SUFFOLK COUNTY COMMUNITY COLLEGE

COLLEGE-WIDE COURSE SYLLABUS

MA70 (MAT126)

 

I.     COURSE TITLE:

Precalculus Mathematics

 

II.    CATALOG DESCRIPTION 2006-2008:

For students with strong mathematics backgrounds planning to enter calculus sequence.  Topics include polynomial, rational, trigonometric, exponential and logarithmic functions; conic sections; translation of axes; linear and nonlinear systems; trigonometric laws and formulas, and applications; DeMoivre's Theorem and complex numbers; polar and parametric equations; and partial fractions.  Prerequisite:  successful completion of three years of college preparatory mathematics (80 or better on the Sequential III or Math B Regents.  Note:  Credit given for MA61 or MA70, but not both.  Credit given for MA62 and MA70, but not both.  Successful completion of both MA61 and MA62 is equivalent to MA70 completion.                                                 A-E-G / 4 cr. hrs.

 

III.  COURSE GOALS:

A.      Introduce the concept of a function, including the algebra and geometry of       functions.

B.      Expose students to a wide variety of elementary functions.

C.      Develop methods of trigonometry, geometry and analytic geometry needed   in calculus and physics.

D.      This course satisfies the SUNY general education requirement for                    mathematics.

 

IV.       STUDENT LEARNING OUTCOMES:

Upon successful completion of this course, students will be able to:

A.      demonstrate an understanding of a mathematical function including such          ideas as the range and domain of functions, symmetric functions, composite   functions, and inverse functions;

B.      sketch graphs of quadratic functions and understand the real and complex       zeros of such functions;

C.      comprehend the significance of the fundamental theorem of algebra and be       able to solve polynomial equations completely by finding the roots;

D.      sketch the graph of polynomial functions;

E.      sketch the graph of rational functions;

F.      sketch the graph of exponential and logarithmic functions;

G.      solve exponential and logarithmic equations;

H.      understand the trigonometric functions, their graphs, and their inverses;

I.              verify trigonometric identities;

J.       solve trigonometric equations and the general triangle, and find the area of a     triangle;

K.      write and do basic computations with complex numbers in both rectangular   and trigonometric form, including the use of DeMoivreÕs Theorem and the      nth root theorem;

L.      analyze, compare, and graph polar functions, conic sections, and parametric   equations;

M.     solve problems involving both linear and non-linear systems of equations        and inequalities;

N.      express and analyze both arithmetic and geometric sequences and series   (optional);

O.      use the principle of mathematical induction to prove identities involving         summations, including the binomial theorem (optional);

P.      use a graphing calculator to perform computations and to graph a variety of   functions.

 

 

V.        Topics Outline with Timeline

 

Topics

Approximate Time

(Including

Examinations)

A.   Quick Review of Algebra and Graphing

1 week

B.    Functions

       1.    domain, range, intercepts
       2.    arithmetic operations and composition
       3.    graphs
       4.    inverses
       5.    special functions: absolute value, split domain,                           greatest integer, etc.
       6.    even and odd functions, symmetry, translations  

1 ½ weeks

C.      Polynomial and Rational Functions

       1.    zeros of polynomials and the fundamental theorem of           algebra

       2.    graphs of polynomial functions

       3.    asymptotes and graphs of rational functions 

2 weeks

D.     Exponential and Logarithmic Functions

       1.    domain and range

       2.    inverse relationship; properties

       3.    graphs with translations

       4.    applications, including compound interest, growth                       and decay

2 weeks

E.      Trigonometric Functions

       1.    domain, range and graphs of the primitive and                            reciprocal functions

       2.    amplitude, period, frequency, and phase shift

       3.    Pythagorean theorem, sum and difference formulas        4.    double angle and half angle formulas

       5.    applications

       6.    domain, range and graphs of inverse trigonometric                       functions

       7.    solving trigonometric equations

3 ½ weeks

F.      Applications of Trigonometry

       1.   laws of sines and cosines

       2.    solving the general triangle

       3.    the area of a triangle

       4.    vectors

       5.    complex numbers Ð rectangular and trigonometric                       form

       6.    DeMoivreÕs Theorem and the nth  root theorem

3 weeks

G.   Polar and Parametric Equations

       1.    polar coordinate system

       2.    graphs of polar functions

       3.    parametric equations and their graphs

 

H.   Conic Sections

       1.    standard and general forms of circle, parabola, ellipse,          hyperbola
       2.    geometric properties, (foci, directrix, focal length,                       eccentricity.)
       3.    graphs

1 week

I.        Systems of Equations and Inequalities

       1.    solution by graphing

       2.    Gaussian elimination and augmented matrices

       3.    partial fractions

       4.    systems of non-linear equations

       5.    systems of inequalities

1 week

J.       Some Special Topics (optional)

       1.    mathematical induction

       2.    binomial theorem

       3.    arithmetic and geometric sequences and series

 

 

 

 

VI.       Evaluation of Student Performance:

            To be determined by the instructor

 

VII.      Programs that require this course:

            None

 

VIII.    Courses that require this course as a prerequisite:

            MA87/MAT141

 

 

IX.       Supporting Information:

Mathematics tutoring services, as well as video and computer aids, are provided for all students through the Math Learning Center (Ammerman Campus, Riverhead 235), the Academic Skills Center Annex (Grant Campus, Health, Sports and Education Center 129), and the Academic Skills Center (Eastern Campus, Orient 213).

 

 

 

 

 

 

 

 

 

 

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