# Mathematics

## Courses

- MAT110 - Algebra 1
- MAT122 - Algebra 1 Accelerated
- MAT210 - Geometry
- MAT222 - Geometry Honors
- MAT310 - Algebra 2
- MAT322 Algebra 2 & Trigonometry Honors
- MAT410 - Probability Statistics & College Algebra
- MAT420 - Pre-Calculus
- MAT422 Pre-Calculus Accelerated
- MAT423 - Pre-Calculus Honors
- MAT510 - Calculus
- MAT512 - Calculus Honors
- MAT515 - AP Calculus AB
- MAT520 - AP Calculus BC
- MAT530 - AP Statistics
- MAT540 - Multivariable Calculus
- MAT541 - Differential Equations
- MAT542 - Linear Algebra
- MAT543 - Advanced Mathematical Proofs
- MAT544 - Graph Theory and Combinatorics

## MAT110 - Algebra 1

**Course Title:**

MAT110 Algebra 1

**Course Description:**

This course is for those students who have completed a pre-algebra course. This course centers around various topics such as the concept of variable, equation solving, polynomials, and linear equations in two variables. Probability and statistics will also be examined. The graphing calculator, as well as other forms of technology, will be used extensively throughout the course. Grade: 9

**Academic Goals:**

- First semester course content will include:
- Algebraic techniques
- Analyzing and solving linear equations
- Ratios and proportions
- Graphing relations and functions

- By the end of the first semester, students will be able to:
- Use order of operations to evaluate expressions and apply the properties of the rational numbers (calculator application).
- Write algebraic equations from verbal sentences, solve single variable algebraic equations, and solve multivariable equations for a specific variable.
- Solve proportions using cross multiplication.
- Solve, write and graph simple equations.
- Plot points in the coordinate plane, write and graph linear equations.

- Second semester course content will include:
- Solving systems of equations
- Operations with polynomials and factoring polynomials
- Radical expressions
- Rational expressions
- Quadratic and exponential equations
- The Pythagorean Theorem
- Inequalities

- By the end of the second semester, students will be able to:
- Simplify, add, subtract, multiply, and divide polynomials.
- Find the greatest common factor for a set of numbers or monomials, factor polynomials, factor polynomials of the form ax
^{2}+ bx +c, solve equations by factoring, use the quadratic formula to solve a quadratic equation, and graph a quadratic or exponential equation (calculator application). - Simplify, add, subtract, multiply, and divide rational or irrational expressions.
- Solve, write and graph simple inequalities.
- Apply various uses of the Pythagorean Theorem
- Solving a system of liner equations

**Instructional Methods:**

- Direct instruction
- Study of text: active reading of text, especially definitions and example problems
- One-on-one instruction (back work)
- Note taking
- On-Line tutorials
- Power point presentations

**Evaluation:**

- There will be a two hour exam at the end of the semester during the exam week in the fall and spring. The fall exam will be approximately 25 questions dealing with topics such as order of operations, solving algebraic equations, proportion, and probability odds. The spring exam will be approximately 25 questions dealing with topics such as quadratic expressions and equations, solving algebraic equations and inequalities and systems of equations, rational and irrational numbers, operations with polynomials, factoring polynomials, simplifying radical expressions, and probability and statistics.
- Tests
- Quizzes
- There will be a writing assignment that all Algebra 1 students will complete.
- Homework

## MAT122 - Algebra 1 Accelerated

**Course Title:**

MAT122 Algebra 1 Accelerated

**Course Description:**

This course is for students who have demonstrated outstanding aptitude and a genuine love of mathematics in their pre-algebra course. It is a fast-paced course centered on the abstract concept of variables, equation solving, and the study of linear equations in two variables. Both the depth and the pace of the course are greater than encountered in Algebra 1, and the expectations of students are much higher. Grade: 9

**Academic Goals:**

- By the end of the first semester, students will be able to:
- Properly handle the order of operations
- Take word phrases or sentences and turn them into algebraic forms and/or equations
- Understand absolute value, especially by using the graphing calculator
- Solve both linear equations and inequalilties
- Graph relations and functions and distinguish their differences

- Second semester course content will include:
- Systems of open sentences
- Factoring of polynomials
- Study of rational and irrational numbers
- Quadratic equations and functions
- Pythagorean Theorem
- Basic Trigonometry

- By the end of the second semester, students will be able to:
- Solve quadratic equations and systems with and without the graphing calculator
- Factor polynomials by several methods
- Handle rational and irrational numbers properly, especially radicals
- Use the basic trigonometric functions
- Use the Pythagorean Theorem in solving right triangle problems
- Use the graphing calculator to deal with quadratic functions

**Instructional Methods:**

- Direct instruction
- Demonstration models
- Question and answer sessions (oral responses)
- Daily work
- One-on-one help sessions (back work)
- Note taking
- Reading and studying of the text

**Evaluation:**

- Graded daily work
- In-class full period tests
- Frequent check of classroom notes
- Quizzes
- Class participation
- Extra credit and./or enrichment problems
- Oral presentations in class
- Semester exams

## MAT210 - Geometry

**Course Title:**

MAT210 Geometry

**Course Description:**

Geometry is the second in our high school series of math courses. The prerequisite for this course is the successful completion of Algebra 1. The topic areas covered in the first semester will be Euclidean Geometry, including parallel and perpendicular lines, equations of lines, angles and triangles. The second semester topics include proportionality, similarity of polygons, special right triangles, quadrilaterals, circles, and areas and volumes. Students will explore these topics by means of constructions, two column and paragraph proofs, using the geometric concepts to set up and solve algebraic equations, presentations of problems and concepts to the class, and writing assignments that demonstrate their mastery of the vocabulary and concepts. Methods of assessment will be homework, daily classroom participation, announced and unannounced quizzes, extended writing assignments describing solutions to problems, tests, and semester exams. Grade: 9-11

**Academic Goals:**

- First semester course content will include:
- Review algebra skills
- Properties of points, lines, segments, rays, and planes
- Inductive reasoning and deductive reasoning
- Angle relationships
- Compass and straightedge constructions
- Discovering and proving triangle properties

- By the end of the first semester, students will be able to:
- Solve linear and quadratic equations
- Use Triangle inequality theorem plus relationships between sides and angles
- Prove basic conjectures
- Find the measure of vertical and linear angles
- Duplicate the basic Euclidean constructions
- Do basic triangle proofs
- Compare and contrast similar polygons
- Write and solve proportions

