Mathematics
SHC Graduation requirement: Three years required; must include Algebra and Geometry.
UC/CSU Admissions requirement: Three years required; four recommended; must include Algebra and Geometry.
The mission of the SHC Mathematics Department is to help our students appreciate math and its practices and to develop their individual reasoning abilities. We are committed to providing a rigorous, college preparatory curriculum that meets the needs of all students, through innovative learning activities, real world applications and problem solving, and connections across disciplines. We aim to teach our students how to use diverse mathematical methods, so they can more critically understand the world of mathematics and arrive at objective conclusions about the problems presented to them in the classroom and our world.
SHC schedules ninth graders in appropriate mathematics courses (Algebra I, Advanced Algebra I or Advanced Algebra II) based on eighth grade mathematics grades, high school placement test scores (HSPT), and results of the SHC Math Placement Test.
Incoming ninth graders who have completed a full year of Geometry in middle school may choose to take a challenge exam on Tuesday, August 11. Please note that there is only one opportunity to test out of the Geometry course at SHC; no retakes will be offered. Detailed information and the registration form will be available on the Class of 2030 page later this year.
The SHC Mathematics department offers courses of advanced mathematics study including AP Calculus BC and AP Statistics. Completion of two tenth-grade math classes facilitates a student’s ability to enroll in an AP Calculus course as an upper-division student.
Alternatively, qualified ninth graders may fulfill their Geometry requirement during the summer after ninth grade, via SHC Summer High School (preferred) or through selected online providers. Students should discuss their options with their counselor to ensure they understand the rigor of an accelerated course and to ensure online courses meet SHC requirements. SHC is under no obligation to accept course credit for courses taken without acquiring the necessary pre-approvals. Students must have the approval of the Math Department Chair to pursue the summer option, obtained via the Geometry Enrollment Agreement found in the Schoology > SHC Announcements Group > Resources > 2026-27 Course Registration folder.
Advanced Algebra I (formerly listed as Algebra Honors) prepares students to solve, graph, and interpret the solutions to real world problems using linear equations and inequalities, exponential functions, and quadratic equations. Students will develop fluency with mathematical vocabulary as they frame real world problems within a mathematical context, develop strategies to address the problem, and interpret the solution(s).
By the end of Advanced Algebra II (formerly listed as Advanced Algebra Trigonometry), students will be able to solve algebra problems using rational, irrational and complex numbers. They will also be able to manipulate algebraic expressions and solve problems including polynomials, rational functions, logarithm expressions and conics. Finally, they will be able to solve basic trigonometric problems involving the six trigonometric functions and they will examine, prove, and use trigonometric identities to solve problems.
Prerequisites: A 3.5 GPA in Advanced Algebra I or a 4.0 GPA in Algebra I.
Students completing this course will have an in-depth grasp of elementary functions and their graphs, analytic trigonometry, plane analytic geometry, sequences, series and limits. The course also includes an introduction to differential calculus. Note: Summer courses in Advanced Algebra II will not facilitate placement into Advanced Pre-Calculus.
Prerequisites: A cumulative 3.5 GPA in Advanced Algebra II.
Algebra I (formerly listed as Algebra 1,2) prepares students to solve, graph, and interpret the solutions to real world problems using linear equations and inequalities, exponential functions, and quadratic equations. Students will develop fluency with mathematical vocabulary as they frame real world problems within a mathematical context, develop strategies to address the problem, and interpret the solution(s).
Students who complete Algebra II (formerly Advanced Algebra) will have mastered topics introduced during their first year of Algebra. They will also be able to solve problems involving linear equations, rational numbers, complex numbers and polynomials. Topics will also include conic sections, rational expressions and equations, inverse functions, radical expressions and equations, logarithms and inverse variation. Note: This class is for 11th graders only.
Prerequisites: Geometry 1,2
At the end of this course, students will be able to solve problems involving conic sections, derivatives, integrals and their applications.
