Shalhevet High School

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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: 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)

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.