Class Descriptions / Math and Math Electives

The 2013-2014 Loudoun County Public Schools Program of Studies can be found here:

2013 2014 LCPS High School Program of Studies

Here is the information about Math Courses available for 2013-2014 (please pay particular attention to the teacher-recommended level for your student when considering a selection):

Algebra I 540000

Grades: 9-12 Credit: 1

Prerequisite:Mathematics 8

Algebra I incorporates all of the concepts and skills necessary for students to pursue the study of rigorous advanced mathematics.The arithmetic properties of numbers are extended to include the development of the real number system.The fundamental concepts of equality, functions, multiple representations, probability, and data analysis guide the activities that allow students to enhance critical thinking skills.Computers are used as tools to enhance the problem solving process and provide students with visual models that augment the learning of algebraic concepts.Graphing calculators are utilized to enhance the understanding of functions and provide a powerful tool for solving and verifying solutions to equations and inequalities. Emerging technologies are incorporated into the curriculum as they become available.

Geometry 550000

Grades: 9-12 Credit: 1

Prerequisite: Algebra I

Geometry is the unified study of plane, solid, and coordinate geometric concepts which provides students with the skills requisite for the study of advanced mathematics. Investigations of lines, planes, congruence, similarity, areas, volumes, circles, and three-dimensional shapes are incorporated to provide a complete course of study. Formal and informal deductive reasoning skills are developed and applied to the construction of formal proofs. Opportunities for inquiry-based learning through hands-on activities and experiences that allow for utilizing computer software to explore major concepts and develop critical thinking skills are provided.An emphasis on reasoning, critical thinking, and proof permeates the course and includes two-column proofs, paragraph proofs, and coordinate proofs.Graphing calculators are utilized to enhance the understanding of functions and provide a powerful tool for solving and verifying solutions to equations and inequalities. Emerging technologies are incorporated into the curriculum as they become available.Mathematical communication, reasoning, are emphasized throughout the course.

Functions, Algebra, and Data Analysis 565000

Grades: 9-12 Credit: 1

Prerequisite: Algebra I

Designing experiments and building mathematical models to describe the experimental results allow students to strengthen conceptual understandings of linear, quadratic, exponential, and logarithmic functions.Within the context of mathematical modeling and data analysis, students will study functions and their behaviors, systems of inequalities, probability, experimental design and implementation, and analysis of data. Data is generated by practical applications arising from science, business, and finance. Students solve problems that require the formulation of linear, quadratic, exponential, or logarithmic equations or a system of equations.Through the investigation of mathematical models and interpretation/analysis of data from real life situations, students strengthen conceptual understandings in mathematics and further develop connections between algebra and statistics.Graphing calculators and other emerging technologies are incorporated into instruction to enhance teaching and learning.Mathematical communication, reasoning, problem solving, critical thinking, and multiple representations are emphasized throughout the course.

Algebra II 560000

Grades: 9-12 Credit: 1

Prerequisite: Algebra I and Geometry

Algebra II provides a thorough treatment of advanced algebraic concepts through the study of functions, including parent functions, families of functions, and transformational graphing.Transformational graphing uses translations, reflections, dilations, and rotations, to generate a family of graphs from a parent graph.The continued study of equations, systems of equations, inequalities, and systems of inequalities builds on Algebra I concepts while polynomials, imaginary numbers in the complex number system, matrices, and sequences and series allow additional opportunities for modeling and practical applications.Graphing calculators and other emerging technologies are incorporated into instruction to enhance teaching and learning.Mathematical communication, reasoning, problem solving, critical thinking, and multiple representations are emphasized throughout the course.

Algebra II/Trigonometry, weighted 0.5 571000

Grades: 9-12 Credit: 1

Prerequisite: Algebra I and Geometry

Algebra II/Trigonometry provides a thorough treatment of advanced algebraic concepts through the study of functions, including parent functions, families of functions, and transformational graphing.Transformational graphing uses translations, reflections, dilations, and rotations, to generate a family of graphs from a parent graph.The continued study of equations, systems of equations, inequalities, and systems of inequalities builds on Algebra I concepts while polynomials, imaginary numbers in the complex number system, matrices, and sequences and series allow additional opportunities for modeling and practical applications.The study of trigonometry includes trigonometric definitions, applications, equations and inequalities. The connections between right triangle ratios, trigonometric functions, and circular functions, are emphasized.Graphing calculators and other emerging technologies are incorporated into instruction to enhance teaching and learning.Mathematical communication, reasoning, problem solving, critical thinking, and multiple representations are emphasized throughout the course.

