## MATH DEPARTMENT

We engage students by creating positive relationships that encourage accountability, initiative and passion as well as pride in themselves and the work they produce in all aspects of their lives.

## COURSES

## AUXILIARY STUDIES

**2109A ALGEBRA 1 AUX **

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 *(c) UC Approved *

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 **

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 *(c) UC Approved *

Prerequisites: Students must be in the Auxiliary Studies Program and have successfully completed Algebra 1 Aux.

**2308A GEOMETRY A **

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 *(c) UC Approved *

Prerequisites: Completion of Algebra 1 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.

**2309A GEOMETRY B**

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 *(c) UC Approved *

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 **

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 *(c) UC Approved *

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 **

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 *(c) UC Approved *

Prerequisites: Completion of Algebra 1 or Algebra 1 Honors with a C or better both semesters. Incoming Freshmen who have met the Algebra 2 benchmark on the SM Math Placement Exam will be placed in this course.

**2308A GEOMETRY A **

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 *(c) UC Approved *

Prerequisites: Completion of Algebra 1 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.

**2309A GEOMETRY B**

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

**Length of Course:**Year

**Open to Grade:**11, 12

*(c) UC Approved*

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.

**2310A GEOMETRY **

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*(c) UC Approved *Prerequisites: Completion of Algebra 2 or Algebra 2 Honors with a C.

**2400A PRECALCULUS **

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 *(c) UC Approved *

Prerequisites: Completion of Algebra 2 and Geometry with a B or better both semesters, or Algebra 2 Honors and Geometry Honors with a C or better both semesters.

**2401A PRECALCULUS STEM **

The course looks at precalculus from a STEM approach – using technology, physics and engineering applications. The topics covered will include functions, trigonometry, linear systems and conic sections. The course will work with the physics course and their laboratory experiments to show problem solving and applications of the math learned. Real world, problem based engineering problems will also be emphasized. TiNspire will be used to enhance problem solving through technology. 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 *(c) UC Approved *

Prerequisites: Completion of Algebra 2 and Geometry with a B or better both semesters, or Algebra 2 Honors and Geometry Honors with a C or better both semesters. This course also requires concurrent enrollment in Physics STEM

**2810AS PROBABILITY AND STATISTICS Paired with Trig or Financial Algebra **

This one semester 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 *(c) UC Approved *

Prerequisites: Completion of Algebra 2 and Geometry with a C or better both semesters.

**2811AS FINANCIAL ALGEBRA Paired with Probability and Statistics **

This is a one semester 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. This semester course may be taken in conjunction with Trigonometry or Probability and Statistics.

**Length of Course:** Semester **Open to Grades:** 11,12 *(g) UC Approved ***2600A STATISTICS**

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 *(g) UC Approved *

Prerequisite: Completion of Algebra 2 with a grade of C or better both semesters or Geometry with a grade of C or better both semesters

**2800AS TRIGONOMETRY Paired with Probability and Statistics **

This is a one semester course for students who wish to broaden their base of mathematical knowledge and strengthen their mathematical experiences. This course will prepare the students for college level math courses who are not yet ready for Precalculus. It is an in-depth study of trigonometric ratios, functions and relations, and involves computation and theoretical processes. This semester course must be taken in conjunction with the semester course Probability and Statistics or Financial Algebra

**Length of Course: **Semester **Open to Grade:** 12 *(c) UC Approved *

Prerequisites: Completion of Algebra 2 and Geometry with a C or better both semesters.

## HONORS

**2110C ALGEBRA 1 HONORS **

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 *(c) UC Approved *Prerequisites: Placement of freshmen is based on A work in 8th grade math and minimum scores of 625 and 610 on math and quantitative sections of the SMCHS entrance examination respectively.

**2200C ALGEBRA 2 HONORS **

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 *(c) UC Approved *

Prerequisites: Completion of Algebra 1 Honors with a B or better both semesters or Algebra 1 with a strong A (95% or above both semesters).

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**Note:** Incoming Freshman who have met the Algebra 2 Honors benchmark on the SM Math Placement Exam and minimum scores of 624 and 610 on the math and quantitative portions of the SMCHS Entrance exam respectively.

**2310C GEOMETRY HONORS **

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 *(c) UC Approved *

Prerequisites: Completion of Algebra 2 Honors with a B or better both semesters or Algebra 2 with a strong A (95% or above) both semesters.

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**2400C PRECALCULUS HONORS **

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 *(c) UC Approved *

Prerequisites: Completion of Algebra 2 Honors and Geometry Honors with a B or better both semesters.

