Pre-Calculus Syllabus

Course Syllabus and Guidelines for PreCalculus – Mr. Beretsky – Room B-230

Course Description

Pre-Calculus is a continuation of Honors Algebra II or Algebra II, which is also a prerequisite.  The Pre-Calculus course reflects the belief that the Belchertown High School educational community fosters academic excellence and responsible citizenship in a positive, safe and respectful environment in order to develop productive contributors to society.


Pre-Calculus students are expected to:

  • Read mathematical problems actively and critically.
  • Write effective solutions to problems and projects
  • Present solutions to problems effectively
  • Use a variety of appropriate resources including the computer and calculator to solve mathematical problems
  • Employ multiple critical and creative thinking strategies in reasoning and problem solving
  • Demonstrate a knowledge and appreciation of how mathematics can be used outside the mathematics classroom
  • And meet all of the course objectives listed below

Topics Include:

  • Understanding Algebra  Basics
  • Functions and Their Graphs
  • Polynomial and Rational Functions
  • Exponential and Logarithmic Functions
  • Matrices
  • Introduction to Trigonometry
  • Analytical Trigonometry
  • Triangle Trigonometry
  • Systems of Equations
  • Analytical Geometry
  • Discrete Algebra

It is a full year course (5 – graduation credits)

Course Objectives

The student will be able to:

  • Apply and demonstrate essential facts about real numbers, algebra and algebraic equations that are needed for Pre-Calculus and Calculus
  • Graph and find equations of lines and circles in the coordinate plane
  • Use numerical, algebraic, and graphical representations of functions and relations in order to solve real-world problems
  • Graphically describe solutions of various algebraic equations
  • Use appropriate technology appropriately to solve mathematical problems
  • Demonstrate how relations and functions can be represented numerically, graphically, algebraically, and/or verbally
  • Explain how the properties of functions and function operations are used to model and analyze real-world applications and quantitative relationships
  • Solve quadratic, polynomial and rational functions by using algebra, graphs and models
  • Solve applications using quadratic, polynomial and rational functions by using algebra graphs and models
  • Solve polynomial and rational inequalities by using algebra and graphs
  • Explain the characteristics of exponential functions and show how are they useful in solving real-world applications
  • Explain the properties of logarithms and show how are they used in manipulating logarithmic expressions
  • Explain the characteristics of logarithmic functions and show how are they useful in solving real-world applications
  • Explain how trigonometric and circular functions model real-world problems and their solutions
  • Explain how trigonometric functions of right triangles model real-world problems and their solutions
  • Describe characteristics of trigonometric and circular functions
  • Use trigonometric identities to simplify, rewrite and prove algebraic expressions and equations
  • Solve trigonometric equations and applications
  • Solve triangles using the laws of cosines and the law of sines
  • Solve applications problems that require using the laws of cosines and the law of sines
  • Solve systems of linear equations and associated applications with two, three or more variables using algebraic and matrix methods
  • Solve systems of non-linear equations and associated applications using algebraic and technological methods
  • Represent conic sections (the circle, the ellipse, the parabola and the hyperbola) graphically and algebraically
  • Demonstrate the ability to identify and evaluate arithmetic and geometric sequences and series
  • Use the binomial expansion to find terms and expand binomials in the form (x+y)n


Pre-Calculus with Limits – Ron Larson/Robert- Houghton Mifflin 2007

Book Web-site:

You need to know the ISBN number 0618660909 to set up an account


Internet Access

I have a homepage on the Internet.

This page will contain a course specific section on which I hope to put all homework assignments, problems of the week, projects, a copy of the course syllabus and links that will be helpful and interesting to you.  Be sure to visit this page regularly.

Email can be sent to me at

You are expected to bring the following materials to class every day:

Notebook (discussed in detail below)

A binder with sections is recommended

– Lined paper

– Graph paper

Ruler – scaled in centimeters

Pencils and erasers


Textbook – covered at all times

A Graphing Calculator such as the TI-83+ or TI-84+ is required.

