linear Variation 1

Direct Linear Variation 2

Quadratic Variation

Inverse Variation

Translating Functions

Unit Review

Unit Test
Honors Algebra I B, Unit 2: Rationals, Irrationals, and Radicals
Are rational numbers very levelheaded? Are irrational numbers hard to reason with? Not really, but rational and irrational numbers have things in common and things that make them different.

Rational Numbers

Terminating and Repeating Numbers

Square Roots

Irrational Numbers

Evaluating and Estimating Square Roots 1

Evaluating and Estimating Square Roots 2

Radicals with Variables 1

Radicals with Variables 2

Using Square Roots to Solve Equations

The Pythagorean Theorem

Higher Roots

Unit Review

Unit Test
Honors Algebra I B, Unit 3: Working with Polynomials
Just as a train is built from linking railcars together, a polynomial is built by bringing terms together and linking them with plus or minus signs. You can perform basic operations on polynomials that work in the same way as when you are adding, subtracting, multiplying, and dividing numbers.

Overview of Polynomials

Adding and Subtracting Polynomials

Multiplying Monomials

Multiplying Polynomials by Monomials

Multiplying Polynomials

The FOIL Method

Unit Review

Unit Test
Honors Algebra I B, Unit 4: Factoring Polynomials
A polynomial is an expression that has variables that represent numbers. A number can be factored, so you should be able to factor a polynomial, right? Sometimes yes and sometimes no. Finding ways to write a polynomial as a product of factors can be quite useful.

Factoring Integers

Properties of Exponents

Dividing Monomials

Dividing Polynomials by Monomials

Common Factors of Polynomials

Factoring Perfect Squares

Factoring Differences of Squares

Factoring Quadratic Trinomials 1

Factoring Quadratic Trinomials 2

Factoring Completely

Finding Roots of a Polynomial

Unit Review

Unit Test
Honors Algebra I B, Unit 5: Quadratic Equations
Solving equations can help answer many kinds of problems. Linear equations usually have one solution, but what about quadratic equations? How many solutions can a quadratic equation have and what do the solutions look like?

Solving Perfect Square Equations

Completing the Square

The Quadratic Formula

The Discriminant

Solving Quadratic Equations

Equations and Graphs: Roots and Intercepts

Applications: Area Problems

Applications: Projectile Motion

Unit Review

Unit Test
Honors Algebra I B, Unit 6: Rational Expressions
A fraction always has a number in the numerator and in the denominator. However, those numbers can be expressions that represent numbers, which means that all sorts of interesting things can happen with fractions. Fractions with variable expressions in the numerator and denominator can help solve many kinds of problems.

Simplifying Rational Expressions

Multiplying Rational Expressions

Dividing Rational Expressions

Adding and Subtracting Rational Expressions 1

Adding and Subtracting Rational Expressions 2

Unit Review

Unit Test
Honors Algebra I B, Unit 7: Logic and Reasoning
Professionals use logical reasoning in a variety of ways. Just as lawyers use logical reasoning to formulate convincing arguments, mathematicians use logical reasoning to formulate and prove theorems.

Hypothesis and Conclusion

Reasoning and Arguments

Forms of Conditional Statements

Inductive and Deductive Reasoning

Analyzing and Writing Proofs

Counterexample

Unit Review

Unit Test
Honors Algebra I B, Unit 8: Semester Review and Test

Semester Review

Semester Test
Honors Project: Sport or Pastime Using Algebra

Project Proposal

Project Outline

Project Paper
Honors Geometry:
Course Overview:
Students learn to recognize and work with geometric concepts in various contexts. They build on ideas of inductive and deductive reasoning, logic, concepts, and techniques of Euclidean plane and solid geometry and develop an understanding of mathematical structure, method, and applications of Euclidean plane and solid geometry. Students use visualizations, spatial reasoning, and geometric modeling to solve problems. Topics of study include points, lines, and angles; triangles; right triangles; quadrilaterals and other polygons; circles; coordinate geometry; threedimensional solids; geometric constructions; symmetry; the use of transformations; and nonEuclidean geometries.
This course includes all the topics in Geometry but has more challenging assignments and includes more optional challenge activities. Each semester also includes an independent honors project.
Course Outline:
SEMESTER ONE
Unit 1: An Introduction
Even the longest journey begins with a single step. Any journey into the world of geometry begins with the basics. Points, lines, segments, and angles are the foundation of geometric reasoning. This unit provides students with basic footing that will lead to an understanding of geometry.

Semester Introduction

Basic Geometric Terms and Definitions

Measuring Length

Measuring Angles

Bisectors and Line Relationships

Relationships between Triangles and Circles

Transformations

Using Algebra to Describe Geometry
Unit 2: Methods of Proof and Logic
Professionals use logical reasoning in a variety of ways. Just as lawyers use logical reasoning to formulate convincing arguments, mathematicians use logical reasoning to formulate and prove theorems. With definitions, assumptions, and previously proven theorems, mathematicians discover and prove new theorems. It is like building a defense, one argument at a time. In this unit, students will learn how to build a defense from postulates, theorems, and sound reasoning.

Reasoning, Arguments, and Proof

Conditional Statements

Compound Statements and Indirect Proof

Definitions and Biconditionals

Algebraic Logic

Inductive and Deductive Reasoning
Unit 3: Polygon Basics
You can find polygons in many places: artwork, sporting events, architecture, and even in roads. In this unit, students will discover symmetry, work with special quadrilaterals, and work with parallel lines and slopes.

