# 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.

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

10th Grade: Geometry, Advanced Algebra 2, or Algebra 2 Honors

11th Grade: Algebra 2, Advanced Precalculus or Precalculus Honors

12thGrade: Precalculus, AP Calculus AB or 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. Students are also introduced to arithmetic and geometric sequences. The TI-84 calculator is an integral part of this course.

Algebra 2 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. The lessons are designed to relate the math concepts to everyday life situations by applying the formulas, rules, and graphs to word problems and then solving them through critical thinking and checking them by using student's common sense. The lessons also invoke the students to improve their logical reasoning skills needed in science courses and SAT and ACT exams. The TI-84 calculator is an integral part of this course.

This course has three principal functions: to review concepts from Algebra II that are central to calculus, to study trigonometry, and to cover miscellaneous mathematics topics needed for advanced math courses. The material central to calculus includes topics focusing on the concept of functions including polynomial, trigonometric, logarithmic, and exponential. Other topics covered include sequences and series, permutations and combinations, and introductory probability and statistics. Throughout the course, students are introduced to the basic facts and techniques of each of these topics, and shown how to use the graphing calculator to solve problems.

This course covers the topics from Pre-calculus in more depth along with the additional topics of conic sections, polar coordinates and parametric equations. Students are expected to stretch what they know by solving problems requiring advanced conceptual understanding. A theoretical approach is utilized to prepare students for the rigors of Advanced Placement Calculus. The TI-84 calculator is an integral part of this course.

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.

In AP Calculus, students are introduced to a different version of mathematics in which they are encouraged to develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment. In this course students learn to model a written description of physical situations with various functions, differential equations, or integrals. They determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement. To understand and learn Calculus better, the teacher uses the mathematical software programs (TI emulator and calculus in motion) extensively. These programs allow students to display, transform, and rotate various shapes and graphs in two or three-dimensional space, which makes the visualizing of, complicated solids significantly easier. The lessons develop students’ mastery of those algebraic techniques necessary for problem solving and mathematical modeling. These lessons also invoke the students to improve their logical reasoning skills needed in other science and business courses. Both AP Calculus courses (AB and BC) are challenging courses reserved for the strongest math students. Calculus BC is extremely challenging and fast-paced and will cover a few additional subjects, including sequences and series, definite integrals, differentiation, and parametric equations. Teacher recommendation is required for entry into either AP Calculus course.

10th Grade: Geometry, Advanced Algebra 2, or Algebra 2 Honors

11th Grade: Algebra 2, Advanced Precalculus or Precalculus Honors

12thGrade: Precalculus, AP Calculus AB or AP Calculus BC

**Ninth Grade Mathematics**

**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)**

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. The TI-84 calculator is an integral part of this course.

**Algebra 2 Honors (10th Grade)**

Algebra 2 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. The lessons are designed to relate the math concepts to everyday life situations by applying the formulas, rules, and graphs to word problems and then solving them through critical thinking and checking them by using student's common sense. The lessons also invoke the students to improve their logical reasoning skills needed in science courses and SAT and ACT exams. The TI-84 calculator is an integral part of this course.

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

This course has three principal functions: to review concepts from Algebra II that are central to calculus, to study trigonometry, and to cover miscellaneous mathematics topics needed for advanced math courses. The material central to calculus includes topics focusing on the concept of functions including polynomial, trigonometric, logarithmic, and exponential. Other topics covered include sequences and series, permutations and combinations, and introductory probability and statistics. Throughout the course, students are introduced to the basic facts and techniques of each of these topics, and shown how to use the graphing calculator to solve problems.

**Precalculus Honors (11th Grade)**

This course covers the topics from Pre-calculus in more depth along with the additional topics of conic sections, polar coordinates and parametric equations. Students are expected to stretch what they know by solving problems requiring advanced conceptual understanding. A theoretical approach is utilized to prepare students for the rigors of Advanced Placement Calculus. The TI-84 calculator is an integral part of this course.

**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 or BC (12th Grade Elective)**

In AP Calculus, students are introduced to a different version of mathematics in which they are encouraged to develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment. In this course students learn to model a written description of physical situations with various functions, differential equations, or integrals. They determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement. To understand and learn Calculus better, the teacher uses the mathematical software programs (TI emulator and calculus in motion) extensively. These programs allow students to display, transform, and rotate various shapes and graphs in two or three-dimensional space, which makes the visualizing of, complicated solids significantly easier. The lessons develop students’ mastery of those algebraic techniques necessary for problem solving and mathematical modeling. These lessons also invoke the students to improve their logical reasoning skills needed in other science and business courses. Both AP Calculus courses (AB and BC) are challenging courses reserved for the strongest math students. Calculus BC is extremely challenging and fast-paced and will cover a few additional subjects, including sequences and series, definite integrals, differentiation, and parametric equations. Teacher recommendation is required for entry into either AP Calculus course.