# Mathematics

## Course Description Key

Descriptions of the courses offered at San Marcos High School are outlined in the following pages. Students should take note of the grade levels at which the course may be taken, prerequisites, and the length of the course (semester or year-long).

### Some of the abbreviations commonly used in this section are explained below.

A-G Designation UC/CSU admission requirements (identifies courses that meet the entrance requirements of that school)

AP Advanced Placement (designates classes to prepare students for the Advanced Placement exams, which may result in a student’s receiving college credit for a course, even though the course was completed in high school

ELD English Language Development (designates English classes for those learning English as a second language).

(P) College preparatory (designates classes accepted by colleges and universities for purposes of meeting their entrance requirements)

(H) Honors (designates honors classes designed to prepare students for Advanced Placement classes)

### ALGEBRA I (P) - 21100

Grade level: 9-12

A-G Designation: C - Mathematics

Recommended Previous Course of Study: Placement determined by middle school math teacher or a B in SMUSD CC Math 8.

The Algebra 1 course is the first course in the high school sequence aligned with the Common Core State Standards for Mathematics (CCSS-M). The purpose of this course is to provide opportunities for students to gain fluency with linear, quadratic and exponential functions. Students will engage in contrasting linear, quadratic and exponential functions, in addition to analyzing, solving and using these functions to model real-world situations. Throughout the course, students will gain understanding and use the formal definition of functions and their notation, and will use them to interpret and build functions. Students will also discover the analogous nature of polynomials with integers, and will begin their study of statistics, focusing on interpreting categorical and quantitative data. In addition to the CCSS-M standards content standards for Algebra 1, students will experience and gain fluency with the eight Standards for Mathematical Practice.

### FINANCIAL ALGEBRA (P) - 21101

Grade level: 9

A-G Designation: Pending

Recommended Previous Course of Study: Placement determined by middle school math teacher

Financial Algebra assists students in making sense of the financial world around them to effectively manage fiscal resources through meaningful mathematical modeling. In the Financial Algebra course, students will study functions and relations with strong attention given to graphing functions, statistics, and data analysis throughout the course. Emphasis will be on the use of mathematics to model and explore real-world financial phenomena including interpreting and justifying reasoning to make data-supported financial decisions. Students will master simplifying, solving, and graphing linear, quadratic, and exponential expressions, equations and functions. Students will show proficiency with linear and higher degree distributions, and work with radical expressions and use graphing calculators and apps to explore relations between functions and their graphs and perform statistical analyses.

### GEOMETRY (P) - 22100

Grade level: 9-12

A-G Designation: C - Mathematics

Recommended Previous Course of Study: Incoming 9th graders: Required C or better in Accelerated Algebra. Current 9th - 12th graders: D or better in Algebra 1, or a teacher recommendation

The Geometry course is the second course in the high school sequence aligned with the California Common Core State Standards for Mathematics (CCSS-M). The purpose of this course is to introduce students to formal geometric proofs and the study of plane figures, culminating in the study of right triangle trigonometry and circles. Throughout the course, students will gain experience in proving results about the plane formally, using previously defined terms and notions. Students will explore transformations, proving geometric theorems, congruence and similarity, right-triangle trigonometry and probability. In addition to the CCSS-M content standards for Geometry, students will experience and gain fluency with the eight Standards for Mathematical Practice.

### GEOMETRY (H) - 22200

Grade level: 9-12

A-G Designation: C - Mathematics

Recommended Previous Course of Study: Required B or better in Accelerated Algebra and a teacher recommendation, Current 9th - 12th graders: Recommended B or better in Algebra 1 and/or teacher recommendation

This course covers the same topics as listed in Geometry in addition to enhanced (+) standards outlined in the California Mathematics Framework for the Geometry course. Students will gain greater understanding of trigonometry through deriving formulas and proving, using, and understanding the application of laws of sines and cosines. In addition, students in Honors Geometry will gain a deeper understanding of using probability models and probability experiments to make decisions.

### ALGEBRA II (P) - 23100

Grade level: 9-12

A-G Designation: C - Mathematics

Recommended Previous Course of Study: Grade of C or better in High School Algebra I and Geometry or teacher’s recommendation. Grade of B or better in Middle School Algebra I and C or better in follow-up Geometry course.

The Algebra 2 course is the third course in the high school sequence aligned with the California Common Core State Standards for Mathematics (CCSS-M). The purpose of this course is to extend and deepen students' understanding of numbers and functions. Throughout the course, students will explore polynomial and rational functions, and their relationship to integers and rational numbers respectively. Students will examine the relationship of a function and its inverse, through exponential and logarithmic functions. Students will study trigonometric functions and expand their knowledge of statistics to include understanding of the normal distribution. In addition to the CCSS-M content standards for Algebra 2, students will experience and gain fluency with the eight Standards for Mathematical Practice.

