# Math Department

**Kathy Boehlert - Resource Teacher**

--Phone: 240-740-1377

-- Related Math

**Darlene Brown -**Honors Geometry, Algebra 2

**Nicholas Chused **- Geometry, Financial Math

**Carolyn Fox **- Honors Algebra 2, Precalculus

**Jennifer Fribush **- Geometry, AP Calculus AB

**Carrie Gaffney **- Financial Math, Honors Precalculus, AP Statistics

**Tara Green **- Honors Algebra 2 and Connections

**Charles Hicks **-Financial Math, Algebra 2

**Matthew Lindsley** -Related Math, Algebra 1, Geometry

**Cashawn Merritt **- 2-Year Algebra 2 C/D, Precalculus

**Noelle Mineart **- Algebra 1, Honors Algebra 2

**Darius Oxley **- Algebra 1, Calculus with Applications

**Seydou Romba **- Related Math, Honors Statistics, SAMM (Statistics and Mathematical Modeling)

**Rui (Ruby) Wang **- Algebra 2, Honors Precalculus

**Justin Yoon **- Geometry, AP Calculus BC, Multivariable Calculus

### Courses

### Algebra 1

**Algebra 1A**

Facilitated by the use of technology, the basic structure of real numbers and functions is covered in this course. Properties of functions and relations are studied. Algebraic skills developed include techniques for the solution of linear sentences and representing distances using absolute value. Mathematical modeling of real-life problems is introduced. Problem solving by construction appropriate linear models and the determination of linear functions to fit data sets are studied.

**Algebra 1B**

The skills developed in Algebra 1A are expanded to include quadratic functions and their graphs. Additional skills developed include the solution of systems of equations and inequalities, simplification of irrational expressions and complex algebraic fractions, and factoring. Quadratic functions and systems, technology, and statistical techniques are used to construct models for problem solving.

### Calculus

**Calculus with Applications A**

The introductory topics of this course includes limits and continuity of functions, derivations of functions, and their applications to problems. Students find derivations numerically, represent derivations graphically, and interpret the meaning of a derivations in real world applications. Models of previously studied functions will be analyzed using calculus concepts. This is designated an advanced level course in the honors program.

**Calculus with Applications B**

The topics developed include the relationship between the derivative and the definite integral. The understanding, properties, and applications of the definite integral are included as students learn to explain solutions to problems. Students will model real-world situations involving rates of change using difference of differential equations. This is designated an advanced level course in the honors program.

**Advanced Placement Calculus AB A and B**

The topics studied in AP Calculus A and B are those traditionally offered in the first year of calculus in college. Calculus A is the first semester of this preparation for advanced placement in mathematics in college. The topics developed in Calculus A include limits and continuity of functions; derivatives of algebraic functions and their applications in problems involving area, volume, work; differentiation and integration of trigonometric functions; Elementary differential equations. All advanced placement courses are in the honors program.

**Advanced Placement Calculus BC A and B**

The BC course includes all topics in the AB course, along with the additional topics of series, vectors, polar and parametric functions. Students in BC Calculus generally receive two semesters of Advanced Placement in mathematics.

### Geometry

**Geometry A**

Geometry is studied through the deductive development of relationships in the plane and in space, developed intuitively in previous years. In Geometry A, the indicators include the recognition of geometry's existence in nature and influence in art; developing geometry as a mathematical system; identifying congruent segments and angles in various relationships; using rules about circles chords, secants, and tangent segments; classifying triangles according to side and angle measure; applying rules for parallel and perpendicular lines and for angle measure in triangles; constructing proofs of triangle congruence: identifying solids of revolution and logic. Students can take the course at the honors level.

**Geometry B**

The indicators of Geometry B extend the formal study of deductive thinking of Geometry A to the use of logic to develop properties of implications, disjunctions, and conjunctions and to applying rules of ratio and proportion to similar triangles; applying the Pythagorean Theorem to right triangles; performing basic geometric constructions; constructing direct and indirect proofs; solving problems involving circle areas and lines; and determining surface area and volume of solids. Students can take the course at the honors level.

