7a. Prerequisite(s): (Course and/or other preparation/experience that is REQUIRED to be completed previous to enrollment in this course.)

Completion of Math 8 with grade of "C" or better, or placement by matriculation assessment process

7b. Co-requisite(s):  (Courses and/or other preparation that is REQUIRED to be taken concurrently with this course.)

7c. Advisory: (Minimum preparation RECOMMENDED in order to be successful in this course.  Also known as “Course Advisory”.)

9b. Catalog Description:

Preparation for calculus. Study of polynomials, rational functions, exponential and logarithmic functions, trigonometric functions, systems of linear equations, matrices, determinants, rectangular and polar coordinates, conic sections, complex number systems, mathematical induction, binomial theorem, and sequences. Recommended for students who plan to take Math. 30. (CAN MATH 16)

10. Student Performance Outcomes: (Outcomes for all credit courses must indicate that students will learn critical thinking and will be able to apply concepts at college level.  Outcomes must be related to items listed in Section 11.)

Through homework assignments, quizzes, exams, projects and classroom discussions, the student will:
1. solve equations, including polynomial, radical, quadratic in form, rational, logarithmic, exponential, and literal with real and imaginary solutions;
2. solve rational, polynomial, and absolute value inequalities;
3. graph polynomial, rational, logarithmic, exponential, and radical functions and find any intercepts, extrema, or asymptotes;
4. solve word problems leading to equations from outcomes #1, 2, 3;
5. solve systems of equations or inequalities using substitution, elimination, graphing Cramer's Rule, and matrices;
6. perform binomial expansion using Pascal's Triangle or combinatorics;
7. identify terms and find finite or infinite sums of arithmetic and geometric sequences and series;
8. apply "Mathematical Induction" method of proof to appropriate problems;
9. evaluate the six trigonometric functions of special angles and their inverses;
10. graph basic trigonometric functions and their transformations and have the ability to identify extreme values, zeros, period, asymptotes and transformations;
11. verify trigonometric identities using valid substitutions and algebraic manipulations;
12. generate solutions to trigonometric equations including the use of trigonometric identities;
13. solve right and oblique triangles and related applications;
14. use polar coordinate system to graph polar equations and evaluate roots and powers of complex numbers;
15. analyze and graph conic sections in rectangular and polar form, labeling the center, vertices, foci, directrices, and asymptotes when applicable;
16. sketch parametric curves and convert parametric equations into rectangular form.

11. Course Content Outline: (Provides a comprehensive, sequential outline of the course content, including all major subject matter and the specific body of knowledge covered.)

I. Algebra Review
A. Polynomial, Radical, quadratic in form, rational, and literal equations with real and imaginary solutions
B. Nonlinear and absolute value inequalities
C. Applications of problems from parts A and B.

II. Functions and Graphs
A. Definition of Function and Evaluation of Functions
B. Graphing of Functions
1. Zeros, or Roots, and Intercepts of Functions
2. Asymptotes of Functions
3. Shifting and Reflection of Functions
4. Symmetry
C. Inverse Functions

III. Exponential and Logarithmic Functions
A. Solving Equations with Exponentials and Logarithms
B. Graphing Exponential and Logarithmic Functions
C. Word Problems with Logarithmic and Exponential Equations

IV. Systems of Equations and Matrices
A. Solving Systems of Equations
1. Substitution
2. Elimination
B. Introduction to Matrices
1. Algebra of matrices
2. Elementary row operations
3. Inverse of a square matrix
C. Matrices as a Method of Solving a System of Equations
1. Elementary row operations
2. Inverse matrices
3. Cramer's Rule

V. Binomial Expansion
A. Pascal's triangle
B. Binomial Theorem

VI. Sequences and Mathematical Induction
A. Arithmetic Sequences
1. Terms
2. Sums
B. Geometric Sequences
1. Terms
2. Sums (finite and infinite)
C. Introduction to Mathematical Induction

VII.Basic Trigonometric Functions
A.Graphing Trigonometric Functions
B.Trigonometric Identities
1.Verify Identities
2.Reciprocal, Ratio, Pythagorean, Sum, Difference, Double Angle, Half Angle
C.Application Problems

VIII.Analytic Trigonometry
A.Inverse Trigonometric Functions
B.Solving Trigonometric Equations
C.Right and Oblique Triangles

IX. Polar Coordinates and DeMoivre's Theorem
A.Polar Coordinates
B.Graphs of Polar Equations
C.Polar Form of Complex Numbers
D.DeMoivre's Theorem

X. More Graphs
A. Conic sections
1. Graphs of conic sections and their transformations in Cartesian coordinates
2. Polar form of conic sections
B. Parametric Equations and Graphs

12. Typical Assignments: (List types of assignments, including library assignments.)

a. Reading Assignments: (Submit at least 2 examples)

1. Read the text selection on sketching hyperbolae with shifted centers and come to class prepared to work on similar problems finding all asymptotes, centers, vertices, and foci.

2. Read the text selection on solving triangles using the Law of Cosines.

b. Writing, Problem Solving or Performance: (Submit at least 2 examples)

1. Find all zeros for a given 5th degree polynomial using the Rational Zeros Theorem, synthetic division, and other relevant theorems discussed in class. Use your results to sketch a graph of the function.

2. Use DeMoivre's Theorem to find all the fourth roots of -1.

c. Other (Terms projects, research papers, portfolios, etc.)

SECTION D

SECTION E

SECTION F

SECTION G