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Mathematics
The goals of the Mathematics Department are:
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to provide all students in all courses with challenging, interesting,
and stimulating mathematical experiences; |
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for all students to develop mathematical power:
the ability to see the mathematics in real-life situations and
to use mathematical techniques to model situations and solve
real-life problems to foster in students an appreciation for
mathematics as a fascina-ting, diverse, and significant area
of human inquiry; |
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to prepare students for further
study in mathematics and mathematics-related fields. |
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The Mathematics Department is guided by two principles: first,
that all students at Lake Ridge Academy have a successful
experience in mathematics; second, that the courses offered
and methods of teaching reflect current thinking in the mathematics
education community, specifically the principles advocated
in the National Council of Teachers of Mathematics Curriculum
and Evaluation Standards.
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Algebra 1 [320]
(full year; 1 credit; 5 sessions per cycle)
Algebra 1 serves as the bridge between arithmetic and more generalized,
abstract mathematics which undergird not only school mathematics
and science courses but all real-world mathematical processes. Learning
to interpret problems and create appropriate mathematical models
is an essential part of this course, as is developing mastery of
the fundamentals involved in the manipulation of expression and
equations – the “grammar” of mathematics. Mathematical
topics studied include linear equations (and systems of equations)
represented and solved algebraically, numerically, and graphically.
Quadratic equations and the quadratic formula are introduced as
well.
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Geometry [330]
(full year; 1 credit; 6 sessions per cycle)
Geometry is an exploration of the essential elements of the oldest
branch of formal mathematics. A central element of the study of
geometry is the emphasis on proof and deductive reasoning, which
is a distinguishing feature of mathematics as a discipline. Students
in geometry gain mathematical power by learning to conjecture and
justify or refute their conjectures with appropriate and precisely
stated mathematical arguments. In addition to classical synthetic
geometry, coordinate geometry and connections with algebra are explored.
Prerequisite: Completion of Algebra 1 with
a grade of C or higher.
Algebra 2 [340]
(full year; 1 credit; 6 sessions per cycle)
Algebra 2 extends the study of algebraic concepts and techniques.
Students refine their understanding of linear and quadratic functions
and are introduced to polynomials and complex numbers, exponential
and logarithmic functions, rational and irrational functions and
right triangle trigonometry. Students learn mathematical processes
used to model and solve increasingly sophisticated problems. Graphing
calculators are an integral part of this course, helping students
explore abstract mathematical relationships and solve complex and
realistic problems.
Prerequisites: Completion of Algebra 1 and
Geometry with a grade of C or higher.
Honors Geometry [331] & Honors Algebra 2
[341]
(full year; 1 credit; 6 sessions per cycle)
These courses are offered only to highly motivated and unusually
capable students. These sections cover more material in greater
depth than regular sections. Formal reasoning and precise mathematical
communication are emphasized and students are often expected to
go beyond what is covered in class by completing special projects
and papers on their own. Students are selected for the honors section
based on out-standing performance in previous math courses, scores
on standardized tests such as the ERB or PSAT, and the recommendation
of the current math teacher.
Qualified students must demonstrate the ability
to learn new concepts quickly, understand and communicate with the
language of mathematics, and use deductive logic to expand their
knowledge of mathematical processes. They must also demonstrate
the ability to apply their knowledge and intuition to solving challenging
problems.
Eligible students will be notified by the
department.
Students who have completed Algebra 2 may elect
the courses below. In keeping with the recommendations of the National
Council of Teachers of Mathematics, these courses offer a range of
mathematical topics which are intended both to serve the needs and
interests of all students and to broaden their mathematical experience.
Successful experiences in any of these courses prepare students to
pursue further studies in mathematics at the college level. Students
should consult with mathematics faculty members to select courses
which best serve their interests and inclinations. Faculty approval
is necessary for the Honors Precalculus and Advanced Placement Calculus
courses. Approval will be based on the same criteria used for Honors
Geometry and Honors Algebra 2, as outlined above.