- Second semester course content will include:
- More review of Algebra skills
- Areas of polygons
- Pythagorean Theorem and special triangles
- Surface area and volume of polyhedrons
- Similarity
- Basic Trigonometry
- Law of Sines and Cosines
- Properties of quadrilaterals
- Properties of circles

- By the end of the second semester, students will be able to:
- Graph linear systems
- Calculate area of triangles, quadrilaterals, and circles
- Solve a right triangle and solve 45-45-90 plus 30-60-90 triangles
- Calculate the surface area and volume of polyhedrons
- Calculate corresponding parts of similar figures
- Use sine, cosine, and tangent to find sides and angles of triangles
- Use Law of Sine and Cosine to find angles and side lengths
- Use direct and indirect proof to verify conjectures.
- Discover quadrilateral properties
- Discover circle properties

**Instructional Methods:**

- Direct instruction
- One-on-one instruction (back work)
- Note taking in class and from reading the book
- Group and individual discovery

**Evaluation:**

- Take-home tests
- In-class tests
- Notebook checks
- Cumulative semester exams. The two-hour exams in both fall and spring will consist of short and long computation and proofs. The exams will include coordinate geometry (slope, distance formula, parallel lines, perpendicular lines), solving linear systems, circles, factoring, solving equations, parabolas, simplifying, right triangle trigonometry, quadratic formula, and locus.
- Extra credit and/or enrichment problems
- Class participation

## MAT222 - Geometry Honors

**Course Title:**

MAT222 Geometry Honors

**Course Description:**

Concepts are presented visually with the extensive use of The Geometer's Sketchpad. Students explore ideas analytically, then inductively, and finally deductively, developing insight, confidence, and increasingly sophisticated mathematical understanding. Topics will include studies of the Euclidean ideals: points, lines, and algebraic; therefore, much time will be spent reviewing algebraic skills and extending these skills to be better prepared for Honors Algebra 2. Grade: 9-10

**Academic Goals:**

- First semester course content will include:
- Review of Algebra skills
- Properties of polygons and circles
- Inductive reasoning and deductive reasoning
- Angle relationships
- Compass and straightedge constructions
- Discovering and proving triangle properties
- Discovering and proving quadrilateral properties
- Discovering and proving circle properties

- By the end of the first semester, students will be able to:
- Solve linear and quadratic equations
- Prove basic conjectures
- Use Triangle inequality theorem plus relationships between sides and angles
- Find the measure of vertical and linear angles
- Duplicate the basic Euclidean constructions
- Do basic triangle proofs
- Do basic quadrilateral proofs
- Do basic circle proofs

- Second semester course content will include:
- More review of Algebra skills
- Areas of polygons
- Pythagorean Theorem and special triangles
- Volume and surface area of polyhedrons
- Similarity
- Basic Trigonometry
- Law of Sines and Cosines
- Proofs

- By the end of the second semester, students will be able to:
- Graph linear systems
- Calculate area of triangles, quadrilaterals, and circles
- Solve a right triangle and solve 45-45-90 and 30-60-90 triangles
- Calculate the surface area and volume of polyhedrons
- Calculate corresponding parts of similar figures
- Use sine, cosine, and tangent to find sides and angles in triangles
- Use Law of Sines and Cosines to find areas, angles, and side lengths
- Use direct and indirect proof to verify conjectures

**Instructional Methods:**

- Study of text; active reading of text, especially definitions and example problems
- Oral questioning
- Daily work (guided practice)
- Collaborative problem sets
- One-on-one instruction (back work)
- Hands-on, real world project
- Cooperative learning strategies
- Note taking in class and from reading the book

**Evaluation:**

- In-class, full period tests
- Take home tests
- Quizzes
- Graded daily work
- Notebook checks
- Section outlines
- Semester exams
- Extended projects that require a formal write up and that will be graded with a rubric
- The exam in both fall and spring will take place during the two-hour slot set aside during exam week. the exam will consist of short and long computation and proofs. Each exam will include coordinate geometry (slope, distance formula, parallel lines, perpendicular lines), solving linear systems, circles, factoring, solving equations, parabolas, simplifying, right triangle trigonometry, 1 derive quad. formula, and a locus problem.
- Students will present to the class a formal presentation of a problem that will be graded with a rubric.

## MAT310 - Algebra 2

**Course Title:**

MAT310 Algebra 2

**Course Description:**

Algebra 2 is a course designed for those students who have successfully completed Geometry. This is the third in our high school math courses. The first semester will deal with solving equation and inequalities. We will explore linear Relations and functions. Students will use these relationships to further develop polynomial and radical equations and inequalities. In the second semester, the students will be introduced to advanced functions, Conic Sections, Trigonometry and Probability and Statistics. Grade: 9-12

**Academic Goals:**

- Second semester course content will include a) Solving Quadratic functions b)Quadratic Formula and the discriminant c) Analyze graphs of quadratic functions d) solve and graph quadratic inequalities e) Remainder and Factor theorems f) Inverse functions and relations g) conic sections h) exponential and logarithmic relations i) trigonometric functions
- By the end of the first semester, students should be able to: a) Simplify and evaluate algebraic expressions b) Classify properties of real numbers c) How to solve and graph different types of equations and inequalities. d) Analyze relations and functions e) Write Linear equations f) Find and use slope of a line g) Solve systems of equations by different methods h) Add, subtract, multiply, and divide polynomials i)perform operations with complex numbers j)solve equations involving roots, radicals, and rational exponents **Calculator skills will be introduced and utilized involving different concepts during the semester
- First semester course content will include: a. Properties of Real Numbers b. solving equations and inequalities c. Absolute Value d. Relations and Functions e. Matrices (if time permits) f. polynomials g. radical equations
- By the end of the first semester, students will be able to: a) Simplify and evaluate algebraic expressions b) Classify properties of real numbers c) How to solve and graph different types of equations and inequalities. d) Analyze relations and functions e) Write Linear equations f) Find and use slope of a line g) Solve systems of equations by different methods h) Add, subtract, multiply, and divide polynomials i)perform operations with complex numbers j)solve equations involving roots, radicals, and rational exponents d)
- By the end of the second semester, students will be able to: a) Solve, write, analyze and graph quadratic equations by different methods b) Find factors and zeros of polynomial by various methods c) Find the composition and determine inverses of functions d) Be able to write equations for parabola, circles, hyperbolas, and ellipses. e) Solve exponential and logarithmic expressions f) Solve problems involving exponential growth and decay g) Find values of trigonometric functions h) solve problems using right triangle trigonometry i) Apply the laws of Cosine and Sine to solve problems ** Calculator skills will also be required in this semester

