MATH 1000 Essentials of Algebra

3 Credit Hour(s)

This course is designed to provide math remediation in preparation for algebra-intensive courses. It covers fundamental topics, including real numbers and operations, essential algebraic concepts such as roots and radicals, polynomial factoring, functions (domain and range), simplifying and solving equations, and rational expressions. Additionally, students will explore the application of these concepts in solving and graphing quadratic equations and working with exponential and logarithmic expressions.

Please note that this course does not fulfill general education math requirements for associate degrees or technical certificates. It is not intended for transfer to four-year universities. Students are advised to verify course recommendations with the college or university to which they plan to transfer, as the receiving institution makes the final decision in determining the transferability of credits.
Student Learning Outcomes:
Upon completion of this course, the student will be able to:

Find the greatest common factor from a group of monomials and polynomials.
Factor by grouping.
Factor trinomials of the form x^(2 )+bx+c.
Factor the difference of two squares, perfect square trinomials, and the sum or difference of two cubes.
Find the domain and range of a relation.
Express equations of functions using function notation.
Solve polynomial equations by factoring.
Evaluate rational functions.
Multiply, divide, add, subtract and simplify rational expressions.
Simplify complex rational expressions.
Identify and solve rational equations.
Find square roots of perfect squares.
Approximate square roots.
Evaluate radical functions.
Use the definition for rational exponents of the form 〖 a〗^(1/n).
Use the definition for rational exponents of the form a^(m/n).
Add, subtract, and multiply radical expressions.
Rationalize denominators of radical expressions.
Solve equations involving one radical expression.
Simplify powers of i and add, subtract, and multiply complex numbers.
Solve quadratic equations using factoring, the quadratic formula, the square root property, and completing the square.
Identify the characteristics of a quadratic function from its graph and graph quadratic functions using translations.
Solve applications involving geometric formulas.
Use vertical and horizontal shifts to graph functions.
Sketch the graphs of exponential functions using transformations.
Demonstrate an understanding of the basic characteristics of exponential functions, including the natural exponential function.
Demonstrate an understanding of the definition of a logarithmic function.

This course is not designed for transfer to four-year universities. Students should check course recommendations with the college or university to which they intend to transfer for a baccalaureate degree. The receiving institution always makes the final decision about transferability of credits.