Polygons and Symmetry

Quadrilaterals and Their Properties

Parallel Lines and Transversals

Converses of Parallel Line Properties

The Triangle Sum Theorem

Angles in Polygons

Midsegments

Slope
Unit 4: Congruent Polygons and Special Quadrilaterals
If two algebraic expressions are equivalent, they represent the same value. What about geometric shapes? What does it mean for two figures to be equivalent? A pair of figures can be congruent the same way that a pair of algebraic expressions can be equivalent. You will learn, use, and prove theorems about congruent geometric figures.

Congruent Polygons and Their Corresponding Parts

Triangle Congruence: SSS, SAS, and ASA

Isosceles Triangles and Corresponding Parts

Triangle Congruence: AAS and HL

Using Triangles to Understand Quadrilaterals

Types of Quadrilaterals

Constructions with Polygons

The Triangle Inequality Theorem
Unit 5: Perimeter, Area, and Right Triangles
If we have a figure, we can take many measurements and calculations. We can measure or calculate the distance around the figure (the perimeter or circumference), as well as the figure's height and area. Even if we have just a set of points, we can measure or calculate the distance between two points.

Perimeter and Area

Areas of Triangles and Quadrilaterals

Circumference and Area of Circles

The Pythagorean Theorem

Areas of Special Triangles and Regular Polygons

Using the Distance Formula

Proofs and Coordinate Geometry
Unit 6: Semester Review and Test

Semester Review

Semester Test
SEMESTER TWO
Unit 1: ThreeDimensional Figures and Graphs
Onedimensional figures, such as line segments, have length. Twodimensional figures, such as circles, have area. Objects we touch and feel in the real world are threedimensional; they have volume.

Semester Introduction

Solid Shapes and ThreeDimensional Drawing

Lines, Planes, and Polyhedra

Prisms

Coordinates in Three Dimensions

Equations of Lines and Planes in Space
Unit 2: Surface Area and Volume
Every threedimensional figure has surface area and volume. Some figures are more common and useful than others. Students probably see pyramids, prisms, cylinders, cones, and spheres every day. In this unit, students will learn how to calculate the surface area and volume of several common and useful threedimensional figures.

Surface Area and Volume

Surface Area and Volume of Prisms

Surface Area and Volume of Pyramids

Surface Area and Volume of Cylinders

Surface Area and Volume of Cones

Surface Area and Volume of Spheres

ThreeDimensional Symmetry
Unit 3: Similar Shapes
A map of a city has the same shape as the original city, but the map is much, much smaller. A mathematician would say that the map and the city are similar. They have the same shape but are different sizes.

Dilations and Scale Factors

Similar Polygons

Triangle Similarity

SideSplitting Theorem

Indirect Measurement and Additional Similarity Theorems

Area and Volume Ratios
Unit 4: Circles
Students probably know what a circle is and what the radius and diameter of a circle represent. However, a circle can have many more figures associated with it. Arcs, chords, secants, and tangents all provide a rich set of figures to draw, measure, and understand.

Chords and Arcs

Tangents to Circles

Inscribed Angles and Arcs

Angles Formed by Secants and Tangents

Segments of Tangents, Secants, and Chords

Circles in the Coordinate Plane
Unit 5: Trigonometry
Who uses trigonometry? Architects, engineers, surveyors, and many other professionals use trigonometric ratios such as sine, cosine, and tangent to compute distances and understand relationships in the real world.

Tangents

Sines and Cosines

Special Right Triangles

The Laws of Sines and Cosines
Unit 6: Beyond Euclidian Geometry
Some people break rules, but mathematicians are usually exceptionally good at playing by them. Creative problemsolvers, including mathematicians, create new rules, and then play by their new rules to solve many kinds of problems.

The Golden Rectangle

Taxicab Geometry

Graph Theory

Topology

Spherical Geometry

Fractal Geometry

Projective Geometry

Computer Logic
Unit 7: Semester Review and Test

Semester Review

Semester Test
Honors Algebra II:
Course Overview:
This course builds upon algebraic concepts covered in Algebra I and prepares students for advancedlevel courses. Students extend their knowledge and understanding by solving openended problems and thinking critically. Topics include functions and their graphs, quadratic functions, inverse functions, advanced polynomial functions, and conic sections. Students are introduced to rational, radical, exponential, and logarithmic functions; sequences and series; data analysis; and matrices.
This course includes all the topics in Algebra II but has more challenging assignments and includes more optional challenge activities. Each semester also includes an independent honors project. This course requires the use of a graphing calculator equivalent to a TI84 and includes tutorials and activities for using a handheld graphing calculator.
Course Outline:
SEMESTER ONE
Unit 1: Numbers, Expressions, and Equations
In this unit, students review the order of operations, set definitions, properties of the real number system, and other symbols and terminology. Various strategies for solving linear and absolute value equations are introduced as are strategies for using formulas to solve realworld applications.

Semester Introduction

Sets of Number

Number Lines and Absolute Value

Number Properties

Evaluating Expressions

Solving Equations

Solving Absolute Value Equations

Applications: Formulas
Unit 2: Linear Equations and Systems
Representations and applications of linear relationships are the focus of this unit. Students interpret and create graphs, tables, and equations that represent linear relationships. In addition to simple linear equations, students also use systems of linear equations to solve realworld problems.

