Mathematics Course Descriptions

Algebra I, Part 1*

Course Code 542000

Grade(s): 9-12

1 Credit

Prerequisite: Pre-Algebra (Mathematics 8)

Algebra I, Part I supports and promotes student success in mathematics coursework necessary to fulfill graduation requirements. While strengthening prerequisite skills in the areas of operations with whole numbers, fractions, decimals, percentages, integers, and rational numbers, algebraic concepts are solidified through modeling and the use of manipulatives, graphing calculators, and computer software where appropriate. A concentration on improving problem solving and communication in mathematics builds student confidence. Students may earn one mathematics credit for the Standard Diploma with Credit Accommodations by successfully completing Algebra I, Part 1.

Algebra I, Part 2*

Course Code 543000

Grade(s): 9-12

(if completed in conjunction with Algebra I, Part 1)

1 Credit

Prerequisite: Algebra I, Part 1

SOL Test Algebra I, Part 2 supports and promotes student success in mathematics coursework necessary to fulfill graduation requirements. The study of linear and quadratic equations, linear inequalities, systems of equations, and functions inherent in Algebra are emphasized in the course.

Graphing calculators and other emerging technologies are used to facilitate problem solving, data analysis, and transformational graphing. Students should consult with their school counselor about the credits that may be used to fulfill the mathematics requirements for a high school diploma.

*These courses may only be used as mathematics credits to fulfill the requirements of a Standard Diploma with Credit Accommodations.

Algebra I

Course Code 540000

Course Code 540V00 Virtual Loudoun Online

Grade(s): 9-12

1 Credit

Prerequisite: Pre-Algebra (Mathematics 8)

SOL Test Algebra I incorporates 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 problem solving skills.

Computers and graphing calculator technologies are incorporated into the curriculum in order to allow students opportunities to explore concepts, provide visual models to support the learning of algebraic concepts, and as powerful tools for solving and verifying solutions to equations and inequalities. Mathematical communication and

reasoning are emphasized throughout the course.

Algebra Intervention

Course Code 557700

Grade(s): 9-12

0.5 Credit

Prerequisite: Successful completion of Algebra 1 and non-passing score on the Algebra 1 SOL

SOL Test Algebra Intervention is designed to provide students with tools to help them master topics found on the end of year Algebra I SOL exam. This course will address topics in operations and linear equations, inequalities, linear functions, and data organizations. Students will use functions to represent, model, analyze, and interpret relationships in problem situations. This course will be assigned as needed, and students will take the Algebra 1 SOL. Credit from this course does not count toward the math graduation requirement.

Algebra I Double Block, Part 1

Course Code 543201

Grade(s): 9-12

1 Math Credit

Algebra I Double Block, Part 2

Course Code 543202

Grade(s): 9-12

1 Elective Credit

SOL Test This course is a full-year, two-credit, daily Algebra course. It supports and promotes student success in mathematics coursework necessary to fulfill graduation requirements. While strengthening prerequisite skills, algebraic concepts are solidified through modeling and the use of manipulatives, graphing calculators, and computer software where appropriate. A concentration on improving problem solving and communication in mathematics builds student confidence.

Students must be concurrently enrolled in Algebra I Double Block, Part 1 – Math 0.5 credit and Algebra I Double Block, Part 1 – Elective 0.5 credit during the first semester. During the second, the student must be concurrently enrolled in Algebra I Part 2 – Math 0.5 credit and Algebra I Double Block Part 2 – Elective 0.5 credit. The student has the potential to earn 1 math credit and 1 elective credit.

Geometry

Course Code 550000

Course Code 550V00 Virtual Loudoun Online

Grade(s): 9-12

1 Credit

Prerequisite: Algebra I

SOL Test Geometry is the combined study of plane, solid, and coordinate geometric concepts that provide students with the skills necessary 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. An emphasis on reasoning, problem solving, and proof is embedded in the course and includes two-column proofs, paragraph proofs, and coordinate proofs.