Statistics and Probability 597700

Grades: 10-12 Credit: 0.5

Prerequisite: Algebra II

Elementary probability and statistics are studied with an emphasis on collecting data and interpreting data through numerical methods. Specific topics include the binomial and normal distributions, probability, linear correlation and regression, and other statistical methods. Students are expected to understand the design of statistical experiments.They are encouraged to study a problem, design and conduct an experiment or survey, and interpret and communicate the outcomes.Through meaningful activities and simulations, students are provided with experiences that models the means by which data are collected, used, and analyzed.This course enables students to be wise users of statistical methods and more critical consumers of statistical materials.The use of computers and calculators should enhance the learning process and provide students with experiences working with emerging technologies.

Discrete Mathematics 599700

Grades: 10-12 Credit: 0.5

Prerequisite: Algebra II

Discrete Mathematics involves applications using discrete variables rather than continuous variables.Modeling and understanding finite systems is central to the development of the economy, the natural and physical sciences, and mathematics itself. Discrete Mathematics introduces the topics of social choice as a mathematical application, matrices and their uses, graph theory and its applications, and counting and finite probability, as well as the processes of optimization, existence, and algorithm construction. Emerging technologies are incorporated into thecurriculum as they become available.

Advanced Functions and Modeling 572000

Grades: 10-12 Credit: 1

Prerequisite: Algebra II

Advanced Functions and Modeling provides opportunities for students to deepen understanding and knowledge of functions based mathematics. Problem solving and critical thinking provide the structure in which functions (polynomial, exponential, logarithmic, transcendental, and rational) are studied. Experimental design provides the foundation for data gathering, curve sketching, and curve fitting in order to provide a graphical interpretation of real world situations.Graphing calculators and other emerging technologies along with the precepts of transformational graphing are incorporated into instruction to enhance teaching and learning.Mathematical communication, reasoning, problem solving, critical thinking, and multiple representations are emphasized throughout the course.

Advanced Algebra/Precalculus 585000

Grades: 10-12 Credit: 1

Prerequisite: Algebra II

Advanced Algebra/Precalculus emphasizes polynomial, exponential, logarithmic, and rational functions, theory of equations, sequences and series, conic sections, limits, mathematical induction, and the Binomial Theorem . Trigonometry topics include triangular and circular definitions of the trigonometric functions, establishing identities, special angle formulas, Law of Sines, Law of Cosines, and solutions of trigonometric equations.Constructing, interpreting, and using graphs of the various function families are stressed throughout the course of study. Students are encouraged to explore fundamental applications of the topics studied with the use of graphing calculators. Emerging technologies are incorporated into the curriculum as they become available.

Mathematical Analysis, weighted 0.5 586000

Grades: 10-12 Credit: 1

Prerequisite: Algebra II/Trigonometry or

Advanced Algebra/Precalculus

Mathematical Analysis introduces mathematical induction, matrix algebra, vectors, and the Binomial Theorem. A detailed treatment of function concepts provides opportunities to explore mathematics topics deeply and to develop an understanding of algebraic and transcendental functions, parametric and polar equations, sequences and series, conic sections, and vectors. Mathematical Analysis also includes precalculus topics such as limits and continuity, the derivative of functions of a single variable and curve sketching.The course of study is enhanced by making connections of the concepts presented to other disciplines. Students routinely use graphing calculators as tools for exploratory activities and for solving rich application problems. Emerging technologies are incorporated into the curriculum as they become available.

Computer Mathematics 593000

Grades: 10-12 Credit: 1

Co-requisite: Algebra II

Computer Mathematics provides students with experiences in workplace computer applications, personal finance, essential algebra skills necessary for college mathematics, and computer programming techniques and skills. Students solve problems that can be set up as mathematical models. Students develop and refine skills in logic, organization, and precise expression, thereby enhancing learning in other disciplines. Programming should be introduced in the context of mathematical concepts and problem solving. Students define a problem; develop, refine, and implement a plan; and test and revise the solution. For students entering the 9th grade for the first time in 2010-2011 or after, Computer Mathematics may not count as one of the four mathematics courses required for an Advanced Studies diploma.