Note: this course includes a summer assignment.
Prerequisites: A cumulative 3.5 GPA in Advanced Pre-Calculus or preparatory Calculus
AP Calculus BC is an introductory college-level calculus course. Students cultivate their understanding of differential and integral calculus through engaging with real-world problems represented graphically, numerically, analytically, and verbally and using definitions and theorems to build arguments and justify conclusions as they explore concepts like change, limits, and the analysis of functions. Students who complete this course will be able to solve problems involving sequences, series, power series, Taylor series, parametric equations, polar coordinates, analytic geometry, vectors, vector applications and matrices.
Prerequisites: 1) A 3.0 GPA in Calculus AB 1,2 or 2) A 4 or 5 on the College Board Calculus AB exam.
This year-long course covers two semesters of a college-level elementary statistics class. Topics include data collection and experiment design, exploratory data analysis (graphical and numerical techniques), probability and statistical inference.
Prerequisites: A cumulative 3.0 GPA in Advanced Pre-Calculus or a cumulative 3.5 GPA in preparatory Pre-Calculus or Statistics 1,2.
This course is designed for students who wish to continue to study the concepts of Pre-Calculus through an introduction to differential and integral calculus. Emphasis will be placed on limits, continuity, differential, and integrals of algebraic and trigonometric functions with one variable.
Prerequisites: A cumulative 3.0 GPA in preparatory Pre-Calculus or a cumulative 2.0 GPA in Advanced Pre-Calculus.
Students completing this course will have mastered the fundamental concepts of plane geometry, properties of similarity, congruence, transformations, triangles, polygons, and circles. Studies will focus on application of these concepts to real life situations and assessed using project based presentations.
Prerequisites: Algebra I
Note: qualified rising sophomores may opt to enroll in Geometry in the summer before tenth grade. Because summer curriculum is accelerated, prerequisites for enrolling in SHC's Summer School Geometry OR in an approved online offering are: 1) 4.0 in Algebra I and a B in Physics or 2) 3.5 in Advanced Algebra I and a B in Physics or 3) 2.0 in Advanced Algebra II.
This course is designed for students who wish to expand their knowledge of trigonometric functions. Students will use trigonometry in a variety of applications and word problems. Students completing this course will have an in-depth grasp of how trigonometric equations and functions relate to an xy-coordinate plane graph. Topics include: elementary functions and their graphs, analytic trigonometry, plane analytic geometry, sequences and series.
Prerequisites for school year: 1) A cumulative 3.5 in Algebra II 1,2 2) A cumulative 2.0 GPA in Advanced Algebra II 1,2. Prerequisites for summer: 4.0 in Algebra II or Advanced Algebra II
Note: Students are not eligible to enter Calculus AB Advanced Placement from this course.
This semester course provides a foundation in elementary statistics for students who might take a statistics course in college. Topics include data collection and experiment design, exploratory data analysis and probability. Students will learn how to use computer software and technology to interpret statistical data. Prerequisites: A cumulative 2.0 GPA in Algebra II.
This yearlong course covers one semester of a college-level elementary statistics class. Topics include data collection and experiment design, exploratory data analysis (graphical and numerical techniques), probability and statistical inference. Students will have the opportunity to take the AP Statistics exam but they are not required to do so.
Prerequisites: A cumulative 3.0 in Algebra II or a 2.0 GPA in Advanced Algebra II.
Students completing this course will have the ability to write and solve problems using the six trigonometric functions. Students will also to be able to create and use the unit circle and all of its trigonometric components for problem solving. Students will have the ability to read and graph periodic trigonometric functions. Students will also examine and prove trigonometric identities. This course will be necessary for any student wishing to take Pre-Calculus in college.
Please note: Students who have completed Advanced Algebra II may not enroll in this course, with the exception for students whose performance in the trigonometry portion of the course resulted in a deficient grade. Prerequisites: A cumulative 2.0 GPA in Algebra II.
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