Mathematics

2023-2024 Course Offerings (4 credits to graduate)

**Please note--there are three summer Mathematics courses at Brophy that are offered as bridge courses for capable students to ascend the curriculum at an expedited pace. These courses do not count against a student's four-credit requirement, however; all students must always be enrolled in a Mathematics course during the regular year.

ALGEBRA I REQUIRED-FULL YEAR

This course is designed to provide students with a basic foundation in algebra. Topics include linear and quadratic equations, factoring, polynomials, functions and inequalities. Students should plan on twenty to thirty minutes of homework per class session.

HONORS ALGEBRA I BY RECOMMENDATION-FULL YEAR

Placement is based upon entrance exam score prior to freshman year. This course covers the same topics as Algebra I, but at a faster pace; the difficulty level is also increased. Thirty minutes of homework can be expected per class session.

HONORS ALGEBRA/GEOMETRY BY TESTING/RECOMMENDATION-FULL YEAR

This course is designed for incoming 9th graders who can demonstrate mastery of concepts within the first semester content of both Algebra I and Geometry, but possess gaps in their understanding of semester two concepts. The course speed-reviews semester one content and then immerses students in work toward mastery of semester two concepts. Students who find success in this course will move into Algebra II or Honors Algebra II as 10th graders and will be on track to take either Honors Calculus or AP Calculus AB as seniors. Students should plan on thirty to forty minutes of homework per class session.

GEOMETRY REQUIRED-FULL YEAR

Prerequisite: Algebra I

This course is designed to acquaint students with the basic structure and vocabulary of geometry as well as develop a proficiency in doing formal proofs. Students can expect approximately thirty minutes of homework per class session.

HONORS GEOMETRY BY RECOMMENDATION-FULL YEAR

Prerequisite: Algebra I and teacher recommendation

This course covers the same topics as Geometry but at a quicker pace and greater difficulty level. Thirty to forty minutes of homework can be expected per class session.

ALGEBRA II REQUIRED-FULL YEAR

Prerequisites: Algebra I, Geometry

This course is designed to prepare students for college-level mathematics. Students can expect approximately thirty to forty minutes of homework per class session.

HONORS ALGEBRA II BY RECOMMENDATION-FULL YEAR

Prerequisite: Algebra I, Geometry, and teacher recommendation

This course covers the same topics as Algebra II but at a faster pace and greater difficulty level. Students can expect approximately forty minutes of homework per class session.

THE FOLLOWING COURSES ARE POST-ALGEBRA II ELECTIVES WHICH COMPLETE THE FOUR-YEAR MATHEMATICS REQUIREMENT FOR SENIORS: ALL PLACEMENTS INCLUDE TEACHER RECOMMENDATIONS.

PRE-CALCULUS FULL YEAR

Prerequisite: Algebra II and teacher recommendation

This course is a full-year pre-calculus course that combines topics from algebra and trigonometry to offer strong preparation for university-level analytical geometry and calculus courses.

AP PRE-CALCULUS FULL YEAR

Prerequisite: Honors Algebra II and teacher recommendation

This course is a full-year advanced pre-calculus course that combines topics from algebra and trigonometry to offer strong preparation for AP Calculus AB, as well as advanced university-level analytical geometry and calculus courses. This full-year course will prepare students to take the AP PreCalculus exam.

HONORS CALCULUS WITH STATISTICAL ANALYSIS FULL YEAR

Prerequisite: Pre-Calculus and teacher recommendation

Honors Calculus With Statistical Analysis combines a project-based approach to studying the fundamental theorem of calculus with a practical, student-centered experience of statistical analysis. Calculus content includes Trigonometric Functions, Modeling using Functions, Rates of Change and Differentials, Accumulation from Rate of Change, Rate of Change from Accumulation, and The Fundamental Theorem of Calculus. This content will be explored through four multi-week, hands-on projects. The course's statistical analysis content builds on introductory statistics and is designed to help students to develop and apply analytical skills that are useful in many areas. These skills include critical thinking, mathematical modeling, statistical analysis, predictive analytics, game theory, optimization and simulation. These skills will be applied to sports in this course, but are equally useful in many areas of study.

AP STATISTICS FULL YEAR

Prerequisite: Solid success in Algebra II or above, and teacher recommendation

The purpose of the AP course in statistics is to introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to four broad conceptual themes: Exploring Data, Sampling and Experimentation, Anticipating Patterns, and Statistical Inference.

AP CALCULUS AB FULL YEAR

Prerequisite: Honors Pre-Calculus and teacher recommendation

This full-year course will prepare students to take the Advanced Placement (AP) Calculus AB exam. Five to six hours of homework per week can be expected.

AP CALCULUS BC FULL YEAR

Prerequisite: “3” or higher on the Calculus AB AP Test and teacher recommendation.

This full-year course will prepare students to take the Advanced Placement (AP) Calculus BC exam. Six to eight hours of homework per week can be expected.

ADVANCED MATH COURSES:

MULTIVARIABLE CALCULUS ONE SEMESTER

Prerequisite: Completion of AP Calculus BC

This course is a look at calculus in three dimensions, exploring the topics usually covered in a Calc 3 university course. Topics include vectors and matrices, partial derivatives, and multiple integrals.

LINEAR ALGEBRA ONE SEMESTER

Prerequisite: Completion of AP Calculus BC & Multivariable Calculus

The course includes the study of systems of linear equations, matrices, determinants, vectors, vector spaces, linear transformations, inner products, eigenvalues and eigenvectors.

DIFFERENTIAL EQUATIONS FULL YEAR

Prerequisite: Completion of Multivariable Calculus and Linear Algebra

This course is an exploration of differential equations including first order differential equations, second order differential equations, systems of differential equations, and LaPlace transforms.