Math 2412 Precalculus Information
LSC-CyFair Math Department
Catalog Description
An integrated treatment of the concepts necessary for calculus, emphasizing elementary functions and their graphs, including polynomial, rational, exponential, logarithmic and trigonometric functions, also includes topics from analytic geometry.
Course Learning Outcomes
The student will:
• Demonstrate and apply knowledge of properties of functions.
• Recognize and apply algebraic and transcendental functions and solve related equations.
• Apply graphing techniques to algebraic and transcendental functions.
• Compute the values of trigonometric functions for key angles in all quadrants of the unit circle measured in both degrees and radians.
• Prove trigonometric identities.
• Solve right and oblique triangles.
• Apply the binomial theorem.
• Determine equations of conic sections, and graph conics, including translation and identification of vertices, foci and asymptotes.
• Perform basic operations and solve applications using vector algebra.
• Perform operations and graph equations using polar and parametric equations.
• Prove statements using mathematical induction.
• Use properties of arithmetic and geometric sequences and series to identify terms, find sums and solve applications.
Contact Hour Information
Credit Hours: 4
Lecture Hours: 4
Lab Hours: 1
External Hours: 0
Total Contact Hours: 80
Prerequisites
Math 1314 and Math 1316 OR placement by testing;
ENGL 0305 or ENGL 0365 OR higher level course (ENGL 1301), OR placement by testing
Corequisites
ENGL 0307
Required Materials
Textbook:
Sullivan, Michael and Sullivan, Michael III, Precalculus Enhanced with Graphing Utilities, 6th edition with MyMathLab Access, Pearson, ISBN Numbers:Textbook Plus MyMathLab Portal Access: 9781256636625
Textbook Only: 9780321795465
MyMathLab Portal Access Only: 9780558357603
Calculator:
Graphing Calculator required. TI 83, TI 84 or TI 86 series calculators recommended.
Calculators capable of symbolic manipulation will not be allowed on tests. Examples include, but are not limited to, TI 89, TI 92, and Nspire CAS models and HP 48 models.
Neither cell phones nor PDA’s can be used as calculators. Calculators may be cleared before tests.
Review Sections and Readiness Check
There are sections of the textbook that should be covered in class (listed below as Textbook Sections) and sections that should be assigned to the students to review on their own at the beginning of the semester (listed below as Self Review Sections). Self Review Sections must NOT be covered in class but students MUST be assessed on these sections as part of their grade. Faculty have the option of using the departmental College Algebra and Trigonometry Readiness Check for Precalculus as an assessment instrument. This instrument is available in print form or in web-based form through MyMathLab.
To access the print version click College Algebra and Trigonometry Readiness Check for Precalculus.
To access the web-based version copy the College Algebra and Trigonometry Readiness Check from the Course ID burghduff61044 in MyMathLab.
Textbook Sections
Note: The following sections are to be covered in class. Self Review Sections, listed below, are to be reviewed by the students on their own outside of class and evaluated.
Chapter 4. Polynomial and Rational Functions
4.4 Properties of a Rational Function
4.5 The Graphs of a Rational Functions
Chapter 5. Exponential and Logarithmic Functions
5.6 Logarithmic and Exponential Equations
5.8 Exponential Growth and Decay; Newton's Law; Logistic Growth and Decay
Chapter 7. Analytic Trigonometry
7.3 Trigonometric Equations
7.4 Trigonometric Identities
7.6 Double-angle and Half-angle Formulas
Chapter 9. Polar Coordinates and Vectors
9.1 Polar Coordinates
9.2 Polar Equations and Graphs
9.3 The Complex Plane; DeMoivre's Theorem
9.4 Vectors
9.5 The Dot Product
Chapter 10. Analytic Geometry
10.1 Conics
10.2 The Parabola
10.3 The Ellipse
10.4 The Hyperbola
10.6 Polar Equations of Conics
10.7 Plane Curves and Parametric Equations
Chapter 11. Systems of Equations and Inequalities
11.1 Systems of Linear Equations: Substitution and Elimination
11.2 Systems of Linear Equations: Matrices
11.3 Systems of Linear Equations: Determinants
11.4 Matrix Algebra
11.5 Partial Fraction Decomposition (optional)
11.6 Systems of Nonlinear Equations (optional)
11.7 Systems of Inequalities
Chapter 12. Sequences, Induction, the Binomial Theorem
12.1 Sequences
12.2 Arithmetic Sequences
12.3 Geometric Sequences, Geometric Series
12.4 Mathematical Induction
12.5 The Binomial Theorem
Self Review Sections
Note: Students are expected to review the following sections on their own. Instructors must evaluate these sections.
Chapter 2. Functions and their Graphs
2.1 Functions
2.2 The Graph of a Function
2.3 Properties of Functions
2.4 Library of Functions; Piece-wise Defined Functions
2.5 Graphing Techniques: Transformations
2.6 Mathematical Models: Building Functions
Chapter 4. Polynomial and Rational Functions
4.1 Polynomial Functions and Models
Chapter 5. Exponential and Logarithmic Functions
5.3 Exponential Functions
5.4 Logarithmic Functions
5.5 Properties of Logarithms
Chapter 6. Trigonometric Functions
6.1 Angles and their Measures
6.2 Trigonometric Functions: Unit Circle Approach
6.3 Properties of the Trigonometric Functions
6.4 Graphs of the Sine and Cosine Functions
6.5 Graphs of the Tangent, Cotangent, Cosecant and Secant Functions
6.6 Phase Shift; Sinusoidal Curve Fitting
Chapter 7. Analytic Trigonometry
7.1 The Inverse Sine, Cosine and Tangent Functions
7.2 The Inverse Trigonometric Functions (continued)
Chapter 8. Applications of Trigonometric Functions
8.1 Right Triangle Trigonometry: Applications
8.2 The Law of Sines
8.3 The Law of Cosines
8.4 Area of a Triangle
