# Math

## Math

High School mathematics offers students the opportunity to develop a deep appreciation for the language of mathematics alongside the chance to develop mathematical skills that are essential to problem solving not just in mathematics but also in the natural and social sciences, engineering, computer science and business.

At Shalhevet, we know that students mature mathematically at different rates and that not all students share the same level of interest in mathematics: where some may see innate beauty of structure and form, others may simply see a tool or technique needed for the sciences of in the life of a successful business person. Shalhevet Mathematics aim to teach students at a pace and depth commensurate with their individual mathematical needs. For students who thrive on the challenges of mathematics, we offer a rigorous Honors track that begins in ninth grade with Honors Geometry and then ends with AP Calculus BC in twelfth grade. Because AP Calculus BC covers two semesters of college calculus, students find that courses in the Honors track move at a fairly fast pace.

Many other students find enjoyment and challenge in our Advanced track which begins in ninth grade with Advanced Geometry and ends in twelfth grade with AP Calculus AB. Because AP Calculus AB covers only one semester of college calculus, students in our Advanced track have ample time in their courses to examine mathematical structures and techniques at a sustained, but not hurried pace.

For students who find mathematics extremely challenging or worrisome, or just have other interests, we offer a third track which provides these students with all of the necessary skills and mathematical ideas to be successful, not just in high school mathematics but also in college mathematics. Students in this track begin with Algebra 1 in ninth grade and may take either Pre Calculus or a mathematics elective in their senior year.

At Shalhevet, we weigh many factors when determining a student’s mathematics placement, including grades in previous mathematics courses, teacher recommendation and performance on standardized tests and placement tests. For students entering Shalhevet in ninth grade, the department communicates with the student’s middle school in order receive teacher recommendation and details about the student’s performance in his or her eighth grade mathematics course. Entering ninth graders also take a placement test in May before starting ninth grade in the fall.

Depending on a student’s placement, students may select from the following list of courses.

Algebra 2 (honors determined by department)

Pre-calculus (honors determined by department)

SAS Statistics

AP Calculus AB

AP Calculus BC

This course teaches students how to work with variables within the context of linear and quadratic equations. Students solve linear equations with one variable and systems of equations with two variables. Students learn how to graph a line given an equation and how to find an equation given a graph or a set of points. Students learn the rules for exponents and simplify rational algebraic expressions. They also are introduced to quadratic equations by learning how to multiply and factor polynomials.

The emphasis of this course is for students to learn deductive reasoning by using the basic postulates and theorems of Euclidean Geometry. They study points, lines, planes, angles, parallel and perpendicular lines, properties of 2-dimensional shapes (triangles, quadrilaterals, circles, etc.) and 3-dimensional shapes (prisms, pyramids, cylinders, etc.), congruency of shapes, similarity of shapes, special right triangles, and area and volume formulas. There is a Geometry Honors option for advanced 9th grade students.

This course emphasizes further development of algebraic skills and focuses on various functions, their properties, graphs and transformations. Students explore polynomial, rational, exponential, and logarithmic functions, inverse functions and the composition of functions. Students solve linear, quadratic, exponential, logarithmic, and rational equations, learn about the complex number system and solve problems involving direct and inverse variation. At the end of the course, students receive an introduction to trigonometry, including unit circle trigonometry.

This course emphasizes further development of algebraic skills and focuses on various functions, their properties, graphs and transformations. Students explore polynomial, rational, exponential, and logarithmic functions, inverse functions and the composition of functions. Students solve linear, quadratic, exponential, logarithmic, and rational equations, learn about the complex number system and solve problems involving direct and inverse variation. Students are also introduced to arithmetic and geometric sequences. At the end of the course, students receive substantial introduction to trigonometry, including unit circle trigonometry and working algebraically with trigonometric identities. The TI-84 calculator is an integral part of this course.

This course bridges the gap between Algebra 2 and college mathematics courses such as statistics and calculus. Students approach linear, polynomial, and exponential functions from a real-life perspective, learn the basics of trigonometry and are introduced to elementary statistics. Upon successful completion of this course, students should be ready for either a basic college level course in elementary statistics or calculus.