## ADVANCED PLACEMENT (AP)

**2700E AP CALCULUS AB **

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 *(c) UC Approved *

Prerequisites: Completion of IB Math SL or Precalculus Honors with a grade of B or better both semesters or Precalculus with a strong A (95% or above) both semesters and successful completion of Summer Calculus Bridge Class.

**Note: **This is a college level course. Students enrolled in this course are required to take the corresponding AP exam.

**2710E AP CALCULUS BC **

This Advanced Placement course is an intensive full-year 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 *(c) UC Approved*

Prerequisites: Completion of Precalculus Honors or Mathematics SL IB with an A both semesters or completion of AP Calculus AB.

**2600E AP STATISTICS **

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:** 11,12 *(c) UC Approved *

Prerequisite: Completion of Precalculus Honors or Math Studies IB with a grade of B or better both semesters, or completion of Precalculus with a grade of A both semesters.

**Note:** This is a college level course. Students enrolled in this course are required to take the corresponding AP exam.

## INTERNATIONAL BACCALAUREATE

**2505F MATHEMATICAL STUDIES IB SL **

This course of study prepares a student for the Mathematical Studies IB exam as well as to encourage an appreciation of mathematics as applied in the real world. This course includes a “project,” which is a piece of written work based on personal research, that provides the student an opportunity to undertake an investigation of a mathematical nature in the context of another subject in the curriculum, a hobby or interest in his/her choice using skills learned before and during the Mathematical Studies course. Curriculum topics include statistics, logic, basic calculus concepts, finance and further study of trigonometry. **Length of Course:** Year **Open to Grades:** 11,12 *(c) UC Approved *

Prerequisites: Completion of Geometry H, Precalculus, PreCalculus Honors or Precalculus Stem with C or better both semesters.

**Note:** This is a college level course. Students enrolled in this course are required to take the corresponding IB exam.

**2610F MATHEMATICS IB SL **

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 *(c) UC Approved *

Prerequisites: Completion of Algebra 2 Honors and Geometry Honors with a B or better both semesters.

**Note: **This is a college level course. Students enrolled in this course are required to take the corresponding IB exam.

**2715F MATHEMATICS IB HL 1 **

This course is the first year of a two-year prerequisite for those students interested in taking the Mathematics HL IB exam. The course includes Calculus topics such as Limits, Derivatives, Curve Properties, Optimization applications, Integrals, Area, Volume, and Kinematics in addition to Related Rates, Implicit Differentiation, Integration by substitution, Integration by parts, First order Differential Equations and Separation of Variables, Slope Fields, Euler’s Method, L’Hopital’s Rule, Sequences and Series. **Length of Course:** Year **Open to Grades:** 11 *(c) UC Approved *

Prerequisites: Completion of Precalculus Honors with a strong A (95% or above) both semesters.

**2716F MATHEMATICS IB HL 2 **

This course is the second year of a two-year prerequisite for those students interested in taking the Mathematics 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 Three-Dimensions. 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 *(c) UC Approved *

Prerequisites: Completion of Mathematics HL 1 IB with a grade of B or better both semesters, and concurrent enrollment or completion of AP Statistics if interested in Statistics option. **Note:** All online classes will have mandatory in class meetings as indicated in the instructor’s syllabus. Every online class will have an orientation at the beginning of the course and in class meetings for all major exams, i.e. the midterm and final.

**2719FL FURTHER MATHEMATICS IB HL 2 **

This course caters to students with an excellent background in mathematics who have been successful with higher level mathematics courses. Most of these students will intend on studying mathematics in college either as a major field of study in and of itself or as a major component of a related subject. The course is designed specifically to allow students to learn a variety of branches of higher level mathematics. It is the expectation of students that are taking this course to know the topics in the core syllabus of IB Math HL and to have studied one of the options in that syllabus. The course consists of the study of one geometry topic and the following four mathematics HL option topics; Statistics and Probability, Sets, Relations, and Groups, Series and differential equations, and Discrete Mathematics. **Length of Course:** Year **Open to Grade:** 12 *(c) UC Approved *

Prerequisites: Completion of Mathematics HL 1 IB and Mathematics HL 2 IB or completion of Mathematics HL 1 IB and concurrent enrollment in Mathematics HL 2 IB.

## ELECTIVES

**6110A INTRODUCTORY PROGRAMMING **

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 *(g) UC Approved *

Prerequisite: Concurrent enrollment in Algebra 2.

**6112E AP COMPUTER SCIENCE A **

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* (g) UC Approved *

Prerequisite: Teacher Approval.

## Faculty & Staff

## 2017-2018 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.