 Loudoun County High School
 Mathematics Course Descriptions

Mathematics Course Descriptions(from the LCPS Program of Studies)Grades: 912 Credit: 1
Prerequisite: Algebra I, Part 1 or 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
Grades: 912 Credit: 1
Prerequisite: Algebra I
Geometry is the unified study of plane, solid, and coordinate
geometric concepts which provides student with the skills
requisite for the study of advanced mathematics. Investigations
of lines, planes, congruence, similarity, areas, volumes, circles, and
threedimensional 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 inquirybased learning through
handson 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
twocolumn 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, will
be emphasized throughout the course.Grades: 912 Credit: 1
Prerequisite: Algebra I
Designing experiments and building mathematical models to
describe the experimental results allows 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 will be
generated by practical applications arising from science, business,
and finance. Students will solve problems that require the
formulation of linear, quadratic, exponential, or logarithmic
equations or a system of equations.The investigation of
mathematical models and interpretation/analysis of data from
real life situations, students will strengthen conceptual
understandings in mathematics and further develop connections
between algebra and statistics.Graphing calculators and other
emerging technologies will be incorporated into instruction to
enhance teaching and learning.Mathematical communication,
reasoning, problem solving, critical thinking, and multiple
representations will be emphasized throughout the course.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 will be incorporated into instruction
to enhance teaching and learning.Mathematical communication,
reasoning,problem solving, critical thinking, and multiple
representations will be emphasized throughout the course.Algebra II/Trigonometry
Grades: 912 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 will include trigonometric definitions,
applications, equations and inequalities.The connections between
right triangle ratios, trigonometric functions, and circular functions,
will be emphasized.Graphing calculators and other emerging
technologies will be incorporated into instruction to enhance
teaching and learning.Mathematical communication, reasoning,
problem solving, critical thinking, and multiple representations will
be emphasized throughout the course.(Takes the place of Advanced Algebra with Trigonometry)
Grades: 1012 Credit: 1
Prerequisite: Algebra II
Advanced Functions and Modeling provides opportunities for
students to deepen understanding and knowledge of functionsbased
mathematics.Problem solving and critical thinking will
provide the structure in which functions (polynomial, exponential.
logarithmic, transcendental, and rational) are studied. Experimental
design will provide 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 will be incorporated into instruction to
enhance teaching and learning.Mathematical communication,
reasoning,problem solving, critical thinking, and multiple
representations will be emphasized throughout the course.Advanced Algebra/Precalculus
(Takes the place of Precalculus)
Grades: 1012 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 will 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.Grades: 1012 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.Grades: 1012 Credit: 1
Corequisite: 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 will solve problems
that can be set up as mathematical models. Students will 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 will define a problem; develop,
refine, and implement a plan; and test and revise the solution.Grades: 1112 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.Grades: 1112 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 multilayered approach including the verbal,
numerical, analytical, and graphical analysis of polynomial,
rational, trigonometric, exponential, and logarithmic functions
and their inverses.The student will be expected to relate the
connections among these approaches. Students will also be
required to synthesize knowledge of the topics of the course to
solve applications that model physical, social, and/or economic
situations.These applications should 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.Grades: 1112 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 collect 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 will be
fully integrated into instruction and students will be 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.Grades: 1012 Credit: 1
Prerequisite: Algebra II
The Advanced Placement Statistics course explores theconcepts 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.
College credit and/or advanced placement in college is available
to those students receiving a qualifying score on the Advanced
Placement Examination.Grades: 1112 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 could include Euclidean 3space, 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.Grades: 1012 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 will model the means
by which data are collected, used, and analyzed.This course will
enable 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.Grades: 1012 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 the
curriculum as they become available.