**Instructional Methods:**

- Direct instruction
- Demonstration techniques
- Study of text; active reading of text, especially definitions and example problems; outlining of text
- Oral questioning
- Daily work (guided practice)
- One-on-one instruction (back work)
- Note taking
- Hands-on, real world project
- Cooperative learning strategies
- Graphing calculator demonstrations and applications

**Evaluation:**

- Take-home tests
- Quizzes
- In-class, full period tests
- Notebook checks
- Essays
- Oral presentations in class
- Section outlines
- Cumulative semester exams
- The Fall Semester Exam contains 28 problems where students must show their work to receive full credit. The breakdown of problems is as follows: 2 inequalities; 1 laws of exponents; 1 simplifying polynomials; 1 factoring; 3 simplifying rational expressions; 3 solving basic equations with real solutions; 1 complex fraction; 2 simplifying radicals; 1 radical equation; 2 arithmetic of imaginary numbers; 3 solving equations with complex solutions; 1 writing equation given complex roots; 1 quadratic inequality; 6 function problems (domain, range, composition, inverses)
- The Spring Semester Exam contains 28 problems where students must show their work to receive full credit. The breakdown of problems is as follows: 3 laws of exponents; 3 functions; 3 conic sections; 5 exponential equations/logarithms; 5 circle geometry; 9 trigonometry

- Extra credit and/or enrichment problems
- Class participation

## MAT322 Algebra 2 & Trigonometry Honors

**Course Title:**

MAT322 Algebra 2 & Trigonometry Honors

**Course Description:**

Course Description: Algebra II (Honors) is a fast-paced course for students who have demonstrated outstanding achievement, consistent work ethic, and a love of mathematics in previous math courses. The study includes quadratic, radical, exponential, logarithmic, rational, and trigonometric functions. Systems of equations, linear programming, sequences and series, and conics are also covered. Both the depth and the pace of the course are greater than encountered in Algebra II, having a higher expectation of difficulty and of independent learning. Grade: 9-11

**Academic Goals:**

- First semester course content will include:
- Basic algebraic principles
- Linear, direct variation, absolute value, and quadratic functions and relations
- Systems of equations and inequalities for two and three variables
- Graphing in two and three dimensions
- Rational, irrational, and complex numbers

- By the end of the first semester, students will be able to
- Perform all basic arithmetic operations with and without the calculator
- Solve equations with and without a calculator
- Solve systems of equations and inequalities by linear combination and substitution, and by graphing with and without a calculator
- Simplify and perform basic operations with rational, irrational, and complex expressions
- Locate and estimate real roots of quadratic equations using the graphing calculator and linear interpolation

- Second semester course content will include:
- Polynomials and polynomial functions
- Radical functions
- Inverse relations and functions
- Exponents and logarithms
- Rational expressions and radical equations
- Conic sections
- Sequences and series
- Triangular and circular trigonometry
- Trigonometric identities and formulas
- Solving triangles

- By the end of the second semester, students will be able to
- Use a variety of methods of factoring to simplify polynomial expressions
- Solve polynomial equations
- Simplify radical and rational expressions
- Perform operations with functions
- Determine the inverse of functions and the composition of functions
- Write and evaluate logarithmic expressions and exponential expressions
- Solve radical, exponential, logarithmic, and rational equations
- Graph, write equations for, and analyze properties of conic sections
- Identify and generate arithmetic and geometric sequences and series
- Evaluate finite and infinite geometric series
- Graph trigonometric functions and their inverses
- Derive and use a number of trigonometric identities
- Solve trigonometric equations

**Instructional Methods:**

- Direct instruction
- Oral questioning
- Daily work (end of period with teacher guidance)
- Demonstration techniques
- Back work (when deemed necessary)
- Note taking
- Cooperative learning

**Evaluation:**

- Graded daily work
- Quizzes
- In-class, full period tests
- Random check of classroom notes
- Extra credit and/or enrichment problems
- Oral presentations in class
- Class participation
- The first semester exam will contain 25 comprehensive questions. Six of the problems will be word problems that involve defining variables, writing equations and solving equations. The exam will include the following:
- Solving equations involving absolute value, rearranging formulas, quadratics, linear systems, fractional equations and radicals.
- Solving systems of equations algebraically, graphically, and by Cramer's Rule.
- Solving inequalities involving one variable, absolute value, and quadratics.
- Graphing linear equations, linear inequalities, and one variable inequalities.
- Composing and evaluating functions.
- Writing equations of lines utilizing information from parallel or perpendicular lines.
- Simplifying expressions containing radicals and exponents.
- Factoring polynomials
- Adding, subtracting, multiplying and dividing polynomials and rational expressions.
- Finding real and complex roots of polynomials.
- Solving quadratic inequalities
- Writing equations conic sections.
- Graphing parabolas, ellipses and hyperbolas using pencil and paper.
- Solving systems of equations over complex numbers.
- Solving problems using inverse, joint and direct proportionality.
- Simplifying radicals.
- Writing quadratic equations.

- The spring semester exam will contain 25 questions reflecting topics from second semester. The exam will contain four word problems that require use of formulas, writing equations and critical thinking. Topics will include the following:
- Finding terms of arithmetic and geometric sequences
- Solving exponential equations.
- Graphing exponential and trigonometric equations.
- Solving logarithmic equations.
- Finding inverse functions.
- Converting degrees to radians.
- Solving triangles.
- Verifying trigonometric identities.
- Using sum and difference formulas to find exact values of trigonometric functions.
- Solving trigonometric equations.
- Solving problems using systems of equations, sequences, series, and trigonometry.