Graphs of Lines

Forms of Linear Equations

Writing Equations of Lines

Applications: Linear Equations

Systems of Linear Equations, Part 1

Systems of Linear Equations, Part 2

Applications: Linear Systems
Unit 3: Functions
Students explore realworld situations regarding input and output and learn how to graph equations and differentiate between functions and relations. Functions that are covered include some that are continuous, discontinuous, and discretevalued. Step functions such as the least and greatest integer functions are introduced. Students learn to estimate and calculate domains and ranges of functions and to compose complicated functions from simpler ones. Students learn to express situations in function notation, calculate domains and ranges, and write sums, differences, products, quotients, and compositions of functions.

Function Basics

Function Equations

Absolute Value Functions

Piecewise Functions

Step Functions

Function Operations, Part 1

Function Operations, Part 2

Function Inverses
Unit 4: Inequalities
In this unit, students solve and graph linear inequalities in one variable including conjunctions, disjunctions, and absolute value inequalities. Students also solve and graph inequalities in two variables and systems of inequalities in two variables. They also use linear programming to solve realworld problems.

Inequalities in One Variable

Compound Inequalities

Absolute Value Inequalities

Inequalities in Two Variables

Systems of Linear Inequalities

Linear Programming
Unit 5: Polynomials and Power Functions
Students learn to identify, evaluate, graph, and write polynomial functions. They review adding, subtracting, and multiplying polynomials as well as algebraic factoring patterns. Students use these patterns and the zeroproduct property to solve polynomial equations. Additionally, students graph power functions and identify the end behavior of various members of the power function graph family. Students also become familiar with the properties of even and odd functions.

Working with Polynomials

Multiplying Polynomials

Factoring Patterns

More Factoring Patterns

Solving Polynomial Equations

Power Functions
Unit 6: Rational Equations
Students learn to add, subtract, multiply, and divide rational expressions. Students learn to simplify compound fractions and solve rational equations. They also explore graphs and end behavior of rational functions including asymptotes and zeros.

Dividing Monomials and Polynomials

Operations with Rational Expressions, Part 1

Operations with Rational Expressions, Part 2

Compound Fractions

Solving Rational Equations, Part 1

Solving Rational Equations, Part 2

Reciprocal Power Functions

Graphing Rational Functions
Unit 7: Radicals and Complex Numbers
Students learn to identify, add, subtract, multiply, and divide radicals, and to factor out perfect squares. Students solve real world problems involving applications of radical equations and convert between rational exponent and radical form of an expression. They learn to identify, graph, find the modulus of, add, subtract, multiply, and divide imaginary and complex numbers.

Simplifying Radical Expressions

Fractional Exponents and Higher Roots

Graphing Radical Functions

Solving Radical Equations

Imaginary Numbers

Complex Numbers

Multiplying and Dividing Complex Numbers

Solving Equations with Complex Solutions
Unit 8: Quadratic Functions
Students learn how to graph quadratic functions and identify the equations of quadratic functions when given a graph. Students also use the zeroproduct property, completing the square, and the quadratic formula to solve quadratic equations. They explore the Quadratic Formula and how factors of quadratic polynomials relate to xintercepts of graphs of quadratic functions. Applications include projectile motion, geometry, and other areas.

Graphing Quadratic Functions

Properties of Quadratic Functions

Solving Quadratic Equations, Part 1

Solving Quadratic Equations, Part 2

Quadratic Inequalities

Finding a Quadratic from Points

Applications: Quadratic Functions
Unit 9: Semester Review and Test

Semester Review

Semester Test
SEMESTER TWO
Unit 1: Solving and Graphing Polynomials
Students learn polynomial long division and the technique of synthetic division to divide polynomials. Additionally, they learn to apply the remainder theorem and they use the factor and rational roots theorems to factor polynomials over the real and complex numbers. Uses of graphs and technology for factoring polynomials and solving polynomial equations are also covered.

Semester Introduction

Polynomial Long Division

Synthetic Division

The Polynomial Remainder Theorem

Factors and Rational Roots

Graphing Polynomials

Factoring Polynomials Completely

Applications: Polynomials
Unit 2: Exponents and Logarithms
Students discover how exponential functions can be used to describe situations in the real world, such as exponential decay and growth. They define the logarithmic function in terms of its relationship with the exponential function and graph both exponential and logarithmic functions. Students learn to apply multiplication and division laws of exponents to exponential and logarithmic expressions and equations.

Exponential Expressions and Equations, Part 1

Exponential Expressions and Equations, Part 2

Graphing Exponential Functions

Applications: Growth and Decay

Logarithms

Using Logs to Solve Exponential Equations

Solving Logarithmic Equations

Graphing Logarithmic Functions

Applications: Logarithms
Unit 3: Sequences and Series
Students explore arithmetic and geometric sequences, learning the concept of series as a sum of terms in a sequence and finding sums of finite arithmetic and geometric series. Students also use and interpret sigma notation to describe sums. Throughout the unit, students use sequences and series to solve several types of realworld problems and use spreadsheets to calculate terms of sequences and series.

Sequences and Patterns

Arithmetic Sequences

Geometric Sequences

Applications: Sequences

Series and Sigma Notation

Arithmetic Series

Geometric Series

Applications: Series

Technology: Sequences and Series
Unit 4: Counting and Probability
Students review counting principles including identifying and calculating permutations and combinations. They calculate probabilities of simple, dependent, independent, and binomial events. They also use probability to make predictions and relate the binomial theorem to Pascal's triangle.

