MATH DEPARTMENT
Santa Margarita's Math Department strives to inspire students to be well balanced individuals and to learn personal responsibility, resourcefulness and tenacity through the lens of mathematics.
Math Department Placement Policy
Students are placed in a Math Class based on the courses they have taken in middle school, scores on the HSPT (High School Placement Test) Exam, and our *SM Math Placement Test as follows:
- If a student has not completed one full year of a high-school equivalent Algebra 1 course in middle school with B or better the student will be placed in Algebra 1. The student is not required to take the SM Math Placement Exam. All other students MUST take the SM Math Placement Exam.
- If a student completed one full year of a high-school equivalent Algebra 1 course in middle school with B or better then they will be placed in either Algebra 1 or Algebra 2 based on a student’s performance on our SM Math Placement Exam.
COURSES
AUXILIARY STUDIES
2109A ALGEBRA 1 AUX
(c) UC Approved, NCAA Approved
This course is designed to develop skills in working with real numbers and polynomials. Students learn to evaluate formulas, to solve first and second degree equations and inequalities, to solve systems of equations, plus additional algebra topics that encourage them to practice and improve logical thought processes.
Length of Course: Year
Open to Grade: 9
Prerequisites: Freshman students must be in the Auxiliary Students Program and placement is based on the mathematics and quantitative sections of the SMCHS Entrance Examination as well as the SM Math Placement Test.
2190A ALGEBRA 2 AUX
(c) UC Approved, NCAA Approved
This course will prepare students for college, deepen their understanding and increase their skills in working with algebraic concepts learned in Algebra 1. This will include the introduction of functions and relations and graphing of linear, quadratic, exponential and logarithmic functions.
Length of Course: Year
Open to Grade: 10
Prerequisites: Students must be in the Auxiliary Studies Program and have successfully completed Algebra 1 Aux.
2308A GEOMETRY A
(c) UC Approved, NCAA Approved
This course is designed for the student who needs a slower paced, more detailed presentation of Geometry topics. It is the first course in a two-part series of Geometry. Together with Geometry B this course comprises a one-year credit equivalent. Students will participate in hands-on activities that will allow them to discover geometric concepts as well as use Geometer’s Sketchpad, a computer software program that supports the curriculum. Practical applications of geometric concepts are presented and emphasized throughout the course and Algebra concepts will permeate throughout the course within context so that these concepts are reinforced and applied.
Length of Course: Year
Open to Grade: 10, 11
Prerequisites: Completion of Algebra 1. Note: Students must be in Auxiliary Studies Program in order to qualify for this course. Geometry A and Geometry B together fulfill the “C requirement of the UC System.
2309A GEOMETRY B
(c) UC Approved, NCAA Approved
This is the second course in a two-year program of Geometry. It was developed for students who can expect to learn Geometry more effectively by having it presented at a slower pace. Coupled with Geometry A the previous year, a comprehensive program in high school Geometry is completed.
Length of Course: Year
Open to Grade: 11, 12
Prerequisites: Completion of Geometry A with a C or better. Note: Students must be in Auxiliary Studies Program in order to qualify for this course. Geometry A and Geometry B together fulfill the “C requirement of the UC System.
ACADEMIC
2110A ALGEBRA 1
(c) UC Approved, NCAA Approved
This course is designed to develop skills in working with real numbers and polynomials. Students learn to evaluate formulas, to solve first and second degree equations and inequalities, to solve systems of equations, plus additional algebra topics that encourage them to practice and improve logical thought processes.
Length of Course: Year
Open to Grade: 9
Prerequisites: Placement of freshmen is based on the mathematics and quantitative sections of the SMCHS Entrance Examination as well as the SM Math Placement Exam
2200A ALGEBRA 2
(c) UC Approved, NCAA Approved
This course will prepare students for college, deepen their understanding and increase their skills in working with algebraic concepts learned in Algebra 1. This will include the introduction and in-depth study of functions and relations and graphing of linear, quadratic, exponential and logarithmic functions. A proficiency in solving word problems will also be stressed.