Discrete Mathematics [382]
(full year; 1 credit; 5 sessions per cycle)
This course explores an important and relatively new branch of mathematics
which has been developed to address situations such as: priority
decision-making in medicine; least cost analyses in business; critical
path determination in transportation and communication networks;
and the theory of games and transaction analysis. Abstract systems,
such as combinatorics and pattern generation, fractals and geometric
growth are also studied. The use of computer spreadsheets and graphical
analysis is emphasized.
Prerequisite: Completion of Algebra 2 with
a second semester grade of C or higher. Offered in alternate years;
not offered in 2001-2002.
Problem Solving [339]
(full year; 1 credit; 5 sessions per cycle)
Few students get the concentrated practice or time necessary to
fully develop their problem-solving skills. By taking this course,
students learn 22 different strategies for problem solving, while
developing new confidence in themselves. These skills are applicable
across the curriculum, preparing students to be logical thinkers
both in other classes and when taking standardized tests such as
college entrance tests.
Prerequisite: Completion of Algebra
2 with a second semester grade of C or higher. Offered in alternate
years; offered in 2001-2002.
Functions [350]
(full year; 1 credit; 6 sessions per cycle)
This course focuses on the study of the major families of functions.
Particular attention is paid to the graphical representations of
functions and to helping students translate among their graphical,
algebraic and numeric representations. A major part of the year
is spent studying circular and trigonometric functions.
Prerequisite: Completion of Algebra 2 with
a second semester grade of C or higher.
Honors Precalculus AB [351]
(full year; 1 credit; 6 sessions per cycle)
This course prepares students to study AP Calculus AB (or Calculus
in college) the following year. Students extend their understanding
of the major families of functions and their ability to use them
to model a variety of situations. Students also study analytic trigonometry,
sequences and series, conic sections, and polar and parametric equations.
Prerequisites: Completion of Honors Algebra
2 with a second semester grade of B or higher and departmental approval.
Honors Precalculus BC [352]
(full year; 1 credit; 6 sessions per cycle)
This course prepares students to take AP Calculus BC the following
year. Students will cover the Precalculus AB curriculum and begin
the study of Calculus in the fourth quarter.
Prerequisites: Completion of Honors Algebra
2 with a second semester grade of A- or higher and departmental
approval.
Introduction to Calculus [362]
(full year; 1 credit; 6 sessions per cycle)
This course extends the students’ precalculus background and
introduces them to calculus. For about half the year, students study
sequences and series, conic sections, vectors, parametric equations
and polar coordinates. The remainder of the year focuses on the
techniques and applications of differential calculus.
Prerequisite: Completion of Functions with
a second semester grade of C or higher.
Advanced Placement Calculus AB [360]
(full year; 1 credit; 7 sessions per cycle)
This course is a college-level course which introduces students
to the concepts and techniques of differential calculus and its
applications, and to the basics of integral calculus, following
the syllabus published by the College Board. Attention is given
to learning the applications of these techniques to model problems
such as arise in economics or the physical sciences. Students in
this course are expected to take the College Board AB Calculus Advanced
Placement examination, which may result in college credit, depending
on the score achieved and the university attended.
Prerequisites: Completion of Honors Precalculus
AB with a second semester grade of B or higher and departmental
approval.
Advanced Placement Calculus BC [361]
(full year; 1 credit; 7 sessions per cycle)
This course is an intense and demanding course which includes all
the topics covered in the Calculus AB plus additional topics such
as divergence and convergence of series, applications using polar
coordinates and parametric equations, vector valued functions and
improper integrals. Students in this course are expected to take
the College Board BC Calculus Advanced Placement examination, which
may result in college credit, depending on the score achieved and
the college attended.
Prerequisites: Completion of Honors Precalculus
BC with a second semester grade of B or higher and departmental
approval.
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May 16, 2002
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