Counting Principles

Permutations and Factorials

Combinations

Basic Probability

Probability With and Without Replacement

Independent and Dependent Events

Mutually Exclusive Events

Binomial probability

Making Predictions
Unit 5: Statistics
Students learn about the measures of center—mode, median, and mean—and the measures of spread—range, variance, and standard deviation. They learn how to produce and interpret bar, boxandwhisker, and scatter plots. Students explore common sampling techniques and learn how to use the properties of normal distributions to compare values.

Measures of Center

Variability

Samples

Graphs of Univariate Data

Frequency Distributions

The Normal Distribution

Lines of Best Fit
Unit 6: Vectors and Matrices
In this unit, students learn how to add, subtract, multiply, and determinants of matrices. Students also use matrices to solve systems of equations, transform figures, and solve realworld problems.

Matrices and Vectors

Operations with Matrices

Matrix Multiplication

Transforming Points and Figures

Determinants and Cramer's Rule, Part 1

Determinants and Cramer's Rule, Part 2

Identity and Inverse Matrices

Using Matrices to Solve Linear Systems
Unit 7: Conic Sections
Students learn about conic sections that are points or lines and curved conic sections, including circles, ellipses, hyperbolas, and parabolas. They learn how to graph conic sections, how to use algebraic reasoning to create equations of conics when given descriptions or graphs, and how to solve realworld problems.

Introduction to Conic Sections

Circles

Ellipses

Hyperbolas

Parabolas

Putting Conics into Graphing Form, Part 1

Putting Conics into Graphing Form, Part 2
Unit 8: Semester Review and Test

Semester Review

Semester Test
Honors Trigonometry:
Course Description:
Honors Trigonometry is designed to be taken after the completion of Algebra II and is designed for students who are looking to better understand trigonometric functions in preparation for their studies of Calculus or Statistics. This comprehensive course reviews topics in Algebra II and covers advanced topics in Trigonometry not often seen before Precalculus.
Students will learn trigonometry by actively engaging with the lectures, notes, project, and resources within the course website. Students can progress at their own rate through this individually paced course. Student knowledge will be assessed by the completion of homework, exams, and a project. Graphing calculators are used throughout the course.
Course Objectives:

The student will analyze, apply, and illustrate the properties of the unit circle.

The student will determine trigonometric values, calculate the transformations of trigonometric functions and graph trigonometric functions on the coordinate plane.

The student will utilize and apply trigonometric identities.

The student will use trigonometry to operate on complex numbers.

The student will study advanced topics in analytic geometry through trigonometric techniques.
List of Topics:
Algebraic Prerequisites:

Graphing Basics

Relationships between Two Points

Relationships among Three Points

Graphing Equations

Function Basics

Working with Functions

Function Domain and Range

Linear Functions: Slope

Equations of a Line

Graphing Functions

Manipulating Graphs: Shifts and Stretches

Manipulating Graphs: Symmetry and Reflections

Quadratic Functions: Basics

Quadratic Functions

Composite Functions

Rational Functions

Graphing Rational Functions

Function Inverses

Finding Function Inverses
The Trigonometric Functions:

Angles and Radian Measure

Right Angle Trigonometry

Applications of Right Triangle Trigonometry

The Trigonometric Functions

Graphing Sine and Cosine Functions

Graphing Sine and Cosine Functions with Vertical and Horizontal Shifts

Graphing Other Trigonometric Functions

Inverse Trigonometric Functions
Trigonometric Identities:

Basic Trigonometric Identities

Simplifying Trigonometric Expressions

Proving Trigonometric Identities

Solving Trigonometric Equations

The Sum and Difference Identities

DoubleAngle Identities

Other Advanced Identities
Applications of Trigonometry:

The Law of Sines

The Law of Cosines

Heron's Formula

Vector Basics

Components of Vectors and Unit Vectors
Complex Numbers and Polar Coordinates:

Complex Numbers

Operations on Complex Numbers

Complex Numbers in Trigonometric Form

Powers and Roots of Complex Numbers

Polar Coordinates
Topics in Analytic Geometry:

Parabolas

Ellipses

Hyperbolas

Identifying Conic Sections

Rotation of Conics

Parametric Equations

Graphs of Polar Equations

Polar Equations of Conics
Honors PreCalculus:
Course Description:
This is a fulllength online Honors Precalculus course for accelerated students. In this course, students will extend topics introduced in Algebra II and learn to manipulate and apply more advanced functions and algorithms. This course provides a mathematically sound foundation for students who intend to study Calculus.
Topics include:

Relations and Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Special Topics

Systems of Equations and Matrices

The Trigonometric Functions

Trigonometric Identities

Applications of Trigonometry

Topics in Analytic Geometry

Limits
List of Topics:
Relations and Functions:

Function Basics

Working with Functions

Function Domain and Range

Equations of a Line

Graphing Functions

Quadratic Functions: The Vertex

Manipulating Graphs: Shifts and Stretches

Manipulating Graphs: Symmetry and Reflections

Composite Functions

Circles
Polynomial and Rational Functions:

Polynomials: Long Division

Polynomials: Synthetic Division

The Remainder Theorem

The Factor Theorem

The Rational Zero Theorem

Zeros of Polynomials

Graphing Simple Polynomial Functions

Rational Functions

Graphing Rational Functions

Inequalities: Rationals and Radicals
Exponential and Logarithmic Functions:

