Four credits in math are required for graduation. Knowledge and competence in the basic ideas of algebra, geometry, and trigonometry are considered necessary for success in college and for full participation in society. Every student is thus required to complete Advanced Algebra & Trigonometry. In spring, the Department issues each continuing student a formal notice of courses she is qualified to take in the following year.
Beyond that, there are options to suit each student. For a student not intending to take calculus in high school, but wishing to further develop math skills for college, College Algebra is recommended. Statistics is valuable for almost any future educational path. The Economics course develops concepts seen in the news and provides practical knowledge for personal finances. For students with strong skills and perhaps an interest in science, Math Analysis is recommended; it is required in order to eventually take AP Calculus at St. Mary’s. For students wishing to advance further, there are Precalculus and AP Calculus. For students prepared for more advanced mathematics, there are online courses available.
Algebra I
This is a required course, to be taken prior to Geometry. It emphasizes the fundamental skills necessary for students to achieve confidence using variables and solving equations. Topics include linear and quadratic equations, inequalities, polynomials, exponential functions, word problems, and the vocabulary and patterns of reasoning used in mathematics. The core concepts of arithmetic are reviewed, with emphasis on practicing and refining algebraic and problem-solving skills.
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Geometry
Prerequisite: Algebra I.
This course provides an overview of Euclidean geometry, covering the essentials for further work in high school and for the SAT and ACT tests. Topics of study include lines, angles, triangles, polygons, circles, the Pythagorean Theorem, area, volume, and similarity. The calculator (TI-84 Plus or Silver) and dynamic geometry software (Geometer’s Sketchpad) will be used. Principles and skills of algebra are applied in this course.
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Honors Geometry
Prerequisite: Algebra I with an A or A–.
This course proceeds at a faster pace and covers more topics than the regular Geometry course (e.g., proofs, deeper study of circles and polygons, more three-dimensional geometry).
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Advanced Algebra & Trigonometry (2 credits; full block each semester)
Prerequisite: Geometry or Honors Geometry.
This year-long course is for students who want to fulfill the Advanced Algebra mathematics requirement at a moderate pace. It includes everything beyond Geometry needed for the math sections of the SAT and ACT. This includes a thorough treatment of linear and quadratic functions; rational exponents; systems of equations; inequalities; polynomials; plane trigonometry; and an introduction to the circular functions. Logarithms, exponential functions, and power functions are introduced. The graphing calculator is used extensively. Upon completion of this course, students may enroll in Statistics, Economics, College Algebra, or Math Analysis. Students must enroll for both semesters of Advanced Algebra.
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Honors Advanced Algebra & Trigonometry
Prerequisite: B+ or better in Geometry or Honors Geometry and Math Department Approval.
This course is for students who are adept at mathematics and want to advance quickly. It is expected that students who take this course will also take College Algebra or Math Analysis. Students who aim to eventually take calculus should take this course. It includes everything beyond Geometry needed for the math sections of the SAT and ACT, including plane trigonometry and the circular functions. (It may not include exponential functions and logarithms.) It develops in depth—in a way that should require little elaboration later—the ideas associated with linear and quadratic functions. The rapid pace of the course demands a substantial time commitment outside of class.
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Statistics
Prerequisite: Advanced Algebra & Trigonometry (or the Honors course).
Statistics is the branch of mathematics dealing with the collection, organization, analysis, and interpretation of information. It can help answer questions in a variety of fields: Is there really a difference or is it just due to chance? How much risk are we willing to take that we make the wrong decision based on a sample? Is there bias in the process? All students who wish to be informed citizens and prepare for a college-level course are welcome in this class.
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Economics
Prerequisite: Advanced Algebra & Trigonometry (or the Honors course).
This course will cover aspects of economic choices that young adults will encounter. Making sound economic choices is an integral part of college life and after; these choices will be enhanced with knowledge and practice through the Stock Market Game, the Budget Game, and many hands-on exercises and activities. Emphasis is on investing, saving, and credit. In addition, general economic principles and current issues are examined including from a global perspective. Recommended for Seniors.
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College Algebra
Prerequisite: Advanced Algebra & Trigonometry (or the Honors course).
This course is for students who do not intend to take calculus in high school but seek an integration of algebraic concepts necessary for college level mathematics and wish to progress at a moderate pace. Topics include relations and functions, advanced algebraic expressions and inequalities, inverse, exponential, and logarithmic functions, systems and matrices, data analysis, and analytic geometry. The course will address how the topics studied are used in real-life applications. The graphing calculator is used extensively in this class.
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Math Analysis
Prerequisite: B or better in Advanced Algebra & Trigonometry and recommendation of teacher.
This course is for students who may eventually take calculus, as well as for students who want to continue in mathematics at an advanced pace. A further precalculus course is needed after this to prepare for calculus. The course provides a thorough development of the properties and modeling applications of functions commonly used in other fields and in calculus—linear, quadratic, exponential, power, and logarithmic functions. General aspects of functions (e.g., rates of change and inverses) and transformations and symmetries are developed and used in the context of the elementary functions. The course also aims to promote fluency in algebra, problem-solving, and communicating mathematics.
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Precalculus
Prerequisite: Math Analysis.
This course is for students who want to and are able to advance quickly toward taking calculus. It covers at a necessarily rapid pace the essentials needed to start calculus—the ideas associated with piecewise, exponential, logarithmic, power, sinusoidal, inverse trigonometric, polynomial, and rational functions. Also covered are advanced aspects of transformations, compositions, and analytic geometry.
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AP Calculus AB (1 credit; full block fall)
Prerequisite: Precalculus.
After a rapid review of preparatory topics, this course covers limits, derivatives and at least the beginning of integration theory. This course must be followed with either AP Calculus AB II or AP Calculus BC.
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AP Calculus AB II (0.5 credit; half block spring)
Prerequisite: AP Calculus AB.
This course is the continuation of AP Calculus AB that will prepare the student for the AP Calculus AB Exam. It continues to develop calculus through applications of integration and elementary differential equations—somewhat further than a first semester university course. A junior taking this option following AP Calculus AB may take AP Calculus BC the next year.
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AP Calculus BC (1 credit; full block spring)
Prerequisite: AP Calculus AB.
This course is the continuation of AP Calculus AB that will prepare the student for the AP Calculus BC exam. This course extends the development of calculus through applications and techniques of integration, differential equations, and power series. It includes the calculus of polar and parametrized curves. The pace and the difficulty of topics are more severe than in AP Calculus AB and AP Calculus AB II.
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