top of page

# Math AP

9-12

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 al-jabr, 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.

• 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 real-world problems.

• 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 never-ending quest to model the real world.

• Graphs

• Equations in Two Variables

• Lines and Intercepts

• Slope

• Slope-Intercept Form

• Point-Slope 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

• 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

• 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

• 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 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 Discriminant

• 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; three-dimensional solids; geometric constructions; symmetry; the use of transformations; and non-Euclidean 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

• 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

• 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: Three-Dimensional Figures and Graphs

One-dimensional figures, such as line segments, have length. Two-dimensional figures, such as circles, have area. Objects we touch and feel in the real world are three-dimensional; they have volume.

• Semester Introduction

• Solid Shapes and Three-Dimensional Drawing

• Lines, Planes, and Polyhedra

• Prisms

• Coordinates in Three Dimensions

• Equations of Lines and Planes in Space

Unit 2: Surface Area and Volume

Every three-dimensional 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 three-dimensional 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

• Three-Dimensional 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

• Side-Splitting 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 problem-solvers, 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 advanced-level courses. Students extend their knowledge and understanding by solving open-ended 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 TI-84 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 real-world 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 real-world 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 real-world 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 discrete-valued. 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 real-world 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 zero-product 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.

• Fractional Exponents and Higher Roots

• Imaginary Numbers

• Complex Numbers

• Multiplying and Dividing Complex Numbers

• Solving Equations with Complex Solutions

Students learn how to graph quadratic functions and identify the equations of quadratic functions when given a graph. Students also use the zero-product 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 x-intercepts of graphs of quadratic functions. Applications include projectile motion, geometry, and other areas.

• Solving Quadratic Equations, Part 1

• Solving Quadratic Equations, Part 2

• Finding a Quadratic from Points

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 real-world 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, box-and-whisker, 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 real-world 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 real-world 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

• Composite Functions

• Rational Functions

• Graphing Rational Functions

• Function Inverses

• Finding Function Inverses

The Trigonometric Functions:

• 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

• Double-Angle 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 Pre-Calculus:

Course Description:

This is a full-length 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

• 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

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 Gauss-Jordan 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

• Double-Angle 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 college-level course. Statistics—the art of drawing conclusions from imperfect data and the science of real-world uncertainties—plays an important role in many fields. Students collect, analyze, graph, and interpret real-world 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 pre-course 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

• Five-Number 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 Least-Squares Regression Line

• The Correlation Coefficient

• Influential Points and Outliers

• Transformations to Achieve Linearity

• Categorical Bivariate Data: Two-Way 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 P-Value

• 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; Single-sample t procedures; Two-sample 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 Least-Squares

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.

• One-Way Tables: Chi-Square for Goodness-of-Fit

• Two-Way Tables: Chi-Square for Association or Independence

• Inference for the Least-Squares 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 Multiple-Choice and Free-Response 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.

1. 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

• One-Sided Limits

• Handout: One-Sided Limits Worksheet

• Assignment: One-Sided 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

• Handout: Limits & Continuity Exam

• Assignment: Limits & Continuity Exam

1. 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

• Handout: Derivatives Exam 3

• Assignment: Derivatives Exam 3

1. 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

1. 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

1. 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

1. 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 full-year course in the calculus of functions of a single variable. It includes all topics covered in Calculus AB plus additional topics. Both courses represent college-level 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 single-variable 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.

1. 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

• One-Sided Limits

• Handout: One-Sided Limits Worksheet

• Assignment: One-Sided 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

• Handout: Limits & Continuity Exam

• Assignment: Limits & Continuity Exam

1. 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

• Handout: Derivatives Exam 3

• Assignment: Derivatives Exam 3

1. 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

1. 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

1. 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

1. Sequences & Series

• Sequences & Series

• 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

• Post-Test

• Assignment: Calculus Post-test

bottom of page