Upper School Mathematics
Each Miami Valley School student is required (at minimum) to complete
the following sequence of courses: Algebra I, Geometry, and Algebra II.
These courses provide each student with a solid foundation for further
study in mathematics, but students are strongly encouraged to consider
elective terms of mathematics beyond Algebra II. Every high school student,
by the time they enter Algebra II, is expected to have a graphing calculator.
The TI-89 is the recommendation of the department, but the TI-83 is supported.
(Most students eventually acquire the TI-89, though, especially for Calculus.)
Algebra I Full year
Algebra I is the foundation for all other courses in mathematics. It supplies
the language and patterns of reasoning needed for future work in this
important subject. Topics of study are equations, inequalities, polynomials,
functions, graphs, systems of linear equations, rational algebraic expressions,
roots, and quadratic equations.
Geometry Full year
Prerequisite: Algebra I
Geometric concepts included in this course are congruency of triangles,
similarity of triangles, area, volume, properties of perpendicular and
parallel lines, right triangles, circles, and special quadrilaterals.
Students will be exploring these concepts by investigation as well as
by the deductive process. Inductive reasoning will be developed through
measuring and drawing conclusions. Application of algebraic skills and
exposure to proofs will be used to improve deductive reasoning.
Geometry Honors Full year
Prerequisite: Algebra I and Departmental Recommendation
This accelerated and enriched course places emphasis on developing critical
thinking skills. Geometric concepts will be studied in depth as deductive
reasoning is developed. Students with a strong aptitude for mathematics
and with a high level of success in Algebra I will be considered as candidates
for this course.
Algebra II Full year
Prerequisite: Geometry
Algebra II is a study of functions and their applications as mathematical
models of real world phenomena. Topics to be studied include linear functions,
quadratic functions, exponential and logarithmic functions, rational algebraic
functions, irrational algebraic functions, systems of equations and inequalities,
conic sections, sequences, and series. A great deal of emphasis will be
placed on graphing, and a considerable amount of work will require the
use of a graphing calculator.
Algebra II Honors Full year
Prerequisite: Geometry (usually Honors) and Departmental Recommendation
This course comprises a rigorous study of advanced algebra using the Algebra
II syllabus but developing each topic more deeply. Some additional topics
are also included, and there is more emphasis on theoretical problems.
This course proceeds at a rapid pace in order to include much more rigor.
MATHEMATICS DEPARTMENT ELECTIVES
Discrete Math Fall Trimester
Prerequisite: Algebra II
This course will cover many mathematical topics related to computer science.
These may include logic, relations, functions, basic set theory, countability
and counting arguments, proof techniques, mathematical induction, graph
theory, combinatorics, discrete probability, recursion, recurrence relations,
and number theory.
Math Lab Winter Trimester (2 days/week)
All sophomores must take the Ohio Graduation Test in late winter, and
this lab will provide access to sample tests, topics covered, and teacher
support and tutoring. Any student who will struggle with passing the math
portion of the OGT is recommended for this course. Such students will
be identified by their current or previous math teachers, or they may
decide on their own to participate in the lab. Evaluation is Pass/Fail.
(Those not achieving minimum attendance will simply not receive
credit for the course.)
Competitive Math Winter Trimester
The goal of this course is to become better prepared for math competitions
such as the Ohio Math League, the American Math Contests (AMC10 and AMC12),
and the American Invitational Math Exam (AIME), in which we participate
yearly. Daily activities will include problem-solving individually and
in groups, sharing solutions, learning computational "tricks,"
and learning competitive approaches to problem-solving.
Geometry Models Spring Trimester (alternate years)
Remember all of the cool projects at the end of the chapters in math courses
you took? Remember how you never had the time to do them? This course
goes back to those times and lingers on interesting, connective, project-based
math. We'll use Geometer's Sketchpad to investigate mathematical phenomena,
learn to do compass and straightedge constructions, investigate the mathematics
behind some of the puzzles in my collection, and much more. Strong math
ability is not necessary, but a curious mind and enthusiasm are required.
Puzzlemaking Spring Trimester (alternate years)
Can't keep your hands off the brainteasers in Room 2? Ever wonder how
people can produce puzzles with such accuracy? Curious about the math
behind those puzzles? Want to make some of your own? Join the Puzzle-Making
class in the spring and experience all of the above. We will visit the
workshops of local puzzle-makers and collectors. We will design and build
many types of puzzles. We will analyze puzzles to figure out how they
work. The class will be taught jointly by math and fine arts teachers.
There is a $20 fee for supplies.
College Algebra Full year
Prerequisite: Algebra II
College Algebra will revisit and extend the concepts found in Algebra
II, as well as introduce new concepts associated with matrices and trigonometry.
Students in this course will also work to improve the mathematical skills
needed for college entrance examinations. It can serve as an additional
year's preparation for Precalculus, or a good way to reenergize Precalculus
skills after a tough year.
Pre-Calculus* Full year
Prerequisite: Algebra II and Departmental Recommendation
This course is designed primarily for math students who intend to continue
their education in mathematics or science at the college level. After
a brief algebra review, trigonometry occupies much of the fall term, because
of its applicability to Physics, which many Pre-calculus students concurrently
take. Winter term includes a thorough study of functions from linear to
logarithmic and logistic functions, along with parametric and polar equations.
In the spring, matrix algebra, discrete mathematics, and conics are covered.
A brief introduction to probability and statistics is also included.
Pre-Calculus Honors* Full year
Reserved for the very best math students, this course completes the Precalculus
curriculum in two terms, so the Calculus may begin in spring term. AP
Calculus (BC) is next, unless the student elects to drop back to the (AB)
level after the first year.
A.P. Statistics* Full Year
Prerequisite: Pre-Calculus, College Algebra, or Departmental Permission
Statistics can be thought of (oxymoronically) as a precise study of uncertainty.
This course serves to introduce students to the major concepts and tools
for collecting, analyzing, and drawing conclusions from data. Students
will be exposed to four broad conceptual themes: exploring and describing
data, planning a study, probability and simulation, and statistical inference.
Students will be able to express their solutions not merely with correct
answers, but also by describing and defending their methodology.
AP Calculus (AB)* Full year
Pre-requisite: Pre-Calculus or Accelerated Pre-Calculus
AB Calculus is a course in single-variable calculus that includes techniques
and applications of the derivative, techniques and applications of the
definite integral, and the Fundamental Theorem of Calculus. It is equivalent
to at least a semester of calculus at most colleges and universities,
perhaps to a year of calculus at some. It is expected that all students
will take the AP examination in the spring.
AP Calculus (BC)* Full year
Pre-requisite: Accelerated Pre-Calculus
BC Calculus is a course in single-variable calculus that includes all
the topics of AB Calculus (techniques and applications of the derivative,
techniques and applications of the definite integral, and the Fundamental
Theorem of Calculus) plus additional topics in differential and integral
calculus (including paraetric, polar, and vector functions) and series.
It is equivalent to at least a year of calculus at most colleges and universities.
Algebraic, numerical, and graphical representations are emphasized throughout
the course. It is expected that all students will take the AP examination
in the spring.
*Seniors taking math courses following Algebra II may depart at the conclusion
of a trimester, and the student will receive credit for successfully completed
work. Such departures must be in the best interest of the student, and
they must be coordinated with the teacher, advisor, and college counselor.
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