PREREQUISITE(S):
MATH 123
COURSE DESCRIPTION:
Real and complex number systems , inequalities, exponential and logarithmic
functions,
mathematical induction , limits, sequences, elementary theory of equations,
linear systems , matrices,
vectors, and topics of analytic geometry.
COURSE COMPETENCIES:
During this course, the student will be expected to:
1. Manipulate fundamental mathematical expressions.
1.1 Describe the complex number system in terms of its subsets and their
properties.
1.2 Identify all the sets to which any given number belongs.
1.3 Interpret rational exponents .
1.4 Solve linear and quadratic equations and inequalities in one variable .
2. Discuss mathematical functions.
2.1 Define a general function using proper terminology.
2.2 Define linear and quadratic functions.
2.3 Define the Cartesian plane and its parts.
2.4 Graph a function using rectangular coordinates.
2.5 Determine if a relation is a function.
2.6 Determine the composition of two functions.
2.7 Obtain the inverse of a function, if it exists.
3. Analyze polynomial and rational functions.
3.1 Define polynomial and rational functions.
3.2 Apply the Fundamental Theorem of Algebra .
3.3 Apply the Intermediate Value , the Remainder, the Factor, and the Rational
Root
theorems to find polynomial roots.
3.4 Sketch polynomial and rational functions.
4. Use exponential and logarithmic functions .
4.1 Define the exponential function with proper terminology.
4.2 State the properties of the exponential function, including its graph.
4.3 Define the logarithmic function as the inverse of the exponential.
4.4 Evaluate logarithmic and exponential functions.
4.5 Solve exponential and logarithmic functions.
5. Compute with sequence and series.
5.1 Define a sequence as a function and recursively.
5.2 Evaluate terms of a sequence.
5.3 Calculate series.
5.3 Verify conjectures by the Induction Principle, when appropriate.
6. Solve systems of equations.
6.1 Solve square and nonsquare linear systems.
6.2 Solve nonlinear systems containing equations of degree two, or less.
6.3 Decompose rational expressions into their partial fraction equivalents .
6.4 Solve systems of inequalities in two variables by graphing .
7. Use matrices.
7.1 Solve a linear system by means of row operations.
7.2 Demonstrate the operations of matrix algebra.
7.3 Determine the inverse of a nonsingular matrix.
7.4 Calculate the determinant of a square matrix.
7.5 Use Cramer's Rule to solve linear systems.
8. Analyze conic sections .
8.1 Write the general and standard form equations for conic sections.
8.2 Write the equations for rotated conics.
8.3 Graph equations in polar coordinates.
8.4 Convert between rectangular and polar forms.
INSTRUCTIONAL MATERIALS:
Textbook(s): For each text used in this course, identify the minimum chapters to
be covered in
this course.
HBJ Advanced Mathematics. Coxford/Payne 1988 (Ankeny, Boone, Urban)
Precalculus. Aufmann/Barker/Nation 2E (Carroll)
Study guide
Transparencies
Test banks
Computer hardware/software
Texas Instruments PC-81 Graphing Calculator Software (Carroll)
Other (example: Laboratory equipment for
biology/chemistry class)
Houghton Mifflin Video Library (Carroll)