Computers and graphing calculator technologies are incorporated into the curriculum in order to allow students opportunities to explore concepts, engage in inquiry-based learning, provide visual models to support the learning of geometric concepts, and as powerful tools for solving and verifying solutions to equations and inequalities. Mathematical communication and reasoning are emphasized throughout the course.

Functions, Algebra, and Data Analysis

Course Code 565000

Grade(s): 9-12

1 Credit

Prerequisite: Algebra I

Designing experiments and building mathematical models to describe the experimental results allows students to strengthen conceptual understandings of linear, quadratic, and exponential functions. Within the context of mathematical modeling and data analysis, students study functions and their behaviors, systems of inequalities, probability, experimental design and implementation, and data analysis.

Data is generated by practical applications arising from science, business, and finance. Students solve problems that require the formulation of linear, quadratic, exponential, or a system of equations. Through the investigation of mathematical models and interpretation/analysis of data from real-life situations, students strengthen conceptual understandings of 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

Course Code 560000

Course Code 560V00 Virtual Loudoun Online

Grade(s): 9-12

1 Credit

Prerequisite: Algebra I

SOL Test Algebra II provides a thorough 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, and imaginary numbers in the complex number system, allow additional opportunities for modeling and practical applications.

Algebra II/Trigonometry H

Course Code 571000

Course Code 571V00 Virtual Loudoun Online H

Grade(s): 9-12

1 Credit

Prerequisite: Algebra I and Geometry

SOL Test Algebra II/Trigonometry thoroughly studies 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, and imaginary numbers in the complex number system, 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.

Data Science

Course Code 594000

Grade(s): 9-12

1 Credit

Prerequisite: Algebra II

Data Science prepares students to think critically about data and develop the tools, techniques, and principles for reasoning about the world with data. Students will engage in a data science problem-solving structure to interact with large data sets as a means to formulate problems, collect and clean data, visualize data, model using data, and communicate effectively about data formulated solutions. Students will use modern data analysis tools, including computer programming languages. Course topics may include big data, data cleaning, data modeling, data mining, artificial intelligence, correlation and causation, and bias and uncertainty.

Probability and Statistics

Course Code 597700

Grade(s): 9-12

0.5 Credit

Prerequisite: Algebra II

Probability and Statistics (semester course) is an activity-based introduction to statistics and probability. Students will use a statistical cycle throughout the course and conduct a well-designed experiment. Course content includes representing, analyzing, and comparing univariate quantitative data sets, theory of probability, and normal probability distributions. Graphing utilities and other relevant technology tools will be used when appropriate to support instruction, especially to allow students to explore graphical, numerical, and symbolic relationships.

Probability and Statistics

Course Code 597600

Grade(s): 9-12

1 Credit

Prerequisite: Algebra II

Probability and Statistics (full-year course) is an activity-based introduction to statistics and probability. Students will use a statistical cycle throughout the course and conduct a well-designed experiment. Course content includes representing, analyzing, and comparing univariate and bivariate quantitative data sets, theory of probability, binomial and normal probability distributions, and inferential statistics.

Graphing utilities and other relevant technology tools will be used when appropriate to support instruction, especially to allow students to explore graphical, numerical, and symbolic relationships. Mathematical communication, reasoning, problem solving, critical thinking, and multiple representations are emphasized throughout the course.

Discrete Mathematics

Course Code 599700

Grade(s): 9-12

0.5 Credit

Prerequisite: Algebra II

Discrete Mathematics (semester course) is an activity-based, introductory course involving logical reasoning, set and number theory, graph theory, and counting methods. As students solve problems, they will analyze and determine whether a solution exists, investigate how many solutions exist, and focus on finding the best solution.

Technology tools will be used to assist in teaching and learning. Graphing technologies facilitate visualizing, analyzing, and understanding algebraic and statistical behaviors and provide a powerful tool for solving and verifying solutions.