Length of Course: Year
Open to Grades: 9, 10
Prerequisites: Completion of Algebra 1. Incoming Freshmen who have met the Algebra 2 benchmark on the SM Math Placement Exam will be placed in this course.
2310A GEOMETRY
(c) UC Approved, NCAA Approved
The purpose of Geometry is to enable students to think logically and to express seemingly complex ideas precisely through problem solving as well as formal proofs. Geometry also encourages the development of imagination, creativity and skills of observation and space perception while continuing to reinforce Algebra skills. Practical applications of geometric concepts are presented and emphasized throughout the course.
Length of Course: Year
Open to Grades: 10, 11
Prerequisites: Completion of Algebra 2.
2400A PRECALCULUS
(c) UC Approved, NCAA Approved
This course is designed to follow Geometry in preparing the student to study Calculus. The topics covered will include functions, trigonometric functions and analysis, linear systems and conic sections. At the end of this course, the students will have the skills necessary to enter a college level Calculus course.
Length of Course: Year
Open to Grades: 11,12
Prerequisites: Completion of Algebra 2 and Geometry with a B or higher.
2700A CALCULUS
(c) UC Approved, NCAA Approved
This is a year long course that covers the elements of beginning college calculus. The course covers limits, derivatives, definite integrals of algebraic and transcendental functions, and the application of derivatives and integrals. Techniques of integration and integrals may also be covered. This course does not follow the curriculum needed to take the Advanced Placement Exam in Calculus. This course is ideal for students who would like an introduction to Calculus for college preparation, but do not desire the rigor or pace of the Advanced Placement Course.
Length of Course: Year
Open to Grades: 10, 11, 12
Prerequisites: Completion of PreCalculus
2811A FINANCIAL ALGEBRA
(c) UC Approved, NCAA Approved
This is a year long course designed for the student who needs to refresh their knowledge of Algebra and Geometry in preparation for college level math courses. It is a comprehensive study of these subjects using application and math modeling. Students are more apt to understand and master mathematical concepts when they can associate those concepts with real life experiences and applications.
Length of Course: Year
Open to Grades: 11, 12
Prerequisites: Completion of Algebra 1, Algebra 2, and Geometry.
2810AS PROBABILITY AND STATISTICS
Paired with Trigonometry
(c) UC Approved, NCAA Approved
This semester long course is designed to enhance statistical literacy by introducing the science of statistics, providing instruction in probability, creating a bridge between probability as an underpinning science and applied inferential statistics and providing students with practical techniques for hypothesis testing. This semester course must be taken in conjunction with the semester course Trigonometry or Financial Algebra.
Length of Course: Semester
Open to Grades: 11, 12
Prerequisites: Completion of Algebra 2 and Geometry.
4922A ACCOUNTING AND FINANCE
(g) UC Approved
Accounting and Finance is a full year course offered to primarily junior and seniors who might be considering majoring in business in college and/or interested in pursuing business interests. It is also designed to help young adults with the personal financial issues they might be facing after high school. Basic financial themes will be explored with an introduction to elementary accounting concepts to help students understand financial statements and decisions. The course will employ real world examples, simplified case studies, and a discussion and analysis approach. Also included will be activities and conversations on business ethics and current events related to the course.
Length of Course: Year
Open to Grades: 11, 12
2600A STATISTICS
(c) UC Approved, NCAA Approved
This math course is a full year of statistics, including applications to probability. The major themes of this course are exploratory analysis, questioning techniques and types of measurement, probability (used for anticipating how the data should appear), and statistical inference.
Length of Course: Year
Open to Grade: 12
Prerequisite: Completion of Algebra 2 and Geometry.
HONORS
2110C ALGEBRA 1 HONORS
(c) UC Approved, NCAA Approved
This accelerated course covers the topics of Algebra 1 in greater depth and includes many additional topics. This enables students who are able to meet the challenge of an accelerated pace to be better prepared for the advanced science and mathematics classes.
Length of Course: Year
Open to Grade: 9
Prerequisites: See Freshmen Placement Policy.
