BRONX COMMUNITY COLLEGE

of the City University of New York

DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE

 

   SYLLABUS:  MTH 30 - Precalculus (4 Credits - 4 Hours per week)

 

Prerequisite:   MTH 6 or equivalent, and if required ENG 2 and RDL 2

TEXT:                                                                           Precalculus Essentials (Fifth Edition) by Robert Blitzer, Pearson

                         ISBN 978-0-13-457815-6               

This course is a Pathways Core B (Mathematical and Quantitative Reasoning) Course:
A course in this area must meet all of the following learning outcomes. A student will:

a)      Interpret and draw appropriate inferences from quantitative representations, such as formulas, graphs, or tables.

b)      Use algebraic, numerical, graphical, or statistical methods to draw accurate conclusions and solve mathematical problems.

c)      Represent quantitative problems expressed in natural language in a suitable mathematical format.

d)     Effectively communicate quantitative analysis or solutions to mathematical problems in written or oral form.

e)      Evaluate solutions to problems for reasonableness using a variety of means, including informed estimation.

f)       Apply mathematical methods to problems in other fields of study.

Course Learning Outcomes                         (Pathways Learning Outcomes contributed to)

On successful completion of this course a student will be able to:

1.      Solve factorable polynomials equations and inequalities of at least 3rd degree in one real variable and 2nd degree rational equations and inequalities in one real variable (b, c, e)

2.      Graph polynomial, rational, exponential, logarithmic, sine and cosine functions (b, d, e, f)

3.      Verify trigonometric identities and solve trigonometric equations (b, d)

4.      Employ transformations of functions algebraically and graphically as problem-solving tools (b, c)

5.      Compute inverse functions and use their properties to obtain more precise algebraic
 and graphical information about the corresponding original functions (a, b, c)

6.      Demonstrate fluency with function notation and operations on functions including composition (b, c)

7.      Identify whether a given graph or algebraic relation represents a function and analyze it to determine its particular properties such as domain and range, end behavior, asymptotes, and periodicity (a, c, d)

8.      Form models to apply them in the solution of real-world problems such as involving exponential growth and decay and optimization in finance, biology, chemistry, or physics (a, b, c, d, e, f)

SECTION             TOPIC                                        SUGGESTED EXERCISES

Functions and Graphs

      1.2       Basics of Functions and their Graphs       176/ 11-31 (odd), 45, 47, 53-57, 71, 72, 75-81

      1.3       More on Functions and their Graphs        195/ 11, 15, 17, 23, 85-92, 97

      1.6       Transformations of Functions                   241/ 1-87 (odd)

      l.7        Combinations of Functions;                      258/ 5-11, 17-33, 51-59, 83-94

                       Composite Functions                                 

      1.8       Inverse Functions                                      269/ 1-5, 11-24, 29-37, 53-58

     

SECTION             TOPIC                                        SUGGESTED EXERCISES

Polynomial and Rational Functions

      2.2       Quadratic Functions                                 330/ 9-55 (odd)

      2.3       Polynomial Functions and Their Graphs   348/ 3-7, 15-21, 25, 27-33, 37, 39, 41-47

2.4              Dividing Polynomials;                              363/ 13, 15, 17-25, 33-41

     Remainder and Factor Theorems        

      2.5       Zeroes of Polynomial Functions               377/ 1-16, 17-31 (odd), 53-55, 58, 59

      2.6       Rational Functions and Their Graphs       398/ 1-14, 21-28, 37-43, 45, 49, 57, 63, 71, 77-80

      2.7       Polynomial and Rational Inequalities       412/ 1-23 (odd), 43-45, 55-57, 69, 70

 

Exponential and Logarithmic Functions

      3.1       Exponential Functions                              448/ 11-17, 19-31, 35-37, 41, 43

      3.2       Logarithmic Functions                              463/ 1-29, 43, 44, 47-53, 55, 59, 63, 71, 75-79, 81-89

      3.3       Properties of Logarithms                          475/ 1-27, 35, 37, 41-57, 67, 71-77, 83-86

3.4              Exponential and Logarithmic Equations  488/ 1-21, 27-43, 49-57, 69-71, 87, 89

                                                                 

Trigonometric Functions

      4.1       Angles and Radian Measure                     532/ 1-10, 13-28, 41-56, 60-63

4.2              Trigonometric Functions:                          547/ 1-55

                 The Unit Circle                                   

      4.3       Right Triangle Trigonometry                    560/ 3-15, 21-31

      4.4       Trigonometric Functions of Any Angle    575/ 1-21, 23-27, 35-43, 61-73

      4.5       Graphs of Sine and Cosine Functions      595/ 1-25 (odd), 43-49

      4.7       Inverse Trigonometric Functions              626/ 1-11, 19-41, 47-53, 63-67

 

Analytic Trigonometry

      5.1       Verifying Trigonometric Identities           658/ 1-35

      5.2       Sum and Difference Formulas                  668/ 1, 3, 5, 13, 15, 21, 23, 33-36

      5.5       Trigonometric Equations                           703/ 11, 15, 19-22, 25-28, 39, 41, 57, 59

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8/06 (MM)

12/06 (AW)

01/16 (EA) for new edition

10/17 (EA) for Pathways compliance

03/18 (YH)