Students complete the College Board’s AB Calculus rubric which is akin to most first semester courses in Calculus offered at the university level. Limits and continuity, derivatives—their techniques and applications—single variable integration, computation of areas as well as the volumes of solids of revolution are covered. Among the theorems stressed in the course are the Intermediate Value Theorem, Extreme Value Theorem, Squeeze Theorem, Rolle’s Lemma, Mean Value Theorem, and The Fundamental Theorem of Calculus. Students in the course also spend about one month reviewing for the AP Exam.

SAS Statistics covers much of the material taught in a traditional college introductory statics class but from a perspective of developing the tools that help students become an informed citizen. Students will learn about the methodology behind medical trials, political surveys, marketing campaigns and crucial sports metrics. Students enrolled in this SAS course will build a portfolio that looks at the statistical methods learned using the lens of a topic and a series of related questions of their individual interest.

**Graduation Requirement:**

At least 3 years, and through Precalculus; 4 years recommended.

*Mathematics Department course placement is determined by teacher recommendation and approval by the Math Department.***Course Offerings for Juniors and Seniors:**

Algebra 2 (honors determined by department)

Pre-calculus (honors determined by department)

SAS Statistics

AP Calculus AB

AP Calculus BC

**Algebra 1 (9th Grade)**

This course teaches students how to work with variables within the context of linear and quadratic equations. Students solve linear equations with one variable and systems of equations with two variables. Students learn how to graph a line given an equation and how to find an equation given a graph or a set of points. Students learn the rules for exponents and simplify rational algebraic expressions. They also are introduced to quadratic equations by learning how to multiply and factor polynomials.

**Geometry (9th or 10th Grade)**

The emphasis of this course is for students to learn deductive reasoning by using the basic postulates and theorems of Euclidean Geometry. They study points, lines, planes, angles, parallel and perpendicular lines, properties of 2-dimensional shapes (triangles, quadrilaterals, circles, etc.) and 3-dimensional shapes (prisms, pyramids, cylinders, etc.), congruency of shapes, similarity of shapes, special right triangles, and area and volume formulas. There is a Geometry Honors option for advanced 9th grade students.

**Algebra 2/Trig (10th or 11th Grade)**

This course emphasizes further development of algebraic skills and focuses on various functions, their properties, graphs and transformations. Students explore polynomial, rational, exponential, and logarithmic functions, inverse functions and the composition of functions. Students solve linear, quadratic, exponential, logarithmic, and rational equations, learn about the complex number system and solve problems involving direct and inverse variation. At the end of the course, students receive an introduction to trigonometry, including unit circle trigonometry.

**Algebra 2/Trig Advanced (10th Grade)**

This course emphasizes further development of algebraic skills and focuses on various functions, their properties, graphs and transformations. Students explore polynomial, rational, exponential, and logarithmic functions, inverse functions and the composition of functions. Students solve linear, quadratic, exponential, logarithmic, and rational equations, learn about the complex number system and solve problems involving direct and inverse variation. Students are also introduced to arithmetic and geometric sequences. At the end of the course, students receive substantial introduction to trigonometry, including unit circle trigonometry and working algebraically with trigonometric identities. The TI-84 calculator is an integral part of this course.

**Algebra 2/Trig Honors**

Algebra 2/Trig Honors is the continuation of the material that students have learned in Algebra 1. The beginning of this course is the review of Algebra 1 topics extensively and in more depth than had been taught in previous years. Then this course introduces students to all different types of function, their graphs, their pattern and their applications. These functions consist of linear, piece-wise, parametric, polynomials, logarithmic, rational, and many others. To grasp the Algebra 2 concept better, students learn how to use the graphing calculators in order to visualize, to compare, and to analyze the behavior of various two-dimensional graphs. At the end of the course, students receive substantial introduction to trigonometry, including unit circle trigonometry and working algebraically with trigonometric identities. The TI-84 calculator is an integral part of this course.