### ALGEBRA II FOR STRATEGIC BUSINESS MANAGEMENT (P) - 23101

Grade level: 9-12

A-G Designation: C - Mathematics

Recommended Previous Course of Study: Grade of C or better in High School I and Geometry or teacher’s recommendation

Building on Financial Algebra, students explore and interpret the behavior of different functions (linear, polynomial, exponential, logarithmic, rational) by modeling real-world relationships found in the finance and business sectors. Through lessons based on consumer economics and business optimization, students deepen their understanding of linear and polynomial functions. Students use case studies of businesses to create, analyze, and interpret functions that influence business decisions. Students investigate the algebra and statistics involved in managing a business, investing, and market research.

### ALGEBRA II (H) - 23200

Grade level: 9-12

A-G Designation: C - Mathematics

Recommended Previous Course of Study: Grade of B or better in Geometry (H) or Grade of B or better in Geometry and teacher recommendation. Grade of A in Algebra 1

This course covers the same topics as listed in Algebra 2 in addition to enhanced (+) standards outlined in the California Mathematics Framework for the Algebra 2 course. Students will examine polynomial identities to include complex numbers and know and apply the Fundamental Theorem of Algebra and the Binomial Theorem. Students will also extend their knowledge of rational expressions by graphing more complex functions and identifying their key features. Students will gain greater understanding of trigonometry by utilizing additional identities and further investigating patterns of the unit circle. In addition, students in Honors Algebra 2 will extend their understanding of probability by analyzing decisions and strategies in more complex situations.

Grade level: 9-12

A-G Designation: C - Mathematics

Recommended Previous Course of Study: Completed two years of high school math

Answering real questions in the world involves analyzing data. This course will teach students to think critically about and with data, developing the tools, techniques, and principles for reasoning. Students form their own questions about the world around them, analyze data using multiple methods, and present their findings through project-based units. Students will be introduced to basic computer programming skills using the language, Python and Tableau, during the research. At the end of the course, students will have a portfolio of their data science work to showcase their newly developed knowledge and understanding. Throughout the course, students will experience and gain fluency with the eight Standards for Mathematical Practice.

### CALCULUS (P) - 25103

Grade level: 11-12

A-G Designation: C - Mathematics

Recommended Previous Course of Study: Grade of C or better in Algebra II.

The major purpose of this course is to provide an introduction to calculus. Topics include functions and trigonometry, limits and continuity, differentiation, applications of derivatives, integration, and applications of the integral.

### AP CALCULUS (A/B) - 25203

Grade level: 11-12

A-G Designation: C - Mathematics

Recommended Previous Course of Study: Grade of C or better in Honors Algebra 2

This course is an intensive study of differential and integral calculus. Topics include limits, derivatives as functions, computation and applications of derivatives, computation and applications of integrals, and differential equations. Students approach calculus concepts and problems when they are represented graphically, numerically, analytically, and verbally, and to make connections amongst these representations. Students learn how to use technology to help solve problems, experiment, interpret results, and support conclusions.

### AP CALCULUS (B/C) - 25204

Grade level: 11-12

A-G Designation: C - Mathematics

Recommended Previous Course of Study: Calculus AB, or an A in Algebra 2H with teacher recommendation.

This course covers the same topics of differential and integral calculus as listed in AP Calculus AB. Additional topics in this course include parametric, polar, and vector functions, additional techniques and applications of integration, and polynomial approximations and series. Students approach calculus concepts and problems when they are represented graphically, numerically, analytically, and verbally, and to make connections amongst these representations. Students learn how to use technology to help solve problems, experiment, interpret results, and support conclusions.

### STATISTICS (P) - 25102

Grade level: 11-12

A-G Designation: C - Mathematics

Recommended Previous Course of Study: Grade of B or better in Algebra II or C

This is a college level introduction to statistics. Students are introduced to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. The course has four broad conceptual themes: 1) exploring data; 2) planning a study 3) anticipating patterns in advance, and 4) statistical inference. Instruction is differentiated in order to provide the depth, complexity, novelty, and pacing required by state gifted standards and to prepare students for the Advanced Placement program.

### AP STATISTICS - 25205

Grade level: 11-12

A-G Designation: C - Mathematics

Recommended Previous Course of Study: Grade of B or better in Algebra II

The AP Statistics course is an intensive study of the major concepts and tools for collecting, organizing, analyzing, and drawing conclusions from data. There are four themes evident in the content, skills, and assessment in the AP Statistics course: exploring data, sampling and experimentation, probability and simulation, and statistical inference. Students use technology, investigations, problem solving, and writing as they build conceptual understanding.