MATHEMATICS COURSES MATHEMATICS COURSES

PreCalculus

Prerequisites: Algebra 2/Trigonometry with a grade of “B-” or better, or departmental approval.

This course provides students with the foundation necessary to take Calculus in Upper School or in college. Topics presented include linear, quadratic, polynomial, and rational functions, exponents and logarithms, analytic geometry, trigonometry, and sequences and series. The concept of function and the connection between the graph and its respective function are emphasized throughout the course. If time permits, limits, probability, linear programming, and/ or matrices are introduced. Using a graphing calculator to analyze graphs and as a problem-solving tool is a significant part of the course.

Honors PreCalculus

Prerequisites: Honors Algebra 2/ Trigonometry with a grade of “B” or better, or departmental approval.

This course is designed to prepare students who have demonstrated a talent for mathematics and possess strong analytical reasoning skills for AP Calculus or a college-level Calculus course. Topics presented include linear, quadratic, polynomial, exponential, rational, logarithmic, and trigonometric functions, conic sections, trigonometry, sequences and series, and probability, time permitting. Limits, optimization, and rate of change are also introduced. Using a graphing calculator to analyze graphs and as a problem-solving tool is a significant part of the course.

Discrete Mathematics

Prerequisites: Precalculus (honors or regular) with a “B” or better, or departmental approval.

Discrete mathematics is the study of mathematical structures that are countable or otherwise distinct and separable. This is in contrast to continuous mathematics, which deals with structures which can range in value over the real numbers, or have some non-separable quality (much of what you study in Calculus). Main topics in Discrete math include combinatorics, probability, set theory, graph theory, and logic and may also include number theory, game theory, cryptography, and computer science applications. For more information on why you should take a Discrete math course, please read https://artofproblemsolving.com/ news/articles/discrete-math. This course will not be designated honors yet will require a strong work ethic and interest in math for you to be successful.

AP Calculus AB

Prerequisites: Honors PreCalculus with a grade of “B” or better, or departmental approval. PreCalculus with a grade of “A”, departmental approval, and independent summer prep work provided by the department.

AP Calculus BC

Prerequisites: AP Calculus AB with a grade of “B” or better, or departmental approval.

Honors Capstone: Data Collection & Analysis

Prerequisites: Algebra 2/Trigonometry with a grade of “B” or better, or departmental approval.

Calculus

Prerequisites: PreCalculus with a grade of “B” or better, or departmental approval.

This introductory course covers the fundamental concepts of differential and integral Calculus. Students learn how these concepts can be applied to the fields of physics, life science, and social sciences. This course presents many of the same topics as AP Calculus AB, but in a less rigorous fashion. Using a graphing calculator to analyze graphs and as a problem solving tool is a significant part of the course.

This course is designed for those students who are planning a major in a subject area in college that requires a Calculus background, or for those who simply have an interest in higher mathematics. Students who successfully complete the course will be prepared for the Advanced Placement Exam (AB) in May. This course offers students a unique opportunity to apply the concepts developed in the Algebra 2-PreCalculus sequence to a wide range of problems. Topics include: limits (computational techniques), differentiation and appropriate formulae, related rates, maximum minimum problems, the mean-value theorem, integration and techniques thereof, the fundamental theorem of Calculus, logarithmic functions, exponential functions, solids of revolutions, and L’Hôpital’s Rule. Students who enroll in the course should realize that the homework load is significant, and they should plan accordingly when arranging their schedules. Using a graphing calculator to analyze graphs and as a problem-solving tool is a significant part of the course.

This course is designed for those students who are planning a major in a subject area in college that requires a Calculus background, or for those who simply have an interest in higher mathematics. Students who successfully complete the course will be prepared for the Advanced Placement Exam (BC) in May. Topics include advanced integration techniques, Simpson’s Rule, related rates, improper integrals, differential equations, slope fields, Euler’s Method, applications to differential equations, infinite series, polar coordinates, vector functions, and parametric functions. Students who enroll in the course should realize that the homework load is significant, and they should plan accordingly when arranging their schedules. Using a graphing calculator to analyze graphs and as a problem-solving tool is a significant part of the course.

This course is similar to an introductory, non-calculus-based, college-level statistics course. Students develop strategies for collecting, organizing, analyzing, and drawing conclusions from data. They will then design, administer, and tabulate results from surveys and experiments. Probability and simulations aid students in constructing models for chance behavior. Sampling distributions provide the logical structure for confidence intervals and hypothesis tests. Students use a TI-nspire graphing calculator, and Web-based applets to investigate statistical concepts. To develop effective statistical communication skills, students are required to prepare frequent written and oral analyses of real data. Students will complete projects throughout the year culminating in a capstone final research project and presentation, applying their knowledge of data collection and analysis to a topic of their choosing.