## MAT410 - Probability Statistics & College Algebra

**Course Title:**

MAT410 Probability Statistics & College Algebra

**Course Description:**

This course is available to seniors who have completed the three years of required high school math and who desire to continue their study of math to prepare for college level courses. The course includes an introduction to statistics and probability, with data analysis, and study of college algebra through the investigation of functions from a graphing calculator point of view. The first semester will be the introduction to Statistics and Probability. We will cover organizing and graphing data, numerical descriptive data, probability and discrete random variables and their probability distribution. During the second semester, the class will cover College Algebra with rates of change. We will specifically study linear, quadratic and power functions and rates of change from real work examples. Grade: 11-12

**Academic Goals:**

- During the first semester students will be an introduced to Descriptive and Inferential Statistics.
- The students will start with the basic terminology and about the different types of variables and sources of data.
- The students will learn how to organize the data and present it in a meaning full manner in different graphs.
- Students will to find measures of central tendencies and dispersion of ungrouped data.
- Students will learn how to find and use the mean, variance and standard deviation of grouped data.
- Students will learn how to predict possible outcomes of experiments with probability.
- Students will learn how to use discrete random variable to predict their probability of distribution.
- At the end of the first semester students will be able to collect and analyze data for themselves and question the data and statistical analyses of others.

- During the second semester students will study college algebra to prepare them to take calculus in college.
- Students will learn how to find the rate of change of a linear function and to write an equation of the function. They will be able to find an equation of a linear function to fit a given data set.
- Students will learn how to find the domain and range of quadratic, piecewise defined, composite and inverse functions.
- Students will learn to use exponential functions and their graphs to show rate so growth, decay and compare how different interest rates effect investments.
- Students will learn to use the sine and cosine functions to model, with an equation, repetitive events.
- Students will learn to model, with a graph, the behavior of polynomial and rational functions.
- At the end of the second semester students will be able to use the equations and graphs of functions to model the behavior of real world events.

**Instructional Methods:**

- Seminar style classes

**Evaluation:**

- In-class, full period tests
- Quizzes
- Graded daily work
- Short papers
- Oral presentations in class
- Semester exams
- Extended projects
- Extra credit and/or enrichment problems
- Class participation
- Both semesters, the final exam will be a traditional 2-hour sit-down exam consisting of both extended and short response problems.

## MAT420 - Pre-Calculus

**Course Title:**

MAT420 Pre-Calculus

**Course Description:**

Students who have completed three years of high school math enroll in Pre-calculus to study in depth the concepts of function, trigonometry, logs and exponents. The course also includes an introduction to limits. A student completing Pre-calculus will be prepared for a rigorous, college-level pre-calculus course or introductory calculus course. Grade: 10-12

**Academic Goals:**

- First semester course content will include:
- The nature of graphs
- Polynomial and rational functions
- Linear Relations and Functions
- Exponential and Logarithmic Functions
- Sequences and series

- By the end of the first semester, students will be able to:
- Graph polynomial and rational functions (calculator application)
- Identify behaviors of graphs
- Solve quadratic equations using a variety of methods (calculator application)
- Analyze quadratic equations using the discriminant and the nature of the roots (calculator application)
- Solve problems involving quadratic equations (calculator application)
- Find composite functions
- Perform operations with functions.
- Find and recognize inverses.
- Write linear equations using the point-slope form and slope-intercept form.
- Find slope of a line and the distance between two points.
- Use the properties of exponents.
- Graph exponential functions, exponential inequalities, logarithmic functions, and logarithmic inequalities.
- Solve exponential equations, exponential inequalities, logarithmic equations, logarithmic inequalities, and equations using the natural logarithm.
- Use the exponential function y = e^x
- Apply annuity formulas to real life problems

- Second semester course content will include:
- Trigonometric identities and equations
- Conics
- Limits, derivatives, and integrals, if time permits
- Trigonometric Functions
- Graphs and inverses of trigonometric functions

- By the end of the second semester, students will be able to:
- Identify and use reciprocal, quotient, sum and difference, double, and half-angle identities
- Write a linear equation in normal form
- Find distance from a point to a line and between parallel lines (calculator application)
- Graph circles, parabolas, ellipses, hyperbolas, and systems of second-degree equations and inequalities (calculator application)
- Use the standard and general forms of the equation of a parabola, ellipse, and hyperbola
- Recognize conic sections by their equations (calculator application)
- Find the derivative of a function
- Use limit theorems to evaluate the limit of polynomial function
- Use integration formulas and the fundamental theorem of calculus, if time permits
- Find the area between a curve and the x-axis by using the limit of areas of rectangles (calculator application)
- Convert radian measure to degree measure, and vice-versa, and determine the arc length or central angle subtended by that arc or radius length of a circle.
- Define periodic function, radian measure, angle in standard position, reference angle, coterminal angles, and sine, cosine, and tangent in terms of a unit circle and in terms of a right triangle.
- Describe the basic propereties of the sine , cosine, and tangent functions, including domain, range, period, amplitude, and graph.
- Apply the Law of Cosines.
- Apply the Law of Sines.
- Apply trigonometric ratios to real life problems.
- Graph trigonometric functions and inverse trigonometric functions.
- Find critical points of polynomial functions

**Instructional Methods:**

- Direct instruction
- Active reading and study of text
- Oral questioning
- Daily work
- Collaborative problem sets

**Evaluation:**

- In-class, full period tests
- Graded homework
- Notebook checks
- Oral presentations
- Semester exams
- Projects
- Labs
- Enrichment problems
- Class participation
- There will be a two hour exam at the end of the semester during the exam week in the fall and spring. The fall exam will be approximately 25 questions dealing with topics such as linear relations and functions, graphing radical and rational functions, quadratic equations and inequalities, sequences and series, and exponential and logarithmic equations. The spring exam will be approximately 25 questions dealing with topics such as trigonometric functions, trigonometric identities and equations, trigonometric curve sketching, conics and calculus topics.