General Classroom Behavior

  • You are expected to respect and value yourself, your school environment and the diversity of the BHS community. 
  • You are expected to contribute to classes and work cooperatively whenever the situation requires. 
  • You are expected to come to class prepared and you are responsible for all missing work
  • You are to be in your assigned seat when the bell rings.  Otherwise you are late which may result in a detention.
  • You are expected not to talk while I am speaking or interrupt while other people are speaking.
  • There will be no getting out of your seat or speaking without permission.  If you want to speak or get of your seat during class, raise your hand and wait to be recognized.
  • There will be no leaving the room except for emergencies, which should not occur often.
  • If you need to leave the room, just take the pass and leave as quietly as possible.
  • Books should be covered at all times.  If you lose your book, report it to me immediately.
  • The bell does not dismiss the class.
  • No eating or drinking in the classroom.
  • The Pass is to be used only in an emergency

 Quarter Grading Policy

Your grade consists of tests, quizzes, homework, class work, journal writing and projects which are assigned a point value.  Quarter grades will be calculated by dividing the total number of points that you have earned by the maximum number of points that you could have earned and calculating a percent.  For example if you earned 600 points out of a possible 800 points, then you get 600/800  = 75%.

Tests will account for about 40% of your grade, Quizzes for 30%, Homework for 15% and all other work (Notebook, Projects, Classwork, etc.) 15%

 Year Grading Policy

Quarter 1 – 20%                                                        A   90 -100

Quarter 2 – 20%                                                        B   80-89

Quarter 3 – 20%                                                        C   70-79

Quarter 4 – 20%                                                        D   65-69

Midyear Exam – 10%                                              F    0-64

Final Exam – 10%


You are advised to keep a well-organized notebook with two sections:

Section 1 – Class Notes

Section 2 – Homework/Class work/Projects

All materials should be neat and dated and each section of your notebook should be in chronological order.

Quizzes and Tests

Quizzes – Generally, short (20-30 minutes) / 6-8 per quarter / Covers selected sections (50 points).  Tests – Full Period – 3 or 4 per quarter / Covers a chapter (100 points).

Intermediate work, if needed, must always be shown to get full credit, even if you use a calculatorI generally give partial credit on tests and quizzes for correct work even if the final answer is incorrect.


Homework is very important when learning mathematics.  Homework assignments (posted on my homepage) will be given daily and will often be graded. Grades will range from 5 to 0.  A 5 indicates that you attempted all problems (work shown) and got most of them correct. 0 indicates you did not do your assignment, missed an assignment and did make it up, or made very little attempt.  Homework may be turned in one day late at reduced credit.  At any time during the year that you score 84% or above on a test or quiz you earn a homework-pass, which gives you full credit for one homework assignment.  This pass is only valid until the next quiz or test.  Repeated failure to complete homework on time may result in a detention.  


Throughout the semester there will be projects and research papers, many of which will require a computer.  (There are computers in the classroom and the library, which are available during study periods and before and after school, if one is not available at home.)  These projects will require class work and home work and will be assigned a numerical value from 25 to 150 points.  Projects will be posted on my Internet homepage.

Midyear Exam

At the end of the second term, you will be given a midyear exam.  This exam will consist of all the material from the beginning of the year to that point.  This will count for 10% of your final grade.  So, this is an important test!!

Make-up Work

If you miss a test, a quiz, project or a significant class work assignment (or a homework assignment (posted on my homepage) for any reason, you are expected to make it up. Generally, you will be given up to one week from the day you return to make up that assignment.  For example, if you are out of school on Monday and return on Tuesday, you have until the following Tuesday to make up your work.  Incomplete work, for any reason, will count as a 0.  Quizzes and tests may be made up, before school, after school or during study periods.


Extra Help

If you are having trouble with any material, you are expected to seek extra help from me.  I will be available after school in room B-230 from Monday to Thursday and before school by appointment on any school day.  I may also be available during your study period.