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Pre-Calculus/Trigonometry

Program Description:

In Precalculus, students will develop and improve competencies as articulated in the Common Core State Standards for mathematics in the third and fourth year of high school.  Students will become proficient in four overarching areas:  (1) number and quantity; (2) algebra; (3) functions; and (4) geometry.

(1) Students will extend their understanding of number and quantity. They will use  quantities for the purpose of descriptive modeling.  Students will use the relation i2= -1and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

(2) Students will use their understanding of Algebra to simplify and manipulate expressions and equations.  They  will complete the square to reveal the maximum or minimum of a quadratic.  They will apply the Remainder Theorem in determining whether something is a factor of the polynomial.  They will identify zeros of polynomials and using those zeros to construct rough graphs of the function.  Students will rewrite simple rational expressions in different forms using long division and synthetic division.  Algebraically and graphically, they  will solve  systems of linear equations consisting of a linear and a quadratic in two variables .  Students will also use  graphing calculators to graph functions and make tables of values to find solutions of a system of equations.

(3) Students will be use functions and will identify the domain and range of functions.  They will use function notation to evaluate functions for inputs in their domain, model a relationship between two quantities, interpret key features of graphs and tables, and sketch graphs showing intercepts, intervals of increasing/decreasing, relative maximums/minimums, symmetries, end behavior, and periodicity.   Students will graph  square root, cube root, rational, exponential, logarithmic, trigonometric functions, and piecewise-defined functions, including step functions and absolute value functions and identifying zeros and asymptotes.  Using properties of exponents, they  will write functions in different but equivalent forms and classify situations as exponential growth or decay.  Students will use logarithms to solve exponential equations by hand and with technology.  They will distinguish  between situations that can be modeled with linear functions and with exponential functions.  Students will use  the unit circle to understand radian measure and extend properties of the unit circle to evaluate trigonometric functions.  They will choose  trigonometric functions to model real-life phenomena and identify amplitude, frequency, period, and shifts.  They will be prove the Pythagorean identity and use it to find other trigonometric values and the specific quadrants the angles are in.

(4) Students will be use geometry to apply the trigonometric identities to triangles.  They will explain and use the relationship between sine and cosine of complementary angles to find other trigonometric functions from a triangle.  

Precalculus students will practice skills in isolation in order to apply them competently in solving real-world problems. Through repeated practice and hands-on activities, they will gain competence in the relevant skills of number and quantity, algebra, functions, and geometry.


Course Outline:
Semester 1
Functions and Their Graphs (Ch 1) – 3 weeks

Polynomial and Rational Functions (Ch 2) – 5 weeks

Exponential and Logarithmic Functions (Ch 3) – 4 weeks

Trigonometric Functions (Ch 4) – 6 weeks 

Semester 2

Analytic Trigonometry (Ch 5) – 6 weeks

Additional Topics in Trigonometry (Ch 6) – 3 weeks

Linear Systems and Matrices (Ch 7) – 4 weeks 

Topics in Analytic Geometry (Ch 9) – 3 weeks

Limits and an Introduction to Calculus (Ch 11) – time permitting

 Materials Needed:

               Each day, bring the following materials to class: 

  1. Pencil and eraser (NO PENS)
  2. Laptop & Graphing Calculator
  3. Paper
  4. Practice from previous class 

Rules:

  1. No shouted answers – raise your hand!
  2. Arrive on time to class each day prepared with the required materials and ready to learn.
  3. Show respect to classmates, yourself, and your teachers. 
  4. Demonstrate acceptable behavior and follow all school rules. 

        

Summative Assessments 100%:

Summative Assessments will always be announced.  These will be in the form of section quizzes and comprehensive tests that will be at the end of each chapter.  Re-do’s will be at TEACHER DISCRETION and will be allowed only on summative assessments.

Formative Assessments:

  1. Assigned practice problems
    1. Precalculus is a class based on skill and in order to improve your skills, you need to practice.  All assigned practice will be designed and selected to prepare you to apply your skills competently in solving real-world applicable problems.  It is expected that you will show the correct solution (just having the answer is not enough).  A solution consists of each and every step that was used to solve the problem, as well as the final answer that you get.

       

    2. Completing the practice problems suggested will prepare students for proficiency and/or mastery on summative assessments.

       

  2. Individual Worksheets/Class Exercises/Activities

 

Academic Success:

  1. Watching the lesson videos and completely filling out the notes that go along with it and the PlayPosit answers are a required part of the class.  

     

  2. Group Activities/Worksheets

 

Folder/Binder:

               Students are required to keep track of their progress throughout the course.  All of your notes, homework, worksheets, and projects should be kept in your folder or binder.  There will be a checklist stating the requirements for each folder on Schoology/and or handed out to you.  Should you request a re-do on a summative assessment, you must provide this information.

Make-up Work Due to Absence:

  • YOU are responsible for make-up work after you have been absent from school.
  • If you are absent, you are to always check Schoology to get the assignment.  There will almost always be an electronic version of the assigned practice.  You may also e-mail me to get other information of what you missed when you were gone or to get help with something you do not understand.
  • All missed summative assessments can only be made-up before school, after school, or during Learning Lab and NOT during class time.  If you decide to make up a summative assessment, you must allow yourself enough time to complete the whole test in one sitting.

 

Extra Help:

I will be available before school, after school, or during Learning Lab should you need to see me for extra help.