## MAT422 Pre-Calculus Accelerated

**Course Title:**

MAT422 Pre-Calculus Accelerated

**Course Description:**

This is a course for students who have completed three years of high school math. Pre-calculus Accelerated covers the concepts of function, trigonometry, logs and exponents,and conic sections, as well as in introduction to limits. Students will learn to solve multi-step problems requiring the application of two or more concepts. Pre-calculus Accelerated is the prerequisite for Calculus AB AP and should be chosen only by those students with a genuine desire to pursue a rigorous math curriculum and who have a consistently high record of achievement in their three previous years of math study. Grade: 10-12

**Academic Goals:**

- First semester course content will include:
- Review of algebra
- Functions
- Polynomial and rational functions
- Logarithmic and Exponetial Functions

- By the end of the second semester, students will be able to:
- Find exact and approximate values of trig functions (calculator application)
- Graph the trigonometric functions with changes in amplitude, period, phase shift and vertical shift (calculator application)
- Use triangle trigonometry to solve height, distance and angle problems (calculator application)
- Write a trigonometric equation that fits a set of conditions
- Solve problems involving two or more equations or inequalities by substitution, combination of equations, or matrices (calculator application)
- Find equations of and graph lines, circles, parabolas, ellipses and hyperbolas (the conic sections)

**Instructional Methods:**

- Direct instruction
- Study of text: active reading of text with special attention to learning the definitions and understanding how the example problems work, required outlining of material
- Questions to the class and individuals
- One-on-one instruction (back work)

**Evaluation:**

- In-class, full period tests
- Take-home tests
- Quizzes
- Graded daily work
- Oral presentations in class
- Section outlines
- Semester exams
- The semester exams will be of the comprehensive, traditional two-hour type. The exams will include short answer problems, problems that involve the application of several concepts to find a solution with multiple steps and problems that involve the analysis of given information.

- Extended problem sets
- Class participation

## MAT423 - Pre-Calculus Honors

**Course Title:**

MAT423 Pre-Calculus Honors

**Course Description:**

This fast-paced course is an option for students identified for Pre-Calculus, but who have demonstrated outstanding achievement, consistent work ethic, and a genuine love of mathematics. Because Pre-Calculus Honors is the prerequisite for Calculus BC AP, students will learn to understand theory, to master proof techniques, and to grasp the concept of limit and derivative. Both the depth and the pace of the course are greater than encountered in Pre-Calculus, and the expectations of students are much higher. Grade: 11-12

**Academic Goals:**

- First semester course content will include:
- Graphs of functions, their inverses and compositions
- Polynomial and rational functions
- Exponential and logarithmic functions
- Trigonometric functions
- Analytical trignometry

- By the end of the first semester, students will be able to:
- Use the graphing calculator to explore the difference between many types of functions
- Understand function notation and the different ways to express a function
- Handle factoring in a number of ways
- Solve equations and inequalities with and without the graphing calculator
- Make use of trigonometric identities in solving trigonometric equations
- Deal with vectors and their uses in two- and three-dimensional space

- Second semester course content will include:
- Systems of equations and inequalities
- Matrices and determinants
- Sequences, probability and statistics
- Conic sections, rotations of these sections and polar graphs
- Introduction to limits
- Limit Theorems
- Derivatives and their applications
- Anti-derivatives

- By the end of the second semester, students will be able to:
- Solve systems of equations and inequalities with and without the use of a calculator
- Use matrices to help solve multi-variable problems
- See the differences between sequences and series in order to handle problems
- Deal with the concept of limit
- Find and use derivatives properly
- Use anti-derivatives to find velocity and position

**Instructional Methods:**

- Concentrated study of the text, especially definitions and sample problems
- Direct instruction
- Demonstration techniques
- Oral questioning
- One-on-one work (help sessions)
- Daily note taking

**Evaluation:**

- In-class, full period tests
- Take-home tests
- The first semester exam will be a two hour exam covering the topics discussed during the semester. The exam will be similar to both the homework and previous test questions. The topics to be covered will be absolute value, rational inequalities, functions, polynomial and rational functions, exponential and logarithmic functions. The second semester exam will also be two hours with an emphasis on the calculus and related concepts that are discussed during the semester. These will include limits of functions, continuity, differentiation, maximum-minimum problems, partial fractions, arithmetic sequences, arithmetic and geometric series, curve sketching, vectors, trigonometric functions of real numbers, trigonometric functions of angles, and analytic trigonometry.
- Quizzes
- Randomly graded daily work
- Random notebook checks
- Oral presentations in class
- Class participation

## MAT510 - Calculus

**Course Title:**

MAT510 Calculus

**Course Description:**

This course is the choice for students who have successfully completed Pre-Calculus or Pre-Calculus Accelerated at McCallie, or who are new to McCallie with a Pre-Calculus credit from another school. It is a senior-level math course for students desiring an introduction to college level Calculus. The course has three components:(1) a thorough review of pre-calculus skills that are crucial to calculus, (2) finding and using the derivative (differential calculus), and (3) an introduction to integrals (integral calculus). The pace of the course is such that students will not be prepared to take the Advanced Placement Calculus Exam in May. Grade: 11-12

**Academic Goals:**

- First semester course content will include:
- Review of algebra skills
- Review of functions
- Limits
- Continuity of a function
- Derivative of a function
- Extrema of functions

- By the end of the first semester, students will be able to:
- Use coordinate algebra to find slopes of lines, graph lines, find the intersection of lines, graph circles, solve algebraic equations
- Find the domain and range of a function, graph functions, set up and solve problems involving one or more functions
- Use the basic trigonometric identities to solve equations, examine graphs of trigonometric functions
- Understand and find limits
- Understand what it means for a function to be continuous and use the definition to show that a function is continuous
- Find the derivative of algebraic functions
- Find relative maximum and minimum values of functions, determine if a function is increasing or decreasing, determine the concavity of functions
- Set up and solve problems to find maximum and minimum values for given conditions

- Second semester content will include:
- Indefinite integrals
- Definite integrals
- Differential equations
- Applications of integrals
- Review of trigonometry

- By the end of the second semester, students will be able to:
- Find the indefinite integral of algebraic and trigonometric functions
- Find the value of the definite integral of alagebraic and trigonometric functions
- Solve differential equations for given initial values
- Use differentials to solve area, volume and work problems
- Use the basic trigonometric identities to solve equations, examine graphs of trigonometric functions
- Find and apply the derivative of trigonometric functions

**Instructional Methods:**

- Study of text: active reading of text with special attention to learning the definitions and comprehension of example problems
- Direct instruction
- Note taking
- Concepts and problem solving techniques demonstrated by instructor
- Completion of homeworks and quizzes containing problems requiring innovative applications of basic concepts, student demonstrations in class and individual review of daily work with the teacher will encourage student engagement and critical thinking.