Function Inverses

Finding Function Inverses

Exponential Functions

Applying Exponential Functions

Logarithmic Functions

Properties and Graphs of Logarithms

Evaluating and Applying Logarithms

Solving Exponential and Logarithmic Equations

Applying Exponents and Logarithms
Special Topics:

Conic Sections: Parabolas

Conic Sections: Ellipses

Conic Sections: Hyperbolas

Identifying Conic Sections

Binomial Coefficients and the Binomial Theorem

Arithmetic and Geometric Sequences

Induction

Combinations, Permutations and Probability
Systems of Equations and Matrices:

Solving Linear Systems by Substitution and Elimination

Linear Systems of Equations in Three Variables

Using Linear Systems: Investments and Partial Fractions

Solving Nonlinear Systems

Operations with Matrices

The GaussJordan Method

Evaluating and Applying Determinants

Using Inverses of Matrices to Solve Linear Systems

Systems of Inequalities

Linear Programming
The Trigonometric Functions:

Angles, Radian Measure, and Arc Length

Right Angle Trigonometry

The Trigonometric Functions

Graphing Sine and Cosine

Graphing Sine and Cosine Functions with Vertical and Horizontal Shifts

Graphing Other Trigonometric Functions

Inverse Trigonometric Functions
Trigonometric Identities:

Basic Trigonometric Identities

Simplifying Trigonometric Expressions

Determining Whether a Trigonometric Function Is Odd, Even, or Neither

Proving Trigonometric Identities

Solving Trigonometric Equations

The Sum and Difference Identities

DoubleAngle Identities

Other Advanced Identities
Applications of Trigonometry:

The Law of Sines

The Law of Cosines

Heron's Formula

Vectors: Operations and Applications

Components of Vectors and Unit Vectors

Complex Numbers in Trigonometric Form

Using DeMoivre's Theorem to find Powers and Roots of Complex Numbers

Functions in Polar Coordinates and their Graphs
Topics in Analytic Geometry:

Rotation of Conics

Parametric Equations

Graphs of Polar Equations

Polar Equations of Conics
Limits:

The Concept of a Limit and Finding Limits Graphically

The Limit Laws

Evaluating Limits

Continuity and Discontinuity
AP Statistics:
Course Overview:
This course is the equivalent of an introductory collegelevel course. Statistics—the art of drawing conclusions from imperfect data and the science of realworld uncertainties—plays an important role in many fields. Students collect, analyze, graph, and interpret realworld data. They learn to design and analyze research studies by reviewing and evaluating examples from real research. Students prepare for the AP Exam and for further study in science, sociology, medicine, engineering, political science, geography, and business.
Course Outline:
SEMESTER ONE
Unit 1: Describing Data
Students take a precourse assessment to be sure they are ready for the challenge of AP Statistics. They explore what statistics is, how it can be used, and how it is misused. They learn some basic statistics terminology and look at the difference between counts and measures and the difference between descriptive and inferential statistics.

What Is Statistics?

Displaying Distributions with Graphs

Describing Distributions Using Numbers

FiveNumber Summaries

More on Describing Distributions
Unit 2: The Normal Distribution
Students learn about the normal distribution and the normal curve—a display of a normal distribution on a graph; the normal curve presents the normal distribution in a form that statisticians can use as a tool in inferential statistics. This unit addresses items in Topic III (The normal distribution) in the College Board's AP Statistics topic outline.

Introduction to the Normal Distribution

Standardized Scores

Determining If a Data Set Is Normal
Unit 3: Bivariate Data
Students learn how statistics can be used to study how one variable affects another—for instance, do people who spend more years in school earn more money? Do people who take an experimental drug suffer fewer heart attacks? To answer questions like these, researchers need to gather data on two variables and then examine the data to see how the variables might be related. This unit addresses items in Topic I (Exploring bivariate data; Exploring categorical data: frequency tables) in the College Board's AP Statistics topic outline.

Introduction to Bivariate Data

The LeastSquares Regression Line

The Correlation Coefficient

Influential Points and Outliers

Transformations to Achieve Linearity

Categorical Bivariate Data: TwoWay Tables
Unit 4: Planning a Study
Students look at some of the most important issues in data gathering. They learn how this can make them smarter consumers of data; when they hear or read about studies, they will be able to determine whether or not they are valid. This unit addresses Topic II (Planning a Study) in the College Board's AP Statistics topic outline.

Methods of Data Collection—Experiments and Studies

Methods of Data Collection—Surveys
Unit 5: Probability
Students look at probability, which is vital for inferential statistics. They determine how likely it is that a sample really represents the population as a whole through proper sampling techniques and the laws of probability. This unit addresses items in Topic III (Law of large numbers; Addition rule, multiplication rule, conditional probability, and independence; Discrete random variables; Mean and standard deviation of a random variable) in the College Board's AP Statistics topic outline. Students review what they have learned and take the semester exam.

What Is Probability?

Introduction to the Basic Rules of Probability

More on Conditional Probabilities and the Probabilities of Combined Events

Probability Distributions

Means and Variances of Random Variables

Review and Exam
SEMESTER TWO
Unit 1: Binomials and Distributions
Students start to work with sampling distributions, which are distributions of possible sample means. This unit addresses items in Topic III (Sampling distribution of a sample proportion; Sampling distribution of a sample mean; Central Limit Theorem) in the College Board's AP Statistics topic outline.

