# Departments & Courses

## Mathematics

*SHC Graduation requirement: Three years required**UC/CSU Admissions requirement: Three years required; four recommended*

#### Our Mission

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.

#### Initial Mathematics Placement

The department schedules ninth graders in appropriate mathematics courses (typically Algebra, Algebra Honors or Advanced Algebra/Trigonometry) based on eighth grade mathematics grades, high school placement test scores, and results of the SHC Math Placement Test.

#### Advanced Study

The SHC Mathematics department offers courses of advanced mathematics study through AP Calculus BC.

Ninth graders who achieve a 3.5 GPA in Algebra Honors or a 4.0 GPA in Algebra may enroll in Geometry and Advanced Algebra/Trig in tenth grade.

Ninth graders who achieve a 2.0 GPA in Advanced Algebra/Trigonometry may enroll in Geometry and Pre-Calculus in tenth grade.

Ninth graders who achieve a 3.5 GPA in Advanced Algebra/Trigonometry may enroll in Geometry and Advanced PreCalculus in tenth grade.

Enrollment in two tenth grade math classes facilitates a student’s ability to enroll in an AP Calculus course during the eleventh or twelfth grades.

Students who qualify for double math as outlined above may also choose to fulfill the Geometry requirement during the summer after ninth grade, via SHC Summer High School or through selected online providers but should discuss online enrollment with their counselor.

Students intending to pursue liberal arts or social science majors in college may be best served by concluding their high school math studies with AP Statistics, Statistics, or Probability & Statistics.

## Courses in this Department

*Prerequisites*: Geometry 1,2

By the end of this course, 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*: Rising **sophomores** must have a 3.5 GPA in Honors Algebra or a 4.0 GPA in Algebra; rising **juniors **must have a 3.0 GPA in Algebra Honors or Algebra.

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/Trig will *not* facilitate placement into Advanced Pre-Calculus.

*Prerequisites*: A cumulative 3.5 GPA in Advanced Algebra/Trig 1,2.

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).

Algebra 1,2Honors 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).

*Algebra 1,2Honors covers additional topics and in greater depth than preparatory Algebra 1,2. Because the UC system does not accord honors credit to ninth grade courses, however, Algebra 1,2 Honors does not confer a weighted grade.*

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 3.0 GPA in Advanced Pre-Calculus or preparatory Calculus

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*: A cumulative 3.0 GPA in Calculus AB 1,2.

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 1,2

**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 1,2 and a B in Physics or 2) 3.5 in Honors Algebra 1,2 and a B in Physics or 3) 2.0 in Advanced Algebra/Trigonometry 1,2

*Prerequisites*: A cumulative 2.0 GPA in Advanced Algebra/Trig 1,2.

*Note*: Students will not be eligible to enter Calculus AB Advanced Placement from this course.

*Prerequisites:*

**A cumulative 2.0 GPA in Advanced Algebra 1,2.**

*Prerequisites:*A cumulative 2.0 GPA in Advanced Algebra/Trigonometry 1,2.

*This course will be necessary for any student wishing to take Pre-Calculus in college.*

*Please note:*Students who have completed Advanced Algebra/Trigonometry may NOT enroll in this course. Exceptions may be granted to students whose performance in the trigonometry portion of the course resulted in a deficient grade.

*Prerequisites:*A cumulative 2.0 GPA in Advanced Algebra 1,2.