### Precalculus

**Precalculus A**

Precalculus completes the formal study of the elementary functions taught in Algebra 1 and 2. Students use the mathematical and modeling skills previously developed to study and apply the trigonometric functions. The use of technology and problem solving are emphasized in units covering data analysis, circular functions, and trigonometric inverses and identities. Students will conduct research and write extensively as they prepare for higher levels of mathematics.

**Precalculus B**

The skills and topics from the first semester study of trigonometry are extended to polar coordinates and complex numbers. Conies and quadratic relations are introduced through a locus definition using polar representation. Discrete functions include the Principal of Mathematical Induction, the Binomial Theorem, and sequences and series, where sequences are represented both explicitly and recursively. An oral and written modeling presentation by students provides culminating synthesis to the concept of function.

**Precalculus with Analysis A**

The formal study of elementary functions is continued with the introduction of the trigonometric functions, Students apply technology, modeling, and problem solving skills to the study of these functions in units on circular functions, trigonometric identities and inverses, and applications of trigonometric functions. Vectors in two and three dimensions are studied. Problem simulations are explored in multiple representations: algebraic, graphical, and numeric. This is designated an advanced level course in the honors program.

**Precalculus with Analysis B**

The topics from the first semester study of trigonometry are applied to the study of polar coordinates and complex numbers. Conic sections and quadratic relations are introduced in polar representation and studies in rectangular representations. The concept of limit is applied to discrete functions such as infinite sequences and series and to rational functions. The formal definition of limit is applied to proofs of the continuity of functions and provides a bridge to calculus. An oral and written modeling presentation by students provides culminating synthesis to the concept of function. This is designated an advanced level course in the honors program.

### Related Mathematics A & B

These courses reinforces the essential pre-algebra concepts and skills necessary to function in authentic problem solving situations. Emphasis is on skills and applications related to success in algebra. Support of attainment of algebra I objectives is provided.

### Statistics

**Statistics & Mathematical Modeling A**

Topics of this course include data analysis, probability, simulations, inferential statistics, normal and binomial distributions, techniques of sampling, confidence intervals, and hypothesis testing. Students use exploratory methods to identify patterns and make decisions. By using a hands-on approach and simulations, students gain a strong understanding of statistical concepts. Emphasis is placed on applications and the use of statistics to solve real-life problems. The TI-83 or TI-83 Plus calculator is required for students taking this course.

**Statistics & Mathematical Modeling B**

Modules presented in this course are chosen from a selections of discrete mathematics topics including cryptography and coding, game theory, graph theory, mathematics and architecture, applications of trigonometry, fairness and apportionment, mathematics and careers, investment and finance, and college placement test review. The course provides an application-based approach to the study of mathematical modeling and provides a bridge from high school mathematics to the mathematical applications commonly encountered in a variety of college disciplines. The TI-83 or TI-83 Plus calculator is required for students taking this course.

### Financial Math

Quantitative Literacy is designed to enhance students’ abilities in mathematical decision-making and financial literacy. Topics in mathematical decision-making include issues in health and social sciences, the mathematics of chance, the mathematics of democracy, and mathematics around the house. Financial literacy topics include individual budgeting, investing, credit and loans. Also included are business topics including starting and maintaining a business. Emphasis is on the mathematical aspects of the topics

### Multivariable Equations/Differential Equations A & B

The first semester covers three-dimensional analytic geometry and vectors; the calculus of functions of more than one variable, including

partial derivatives, vector-valued functions, multiple integrals, volumes, surface area, and the classical theorems of Green, Stokes, and

Gauss. The second semester introduces the basic concepts of ordinary differential equations. Must earn 4 or 5 on AP Calculus BC

exam.