This course serves as a capstone to a student’s study of high school mathematics. Polynomials and rational functions are reviewed extensively, including factoring and graphing techniques. Next students spend time with exponential and logarithms before turning their attention to extensive study of unit circle trigonometry. Systems of equations and an introduction to sequences and series are also covered. Time permitting, an introduction to the derivative is also included. Students who take this course prior to their senior year are eligible to take SAS Statistics the following year.

**Pre-calculus**This course serves as a capstone to a student’s study of high school mathematics. Polynomials and rational functions are reviewed extensively, including factoring and graphing techniques. Next students spend time with exponential and logarithms before turning their attention to extensive study of unit circle trigonometry. Systems of equations and an introduction to sequences and series are also covered. Time permitting, an introduction to the derivative is also included. Students who take this course prior to their senior year are eligible to take SAS Statistics the following year.

**Advanced Pre-Calculus**

This course is taught with an eye toward preparing students to take AP Calculus AB the following school year. As such, students spend extensive time studying algebraic and transcendental functions from algebraic, numerical, graphical and verbal perspectives. Graphs and their transformations receive extensive coverage. Systems of equations and an introduction to sequences and series are also covered. Extensive use of a College Board-approved graphing calculator is required inside and outside of class. Students are introduced to making arguments using mathematical facts, as a way of readying them for the AP Calculus AB the subsequent year.

This course is required for the student who wishes to take AP Calculus BC the following school year. Polynomials and rational functions are studied in-depth from both a mechanical and theoretical standpoint. The concept of a limit is breached early on in the course. From there, students complete a rigorous treatment of exponential, logarithmic and trigonometric functions. Sequences, series, and analytic geometry receive substantial treatment as well. Students receive extensive exposure to parametric curves and polar coordinates. Finally, students begin the study of differential calculus in which they work with both polynomial and transcendental functions.

**Precalculus Honors**This course is required for the student who wishes to take AP Calculus BC the following school year. Polynomials and rational functions are studied in-depth from both a mechanical and theoretical standpoint. The concept of a limit is breached early on in the course. From there, students complete a rigorous treatment of exponential, logarithmic and trigonometric functions. Sequences, series, and analytic geometry receive substantial treatment as well. Students receive extensive exposure to parametric curves and polar coordinates. Finally, students begin the study of differential calculus in which they work with both polynomial and transcendental functions.

**Functions, Statistics and Trigonometry**

This course bridges the gap between Algebra 2 and college mathematics courses such as statistics and calculus. Students approach linear, polynomial, and exponential functions from a real-life perspective, learn the basics of trigonometry and are introduced to elementary statistics. Upon successful completion of this course, students should be ready for either a basic college level course in elementary statistics or calculus.

**AP Calculus AB**

Students complete the College Board’s AB Calculus rubric which is akin to most first semester courses in Calculus offered at the university level. Limits and continuity, derivatives—their techniques and applications—single variable integration, computation of areas as well as the volumes of solids of revolution are covered. Among the theorems stressed in the course are the Intermediate Value Theorem, Extreme Value Theorem, Squeeze Theorem, Rolle’s Lemma, Mean Value Theorem, and The Fundamental Theorem of Calculus. Students in the course also spend about one month reviewing for the AP Exam.

**AP Calculus BC**

Students complete the College Board’s BC Calculus rubric, which covers roughly the same material as the first two semesters of college calculus. In addition to the material covered in AP Calculus AB (outlined above), the course covers the remaining basic concepts of single variable calculus: techniques of integration, integration in polar coordinates, infinite sequences and series, basic calculus of vector functions and an introduction to differential equations. Students in the course also spend about two weeks reviewing for the AP Exam.

**SAS Statistics**

SAS Statistics covers much of the material taught in a traditional college introductory statics class but from a perspective of developing the tools that help students become an informed citizen. Students will learn about the methodology behind medical trials, political surveys, marketing campaigns and crucial sports metrics. Students enrolled in this SAS course will build a portfolio that looks at the statistical methods learned using the lens of a topic and a series of related questions of their individual interest.