Mathematics

ALGEBRA 1
Full Year - Grades 7-9

This course begins with a study of the axioms of multiplication, addition, and equality. Students are introduced to operations on polynomials, solving quadratic equations, and solving systems of equations and inequalities. Throughout the course, students learn graphing techniques using pencil and paper, graphing calculators, and computers. Students also work with algebraic fractions and trigonometric and quadratic functions, as well as solve word problems requiring a wide variety of algebraic techniques.

Prerequisite: Successful completion of pre-algebra or departmental recommendation

GEOMETRY
Full Year - Grades 9-10

Geometry introduces high school students to concepts of formal logic. Students study the material of Euclidean plane geometry, in particular, the properties of geometric figures, including triangles, polygons, and circles. Congruence and similarity of figures is covered as well as the calculation of area and volume of two and three-dimensional figures. Transformations of geometric figures in the plane are studied in depth. Students perform straightedge and compass constructions, as well as constructions using the Geometer’s Sketchpad software. The Pythagorean Theorem and right-triangle trigonometry are key concepts of the course. Algebra skills are incorporated throughout the course to maintain readiness for Algebra II.

Prerequisite: Successful completion of Algebra 1

ALGEBRA 2/TRIGONOMETRY
Full Year - Grades 9-11

Algebra II students should have mastery of Algebra I material and a thorough familiarity with coordinate geometry. Topics include solving and graphing linear, quadratic, polynomial, rational, exponential, logarithmic and trigonometric equations, functions, relations, and inequalities. Students also learn complex numbers, matrices and determinants, conic sections, sequences and series, and combinatorics and probability.

Prerequisite: Successful completion of Algebra 1 and Geometry

ALGEBRA 2/TRIGONOMETRY HONORS
Full Year - Grades 9-11

This course expands on the basic concepts of algebra and introduces the student to new concepts such as matrices, trigonometry, exponential and logarithmic functions, and complex numbers. All the topics of standard Algebra II are covered, but they are studied in greater depth and at a more rigorous pace. Use of technology is extensive. A graphing calculator (such as a TI-83 or TI-89) is used daily to solve problems and do investigations.

Prerequisite: Successful completion of Algebra 1 and Geometry and departmental recommendation

 

PRE-CALCULUS
Full Year - Grades 10-12

Pre-Calculus students expand their graphing techniques and algebra skills in preparation for calculus. The course provides an advanced treatment of polynomial equations and inequalities, exponents and logarithms, trigonometric functions, triangle trigonometry, polar coordinates, and conic sections. Also introduced are vectors, the binomial theorem, and derivatives. Thorough knowledge of the material in this course is essential for success in calculus. Successful completion of this course qualifies students to enroll in Advanced Placement Calculus AB.

Prerequisite: Successful completion of Algebra 2 and Geometry

PRE-CALCULUS HONORS (UC honors weighted course)
Full Year - Grades 10-12

Pre-Calculus Honors covers all material in the standard Pre-Calculus course but at a faster pace. It proceeds to an introduction to calculus during the fourth quarter. Calculus topics include limits, continuity, the derivative, and differentiation. Successful completion of this course qualifies students to enroll in Advanced Placement Calculus BC.

Prerequisite: Successful completion of Algebra 2 and Geometry and departmental recommendation

ADVANCED PLACEMENT
CALCULUS AB
Full Year - Grades 11-12

Calculus covers the Cartesian plane, limits, and differentiation and integration of algebraic and transcendental functions. Students learn advanced methods of curve sketching and apply calculus to problems in physics, business, and economics. Conceptual understanding is emphasized rather than focus on computational techniques. The graphing calculator is used extensively. Specific topics include Rolle's Theorem, the Mean Value Theorem, and the Fundamental Theorem of Calculus. Enrolled students are required to take the AP Calculus AB exam in May.

Prerequisite: Successful completion of Pre-Calculus and departmental recommendation

ADVANCED PLACEMENT
CALCULUS BC
Full Year - Grades 11-12

This course includes all the material of Calculus AB with additional topics including infinite sequences and series. Calculus BC is concerned with developing the students’ understanding of the concepts of differential and integral calculus and providing experience with methods and applications. The level of work is comparable to a full year of calculus offered in most colleges and universities. The course emphasizes a multi-representational approach to calculus with concepts and problems being expressed graphically, analytically, numerically, and verbally. Broad concepts and wide applications are emphasized rather than focusing on techniques of computation, although techniques of computation will be thoroughly covered. Unifying themes are derivatives, integrals, limits, methods of approximation and applications, and modeling. The technology of the graphing calculator is incorporated into all aspects of the course. Enrolled students are required to take the AP Calculus BC exam in May.

Prerequisite: Successful completion of Pre-Calculus Honors or AP Calculus AB and departmental recommendation

MULTIVARIATE CALCULUS
Grades 10–12 (If mathematically qualified.)

Multivariate Calculus will start with vectors and the geometry of space, focusing on vector functions. We will cover multiple integrals and their applications. A prominent topic will be partial derivatives with maximum and minimum calculations and some work with tangent planes, directional derivatives and gradient vectors. We will finish the year with vector calculus including both Green’s and Stoke’s theorems and the fundamental theorem of line integrals.

Prerequisite: Calculus BC or consent by instructor

ADVANCED PLACEMENT
ECONOMICS
Full Year – Grades 11-12

This course prepares students for both the AP Microeconomics and AP Macroeconomics exams in May. After a brief introduction to basic economic concepts of supply and demand, scarcity, comparative advantage and specialization, economic systems, and marginal analysis, the course blends quantitative reasoning/mathematical models with social science in the study of individual choice and markets (microeconomics) and inflation, unemployment, business cycles, international trade and currencies, and national economic growth (macroeconomics). Micro topics include: the nature and function of product markets, factor markets, market failures, and the role of government at the individual and firm levels. Macro topics include: national measurements of economic performance, aggregate supply and demand models, money and banking, the role of banks and the Federal Reserve Bank in money creation and economic growth, the role of fiscal and monetary policy on unemployment and inflation, and foreign exchange markets and international trade.

Prerequisite: Pre-Calculus or instructor approval

ADVANCED PLACEMENT
STATISTICS
Full Year - Grades 11-12

AP Statistics has four main components: describing and analyzing one and two-variable sets of data, planning studies, anticipating patterns, and developing and confirming statistical models. Students design surveys and explore bias, correlation, sampling error, randomization, control groups, and generalization of results. Statistical models are produced using probability, simulation, and statistical inference. Students explore confidence intervals and tests of significance. AP Statistics focuses on word problems using real world data. Mastery of data analysis is a key component of the course. Enrolled students are required to take the AP Statistics exam in May.

Prerequisite: Successful completion of Pre-Calculus or Algebra 2 and departmental recommendation

DISCRETE MATHEMATICS
Full Year - Grades 11-12

Students will study descriptive statistics including standard deviation, percentiles, and the normal distribution; linear regression; statistical tests; theoretical and experimental probability; Venn diagrams; advanced algebra topics including sequences and series; introductory differential calculus; and financial math. Students will use a TI graphing calculator to explore mathematical functions and linear regression. This course will provide the necessary foundation for quantitative courses offered in college.

Prerequisite: Algebra 2/Trigonometry