PREREQUISITE(S): MAT 073 or two years of high
school algebra
COURSE DESCRIPTION:
This course provides an intensified study of algebraic techniques and
prepares students for future study in mathematics. The central theme of this
course is the concept of a function and its graph. Topics include functions,
exponents, logarithms, systems of equations, matrices, polynomials, and conic
sections .
COURSE COMPETENCIES:
During this course, the student will be expected to:
1. Discuss equations, inequalities, and mathematical
models.
1.1 Graph equations and inequalities.
1.2 Solve linear , quadratic, polynomial, rational, radical, and absolute value
equations .
1.3 Describe real -world situations through math modeling.
1.4 Simplify complex numbers .
2. Discuss functions.
2.1 Calculate slope of linear functions .
2.2 Calculate midpoint and distance between two points.
2.3 Identify domain and range.
2.4 Apply vertical line test.
2.5 Discuss properties of functions .
2.6 Discuss transformations of functions.
2.7 Analyze combinations of functions .
2.8 Calculate inverse functions.
3. Discuss and graph polynomial functions .
3.1 Discuss and graph quadratic functions .
3.2 Calculate zeros of polynomial functions.
3.3 Divide polynomials using long division.
3.4 Divide polynomials using synthetic division.
4. Analyze rational functions and their graphs.
4.1 Discuss and graph rational functions.
4.2 Identify domain and range.
4.3 Identify asymptotes.
4.4 Calculate practical applications using variation.
5. Analyze radical functions and their graphs.
5.1 Discuss and graph radical functions.
5.2 Identify domain and range.
5.3 Apply radical functions to models.
6. Calculate and graph exp onential and logarithmic
functions.
6.1 Identify domain and range.
6.2 Calculate values of logarithms.
6.3 Solve exponential and logarithmic equations.
6.4 Calculate and analyze practical applications, using exponential and
logarithmic functions.
7. Setup and solve systems of equations.
7.1 Calculate solutions of linear systems.
7.2 Perform partial fraction decomposition .
7.3 Algebraically solve nonlinear equations in two variables.
7.4 Graphically solve systems of linear inequalities.
7.5 Solve linear programming involving objective functions.
8. Use and understand matrices and de terminants .
8.1 Use Gaussian elimination to calculate matrix solutions to linear systems.
8.2 Perform matrix operations.
8.3 Calculate multiplicative inverses.
8.4 Identify and solve matrix equations.
8.5 Solve systems of equations, using Cramer’ s Rule .
9. Calculate conic sections: ellipse, hyperbola, and
parabola.
9.1 Transform equations to standard form.
9.2 Identify centers, foci, and vertices.
9.3 Graph conic sections.
COMPETENCIES REVIEWED AND APPROVED BY:
DATE: _________________
FACULTY:
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