Introduction to Inferential Statistics

Binomial Distributions

Geometric Distribution

Sampling Distributions: Means and Proportions
Unit 2: Introduction to Inference
Students look at concepts of sampling, probability, and distributions and are introduced to processes that researchers use to do statistical inference. This unit addresses items in Topic IV (The meaning of a confidence interval; Large sample confidence interval for a mean; Logic of significance testing; Large sample test for a mean) in the College Board's AP Statistics topic outline.

Confidence Intervals for Means

Statistical Significance and PValue

Significance and Hypothesis Testing: Means

Errors in Hypothesis Testing
Unit 3: t Distribution for Means
Students review and reinforce many concepts that they may already know about statistical inference, learning a new dimension that is vital to anyone doing inferential statistics in the real world. This unit addresses items in Topic IV (Large sample confidence interval for a difference between two means; t distribution; Singlesample t procedures; Twosample procedures) in the College Board's AP Statistics topic outline.

Confidence Intervals and Hypothesis Testing for a Single Mean

Confidence Intervals for the Difference between Two Means

Confidence Intervals and Hypothesis Tests for Two Independent Samples
Unit 4: Inference for Proportions
Students learn the basics of how to infer a population proportion based on a sample. This unit addresses items in Topic IV (Confidence intervals and significance tests for proportions and the differences between two proportions) in the College Board's AP Statistics topic outline.

Confidence Intervals and Hypothesis Tests for a Single Population Proportion

The Difference between Two Proportions
Unit 5: Inference for Tables and LeastSquares
Students build on what they have learned about analyzing bivariate sample data. They go beyond looking at the sample and make inferences about the population. This unit addresses items in Topic IV (Statistical Inference: Confirming Models) in the College Board's AP Statistics topic outline.

OneWay Tables: ChiSquare for GoodnessofFit

TwoWay Tables: ChiSquare for Association or Independence

Inference for the LeastSquares Line
Unit 6: Final Preparation for the AP Statistics Exam
Students review what they have learned and take the final exam.

General Preparation Strategies

Strategies and Practice for MultipleChoice and FreeResponse Questions

Putting It Together: Practice Exam and Mixed Practice

Final Exam
AP Calculus AB:
Course Description:
This is designed to be taught over a full high school academic year. It is possible to spend some time on elementary functions and still cover the Calculus AB curriculum within a year. However, if students are to be adequately prepared for the Calculus AB examination, most of the year must be devoted to topics in differential and integral calculus. These topics are the focus of the AP Exam.
AP Calculus AB is the study of limits, derivatives, definite and indefinite integrals, and the Fundamental Theorem of Calculus. Consistent with AP philosophy, concepts will be expressed and analyzed geometrically, numerically, analytically, and verbally.

Limits & Continuity

An Introduction to Limits & Continuity

Quiz: Introduction to Limits & Continuity

Tangent Lines & Rates of Change

Handout: Tangent Lines & Rates of Change Worksheet

Assignment: Tangent Lines & Rates of Change

The Limit

Handout: The Limit Worksheet

Assignment: The Limit

OneSided Limits

Handout: OneSided Limits Worksheet

Assignment: OneSided Limits

Computing Limits

Handout: Computing Limits Worksheet

Assignment: Computing Limits

Infinite Limits

Handout: Infinite Limits Worksheet

Assignment: Infinite Limits

Limits at Infinity

Handout: Limits at Infinity Worksheet

Assignment: Limits at Infinity

Continuity

Handout: Continuity Worksheet

Assignment: Continuity

Additional Resources

Handout: Limits & Continuity Exam

Assignment: Limits & Continuity Exam

Derivatives

Introduction to Derivatives

Definition & Interpretation of the Derivative

Handout: Definition & Interpretation of the Derivative Worksheet

Assignment: Definition & Interpretation of the Derivative

Differentiation Formulas

Handout: Differentiation Formulas Worksheet

Handout: Derivatives Exam 1

Assignment: Differentiation Formulas

Assignment: Derivatives Exam 1

Product & Quotient Rule

Handout: Product & Quotient Rule Worksheet

Assignment: Product & Quotient Rule

Derivatives of Trig Functions

Handout: Derivatives of Trig Functions Worksheet

Assignment: Derivatives of Trig Functions

Derivatives of Exponential & Logarithm Functions

Handout: Derivatives of Exponential & Logarithm Functions Worksheet

Assignment: Derivatives of Exponential & Logarithm Functions

Derivatives of Inverse Trig Functions

Derivatives of Hyperbolic Functions

Handout: Derivatives of Inverse & Hyperbolic Trig Functions Worksheet

Assignment: Derivatives of Inverse & Hyperbolic Trig Functions

The Chain Rule

Handout: The Chain Rule Worksheet

Handout: Derivatives Exam 2

Assignment: The Chain Rule

Assignment: Derivatives Exam 2

Implicit Differentiation

Handout: Implicit Differentiation Worksheet

Assignment: Implicit Differentiation

Related Rates

Handout: Related Rates Worksheet

Assignment: Related Rates

Higher Order Derivatives

Handout: Higher Order Derivatives Worksheet

Assignment: Higher Order Derivatives

Additional Resources

Handout: Derivatives Exam 3

Assignment: Derivatives Exam 3

Applications of Derivatives

What’s the Big Deal About Derivatives, Anyway?