Trigonometry/Advanced Algebra

Course Code 573000

Grade(s): 10-12

1 Credit

Prerequisite: Geometry and Algebra II

Trigonometry/Advanced Algebra explores topics in fundamental trigonometry and extends students' understanding of algebraic functions. Trigonometry concepts include the study of trigonometric definitions, applications, graphing, and solving trigonometric equations and inequalities. Advanced Algebra concepts include the study of polynomial, rational, piecewise, absolute value, radical, step functions, exponential, and logarithmic functions.

Precalculus

Course Code 585000

Course Code 585V01 Virtual Loudoun Online

Grade(s): 9-12

1 Credit

Prerequisite: Geometry and Algebra II

Precalculus emphasizes polynomial, exponential, logarithmic, and rational functions, sequences and series, conic sections, and limits. Trigonometry topics include triangular and circular definitions of the trigonometric functions, establishing identities, special angle formulas, the Law of Sines, the 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. Mathematical communication, reasoning, problem solving, critical thinking, and multiple representations are emphasized throughout the course.

Precalculus DE

Course Code 585006

Grade(s): 9-12

Prerequisite: Geometry and Algebra II

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. Mathematical communication, reasoning, problem solving, critical thinking, and multiple representations are emphasized throughout the course. This course awards 6 college credits. Precalculus DE is taught by LCPS teachers who are also adjunct faculty members at participating colleges.

Mathematical Analysis H

Course Code 586000

Course Code 58670V Virtual Loudoun Online H

Grade(s): 9-12

1 Credit

Prerequisite: Algebra II/Trigonometry or Precalculus

Mathematical Analysis introduces matrix algebra, parametric and polar equations, and vectors. 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 an introduction to calculus topics including limits and continuity; the derivative of functions of a single variable; the first and second derivative tests; and curve sketching. The course of study is enhanced by making connections to the concepts presented in other disciplines.

Students routinely use graphing calculators as tools for exploratory activities and for solving rich application problems. Mathematical communication, reasoning, problem solving, critical thinking, and multiple representations are emphasized throughout the course.

AP Precalculus

Course Code 584200

Grade(s): 9-12

1 Credit

Prerequisite: Geometry and Algebra II

AP Precalculus explores everyday situations and phenomena using mathematical tools and lenses. Students will explore polynomial, rational, exponential, logarithmic, trigonometric, and polar functions. As well as functions involving parameters, vectors, and matrices. Students build deep mastery of modeling and functions, and they examine scenarios through multiple representations. They will learn how to observe, explore, and build mathematical meaning from dynamic systems, and important practice for thriving in an ever-changing world. Students have the opportunity to take the AP Precalculus exam in May with the possibility to earn college credit.

AP Calculus AB

Course Code 585100

Grade(s): 10-12

1 Credit

Prerequisite: Precalculus, AP Precalculus, or Mathematical Analysis

AP Calculus AB explores the topics of limits/continuity, derivatives, and integrals. These ideas are examined using a multilayered 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. Students have the opportunity to take the AP Calculus AB exam in May with the possibility to earn college credit.

AP Calculus BC

Course Code 586100

Grade(s): 10-12

1 Credit

Prerequisite: AP Precalculus, Mathematical Analysis or AP Calculus AB

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 AP Calculus AB course are included, the course 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 AP Calculus BC. Among these are advanced integration techniques including integration by parts, partial fractions and improper integrals; Euler’s method; logistic model with differential equations; arc length of a curve; parametric, polar, and vector functions; the study of infinite sequences and series with radius of convergence and error bounds; and Taylor polynomials and series. The use of the graphing calculator is fully integrated into instruction and students are expected to confirm and interpret results of problem situations that are solved using available technology. Emerging technologies are incorporated into the curriculum and as they become available. Students have the opportunity to take the AP Calculus BC exam in May with the possibility to receive college credit.

AP Statistics

Course Code 598100

Grade(s): 9-12

1 Credit

Prerequisite: Algebra II

The AP Statistics course explores the concepts and skills according to the syllabus available through the College Entrance Examination Board. These topics include collecting 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. Students have the opportunity to take the AP Statistics exam in May with the possibility of earning college credit.

