The main goal of the Shalhevet Mathematics Department is to provide students with the tools to reason abstractly, think sequentially, and solve problems systematically. Upon graduation, our students should be ready for the mathematics that they will encounter in later schooling, mainly calculus and/or statistics. We also want our students to be prepared to use mathematics in their everyday life and to appreciate the relevance and importance of mathematics. Successful completion of the Shalhevet math program provides students with a mathematical foundation upon which their college education will flourish. Shalhevet graduates will be prepared to continue their education in any field they choose to pursue.

9th Grade: Basic Algebra, Algebra 1 or Geometry Honors

10th Grade: Geometry or Algebra 2 Honors

11th Grade: Algebra 2 or Precalculus Honors

12thGrade: Precalculus or AP Calculus AB or 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 (10th or 11th Grade)**

Students continue their study of algebra by reviewing linear equations and expanding their knowledge of quadratics by graphing quadratic equations, solving using the quadratic formula, and exploring the concept of the complex number system. Students expand their knowledge of functions by studying polynomial, rational, exponential, and logarithmic functions, inverse functions and the composition of functions. Students are also introduced to sequences and series, and conic sections. The TI-84 calculator is an integral part of this course. There is an Algebra 2 Honors option for advanced 10th grade students.

**Precalculus (11th or 12th Grade)**

This course prepares students for success in Calculus by offering a thorough exploration of trigonometric functions—their definitions, graphs, properties, and identities. Students also review polynomial, rational, exponential, and logarithmic functions using a three-tiered (numeric, algebraic, and graphic) approach. Other topics covered include polar coordinates, parametric equations, and sequences and series. There is a Precalculus Honors option for advanced 11th grade students.

**Calculus (12th Grade Elective)**

In this course, students will analyze graphs of functions, limits of functions, asymptotic and unbounded behavior of functions, and the continuity of functions. Students will learn the concept of a derivative and evaluate the derivative at a point, the derivative as a function, the second derivative, and applications of derivatives. Students will finish the course with a thorough evaluation of the integral, including evaluating integrals, applications of integrals, and study of the Fundamental Theorem of Calculus. The focus of Regular Calculus is to promote the conceptual understanding of calculus which will allow students to appreciate some of the greatest achievements of the human mind and to be better prepared to excel in college level calculus classes.

**AP Calculus AB (12th Grade Elective)**

This course covers the equivalent of 1-semester of college calculus. Students may take the Calculus AB Advanced Placement exam at the end of the year to earn college credit. In this course, students will analyze graphs of functions, limits of functions, asymptotic and unbounded behavior of functions, and the continuity of functions. Students will learn the concept of a derivative and evaluate the derivative at a point, the derivative as a function, the second derivative, and applications of derivatives. Students will finish the course with a thorough evaluation of the integral, including evaluating integrals, applications of integrals, and study of the Fundamental Theorem of Calculus.

**AP Calculus BC (12th Grade Elective)**

This course covers the equivalent of 2-semesters of college calculus and therefore is taught at a very fast pace. Students may take the Calculus BC Advanced Placement exam at the end of the year to earn college credit. In addition to the topics covered in Calculus AB, students in Calculus BC will learn the concept of a series, in particular how to determine convergence of a series and how to work with Taylor Series.