2200C ALGEBRA 2 HONORS
(c) UC Approved, NCAA Approved
This accelerated course covers the concepts of Algebra 2 in greater depth and involves higher order critical thinking skills. Strong emphasis is placed on understanding mathematics conceptually, its structures and processes. Students who excel in the area of mathematics and who are planning further study in mathematics or science-related fields are encouraged to take this course. This course includes concepts that are part of the IB curriculum.
Length of Course: Year
Open to Grades: 9, 10
Prerequisites: Completion of Algebra1 or Incoming Freshman who have met the Algebra 2 Honors benchmark on the SM Math Placement Exam and minimum scores of 1235 combined on the math and quantitative portions of the SMCHS Entrance exam.
*Note: To move from Academic to Honors classes requires an “A” both semesters & a passing score on the placement exam in May.
2310C GEOMETRY HONORS
(c) UC Approved, NCAA Approved
The purpose of Geometry Honors is to move beyond the basic material presented in the regular course in order to provide a sufficient challenge for the outstanding math student. The basic terminology, principles, properties and concepts are presented with a much greater level of profundity. Students pay particular attention to the logical development of organized, reasonable and creative formal proofs. This course includes concepts that are part of the IB curriculum.
Length of Course: Year
Open to Grades: 10, 11
Prerequisites: Completion of Algebra 2.
*Note: To move from Academic to Honors classes requires an “A” both semesters & a passing score on the placement exam in May.
2400C PRECALCULUS HONORS
(c) UC Approved, NCAA Approved
This accelerated course covers the topics of Precalculus at a faster pace and in greater depth, and also includes additional material. Its purpose is to give the students a solid foundation for Calculus, to gain an appreciation of mathematics as a logical science and to show the usefulness of the subject matter through a variety of applied problems from many different disciplines. After successful completion of this course, the students will be prepared to take Advanced Placement Calculus in high school or Calculus at the college level. This course also prepares sophomores for the Mathematics HL IB courses. Length of Course: Year
Open to Grades: 10, 11, 12
Prerequisites: Completion of Algebra 2 Honors and Geometry Honors.
*Note: To move from Academic to Honors classes requires an “A” both semesters & a passing score on the placement exam in May.
ADVANCED PLACEMENT (AP)
2700E AP CALCULUS AB
(c) UC Approved, NCAA Approved
This Advanced Placement course covers the entire “AB” syllabus published by the College Board and is designed for the students who are prepared to pursue college level studies while in high school. An attempt is made to strike a balance between the theory, technique and application of the Calculus. Calculus AB is primarily concerned with an “intuitive” understanding of the concepts of Calculus and experience with its methods and applications. Upon completion of this course, the students will be adequately prepared for the Calculus AB examination. Success on this examination will possibly enable them to receive appropriate credit and placement at the college they will attend. The customary policy of most colleges and universities is, upon completion of a passing grade on the AP Calculus AB examination, to give a semester of college math credit and place the student into a second semester Calculus course.
Length of Course: Year
Open to Grades: 11, 12
Prerequisites: Completion Precalculus Honors
*Note: To move from Academic to Honors classes requires an “A” both semesters & a passing score on the placement exam in May.
2710E AP CALCULUS BC
(c) UC Approved, NCAA Approved
This Advanced Placement course is an intensive year long course in the Calculus of functions of a single variable. In addition to the topics covered in Calculus AB, the Calculus BC course includes all additional topics listed in the “BC” syllabus published by The College Board. Upon completion of this course, the student will be adequately prepared for the Calculus BC examination. Success on this examination will possibly enable them to receive appropriate credit and placement at the college they will attend. The customary policy of most colleges and universities is, upon completion of a passing grade on the AP Calculus BC examination, to give a year of college math credit and place the student into a third semester Calculus course.
Length of Course: Year
Open to Grades: 11, 12
Prerequisites: Completion of Precalculus Honors or Mathematics AA IB SL with a 95% or better
*Note: To move from Academic to Honors classes requires an “A” both semesters & a passing score on the placement exam in May.