**Evaluation:**

- Brief, daily free-response quizzes covering concepts and application of concepts
- Full period tests at appropriate intervals covering all material
- Semester exam; a two-hour exam covering the entire semester containing multiple-choice and free response questions

## MAT512 - Calculus Honors

**Course Title:**

MAT512 Calculus Honors

**Course Description:**

**Academic Goals:**

- First semester course content will include:
- Review of algebra skills
- Review of functions
- Limits
- Continuity of a function
- Derivative of a function
- Extrema of functions

- By the end of the first semester, students will be able to:
- Use coordinate algebra to find slopes of lines, graph lines, find the intersection of lines, graph circles, solve algebraic equations
- Find the domain and range of a function, graph functions, set up and solve problems involving one or more functions
- Use the basic trigonometric identities to solve equations, examine graphs of trigonometric functions
- Understand and find limits
- Understand what it means for a function to be continuous and use the definition to show that a function is continuous
- Find the derivative of algebraic functions
- Find relative maximum and minimum values of functions, determine if a function is increasing or decreasing, determine the concavity of functions
- Set up and solve problems to find maximum and minimum values for given conditions

- Second semester content will include:
- Indefinite integrals
- Definite integrals
- Differential equations
- Applications of integrals
- Review of trigonometry

- By the end of the second semester, students will be able to:
- Find the indefinite integral of algebraic and trigonometric functions
- Find the value of the definite integral of alagebraic and trigonometric functions
- Solve differential equations for given initial values
- Use differentials to solve area, volume and work problems
- Use the basic trigonometric identities to solve equations, examine graphs of trigonometric functions
- Find and apply the derivative of trigonometric functions

**Instructional Methods:**

- Study of text: active reading of text with special attention to learning the definitions and comprehension of example problems
- Direct instruction
- Note taking
- Concepts and problem solving techniques demonstrated by instructor
- Completion of homeworks and quizzes containing problems requiring innovative applications of basic concepts, student demonstrations in class and individual review of daily work with the teacher will encourage student engagement and critical thinking.

**Evaluation:**

- Brief, daily free-response quizzes covering concepts and application of concepts
- Full period tests at appropriate intervals covering all material
- Semester exam; a two-hour exam covering the entire semester containing multiple-choice and free response questions

## MAT515 - AP Calculus AB

**Course Title:**

MAT515 AP Calculus AB

**Course Description:**

This challenging course is the choice for students who have excelled in Pre-Calculus Accelerated or successfully completed Pre-Calculus Honors at McCallie, or who are new to McCallie with a rigorous Pre-Calculus credit from another school. It includes all of the topics of a one-semester college calculus course including limits, derivatives with applications, and the definite integral with applications. Students will frequently practice multiple choice and free-response questions similar to those that appear on the AP exam. All students are expected to take the AB Advanced Placement exam in May. Grade: 10-12

**Academic Goals:**

**Instructional Methods:**

- Direct instruction
- Demonstration techniques
- Study of text: active reading of text, especially definitions and example problems
- Oral questioning
- Daily work (guided practice)
- One-on-one instruction (back work)
- Note taking
- Hands-on, real world project
- Cooperative learning strategies
- Graphing calculator demonstrations and applications

**Evaluation:**

- In-class, full period tests
- Take-home tests
- Quizzes
- Graded daily work
- Graded multiple choice and free response essay questions
- Practice AP exams
- Cumulative semester exam
- The fall semester exam will be a three-hour, sit-down exam designed to mirror the AP Calculus exam format and length. As on the actual AP exam, this exam will contain both multiple choice and free response questions of calculator and non-calculator variety. The students will be provided with extensive review materials, including a set of multiple choice problems from which the actual exam questions will be taken.

- Year-long cumulative review take-home problem sets.
- Extra credit and/or enrichment problems

## MAT520 - AP Calculus BC

**Course Title:**

MAT520 AP Calculus BC

**Course Description:**

This challenging course is the choice for students who have successfully completed Pre-Calculus Honors at McCallie, or who are new to McCallie with a rigorous Pre-Calculus credit from another school. It includes all the topics of a full year college Calculus course including limits, derivatives with applications, the definite integral with applications, parametric and polar equations, vectors, and sequences and series. Students will frequently practice multiple choice and free-response questions similar to those that appear on the AP exam. All students will be expected to take the BC Advanced Placement exam in May. Grade: 10-12

**Academic Goals:**

- First semester course content will include:
- Limits and continuity
- Derivatives and rules for differentiation
- Applications of the derivative
- Integrals
- Applications of the definite integral

- By the end of the first semester, students will be able to:
- Find the limits algebraically and with the aid of a calculator and determine where functions are continuous
- Find derivatives of functions which are given by rules, graphs, or tables
- Determine local extrema and concavity, solve optimization problems
- Understand the relationships between position, velocity and acceleration
- Find the integrals of functions that are given in terms of a rule or a graph
- Understand the relationship between a definite integral and a Riemann sum
- Find areas, volumes, arc length, and surface area using a definite integral
- Use the calculator to find numerical derivatives and definite integrals of functions

- Second semester course content will include:
- Transcendental functions
- Techniques of integration
- Parametric equations and polar coordinates
- Infinite series
- Vector-valued functions
- Variable separable differential equations

- By the end of the second semester, students will be able to:
- Find the derivatives and integrals of the transcendental functions
- Integrate using parts, trigonometric substitution, and miscellaneous substitutions
- Find arc length and surface using parametric equations
- Work with integrals using polar coordinates
- Determine the conditions for the convergence of sequences and series
- Apply the Maclaurin and Taylor series and the Lagrange error estimate
- Find the derivatives and integrals of vector-valued functions
- Use slope fields and Euler's method to solve differential equations

**Instructional Methods:**

- Concentrated study of the text, especially definitions and sample problems
- Direct instruction
- Demonstration techniques
- Oral questioning
- One-on-one work (help sessions)
- Daily note taking

**Evaluation:**

- In-class, full period tests
- Take-home tests
- The first semester exam will be a two hour exam and will be similar to both the homework and previous test questions. The topics to be covered will be limits and derivatives, differentiation rules, applications of differentiation, integrals, and applications of integrals. In May, the students will take the Advanced Placement in lieu of a second semester exam. The AP exam will cover all of the items included in the first semester plus parametric equations and polar coordinates, infinite sequences and series and derivatives and integrals of vector functions. In addition, the student is expected to be able to recall and use concepts from Arithmetic through Precalculus. The AP exam will consist of 28 multiple choice questions without the use of a calculator, 17 multiple choice questions with the use of a calculator, 3 free response questions without the use of a calculator and 3 free response questions with the use of a calculator.
- Quizzes
- Randomly graded daily work
- Random notebook checks
- Oral presentations in class
- Class participation