Computer Science A

Advanced Placement, weighted 1.0 with AP exam 595100

Grades: 11-12 Credit: 1

Prerequisite: Computer Mathematics

Advanced Placement Computer Science A is taught according to the syllabus for Computer Science A available through the College Entrance Examination Board.Major topics in AP Computer Science A include programming methodology, algorithms, and data structures.Topics are extended to include constructs,data types, functions, testing, debugging, algorithms, and data structures.The JAVA programming language is used to implement computer based solutions to meaningful problems.Treatments of computer systems and the social implications of computing are integrated into the course.College credit and/or advanced placement in college is available to those students receiving a qualifying score on the Advanced Placement Examination. AP final grades are “weighted”by 1.0 if the student passes the course and elects to take the related AP examination.

Calculus AB

Advanced Placement, weighted 1.0 with AP exam 585100

Grades: 11-12 Credit: 1

Prerequisite:Mathematical Analysis or

Advanced Algebra/Precalculus

Advanced Placement Calculus AB explores the topics of limits/continuity, derivatives, and integrals.These ideas are examined using a multi-layered approach including the verbal, numerical, analytical, and graphical analysis of polynomial, rational, trigonometric, exponential, and logarithmic functions and their inverses.The student is expected to relate the connections among these approaches. Students are also required to synthesize knowledge of the topics of the course to solve applications that model physical, social, and/or economic situations.These applications emphasize derivatives as rates of change, local linear approximations, optimizations and curve analysis, and integrals as Reimann sums, area of regions, volume of solids with known cross sections, average value of functions, and rectilinear motions. Emerging technologies are incorporated into the curriculum as they become available. College credit and/or advanced placement in college is available to those students receiving a qualifying score on the Advanced Placement Examination. AP final grades are “weighted”by 1.0 if the student passes the course and elects to take the related AP examination.

Calculus BC

Advanced Placement, weighted 1.0 with AP exam 586100

Grades: 11-12 Credit: 1

Prerequisite:Mathematical Analysis or

Calculus AB—Advanced Placement

Advanced Placement Calculus BC is intended for students who have a thorough knowledge of analytic geometry and elementary functions in addition to college preparatory algebra, geometry, and trigonometry. Although all of the elements of the Advanced Placement Calculus AB course are included, it provides a more rigorous treatment of these introductory calculus topics. The course also includes the development of the additional topics required by the College Entrance Examination Board in its syllabus for Advanced Placement Calculus BC. Among these are parametric, polar, and vector functions; the rigorous definition of limit; advanced integration techniques; Simpson’s Rule; length of curves; improper integrals; Hooke’s Law; and the study of sequences and series.The use of the graphing calculator is fully integrated into instruction and students are called upon to confirm and interpret results of problem situations that are solved using available technology. Emerging technologies are incorporated into the curriculum as they become available. College credit and/or advanced placement in college is available to those students receiving a qualifying score on the Advanced Placement Examination. AP final grades are “weighted”by 1.0 if the student passes the course and elects to take the related AP examination.

Statistics

Advanced Placement, weighted 1.0 with AP exam 598100

Grades: 10-12 Credit: 1

Prerequisite: Algebra II

The Advanced Placement Statistics course explores the concepts and skills according to the syllabus available through the College Entrance Examination Board.These topics includecollecting and interpreting data through numerical methods, binomial and normal distribution, probability, linear correlation and regression, analysis of variance, and other descriptive statistical methods. Students should be able to transform data to aid in data interpretation and prediction and test hypotheses using appropriate statistics. Emerging technologies are incorporated into the curriculum as they become available. College credit and/or advanced placement in college is available to those students receiving a qualifying score on the Advanced Placement Examination. AP final grades are “weighted”by 1.0 if the student passes the course and elects to take the related AP examination.

Multivariable Calculus (only offered through NVCC--see Counselor)

Dual Enrollment, weighted 0.5 583000

Grades: 11-12 Credit: 1

Prerequisite: Calculus BC—Advanced Placement

Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus in several variables.Topics may include Euclidean 3-space, vector functions, derivatives and curvature and torsion, Rn space, surface normals, the Taylor polynomial, power and Taylor series, multivariable integration, vector function integration, and theorems by Gauss, Green, and Stokes.