Algebra I establishes the vocabulary and symbolism of algebra and includes evaluating expressions, properties of real numbers, rational and irrational numbers, square roots, function theory, solving and graphing linear equations and systems, solving and graphing linear inequalities and systems, applying exponent properties, scientific notation, simplifying polynomial expressions, solving polynomial equations, basic factoring, solving and graphing quadratic functions, exponential growth and decay, and word problems. Students are introduced to matrices, probability, data analysis, and simplifying and solving rational expressions and equations.
Courses in Algebra II serve as a natural extension of topics covered in Algebra I. The content and pace of the course are rigorous and require students to develop higher-order thinking skills in preparation for precalculus. Topics include polynomial and rational expressions and functions, systems of equations and inequalities, functions, radicals, irrational numbers, complex numbers, synthetic substitution, graphing polynomial functions, composition of functions, inverses, exponential and logarithmic functions, and curve fitting.
Honors Algebra II covers all topics, however, more difficult problems are explored with the expectation that students are highly proficient in Algebra I topics, can work at a very fast pace, will complete extensive assignments, and require minimal extra help from the instructor. Additional topics include advanced problem-solving along with an in-depth examination of functions.
Geometry courses require mastery of the concepts of algebra including quadratics and radical expressions. Students explore both Euclidean and solid geometries with a particular emphasis on plane geometry. Topics of study include an introduction to logic and proofs, triangles, special quadrilaterals, polygons, perimeter and area of figures, surface area and volume of solids, similar shapes (ratio and proportion), circles, and trigonometry. Applications of these topics are incorporated into the lessons and assignments.
Honors Geometry studies additional topics which may include: indirect proofs, sequences, pattern recognition, vectors, volumes of revolution, equations of lines in three space and planes. However, important differences lie in the pacing and emphasis of the course. Additionally, an emphasis is placed on independent learning and higher-level thinking skills. Students are routinely expected to successfully tackle the more challenging problems in planar and solid geometry.
PRECALCULUS & TRIG COURSES
Students in Precalculus/Trig are expected to work at a rigorous pace and to spend a significant amount of time on homework assignments and related activities. Precalculus/Trig topics include conic sections, binomial theorem, sequences and series, counting principles, and introductory probability concepts, compositions of functions, inverse functions, exponential and logarithmic functions. Trigonometry is explored with the emphasis on the circular functions. Students will work extensively on graphing, identities, solutions of right and oblique triangles, and inverse functions and their graphs. Students also study proofs, parametric functions, and complex numbers.
Honors Precalculus/Trig covers all of the topics covered in Precalculus/Trig as well as additional topics in vectors, complex numbers, graphing techniques, end-behavior models, applications, inequalities, parametric and polar equations, conic sections, partial fractions, combinatorics, probability, and sequences and series. Additionally, an emphasis is placed on independent learning and higher-level thinking skills.
In Calculus and AP Calculus AB* courses, the theory of calculus, understanding why and how techniques work and when to use them, is a central focus each time a new topic is presented. The course follows closely, but is not limited to, the topics and techniques specified by The College Board. The differential calculus topics include limits, continuity, curve sketching, derivatives of polynomial functions, exponential/ logarithmic functions, trigonometric and inverse trigonometric functions, and optimization and related rates applications. The integral calculus topics include Riemann sums, the Fundamental Theorem of Calculus, methods of integration, area under a curve, volumes of revolution, differential equations, slope fields, and applications (such as exponential growth and decay).
AP Calculus BC* is a challenging course that continues from where Calculus left off. Students need to have already mastered differentiation and basic integration. The course will review some of the concepts covered in AP Calculus AB but at a higher level. The course follows closely but is not limited to the topics and techniques specified by The College Board. Topics include L’Hopital’s Rule, advanced methods of integration, improper integrals, the calculus of polar functions, infinite sequences and series, Taylor and power series, vector functions, polar calculus, and first-order differential equations and slope fields. Applications will focus on area accumulation, volume, surface area, applied differential equations, growth models, approximation techniques, work, fluid force, center of mass, and business applications.
Multivariable Calculus continues from where AP Calculus BC ended. Specific topics include: three-dimensional coordinate systems, lines, planes, and quadric surfaces; vector-valued functions, parametric equations, and curves in two- and three-dimensional space; arc length and curvature; differential calculus of functions of more than one variable with limits, continuity, partial derivatives differentials, tangent planes, the chain rule, directional derivatives and gradients; maximizing and Lagrange multipliers; integral change of variables; multiple integration in various coordinate systems; line integrals and surface integrals; curl and divergence; The Fundamental Theorem of Line Integrals, Green's Theorem, Stokes' Theorem and the Divergence Theorem.
Students in Statistics and AP Statistics* learn mathematical skepticism and rigorously controlled experimental design and analysis. Topics include counting principles, probability, sampling techniques, exploratory data analysis, probability, probability distributions, normal distributions, and hypothesis testing. Students also engage in a rich and varied experience with applied mathematical concepts including data analysis and interpretation, methods of data collection, and planning and conducting studies. Major topics include descriptive statistics, probability, normal, Chi-Square and t-distributions, confidence intervals and tests of significance. Data analysis requires the use of statistical graphing calculators and modern statistical software.
*Advanced Placement and honors-level courses cover material that is found in regular classes but at a much faster pace, depth, and breadth.