## MAT530 - AP Statistics

**Course Title:**

MAT530 AP Statistics

**Course Description:**

AP Statistics is a challenging course designed as an elective for those students who have completed or are currently in a Calculus course. This course will introduce students to the major tools for collecting, analyzing, and drawing conclusions from data. Students who successfully complete the course and AP exam during the second semester may receive credit, advanced placement, or both for a one-semester introductory college statistics course. Grade: 11-12

**Academic Goals:**

- Exploring Data: Describing patterns and departures from patterns (20%-30%). Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis should be placed on interpreting information from graphical and numerical displays and summaries.
- Constructing and interpreting graphical displays of distributions of univariate data (dotplot, stemplot, histogram, cumulative frequency plot)
- Summarizing distributions of univariate data
- Comparing distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots)
- Exploring bivariate data
- Exploring categorical data

- Sampling and Experimentation: Planning and conducting a study (10%-15%). Data must be collected according to a well-developed plan if valid information on a conjecture is to be obtained. This plan includes clarifying the question and deciding upon a method of data collection and analysis.
- Overview of methods of data collection
- Planning and conducting surveys
- Planning and conducting experiments
- Generalizations that can be drawn from results and types of conclusions that can be drawn from observational studies, experiments and surveys

- Anticipating Patterns: Exploring random phenomena using probability and simulation (20%-30%). Probability is the tool used for anticipating what the distribution of data should look like under a given model.
- Probability
- Combining independent random variables
- The normal distribution
- Sampling distributions

- Statistical inference: Estimating population parameters and testing hypotheses (30%-40%). Statistical inference guides the selection of appropriate models
- Estimation (point estimators and confidence intervals)
- Tests of significance

**Instructional Methods:**

- Direct instruction
- Demonstration techniques
- Study of text; active reading of text, especially definitions and example problems
- Oral questioning
- Daily work (guided practice)
- One-on-one instruction (backwork)
- Note taking
- Hands-on, real world project
- Cooperative learning strategies
- Graphing calculator demonstrations and applications

**Evaluation:**

- In-class, full period tests
- Take-home tests
- The first semester exam will be a two hour exam and will be similar to both the homework and previous test questions. The topics to be covered will be exploratory analysis as well as planning and conducting a statistical study. In May, the students will take the Advanced Placement in lieu of a second semester exam. The AP exam will cover all of the items included in the first semester exploratory analysis (20%-30% of the exam), planning and conducting a study (10%-15% of the exam), in addition to probability (20%-30% of the exam), and statistical inference (30-40% of the exam).
- Quizzes
- Randomly graded daily work
- Random notebook checks
- Oral presentations in class
- Class participation

## MAT540 - Multivariable Calculus

**Course Title:**

MAT540 Multivariable Calculus

**Course Description:**

This course is for the exceptional math student who has completed Advanced Placement BC Calculus before his senior year. Topics include vectors and surfaces, vector valued functions, partial differential equations and multiple integrals, and vector calculus. Semester Course. Fall only. Grade: 11-12

**Academic Goals:**

- Course content will include:
- Vectors and the geometry of space
- Vector functions
- Partial derivatives
- Multiple integrals
- Vector calculus

- Students will be able to:
- Find dot products, cross products and equations of planes and lines
- Become familiar with cylindrical and spherical coordinates
- Find derivatives and integrals of vector functions
- Understand arc length and curvature
- Work with motion in space: velocity and acceleration
- Find partial derivatives
- Find maximum and minimum values using gradient vectors
- Extend the chain rule to include functions of several variables
- Find double integrals over general regions and in polar coordinates
- Find triple integrals using cylindrical and spherical coordinates
- Work with line integrals and surface integrals
- Understand Green's Theorem and Stokes Theorem

**Instructional Methods:**

- Concentrated study of the text, especially definitions and sample problems
- Direct instruction
- Demonstration techniques
- Oral questioning
- One-on-one work (help sessions)
- Daily note taking

**Evaluation:**

- Due to the nature of the material the students will receive a series of take-home exams.
- The semester exam will be a comprehensive take home exam and the students will have approximately two weeks to complete it. The exam will be similar to both the homework and previous test questions. The topics to be covered will be vectors and geometry of space, vector functions, partial derivatives, multiple integrals and vector calculus.
- Quizzes
- Randomly graded daily work
- Random notebook checks
- Oral presentations in class
- Class participation

## MAT541 - Differential Equations

**Course Title:**

MAT541 Differential Equations

**Course Description:**

This course is for the exceptional math student who has completed Advanced Placement BC Calculus before his senior year. Topics include first order differential equations, second order linear equations, and higher order linear equations. Additional topics may include series solutions of second order linear equations, the Laplace transform, or systems of first order linear equations. Semester Course. Spring only. Grade: 11-12

**Academic Goals:**

- Course content will include:
- First order differential equations
- Mathematical models and numerical methods
- Linear equations of higher order
- Introduction to systems of differential equations
- Linear systems of differential equations
- Laplace transform methods
- Series solutions of Differential Equations(time permitting)

- Students will be able to:
- Solve separable and linear first order equations
- Become familiar with population models, acceleration-velocity models, and the Runge-Kutta Method
- Solve second order linear equations, homogeneous and nonhomogeneous equations
- Work with first order systems using elimination and numerical methods for systems
- Use matrices with linear systems, eigenvalues, and matrix exponentials
- Become familiar with laplace transforms, translation, derivatives, integrals, and products of transforms

**Instructional Methods:**

- Concentrated study of the text, especially definitions and sample problems
- Direct instruction
- Demonstration techniques
- Oral questioning
- One-on-one work (help sessions)
- Daily note taking

**Evaluation:**

- Due to the nature of the course the students will have a series of take-home exams
- The course is offered during the second semester, and there will not be a semester exam.
- Quizzes
- Randomly graded daily work
- Random notebook checks
- Oral presentations in class
- Class participation

