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# 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.

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, 3rd Edition. Lial, Hornsby, and Schneider. Pearson, Addison Wesley, 2005.

Required Text Coverage:
1.1 Linear Equations
1.3 Complex Numbers
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
3.2 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
6.2 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