Math
Mathematics is essential to all scientific research and technology. As a critical component of knowledge, it can be used effectively to refine the thinking abilities of maturing minds for which there exists a great need. In teaching the courses described below, the Mathematics Department seeks to provide a setting in which AOA students will:
- Be exposed to the mathematics curricula needed to accomplish intended career goals.
- Be called upon to demonstrate competency on all levels of the cognitive domain from knowledge to evaluation.
- Utilize the logical problem solving techniques when confronted with mathematical and non-mathematical problems.
The many colleges and universities that our students have attended and hope to attend are increasingly recommending four years (credits) of mathematics courses at the high school level. Even undergraduate programs where mathematics courses play little role, the logical and sequential thought processes nurtured in high school mathematics prove valuable to the professional development and training in virtually all disciplines. Effort is consequently made to incorporate as many application oriented and thought provoking experiences as is possible in our courses.
The major focus of technology for the mathematics courses centers about the appropriate use of calculators both in and out of the classroom. Students regularly use the graphing calculator models from the Algebra Two courses to the Calculus courses while more basic models are used in the Middle School and early Upper School courses.
Any future development of the overall curriculum of AOA can and must be focused around the connection of the various disciplines to one another and to the thinking processes necessary to meet the challenges that our students will certainly face.
Algebra I
Full year - 1 credit ~ Prerequisite: Departmental Approval
Designed for those students who have successfully completed the concepts and skills of Pre-Algebra, this course incorporated the classical topics of beginning Algebra, including operations with signed numbers, writing and solving equations with signed numbers, writing and solving equations and inequalities, exponents, graphing, factoring, and radicals.
Algebra I Honors
Full year - 1 credit ~ Prerequisite: Departmental Approval
Intended for the strong student of mathematics, this course includes the classical topics of beginning Algebra taught in considerable depth and at an accelerated pace. Those eighth grade students who have successfully completed the Pre-Algebra Honors are eligible for this course, as well as strong ninth grade students who are new to the school.
Geometry and Art
Full year - 1 credit ~ Prerequisite: Algebra I
This is the traditional, formal Euclidean geometry course. The nature of the deductive proof is explored, through not emphasized. Students also continue to use their algebraic skills in solving numerical problems dealing with geometric relationships. Topics include congruence, similarity, triangles, other polygons, circles, parallel and perpendicular lines, area, and volume. This course will include four integrated projects involving the art applications of geometry. These projects will be team taught by the Mathematics and Art Departments, allowing the students the added experience of learning mathematics through art.
Geometry and Art Honors
Full year - 1 credit ~ Prerequisite: Algebra I, Departmental Approval
This course is intended for the more advanced student of mathematics. The content of the course is similar to that of Geometry and Art as previously described, but the pace is faster, and the concepts are studied in greater depth. The course will include four integrated projects involving the art applications of geometry. These projects will be team taught by the Mathematics and Art Departments, allowing students the added experience of learning mathematics through art.
Algebra II
Full year - 1 credit ~ Prerequisite: Algebra I
The central ideas of Algebra I are reviewed as students move on the more advanced topics in algebra, including quadratic systems, logarithms, variation, graphing, conic sections, and problem solving. A student-provided graphing calculator is a course requirement. **
Algebra II Honors
Full year - 1 credit ~ Prerequisite: Algebra I, Departmental Approval
Intended for strong students of mathematics, this course continues the study of algebraic concepts in greater depth and at a faster pace. Topics include quadratic systems, logarithms, variation, graphing, conic sections, functions and determinants. A student-provided graphing calculator is a course requirement. **
Pre-Calculus
Full year - 1 credit ~ Prerequisites: Algebra II, Departmental Approval
Pre-Calculus is an elective course for seniors who are above average in their skills and who wish to take four years of mathematics, The content is much the same as that described for the honors Pre-Calculus course but included greater emphasis on applications and problem solving than on theory. A student-provided graphing calculator is a course requirement. **
Pre-Calculus Honors
Full year - 1 credit ~ Prerequisites: Algebra II, Departmental Approval
An elective for honors mathematics students, this course places considerable emphasis upon the thorough investigation of elementary functions and their applications, including those which are trigonometric, logarithmic, exponential, rational, or polynomial in nature. A student-provided graphing calculator is a course requirement. **
To qualify for Pre-Calculus, students must earn at least a B- in the second semester of Algebra II and at least a C- on the Algebra II second semester examination.
Calculus AP
Full year - 1 credit ~ Prerequisites: Pre-Calculus Honors, Departmental Approval
Students expand their understanding of functions as applied to the concepts of limits, derivatives, integrals, and the applications of derivatives and integrals. It is expected that students in this course will take the AP examination in Calculus. A student-provided graphing calculator is a course requirement. **
Probability and Statistics
Fall semester - 1/2 credit ~ Prerequisite: Algebra II
This course is designed to provide students with the fundamental concepts of probability and an introduction to descriptive and basic inferential statistics. It also may be taken concurrently with either Pre-Calculus or Calculus AP courses. A student-provided graphing calculator is a course requirement. **
Functions and Applications
Spring semester - 1/2 credit ~ Prerequisite: Algebra II
This course is designed for students who have not met the requirements for Pre-Calculus. Course content includes a thorough review of exponent and simplification operations and an introduction to basic functions, trigonometric ratios, exponential and logarithmic functions and their applications. A student-provided graphing calculator is a course requirement. **
Applied Differential Calculus
Spring semester - 1/2 credit ~ Prerequisite: Pre-Calculus
This course is designed for students who have not met the requirements for AP Calculus. Course content includes the concept of a limit and the derivatives of polynomial, rational, algebraic, exponential and logarithmic functions, and various applications using those concepts and functions. A student-provided graphing calculator is a course requirement. **
**The Texas Instrument graphic calculator models TI-83, TI-83 Plus, and TI-84 are recommended and will be used in classroom demonstrations.