# Precalculus Course Outline

**Course: **MATH 1285, Precalculus

**Catalog Description:** This course covers topics in
college algebra and plane trigonometry. It is designed for

students who will take MATH 2554.

**Prerequisite:** Appropriate placement scores or
consent of the instructor. NOTE: No credit can be given for those

who have completed MATH 1204 and/or MATH 1213.

**Credit/Contact/Load Hours:** 5 credit hours, 5
contact hours, 5 load hours

**Target Audience and Transfer:** This course is
designed for students who plan to continue into the Calculus

sequence. Transfer depends on the receiving institution.

**Core Course Objectives: **Although each instructor
has his or her own specific objectives, there are some shared by

all. A student who is successful in Precalculus should be able to:

1) Write the equation of a line in slope-intercept form

2) Write or analyze the equation of a secondary function using translations,
reflections, and shrinks/stretches

of a “basic” graph

3) Find the zeros of a polynomial function using the Rational Zeros Test and
synthetic division

4) Algebraically solve various types of equations including quadratic, rational,
exponential, and logarithmic

5) Algebraically solve application problems involving quadratic and exponential
equations

6) Solve a system of two or three linear equations using Gauss-Jordan
elimination with matrices (or Gaussian

elimination with back-substitution and matrices)

7) Algebraically solve a quadratic inequality

8) Find the domain, intercepts, and difference quotient of a function

9) Find the sum, difference, product, quotient, and composition functions when
given two functions

10) Graph various types of functions by hand; including polynomial, piece-wise,
rational, exponential, and

logarithmic

11) Use a graphing calculator for graphing the various types of functions in
objective 10, for regression

analysis, and for finding extrema and zeros

12) Determine if a function has an inverse function and, if so, algebraically
find the inverse function

13) Find the nth term and sum of an arithmetic or geometric sequence

14) Find the partial fraction decomposition of a rational expression

15) Graph by hand or write the equation of a parabola, ellipse, and/or hyperbola

16) Find the six trigonometric function values for an angle given a point on its
terminal side

17) Find the other five trigonometric function values for an angle given one of
the trigonometric function’s

values and the quadrant in which the terminal side of the angle lies

18) Use trigonometry to solve application problems involving right triangles

19) Graph a trigonometric function by hand over two periods involving phase
shifts, amplitude changes,

changes in period, and vertical translations

20) Verify and apply trigonometric identities

21) Evaluate inverse trigonometric functions

22) Solve a trigonometric equation

23) Apply the Law of Sines and the Law of Cosines

24) Convert between rectangular and polar coordinates and graph a polar equation
by hand

*For a more detailed list of problem types, contact the Math Department for a
copy of the Departmental
Review Sheet for Precalculus.*

**Required Text:**__ __Precalculus, 3^{rd} Edition__.__ Lial,
Hornsby, and Schneider. Pearson, Addison Wesley, 2005.

**Required Text Coverage:
**1.1 Linear Equations

1.3 Complex Numbers

1.4 Quadratic Equations

1.5 Applications and Modeling with Quadratic Equations

1.6 Other Types of Equations

1.7 Inequalities (optional topic: rational inequalities)

2.2 Functions

2.3 Linear Functions

2.4 Equations of Lines; Curve Fitting

2.5 Graphs of Basic Functions

2.6 Graphing Techniques

2.7 Function Operations and Composition

3.1 Quadratic Functions and Models

3.2 Synthetic Division

3.3 Zeros of Polynomial Functions

3.4 Polynomial Functions: Graphs, Applications, and Models (optional topics: Intermediate Value and

Boundedness Theorems)

3.5 Rational Functions: Graphs, Applications, and Models (optional topic: slant asymptotes)

4.1 Inverse Functions

4.2 Exponential Functions

4.3 Logarithmic Functions

4.4 Evaluating Logarithms and the Change-of-Base Theorem

4.5 Exponential and Logarithmic Equations

4.6 Applications and Models of Exponential Growth and Decay

5.1 Angles

5.2 Trigonometric Functions

5.3 Evaluating Trigonometric Functions

5.4 Solving Right Triangles

6.1 Radian Measure

6.2 The Unit Circle and Circular Functions

6.3 Graphs of the Sine and Cosine Functions

6.4 Graph of the Other Circular Functions

7.1 Fundamental Identities

7.2 Verifying Trigonometric Identities

7.3 Sum and Difference Identities

7.4 Double-Angle Identities and Half-Angle Identities

7.5 Inverse Circular Functions

7.6 Trigonometric Equations

8.1 The Law of Sines

8.2 The Law of Cosines

8.7 Polar Equations and Graphs

9.2 Matrix Solution of Linear Systems (optional topic: nonsquare systems)

9.4 Partial Fractions

10.1 Parabolas

10.2 Ellipses

10.3 Hyperbolas

10.4 Summary of the Conic Sections

11.1 Sequences and Series

11.2 Arithmetic Sequences and Series

11.3 Geometric Sequences and Series

**A variety of application problems from each required topic
should be assigned.**

**Optional Sections: **1.2, 6.5, 7.7, 8.3, 8.4, 8.5, 8.6, 9.5,
9.6

**Required Instructional Activities: **The content of the
course should be taught with graphing calculator usage as an

integral part of the curriculum. However, no TI-89, TI-92, or comparable
calculators are allowed.

**Required Forms of Assessment: **Each instructor must include
a set of 6 departmental final exam questions on his

or her final exam. These questions will be in direct support of the specific
objectives stated in the Core Course

Objectives, will be based on material covered in the Required Text Coverage
section, and be similar to the questions

on the Departmental Review Sheet for Precalculus. These questions will compose
at least 10% of the students'

overall grade in the course and will be graded according to a standard grading
rubric. The results of these questions

and overall student performance will be reported when final grades are turned
in. *Please note that the only
resource other than a graphing calculator allowed for use by students during the
final exam will be a
departmental formula sheet for trigonometry.*

**Instructor Resources:
**1) Instructor’s Annotated Edition

2) Instructor’s Solutions Manual

3) Instructor’s Testing Manual

4) TestGen-EQ with Quizmaster-EQ

5) Adjunct Support Manual

6) PowerPoint Lecture Presentation

7) Adjunct Support Center

8) MyMathLab

**Student Resources:
**1) Student’s Solutions Manual

2) Graphing Calculator Manual

3) Instructional Videotapes and DVD’s (available in library)

4) Additional Skill & Drill Manual

5) A Review of Algebra

6) Addison Wesley Math Tutor Center—Accessible via toll-free telephone, toll-free fax, e-mail, and the

Internet