PreCalculus

  • NORTHEASTERN CLINTON CENTRAL SCHOOL

    Pre-Calculus I

    Course Syllabus

    Fall/Spring 2017-2018

     

    Paul Smith’s College Course Precalculus-MAT 180

    Instructor:                M. Dudyak

    Contact Hours:       3

    Credit Hours:           3

    Textbook:                 Precalculus: Functions and Graphs, A Graphing Approach, 4th edition; Larson, Hostetler, & Edwards.  Houghton Mifflin.

                                        ISBN #0-618-39476-1

                            Calculus: Early Transcendentals, 7th edition; Anton, Bivens and Davis. ISBN #0-471-38156-X

    Required Materials:           A graphing calculator (i.e. TI-83 plus, or TI-84 plus)

    Prerequisite:            Alegabra2/Trigonometry

     

    Course Description:

    This course will cover topics that prepare a student to study in many different technical venues.  Topics covered will prepare the student for further work in more advanced math courses particularly the Calculus sequence.  Topics that will be covered are a very brief review of algebra concepts, with a more in depth treatment of linear equations and inequalities, quadratic equations and inequalities, graphing and modeling basic functions to include polynomial, rational, exponential, and logarithmic functions.  Additionally students will study systems of equations, conic sections, binomial expansion, and an introduction to limits.  In addition, students will begin to study calculus

    topics such as: Functions, Limits and Continuity, and Derivatives.

     

    Attendance Policy:

    Students must follow Northeastern Clinton Central School attendance policy.

     

                            Note: If you miss a class, it is your responsibility to copy lecture notes from a classmate and complete any missed work.

     

    Grading Policy:

    Each Quarterly grade:

    Major Grades (i.e. Tests, Projects)                                                40%

    Minor Grades (i.e. Quizzes)                                                           40%

    Classwork/Bell Grades                                                                   20%

     

    Test, projects and quizzes are announced.  Homework and Classwork grades

     may or may not be announced.  The final grade is the calculation of 6 scores,

     the 4 quarterly grades (20% each), mid-year exam and the final exam(10%

     each).

     

     

    Grade Scale (Paul Smith’s College):

    A+   100-95                      B    84-80                               D+  69-65

    A   94-90                         C+  79-75                               D    64-60

    B+  89-85                         C    76-73                               F    59-0

     

    ***Northeastern Clinton’s grades will still be a numerical grade.

     

    Course Objectives (Including General Education Objectives):

    As a result of instructional activities, students will be able to:

    1.            Use basic Algebraic concepts that include linear and quadratic equations and inequalities, systems of linear equations and bimomial expansion to accomplish the procedures necessary to the study of Precalculus

    2.            Find and use the slope of a line to write and graph linear equations.

    3.            Find the intercepts of the graph of a function algebraically and graphically.

    4.            Determine whether a relation is a function given its graph, equation, or table of values.

    5.            Find the relative extrema of a graph of a function using the graphing calculator.

    6.            Interpret the domain and range of a function from its equation and its graph.

    7.            Identify even and odd functions.

    8.            Use reflections, translations, and nonrigid transformations to sketch graphs of functions.

    9.            Use graphs of functions to decide whether functions have inverses.

    10.         Find arithmetic combinations and composition of functions.

    11.         Find the inverse of a given one-to-one function graphically and algebraically.

    12.         Choose an appropriate regression model, if any, for a given set of data.

    13.         Use the graphing calculator to find a regression model for a given set of data.

    14.         Find the maximum or minimum of a quadratic function algebraically.

    15.         Use the leading coefficient to determine the end behavior of graphs of polynomial functions.

    16.         Write the equation of a polynomial function given its zeros.

    17.         Perform long and synthetic division of polynomials.

    18.         Apply the Rational Zero Test to find all the possible rational zeros of a polynomial functions.

    19.         Add, Subtract, multiply and divide complex numbers.

    20.         Find all Zeros of polynomial functions, including complex ones.

    21.         Determine the vertical, horizontal, and slant asymptotes of rational functions algebraically and graphically.

    22.         Graph exponential and logarithmic functions and identify their domain and range.

    23.         Convert exponential expressions to logarithmic, and vice versa.

    24.         Use the properties of logarithms to simplify or expand logarithmic expression.

    25.          Solve exponential and logarithmic equations.

    26.         Solve applications of exponential growth, exponential decay, logarithmic, and logistic functions.

    27.         Convert from radians to degrees, and vice versa.

    28.         Use right triangle trigonometry to solve applications.

    29.         Find the 6 trigonometric functions of any angle.

    30.         Graph the sine, cosine, and tangent curves by hand.

    31.         Determine the amplitude, period domain and range of sine and cosine functions.

    32.         Determine the domain, range, and asymptotes of the tangent function.

    33.         Use sine and cosine functions to model real-life data.

    34.         Use the inverse trigonometric functions to determine an angle.

    35.         Prove basic trigonometric identities.

    36.         Solve trigonometric equations algebraically and graphically.

    37.         Limits and continuity of functions including trigonometry functions.

    38.         Derivative of functions including chain rule and implicit derivatives.

     

     

    General Topics Outline:

           I.        Review of Elementary Algebra including graphing, linear equations, solving

                     equations, geometry, using the graphing calculator

     

    II.            Functions including function definitions, graphing by hand and using the

               graphing calculator, graphical transformations, and inverse function

     

    III.           Polynomial and Rational Functions including quadratics functions, higher

               degree functions, zeros of polynomial functions, complex numbers,

               fundamental theorem of algebra, rational functions, graphs of rational

               functions, asymptotes

     

    IV.          Exponential and Logarithmic Functions including definitions and graphs,

               properties of logarithms, solving equations and applications

     

    V.           Trigonometric Functions including radian and degree measure, the

               unit circle, right triangle trigonometry, graphs of trigonometric

               functions, inverse trig functions

     

    VI.          Analytical Trigonometry including fundamental identities, solving

               trigonometric equations

     

    VII.         Additional Topics in Trigonometry including laws of sines and cosines

     

    VIII.       Limits and Continuity

     

    IX.          Derivative of many functions