Algebra 1 - This first year course in algebra provides an important base for all high school mathematics. Topics include factoring; rational expressions; systems of equations; lines; solving linear, fractional and quadratic equations; solving inequalities; rational and irrational numbers; and exponents including negative exponents.
Geometry - Prerequisite: Algebra 1. This proof-based course in plane and solid geometry focuses on teaching students logical methods. Topics include segments, angles, deductive reasoning, parallel and perpendicular lines, coordinate geometry, congruent and similar triangles, quadrilaterals, right triangle trigonometry, circles, and area and volume. Proper presentation of a mathematical proof in two-column form is a major point of emphasis.
Geometry (Honors) - Requires departmental approval. Prerequisite: Superior performance in Algebra 1. This enriched course in plane and solid geometry includes the topics listed above for Geometry but approaches the topics in a more formal, axiomatic way. Euclidean Geometry serves as an excellent introduction to the advanced young student of the beauty and rigor of a formal mathematical system, and great emphasis is put on proofs with thorough justification via definitions, postulates, and theorems.
Algebra 2 - Prerequisite: Algebra 1 and Geometry. This second year algebra course prepares students for the study of Pre-calculus. Topics include review of Algebra I concepts; rational expressions; radicals; rational exponents; equations and linear inequalities; functional analysis including graphs, transformations, piecewise and composite functions, quadratics and polynomials, and rational functions; rational and polynomial inequalities; probability and counting; inverse functions; exponential and logarithmic functions; systems of equations; circles and parabolas; sequences and series; and an introduction to trigonometry including radians, the unit circle, and right triangles.
Algebra 2 (Honors) - Requires departmental approval. Prerequisite: Superior performance in Algebra 1 and Geometry. This rigorous course in algebra and pre-calculus covers a large amount of material in greater depth than the standard two year Algebra 2 – Pre-calculus sequence. Students who successfully complete this course may proceed directly to AB Calculus (AP).
Functions and Discrete Mathematics - Requires departmental approval. Prerequisite: Algebra 2 This course offers a brief review of algebra concepts, a preview of Pre-calculus topics, and an introduction to discrete mathematics. Topics include exponential and trigonometric functions, sequences, statistics, voting and apportionment, and operations science. These topics will be studied through applications, including those in economics, finance, and environmental science, and will rely heavily on both the TI-83 graphing calculator (or equivalent) and Microsoft Excel. This course is for fifth-form students who have completed Algebra II and wish to strengthen and broaden their mathematical backgrounds before taking Pre-calculus or AP Statistics.
Pre-Calculus - Requires departmental approval. Prerequisite: Good performance Algebra 2. This course in pre-calculus mathematics is designed to prepare students for the study of calculus. Topics include analysis and graphing of a variety of functions (polynomials, rational, exponential and logarithmic, and trigonometric), trigonometry (verifying identities, applications for both right triangles and non-right triangles), conic sections, systems of equations, probability and statistics.
Pre-Calculus (Honors) - Requires departmental approval. Prerequisite: Superior performance in Algebra 2 or Algebra 2 (Honors). This course is an enriched course in pre-calculus mathematics, studying topics in greater depth than in the regular Pre-calculus course. Topics include those in Pre-calculus as well as additional topics including matrices and an introduction to calculus.
Statistics - Requires departmental approval. Prerequisite: Algebra 2. This course in probability and statistics covers a wide range of statistical material, including displays of quantitative and categorical data (e.g. boxplots, scatterplots, contingency tables), measures of spread, relationships between quantitative variables (including linear regression), randomness and probability, data collection (experiment and surveys), random variables in probability models, and statistical inference (hypothesis testing and confidence intervals). This course does not prepare students for the Advanced Placement exam.
Statistics (AP) (Honors) - Requires departmental approval. Prerequisite: Pre-calculus or Functions and Discrete Mathematics. This honors course in probability and statistics covers a wide range of statistical material, including displays of quantitative and categorical data (e.g. boxplots, scatterplots, contingency tables), measures of spread, relationships between quantitative variables (including linear regression), randomness and probability, data collection (experiments and surveys), random variables in probability models, and statistical inference (hypothesis testing and confidence intervals). Special emphasis is placed on the interpretation of those topics, and practical applications are emphasized. This course prepares students for the Advanced Placement Exam in Statistics.
Calculus - Requires departmental approval. Prerequisite: Good performance in Pre-calculus or Pre-Calculus (Honors). This introductory course in calculus emphasizes differential calculus, but some time is also spent on integral calculus. Topics include limits, derivatives, antiderivatives, integrals including the Fundamental Theorem of Calculus, and applications of the derivative including graphical analysis and relative and absolute extrema problems. This non-honors calculus course does not prepare students for the Advanced Placement exam.
Calculus AB (AP) (Honors) - Requires departmental approval. Prerequisite: Superior performance in Algebra 2 (Honors) or Pre-calculus or Pre-Calculus (Honors). This honors level course studies topics in both differential and integral calculus. Topics include limits and continuity; derivatives including implicit, exponential, logarithmic, and inverse trigonometric functions; applications of derivatives including graphing, first and second derivative tests, rectilinear motion, and maximum and minimum problems; antiderivatives and integration including the Fundamental Theorem of Calculus; area between two curves and volumes by slicing; and separable differential equations. This course prepares students for the Advanced Placement exam for Calculus AB.
BC/Multivariable Calculus (AP) (Honors) - Requires departmental approval. Prerequisite: Successful completion of Calculus AB (AP). This course continues the calculus sequence started in Calculus AB (AP). The topics covered at the start of the course complete the study of single variable calculus including methods of integration, sequences and series, and polar and parametric functions. Included among the topics for multivariable calculus are three dimensional space, vectors, vector-valued functions, curvature, partial derivatives, multiple integrals and their applications including Green’s Theorem and Stokes’ Theorem. This course prepares students for the Advanced Placement exam for Calculus BC.
Graph Theory and Proof (Honors) - Requires departmental approval. This course is for those students who have completed or are concurrently taking BC/Multivariable Calculus (AP/Honors). This is a course in discrete mathematics, methods of mathematical proof, and introductory graph theory. Emphasis will be placed on daily presentation of material from the reading. Topics include logic, congruence, induction and recursion, algorithms, graphs, and applications. (Not offered 2011-2012)
Advanced Mathematics Seminar (Honors) - Requires departmental approval. This course is for those students who have completed or are concurrently taking BC/Multivariable Calculus (AP/Honors). Topics in undergraduate mathematics will be studied as chosen by the instructor. Topics may include, but are not limited to, Chaotic Dynamical Systems, Logic and Set Theory, Number Theory, Advanced Geometry, Stochastic Processes, Mathematical Modeling, Complex Analysis, Linear Algebra, and Differential Equations.