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MATH 121: COLLEGE ALGEBRA
I: Algebra
Students will be able to:
1. Perform operations on polynomials: +, -, x, ), including synthetic ), and raising to a power
2. Factor expressions
a. by grouping
b. by synthetic division that are the sum or difference of cubes
c. containing negative and fractional exponents
3. Perform operations on rational expressions
a. Reduce, +, -, x, )
b. Simplify a complex fraction
4. Perform operations on radical expressions
a. Simplify, +, -, x, ), raise to a power including complex numbers
b. Rewrite radicals using fractional exponents
5. Perform operations on expressions with fractional and negative exponents
a. Simplify, +, -, x, ), raise to a power
b. Rewrite fractional exponents using radicals
6. Solve the following Equations algebraically and graphically on the TI-83 Plus calculator
a. Linear
b. Quadratic -- Algebraically by: Factoring, Quadratic Formula with Real and Complex Roots, Extracting the
Roots with Real and Complex Roots, Completing the Square Method with Real and Complex Roots
c. Higher Degree (Polynomials)
d. Rational
e. Radical
f. Absolute Value
7. Solve the following Inequalities algebraically and graphically on the TI-83 Plus calculator and express the
solution in Interval Notation
a. Linear
b. Quadratic
c. Rational
d. Absolute value
8. Perform the following in regard to Relations and Functions
a. Find the value of a function using functional notation
b. Determine whether a relation represents a function (from a set of ordered pairs and from a graph)
c. Find the domain and range of a function
d. Find the sum, difference, product and quotient of two functions
e. Find the composite of a pair of functions (and its domain)
f. Find the Difference Quotient of a Polynomial, Rational, and Radical Function
9. Hand graph the following functions
a. Linear using Slope Y-Intercept (find the slope of a line and write an equation of a line).
b. Quadratic (Find x and y-intercepts, find the axis of symmetry, and find the vertex
c. Cubic
d. Rational and determine asymptotes
e. Radical
f. Absolute Value
g. Restricted domain, Split domain or Piecewise
h. Greatest Integer
10. Using the graphing calculator
a. To graph a function and find/determine (x-and y-intercepts, zeros, intervals on which the function is
increasing and decreasing, maximum and minimum and local minima and maxima, obtain information from
or about the graph of a function
b. Regression Program to find the Curve of Best Fit (linear, quadratic, power, polynomial – cubic, exponential,
logarithmic)
11. Solve systems of equations algebraically and graphically, by hand and graphing
calculator
a. That are linear and nonlinear, two variables
b. *That are linear, three variables
II. Trigonometry
Students will be able to:
1. Solve a right triangle using Right Triangle Trig and The Pythagorean Theorem
2. Convert between degrees, minutes, seconds and decimal form for angles
3. Convert from degrees to radians and from radians to degrees
4. Find the trigonometric functions of an angle of any size
5. Solve oblique triangles using the Law of Sines and Law of Cosines
6. Graph trigonometric functions
7. *Graph and solve vector problems
III. Elementary Transcendental Functions
Students will be able to:
1. Use the Properties of logarithms to expand a log expression, and vice versa
2. Solve logarithm equations algebraically and graphically on the calculator
3. Graph logarithmic functions by hand and graphing calculator
4. Solve exponential equations algebraically and graphically on the calculator
5. Graph exponential functions by hand and the graphing calculator