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Mathematics Department Courses
Every student is expected to take mathematics each year.
Students must make at least a C- in order to continue in the
mathematics sequence. Mathematics courses taken in the summer
are for remedial purposes only. In general, the Mathematics
Department does not endorse summer courses in place of courses taken
during the regular school year. Enrichment or remediation courses
taken over the summer are supported.
Students new to Moravian Academy may be required to take a placement
test.
The following is the sequence of math courses for Moravian
Academy students:
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Algebra One |
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Algebra Two |
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Geometry or Geometry (Honors) |
*After Geometry, students are placed in the appropriate courses
chosen from the following:
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Advanced Algebra |
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Precalculus or Precalculus (Honors) |
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Calculus or AP Calculus (AB or BC) |
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Calculus II or college course (usually
Calculus III) |
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Linear Algebra (Honors) |
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Probability & Statistics (elective) |
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AP Statistics (elective) |
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Studies page. |
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| Course Offerings: |
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course descriptions. |
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| Course Descriptions |
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| Algebra I |
2 Semesters, 1 Credit |
| An introduction to modern
algebra. Topics include: polynomials in one and two
variables, solution of linear equations and inequalities,
linear functions and graphing, systems of two equations in
two unknowns, rational algebraic expressions, quadratic
equations solved by factoring, proportions and percents,
square roots, and application problems. |
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| Algebra II |
2 Semesters, 1 Credit |
| A continuation from the Algebra I
study of linear equations. Linear systems and inequalities
are further developed. This course will continue the study
of the complex number system focusing on irrational and
imaginary numbers as solutions to equations. Algebraic
skills for symbolic manipulation of rational and polynomial
expressions are further developed. The concept of linear,
rational, and quadratic functions including their graphs and
methods for solving equations will be developed. |
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| Geometry |
2 Semesters, 1 Credit |
| Euclidean plane geometry is the
focus of this course. Topics include: basic undefined terms,
formal and informal definitions, deductive reasoning,
parallel lines, congruent triangles, quadrilaterals, similar
triangles, right triangles and Pythagorean theorem, right
triangle trigonometry, circles, construction, coordinate
geometry, areas and volumes of plane and solid figures. In
addition, algebra topics are reviewed frequently throughout
the course. |
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| Geometry
(Honors) |
2 Semesters, 1 Credit |
| A rigorous course covering in
detail all the topics included in the Geometry course.
Exercises and problems are more difficult than those in the
Geometry course, proof is emphasized, and the pace is
faster. Special topics include an introduction to
fractal geometry and transformations in the plane. In
addition, algebra topics are reviewed periodically
throughout the course.
Prerequisite: A minimum grade of "B+" in
Algebra II |
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Offerings |
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| Precalculus
(Honors)
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2 Semesters, 1 Credit |
| An intensive course in
preparation for AP Calculus (AB or BC), this course is
rigorous, fast paced, and includes the study of the
properties, techniques of advanced graphing, and techniques
for solving equations of the elementary functions
(specifically polynomial, rational, power, piecewise,
exponential and logarithmic, logistic, and trigonometric),
polar and parametric representation of functions, complex
numbers, sequences and series, and an introduction to matrix
algebra.
Prerequisite: A minimum grade of "B+" in
Geometry (Honors) |
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| Precalulus |
2 Semesters, 1 Credit |
| Elementary functions
(specifically polynomials, rational, power, piecewise,
logarithmic, exponential, and trigonometric), skills for
algebraic manipulation, and methods for solving equations
will be developed. The focus will be on a deep understanding
of the algebraic elementary functions and an introductory
level exposure to logarithmic, exponential, and
trigonometric functions.
Prerequisite: Geometry or Geometry (Honors) |
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| Calculus
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2 Semesters, 1 Credit |
| This course provides the student
with an opportunity to explore the concepts of calculus in a
non-AP setting. Topics to be studied include: the
derivative, tangents to a graph of a function, optimization
analysis, curve sketching, anti-derivatives, area under a
curve, volumes of solids, and differential equations. Other
advanced topics may be explored as time permits. Upon
completion of this course, students should be able to
successfully complete a college-level calculus course.
Prerequisite: Precalculus
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| AP Calculus AB
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2 Semesters, 1 Credit |
| This course covers differential
calculus in the first semester and integral calculus in the
second semester. The use of graphical, numerical, and
analytical methods is emphasized; the graphing calculator is
incorporated throughout. Topics to be studied include: the
derivative, function analysis and curve sketching,
optimization, anti-derivatives, definite integrals and area
under a curve, volumes of solids, differential equations,
and applications of calculus. The syllabus follows the
curriculum outline for Advanced Placement and prepares
students for the AP Calculus AB examination.
Prerequisite: Precalculus (Honors) |
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Offerings |
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| AP
Calculus BC |
2 Semesters, 1 Credit |
| This is a full year
course completely covering the calculus of a single
variable. It consists of all topics covered in AP Calculus
AB plus additional topics including properties of functions
given in parametric, polar, and vector form, more
applications of integrals and integration techniques, and a
thorough study of infinite series. The syllabus follows the
curriculum outline for Advanced Placement and prepares
students for the AP Calculus BC examination.
Prerequisite: A minimum grade of “A-“ in Precalculus
(Honors) |
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Calculus
II (Honors)
(not offered in 2008-2009)
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Fall Semester, ½ Credit |
| A continuation of
the AP Calculus AB syllabus covering those topics in the BC
course not covered in the AB course. These include:
further techniques and applications of integration, improper
integrals, differential equations, infinite series, and
functions given in parametric, polar, and vector form.
Prerequisite: Successful completion of Calculus or AP
Calculus AB
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| Linear
Algebra (Honors) |
Spring Semester, ½ Credit |
| A modern elementary introduction
to linear algebra with an emphasis on techniques and
applications. Topics include: matrix operations, properties
of determinants, vectors in two and three dimensions, linear
transformations, eigenvalues, and eigenvectors.
Prerequisite: Successful completion of AP Calculus
BC or Calculus II |
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Offerings |
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| Advanced
Algebra |
2 Semesters, 1 Credit |
| This course begins with an
extensive review of the topics covered on the SAT. After
that the topics covered will include: linear equations and
inequalities, quadratic equations and inequalities,
polynomial equations and inequalities of high degrees,
rational equations and inequalities. As time permits, topics
in sequences and series will be included as well as an
introduction to statistics and probability.
Prerequisite: Geometry (seniors only) |
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| Probability
& Statistics |
Fall Semester, ½ Credit |
| This one semester course
emphasizes an understanding of data-collecting, interpreting,
and presenting data graphically and analytically.
There is an introduction to inferential statistics.
Elementary probability theory is studied. The TI-84 graphing
calculator is an essential tool in the course.
Prerequisites: Precalculus or Precalculus (Honors) |
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Offerings |
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| AP Statistics |
Spring Semester, ½ Credit |
| This is a one semester course
that expands upon the concepts covered in the fall semester
Probability & Statistics course. Additional topics
include: tests of significance (inference for
distributions), the Chi-Square test, and inference for
regression. The syllabus follows the curriculum
outline for Advanced Placement and prepares students for the
AP exam.
Prerequisites: Probability & Statistics with a
minimum grade of "B" |
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