Multivariable Calculus

Course Code 583302

Multivariable Calculus DE

Course Code 583006

Grade(s): 11-12

1 Credit

Prerequisite: AP Calculus BC (Students must receive a 4 or higher on the AP exam)

Multivariable Calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus in several variables. Topics include: Euclidean 3- space; vectors and the dot and cross products; vector functions and their differentiation and integration; normal and bi-normal vectors, curvature and torsion; Rn space; partial derivatives; surface normal; double in Cartesian and polar coordinates; triple integrals in Cartesian, cylindrical and spherical coordinates; and change of variables in multiple integrals. The course culminates with the development of Green’s and Stokes’ theorems and the Divergence theorem which lay the foundation for applied mathematics and physics. The Multivariable Calculus DE course awards 4 college credits.

Computer Mathematics

Course Code 593000

Grade(s): 9-12

1 Credit

Prerequisite: Algebra I

NOTE: LCPS awards a Math credit for this course only. It does not count for a Science or CTE credit.

Computer Mathematics serves as an introduction to Computer Science and to object-oriented programming using JAVA. Students will learn to design graphical interfaces, write browser applets, and create their own games using the principles of OOP (object-oriented programming) using user defined objects, encapsulation of data, and libraries. Students develop and refine skills in logic, organization, and precise expression, thereby enhancing learning in other disciplines. Programming is 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.

AP Computer Science A

Course Code 595100

Grade(s): 10-12

1 Credit

Prerequisite: Computer Mathematics or AP Computer Science Principles

NOTE: LCPS awards a Math credit for this course only. It does not count for a Science or CTE credit.

AP Computer Science A is taught according to the syllabus for Computer Science A, available through the College Entrance Examination Board. Major topics in the course 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. Students have the opportunity to take the AP Computer Science A exam in May with the possibility of earning college credit.

Data Structures DE

Course Code 588800

Grade(s): 11-12

1 Credit

Prerequisite: AP Computer Science A, 3 or higher on exam

NOTE: LCPS awards an elective Math credit for this course only. It does not count for a Science or CTE credit.

This course provides a comprehensive overview of advanced programming topics in Java through Object- Oriented Design. Students will cover Abstract Data Type (ADT) implementations, recursion, inheritance and polymorphism, file handling and exception management. Students will analyze algorithms, study various data structures, and searching and sorting algorithms. Real-world applications illustrate the practical relevance of the learned concepts. Students may earn up to 8 college credits.

AP Computer Science Principles

Course Code 597000

Grade(s): 9-12

1 Credit

Prerequisite: Algebra I

NOTE: LCPS awards an elective credit for this course only. It does not count for a Math, Science or CTE credit.

Following the College Board's suggested curriculum designed to parallel college-level computer science principles courses, the AP CSP course will introduce students to the fundamental ideas of CS and how to apply computational thinking across multiple disciplines. This course will teach students to apply creative designs and innovative solutions when developing computational artifacts. This course will cover such topics as creative development, data, algorithms and programming, computer systems and networks, and the impact of computing.

Cloud Computing H

Course Code 588500

Grade(s): 11-12

1 Credit

Prerequisite: AP Computer Science A

NOTE: LCPS awards an elective credit for this course only. It does not count for a Math, Science or CTE credit.

The Cloud Computing course is a post AP Computer Science A guided independent study course that will introduce students to the fundamental ideas of cloud computing. This course will provide a detailed overview of cloud concepts including: infrastructure, deployment, security and architecture. Students will prepare for the AWS Certified Cloud Practitioner exam.

Data Structures/Artificial Intelligence H

Course Code 588600

Grade(s): 11-12

1 Credit

Prerequisite: AP Computer Science A

NOTE: LCPS awards an elective credit for this course only. It does not count for a Math, Science or CTE credit.

The Data Structures/Artificial Intelligence course is an advanced guided independent study course that will introduce students to data structures including stacks, queues, deques, linked lists, dictionaries, sets, maps and trees. Students will also cover artificial intelligence topics including data collection, linear regression, k nearest neighbor, and neural networks.