## MAT542 - Linear Algebra

**Course Title:**

MAT542 Linear Algebra

**Course Description:**

This fall semester course is available to advanced math students who anticipate taking college level mathematics beyond calculus. For students who successfully completed Advanced Placement AB Calculus earlier, it is paired with Advanced Placement C Calculus to give these students a full-year mathematics option. Linear Algebra may also be taken as an elective concurrently with (but not instead of) Advanced Placement BC Calculus or Multivariable Calculus. Finally, it is available to any student who has successfully completed Multivariable Calculus and Differential Equations. Rather than starting with the abstract definition of a vector space and treating the topics from an entirely theoretical point of view, the intent of this course is to first present the fundamentals if linear algebra through the clearest possible way, through examples, and then to move on to the abstract set of axioms. Topics will include systems of linear equation with matrix solutions, determinates, two and three space vectors, n-dimensional Euclidean spaces, abstract vector spaces, inner product spaces, eigenvalues and eigenvectors, and linear transformations. The course will be conducted in a seminar format with the write up of problems, take-home problem sets, and verbal presentation of problems as a major component to the students' evaluation. Semester Course. Grade: 12

**Academic Goals:**

- Course content will include:
- Introduction to systems of linear equations
- Introduction to matrices
- Determinants
- Vectors in 2-space and 3-space
- Abstract vector spaces
- Inner product spaces
- Eigenvalues and eigenvectors
- Linear transformations

- Students will be able to:
- Read and understand a college level mathematics textbook
- Present problems and proofs orally
- Solve problems in 2- and 3-space applying vector methods
- Understand the logic of proof techniques
- Communicate proofs through written expression
- Work together to solve problems
- Apply abstract theorems and definitions to solve specific problems

**Instructional Methods:**

- Concentrated study of the text
- Direct instruction
- Classroom discussions
- Cooperative problem solving

**Evaluation:**

- Oral presentation of problems
- Oral questioning
- Take-home problem sets
- Written expression of problems and proofs
- Participation in group problem solving activities
- Participation in classroom discussions
- A final presentation masterpiece on an application of Linear Algebra.

## MAT543 - Advanced Mathematical Proofs

**Course Title:**

MAT543 Advanced Mathematical Proofs

**Course Description:**

A second semester course, Abstract Algebra is intended for the very advanced math student who anticipates taking college level mathematics beyond calculus. This course is available to any student who has completed Multivariable Calculus and Differential Equations. Abstract Algebra may also be taken as an elective concurrently with (but not instead of) Advanced Placement BC Calculus or Differential Equations. It is assumed that this will be the first actual theory course the student will have encountered, so the main emphasis of Abstract Algebra will be proof and proof techniques. Since the student will move slowly though the content, this course is not intended to replace a college level Abstract Algebra course that would normally be required for a mathematics major. Topics will include introduction to group theory, homomorphisms and factor groups, rings, fields, and integral domains. The course will be conducted in a seminar format with the write up of problems and verbal presentation of problems as a major component to the students' evaluation. Semester Course. Grade: 12

**Academic Goals:**

- Course content will include:
- Group theory: Finite, Cyclic, and Permutation
- Isomorphism and homomorphism
- Direct products
- Cosets and LaGrange's Theorem
- Normal Subgroups and Factor Groups
- Fundamental Theorem of Finite Abelian Groups
- Introduction to Rings, Fields, Integral Domains, and Ideals.

- Students will be able to:
- Read and understand a college-level math textbook
- Understand the definitions of the abstract structures
- Write original proofs
- Present proof and problem solutions orally
- Communicate proofs and problem solutions in writing
- Understand the logic of proof and be able to apply it to the abstract structures
- Work together in a cooperative manner on group problem solving activities

**Instructional Methods:**

- Concentrated study of the text
- Direct instruction
- Classroom discussion
- Collaborative problem solving

**Evaluation:**

- Oral presentation of problems
- Oral questioning
- Take-home problem sets
- Written expression of problems and proofs
- Participation in group problem solving activities
- Participation in classroom discussions
- The final exam will be oral

## MAT544 - Graph Theory and Combinatorics

**Course Title:**

MAT544 Graph Theory and Combinatorics

**Course Description:**

Graph Theory and Combinatorics with Applications has honors designation, and is designed for students wishing to take a second math course stemming from a genuine desire to study high-level mathematics. There is no pre-requisite other than mathematical maturity and a willingness to spend long hours working on problems which, in the end, will often prove that mathematics gets to win once in a while. It is classified as an elective, but may not be taken as a replacement for the normal calculus-bound sequence, i.e. it must be taken concurrently with Advanced Placement Calculus (either AB or BC), Calculus C, or Differential Equations/Multivariable Calculus. A student in Honors Pre-Calculus may enroll, but only by special appeal to the instructor. Topics will include Introductory Graph Concepts, Trees, Planarity, Graph Coloring, Matching, Ramsey Theory, Basic Counting Techniques, Generating Functions, Polya's Counting Theorem, and a little bit on Infinite Graphs and Combinaorics. The course will be conducted in a seminar format with the write up of problems and verbal presentation of problems as a major component to the students' evaluation. Students will be expected to research topics and present the concepts to the class. It is a full-year, two semester course.

**Academic Goals:**

Students will be able to

1. Read and understand a college-level math textbook.

3. Write original proofs and solve combinatorial problems.

4. Present proof and problem solutions orally.

5. Communicate proofs and problem solutions in writing.

6. Understand the logic of proof and be able to apply it to reading and writing mathematics.

7. Work together in a cooperative manner on group problem solving activities.

8. Lead a seminar group for an entire body of material.

**Instructional Methods:**

3. Classroom discussion

4. Collaborative problem solving

**Evaluation:**

3. Take-home problem sets

4. Written expression of problems and proofs

5. Participation in group problem solving activities

6. Participation in classroom discussions

7. The final exam will be oral.

## Meet the Faculty

### Bailey Adams

**Titles:**Math Teacher

**Degrees:**B.S., University of Mississippi

M.A., Reformed Theological Seminary

M.S., Mississippi College

### Jim Carlone

**Titles:**Mathematics Teacher, Endowed Alumni Chair of Mathematics

**Degrees:**B.A., Kenyon College

### Rob Lyons

**Titles:**Mathematics Department Head, Mathematics Teacher

**Degrees:**B.A., M.S., University of Tennessee at Chattanooga

### Brian Maskarinec

**Titles:**Mathematics Teacher

**Degrees:**B.S., University of Georgia

M.Ed., University of Tennessee

Specialist in Curriculum and Instruction, Lincoln Memorial University