Rates of Change

Critical Points & Extrema

Handout: Critical Points & Extrema Worksheet

Assignment: Critical Points & Extrema

The Shape of a Graph

Handout: The Shape of a Graph Worksheet

Assignment: The Shape of a Graph

The Mean Value Theorem

Handout: The Mean Value Theorem Worksheet

Assignment: The Mean Value Theorem

Optimization

Handout: Optimization Worksheet

Assignment: Optimization

L’Hopital’s Rule

Handout: L’Hopital’s Rule Worksheet

Assignment: L’Hopital’s Rule

Linear Approximations

Handout: Linear Approximations Worksheet

Assignment: Linear Approximations

Differentials

Handout: Differentials Worksheet

Assignment: Differentials

Newton’s Method

Handout: Newton’s Method Worksheet

Assignment: Newton’s Method

Handout: Motion Part 1 Worksheet

Handout: Motion Part 2 Worksheet

Handout: Motion Part 3 Worksheet

Assignment: Motion Part 1

Assignment: Motion Part 2

Assignment: Motion Part 3

Integrals

Working Backwards

Indefinite Integrals

Handout: Indefinite Integrals Worksheet

Assignment: Indefinite Integrals

Computing Indefinite Integrals

Handout: Computing Indefinite Integrals Worksheet

Assignment: Computing Indefinite Integrals

Substitution Rule for Indefinite Integrals

Handout: Substitution Rule Worksheet

Handout: Integrals Exam 1

Assignment: Substitution Rule

Assignment: Integrals Exam 1

Area Problem

Handout: Area Problem Worksheet

Assignment: Area Problem

Definite Integrals

Handout: Definite Integrals Worksheet

Assignment: Definite Integrals

Computing Definite Integrals

Handout: Computing Definite Integrals Worksheet

Assignment: Computing Definite Integrals

Substitution Rule for Definite Integrals

Handout: Substitution Rule for Definite Integrals Worksheet

Assignment: Substitution Rule for Definite Integrals

Integration by Parts

Handout: Integration by Parts Worksheet

Assignment: Integration by Parts

Partial Fractions

Handout: Partial Fractions Worksheet

Assignment: Partial Fractions

Improper Integrals

Handout: Improper Integrals Worksheet

Assignment: Improper Integrals

Additional Resources

Handout: Motion Part 4 Worksheet

Handout: Motion Part 5 Worksheet

Assignment: Motion Part 4

Assignment: Motion Part 5

Applications of Integrals

What’s the Big Deal About Integrals, Anyway?

Area Between Curves

Handout: Area Between Curves Worksheet

Assignment: Area Between Curves

Volumes of Solids of Revolution (Part 1)

Handout: Method of Rings Worksheet

Assignment: Method of Rings

Volumes of Solids of Revolution (Part 2)

Handout: Method of Cylinders Worksheet

Assignment: Method of Cylinders

Volume

Work

Handout: Work Worksheet

Assignment: Work

Handout: Applications of Integrals Exam

Assignment: Applications of Integrals Exam

Review & Test Preparation

Exam Format & Scoring

Exam Strategies & Tips

Practice, Practice, Practice

Handout: Calculus AB Section I Part A

Handout: Calculus AB Section 1 Part B

Handout: Calculus AB Section II Part A

Handout: Calculus AB Section II Part B

Assignment: AP Calculus AB Practice – Section I Part A

Assignment: AP Calculus AB Practice – Section I Part B

Assignment: AP Calculus AB Practice – Section II Part A

Assignment: AP Calculus AB Practice – Section II Part B
AP Calculus BC:
Course Description:
This is a fullyear course in the calculus of functions of a single variable. It includes all topics covered in Calculus AB plus additional topics. Both courses represent collegelevel mathematics for which most colleges grant advanced placement and credit. The content of Calculus BC is designed to qualify the student for placement and credit in a course that is one course beyond that granted for Calculus AB.
AP Calculus BC is the study of limits, derivatives, definite and indefinite integrals, polynomial approximations and (infinite) series. Though this is considered a study of singlevariable calculus, parametric, polar, and vector functions will be studied. Consistent with AP philosophy, concepts will be expressed and analyzed geometrically, numerically, analytically, and verbally. Calculus BC covers topics that are usually included in the first 3 semesters of college calculus.