2600E AP STATISTICS
(c) UC Approved, NCAA Approved
The purpose of the Advanced Placement 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: 1. Exploring data: Observing patterns and departures from patterns 2. Planning a study: Deciding what and how to measure 3. Anticipating patterns in advance: Producing models using probability and simulation 4. Statistical inference: Confirming models Students who successfully complete this course and the Advanced Placement examination may receive credit and/or advanced placement for a one semester introductory college statistics course.
Length of Course: Year
Open to Grades: 12
Prerequisite: Completion of Precalculus Honors.
*Note: To move from Academic to Honors classes requires an “A” both semesters & a passing score on the placement exam in May.
INTERNATIONAL BACCALAUREATE
2402C PRECALCULUS H AI IB
(c) UC Approved
This course is designed to follow Geometry or Geometry H. It is the first year in a 2 year sequence culminating in either Math SL AI or Math HL AI, depending on the performance in year 1. The topics covered will include algebraic, rational and exponential functions, trigonometric functions and analysis, linear systems, sequences and series, polar graphs, statistics, and calculus. At the end of this course, the students will have the skills necessary to enter a college level Calculus course. This course recognizes the increasing role that mathematics and technology play in a diverse range of fields in a data-rich world. As such, it emphasizes the meaning of mathematics in context by focusing on topics that are often used as applications or in mathematical modelling. The course makes extensive use of technology to allow students to explore and construct mathematical models.
Length of Course: Year
Open to Grades: 11, 12
Prerequisites: Completion of Geometry
*Note: To move from Academic to Honors classes requires an “A” both semesters & a passing score on the placement exam in May.
2720F MATHEMATICS AA IB SL
(c) UC Approved
This course is a Prerequisite for those students interested in taking the Mathematics SL exam. The course includes Precalculus topics such as Functions and Equations, Circular Functions and Trigonometry, Matrices, and Vectors. Probability and Statistics concepts including Probability Distributions will also be part of the course. The third quarter of this course includes Calculus topics such as Limits, Derivatives, Curve Properties, Optimization Applications, Integrals, Area, Volume and Kinematics. Students will also complete a mathematical exploration which is a project-oriented assessment and will comprise 20% of their IB grade.
Length of Course: Year
Open to Grades: 11, 12
Prerequisites: Completion of Algebra 2 Honors and Geometry *Note: To move from Academic to Honors classes requires an “A” both semesters & a passing score on the placement exam in May.
2711F MATH AA IB HL1
(c) UC Approved, NCAA Approved
This Advanced Placement course is an intensive year long course in the Calculus of functions of a single variable. In addition to the topics covered in Calculus AB, the Calculus BC course includes all additional topics listed in the “BC” syllabus published by The College Board. Upon completion of this course, the student will be adequately prepared for the Calculus BC examination. Success on this examination will possibly enable them to receive appropriate credit and placement at the college they will attend. The customary policy of most colleges and universities is, upon completion of a passing grade on the AP Calculus BC examination, to give a year of college math credit and place the student into a third semester Calculus course.
Length of Course: Year
Open to Grades: 11, 12
Prerequisites: Completion of Precalculus Honors or Mathematics AA IB SL with a 95% or better.
*Note: To move from Academic to Honors classes requires an “A” both semesters & a passing score on the placement exam in May.
MATH AI IB HL1
(c) UC Approved
This course is designed to follow Geometry or Geometry H. It is the first year in a 2 year sequence culminating in either Math SL AI or Math HL AI, depending on the performance in year 1. The topics covered will include algebraic, rational and exponential functions, trigonometric functions and analysis, linear systems, sequences and series, polar graphs, statistics, and calculus. At the end of this course, the students will have the skills necessary to enter a college level Calculus course. This course recognizes the increasing role that mathematics and technology play in a diverse range of fields in a data-rich world. As such, it emphasizes the meaning of mathematics in context by focusing on topics that are often used as applications or in mathematical modelling. The course makes extensive use of technology to allow students to explore and construct mathematical models. Length of Course: Year
Open to Grades: 11, 12
Prerequisites: Completion of Geometry
*Note: To move from Academic to Honors classes requires an “A” both semesters & a passing score on the placement exam in May.
