## Mathematics

*“Pure mathematics is, in its way, the poetry of logical ideas.” – Albert Einstein*

Our typical student takes Algebra I in middle school and then progresses through Algebra II, Geometry, Precalculus, and either Advanced Placement Calculus or Advanced Placement Statistics. Students who have accelerated their math study take Advanced Placement Calculus in their junior year and Advanced Placement Statistics in their senior year. Students who go beyond Cambridge Prep's course offerings can opt for college-level courses in linear algebra, discrete mathematics, multivariate calculus, or differential equations or a directed study in mathematics to explore advanced topics such as number theory, combinatorics, and topology.

Students are required to take 4.0 credits of mathematics to graduate and must take one full year of mathematics each academic year.

**Algebra I**- Algebra I investigates traditional algebraic concepts using a variety of problem-solving strategies. Algebra skills are continually reinforced and applied to new topics as students learn to make connections between algebra and real-world situations. Students are expected to become proficient at graphing and solving linear and quadratic equations and at solving linear systems and word problems. Additional topics include radicals and exponents.
**Algebra I Honors**- Algebra I Honors is a fast-paced course, designed for students who have a thorough mastery of pre-algebra skills. Students investigate traditional algebraic concepts using a variety of problem-solving strategies, challenging them to develop skills quickly and then apply them to more complex problems. Students are expected to become proficient not only in the mechanics of a given topic, but also in its application to word problems. Mastery is expected in solving, writing, and graphing linear equations, inequalities, and systems as well as in solving and graphing quadratic equations. Other topics include radicals, exponents, and rational expressions.
**Algebra II**- Algebra II prepares students for trigonometry and precalculus. Students explore polynomial, rational, irrational, and transcendental functions, while developing skills in solving various types of systems of equations and inequalities, manipulating expressions, and graphing. The course is designed so that it promotes inquisitiveness, objectivity, and perseverance in students. In the use of mathematical models of real world phenomena, students learn to apply a variety of mathematical concepts and functions while making interpretations about the real world based on their results. The topics are presented as the study of classes of functions and as the foundation for calculus. In recognizing expressions as a composition of functions, students identify methods for manipulating variables, solving equations and graphing.
**Algebra II Honors**- Algebra II Honors provides students with an in-depth study of second-year algebra with greater breadth, depth, and rigor than is required for the standard Algebra II course. Topics include: polynomial equations and inequalities; functions and their inverses; linear, quadratic, polynomial, and rational functions and their graphs; logarithmic and exponential functions; sequences, and series; and systems of equations, including matrix solutions. Graphing calculators are used to reinforce students’ understanding of the concepts presented.
**Geometry**- This course stresses the development of a system of logic based on deductive reasoning. Students learn definitions and postulates, prove theorems, and build the system of geometry. They also gain the ability to analyze a problem, to hypothesize a conclusion, and then to write a logical, two column formal proof. The class also includes the study of angle relationships of parallel and perpendicular lines; similarity and congruence of polygons; circles, arc, and associated angles; coordinate geometry; area and volume; and constructions.
**Geometry Honors**- This course provides an in-depth study of Euclidean geometry as well as an introduction to transformational, coordinate, and three-dimensional geometries. This course stresses the development of a system of logic based on deductive reasoning. Students learn definitions and postulates, prove theorems, and build the system of geometry. They also gain the ability to analyze a problem, to hypothesize a conclusion, and then to write a logical, two column formal proof.
**Precalculus**- This consists of two parts: mathematical analysis and trigonometry. Mathematical analysis covers topics such as linear systems, polynomial functions, rational functions, exponential and logarithmic functions, conic sections, sequence and series, probability, and basic statistics. Trigonometry uses the techniques that students have previously learned from the study of algebra and geometry. The trigonometric functions studied are defined geometrically rather than in terms of algebraic equations. Facility with these functions and the ability to prove basic identities regarding them are especially important for students intending to study calculus, more advanced mathematics, physics and other sciences, and engineering in college.
**Precalculus Honors**- This course is open to students with strong algebra and geometry skills who show creativity in solving problems, enjoy mathematics, and are interested in studying the subject in depth. In addition to a review of algebra, all of the elementary functions are studied. These functions include polynomials, rational functions, exponential and logarithmic functions, and the circular and trigonometric functions. Other topics include complex numbers, sequences and series, analytic geometry, and matrices and determinants. Graphing calculators help extend each student’s ability to explore and to do more interesting and difficult problems.
**Advanced Placement Calculus AB**- Advanced Placement Calculus AB is primarily concerned with developing the students’ understanding of the concepts of calculus and providing experience with its methods and applications. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally, demonstrating connections among these representations. Topics include functions, graphs, limits, differentiation, and integration.
**Advanced Placement Calculus BC**- Advanced Placement Calculus BC is an extension to Advanced Placement Calculus AB and is recommended for students who excel in mathematics and/or wish to pursue math, science, or engineering in college. It covers all of the topics presented in Advanced Placement Calculus AB to a greater depth and includes polynomial approximations and series.
**Advanced Placement Statistics**- Advanced Placement Statistics introduces students to the major concepts and tools for collecting, analyzing and drawing conclusions from data . Students are exposed to four broad conceptual themes: 1) Exploring Data: describing patterns and departures from patterns; 2) Sampling and Experimentation: planning and conducting a study; 3) Anticipating Patterns: exploring random phenomena using probability and simulation; and 4) Statistical Inference: estimating population parameters and testing hypotheses.
**Multivariate Calculus**- This is a college-level course designed for students who wish to continue the study of calculus with respect to multiple variables and tailored for students who expect to major in chemistry, mathematics, physics, or engineering. Topics include: vectors in 2-D and 3-D, partial derivatives, gradients, multiple integrals, line integrals and their applications, solid analytical geometry in 3-D, parametric curves, optimization in several variables, Green's Theorem, Stoke's Theorem, and the Divergence Theorem.
**Linear Algebra**- Coming soon...
**Discrete Mathematics**- Coming soon....
**Differential Equations**- Coming soon...
**Directed Study in Mathematics**- Students wishing to pursue advanced work in mathematics may propose a directed course of study. Potential courses of study include number theory, combinatorics, and topology.