Limits & Continuity

An Introduction to Limits & Continuity

Quiz: Introduction to Limits & Continuity

Tangent Lines & Rates of Change

Handout: Tangent Lines & Rates of Change Worksheet

Assignment: Tangent Lines & Rates of Change

The Limit

Handout: The Limit Worksheet

Assignment: The Limit

OneSided Limits

Handout: OneSided Limits Worksheet

Assignment: OneSided Limits

Computing Limits

Handout: Computing Limits Worksheet

Assignment: Computing Limits

Infinite Limits

Handout: Infinite Limits Worksheet

Assignment: Infinite Limits

Limits at Infinity

Handout: Limits at Infinity Worksheet

Assignment: Limits at Infinity

Continuity

Handout: Continuity Worksheet

Assignment: Continuity

Additional Resources

Handout: Limits & Continuity Exam

Assignment: Limits & Continuity Exam

Derivatives

Introduction to Derivatives

Definition & Interpretation of the Derivative

Handout: Definition & Interpretation of the Derivative Worksheet

Assignment: Definition & Interpretation of the Derivative

Differentiation Formulas

Handout: Differentiation Formulas Worksheet

Handout: Derivatives Exam 1

Assignment: Differentiation Formulas

Assignment: Derivatives Exam 1

Product & Quotient Rule

Handout: Product & Quotient Rule Worksheet

Assignment: Product & Quotient Rule

Derivatives of Trig Functions

Handout: Derivatives of Trig Functions Worksheet

Assignment: Derivatives of Trig Functions

Derivatives of Exponential & Logarithm Functions

Handout: Derivatives of Exponential & Logarithm Functions Worksheet

Assignment: Derivatives of Exponential & Logarithm Functions

Derivatives of Inverse Trig Functions

Derivatives of Hyperbolic Functions

Handout: Derivatives of Inverse & Hyperbolic Trig Functions Worksheet

Assignment: Derivatives of Inverse & Hyperbolic Trig Functions

The Chain Rule

Handout: The Chain Rule Worksheet

Handout: Derivatives Exam 2

Assignment: The Chain Rule

Assignment: Derivatives Exam 2

Implicit Differentiation

Handout: Implicit Differentiation Worksheet

Assignment: Implicit Differentiation

Related Rates

Handout: Related Rates Worksheet

Assignment: Related Rates

Higher Order Derivatives

Handout: Higher Order Derivatives Worksheet

Assignment: Higher Order Derivatives

Additional Resources

Handout: Derivatives Exam 3

Assignment: Derivatives Exam 3

Applications of Derivatives

What’s the Big Deal About Derivatives, Anyway?

Rates of Change

Critical Points & Extrema

Handout: Critical Points & Extrema Worksheet

Assignment: Critical Points & Extrema

The Shape of a Graph

Handout: The Shape of a Graph Worksheet

Assignment: The Shape of a Graph

The Mean Value Theorem

Handout: The Mean Value Theorem Worksheet

Assignment: The Mean Value Theorem

Optimization

Handout: Optimization Worksheet

Assignment: Optimization

L’Hopital’s Rule

Handout: L’Hoptial’s Rule Worksheet

Assignment: L’Hopital’s Rule

Linear Approximations

Handout: Linear Approximations Worksheet

Assignment: Linear Approximations

Differentials

Handout: Differentials Worksheet

Assignment: Differentials

Newton’s Method

Handout: Newton’s Method Worksheet

Assignment: Newton’s Method

Midtest

Assignment: Calculus Midtest

Handout: Motion Part 1 Worksheet

Handout: Motion Part 2 Worksheet

Handout: Motion Part 3 Worksheet

Assignment: Motion Part 1

Assignment: Motion Part 2

Assignment: Motion Part 3

Integrals

Working Backwards

Indefinite Integrals

Handout: Indefinite Integrals Worksheet

Assignment: Indefinite Integrals

Computing Indefinite Integrals

Handout: Computing Indefinite Integrals Worksheet

Assignment: Computing Indefinite Integrals

Substitution Rule for Indefinite Integrals

Handout: Substitution Rule Worksheet

Handout: Integrals Exam 1

Assignment: Substitution Rule

Assignment: Integrals Exam 1

Area Problem

Handout: Area Problem Worksheet

Assignment: Area Problem

Definite Integrals

Handout: Definite Integrals Worksheet

Assignment: Definite Integrals

Computing Definite Integrals

Handout: Computing Definite Integrals Worksheet

Assignment: Computing Definite Integrals

Substitution Rule for Definite Integrals

Handout: Substitution Rule for Definite Integrals Worksheet

Assignment: Substitution Rule for Definite Integrals

Integration by Parts

Handout: Integration by Parts Worksheet

Assignment: Integration by Parts

Partial Fractions

Handout: Partial Fractions Worksheet

Assignment: Partial Fractions

Improper Integrals

Handout: Improper Integrals Worksheet

Assignment: Improper Integrals

Handout: Motion Part 4 Worksheet

Handout: Motion Part 5 Worksheet

Assignment: Motion Part 4

Assignment: Motion Part 5

Applications of Integrals

What’s the Big Deal About Integrals, Anyway?

Area Between Curves

Handout: Area Between Curves Worksheet

Assignment: Area Between Curves

Volumes of Solids of Revolution (Part 1)

Handout: Method of Rings Worksheet

Assignment: Method of Rings

Volumes of Solids of Revolution (Part 2)

Handout: Method of Cylinders Worksheet

Assignment: Method of Cylinders

Volume

Work

Handout: Work Worksheet

Assignment: Work

Handout: Applications of Integrals Exam

Assignment: Applications of Integrals Exam

Sequences & Series

Sequences & Series

Additional Resources

Sequences

Handout: Sequences Worksheet

Assignment: Exploration: The Limit of a Sequence

Assignment: Sequences

Series: The Basics

Handout: Series Worksheet

Assignment: Series

Series: Convergence & Divergence

Special Series

Integral Test

Essay: Integral Test

Comparison Test

Handout: Comparison Test Worksheet

Assignment: Comparison Test

Alternating Series Test

Handout: Alternating Series Test Worksheet

Assignment: Alternating Series Test

Absolute Convergence

Handout: Absolute Convergence Worksheet

Assignment: Absolute Convergence

Ratio & Root Tests

Handout: Ratio & Root Test Worksheet

Assignment: Ratio & Root Test

Strategy for Series

Estimating the Value of a Series

Power Series

Handout: Power Series Worksheet

Taylor Series

Handout: Taylor Series Worksheet

Assignment: Power Series

Assignment: Taylor Series

PostTest

Assignment: Calculus Posttest