2721F MATHEMATICS AA IB HL 2
(c) UC Approved
This course is the second year of a two-year prerequisite for those students interested in taking the Mathematics AA HL IB exam. The course includes Extensive Probability and Statistics concepts which will include Bayes’ Theorem, Expected Value, Probability Distributions such as the Poisson Distributions. Precalculus extended topics will include Mathematical Induction, Complex Numbers, DeMoivre’s Theorem, and Vectors in ThreeDimensions. Homogeneous differential equations and the integrating factor will also be considered. Students will also complete portfolio assignments which are project-oriented assessments and comprise 20% of their IB grade.
Length of Course: Year
Open to Grade: 12
Prerequisites: Completion of AP Calculus BC or Mathematics HL 1 IB and concurrent enrollment or completion of AP Statistics if interested in Statistics option.
*Note: To move from Academic to Honors classes requires an “A” both semesters & a passing score on the placement exam in May.
2722F MATH AI IB HL 2
(c) UC Approved
This class emphasizes the meaning of mathematics in context by focusing on topics that are often used as applications or in mathematical modelling. To give this understanding a firm base, this course also includes topics that are traditionally part of a preuniversity mathematics course such as calculus and statistics. The course makes extensive use of technology to allow students to explore and construct mathematical models. Mathematics: applications and interpretation will develop mathematical thinking, often in the context of a practical problem and using technology to justify conjectures.
Length of Course: Year
Open to Grade: 12
Prerequisites: Completion of Precal H AI IB
PROGRAMMING
6113A CYBER SECURITY
(g) UC Approved
Cyber Security prepares students for success in postsecondary information technology majors and for careers in network administration and information technology support services with a focus on cyber security. The course includes a series of technical modules that provide hands-on learning as well as knowledge and skills development in computer hardware, operating systems, networking, coding, and security infrastructures. Industry-based curricula are utilized in network and virtual image environments to emulate real-life scenarios and prepare students for industry recognized certifications. Students research and address ethical and legal standards related to information security. Students mitigate cyber vulnerabilities through intricate problem-solving scenarios requiring critical thinking, incident response and analysis, and collaboration. Ethical hacking and penetration testing concepts will be introduced with an emphasis on information security research. Students will be expected to us network scanners, network packet capture, network security and auditing tools to accomplish tasks. The Cybersecurity curriculum is designed to ensure a deep understanding of privacy, reliability, and integrity of information systems for students preparing for majors and careers in Cyber Security and Information and Communications Technology.
Length of Course: Year
Open to Grades: 9, 10, 11, 12
6110A INTRODUCTORY PROGRAMMING
(g) UC Approved
A first course in programming using Java to introduce and develop initial programming skills. Structured programming will be stressed through proper control flow and simple data types. Problem solving, critical thinking, and logical thinking skills are essential and will be developed during the class. This course also covers various computer ethics and current technology trends.
Length of Course: Year
Open to Grades: 9, 10, 11, 12
Prerequisite: Concurrent enrollment in Algebra 2.
6112E AP COMPUTER SCIENCE A
(g) UC Approved
The AP Computer Science A course is an introductory course in computer science. Because the design and implementation of computer programs to solve problems involve skills that are fundamental to the study of computer science, a large part of the course is built around the development of computer programs that correctly solve a given problem. These programs should be understandable, adaptable, and when appropriate, reusable. At the same time, the design and implementation of computer programs is used as a context for introducing other important aspects of computer science, including the development and analysis of algorithms, the development and use of fundamental data structures, the study of standard algorithms and typical applications, and the use of logic and formal methods. In addition, the responsible use of these systems is an integral part of the course.
Length of Course: Year
Open to Grades: 10, 11, 12
Prerequisite: Teacher Approval.
*Note: To move from Academic to Honors classes requires an “A” both semesters & a passing score on the placement exam in May.