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MAT092 - Algebra 1
Catalog Description: Students move through a series of content modules using a mastery learning approach, making extensive use of computer software for content delivery, practice of skills, and assessment (graded homework, quizzes, and module pre- and post-tests). Topics include simplifying variable expressions, solving linear equations and inequalities, graphing linear equations in two variables, solving systems of linear equations in two variables, operations with exponential pressions and polynomials, factoring polynomials, simplifying radical expressions (square roots), and solving quadratic equations. Prerequisite: MAT 091 or by placement.
Lecture: 4 hrs.
Course Learning Outcomes (CLOs):
Upon successful completion of this course, the student will be able to:
1. Use the Order of Operations Agreement to correctly evaluate numerical expressions involving any combination of addition, subtraction, multiplication, division, whole number exponents, and grouping symbols (e.g., parentheses and brackets).
2. Solve linear equations and inequalities in one variable that may include variable and/or constant terms on both sides of the equation (or inequality) and may include expressions in parentheses; graph open, closed, and half-open intervals of real number solutions of linear inequalities on a number line.
3. Add, subtract, and/or multiply any combination of two polynomials; then simplify and write the result in descending order.
4. Simplify exponential expressions involving negative and/or positive integers or zero as exponents and involving multiplication, division, and/or raising a monomial to a power, and express the answers in a form that uses only positive integers as exponents.
5. Convert given numbers from scientific notation to standard decimal form and from standard decimal form to scientific notation.
6. Completely factor polynomials using appropriate combinations of factoring techniques, or state that a given polynomial is non-factorable/prime. Factoring techniques needed may include factoring out a monomial GCF (greatest common factor) of the terms, factoring out a common binomial, factoring a polynomial of 4 terms by grouping, factoring a trinomial using "Trial Factors" (sometimes called trial and error) or the "ac Grouping Method," and factoring a Difference of Perfect Squares.*
7. Draw the graph of a line when given its equation in either standard form (Ax + By = C) or in slope-intercept form (y = mx + b).
8. Given a system of two linear equations in two variables, solve the system using the Graphing Method, the Substitution Method, or the Addition/Elimination Method, as appropriate, or identify that the system is Inconsistent (with no solution), or Dependent (with many solutions).
9. Write numerical square root expressions (involving a single radical or addition, subtraction, multiplication, and/or division of radical expressions) in their simplest radical form, and rationalize any denominators before writing the final answer.
10. Solve a quadratic equation by using factoring or taking square roots or using the Quadratic Formula, as appropriate, and write the solutions in simplest form or indicate that there are no real roots if the solutions include square roots of negative radicands.
11. Use the Pythagorean Theorem to calculate the length of the remaining side of a right triangle when given the lengths of any two sides, and express the final answer in simplest radical form if it is not an integer.
* This course objective has been identified as a student learning outcome that must be formally assessed as part of the Comprehensive Assessment Plan of the college. All faculty teaching this course must collect the required data and submit the required analysis and documentation at the conclusion of the semester to the Office of Institutional Research and Assessment.
A. Review of Foundational Skills and Vocabulary
Absolute value; operations with integers; exponential notation; the Order of Operations Agreement; properties of addition and multiplication with real numbers
B. Variable Expressions and Review of Operations with Rational Numbers
Operations with fractions and decimals, evaluating and simplifying variable expressions; translating English phrases and algebraic expressions
C. Linear Equations and Inequalities
Solving linear equations of the form ax + b = cx + d
and equations involving parentheses; solving linear inequalities; graphing intervals of real numbers on a number line; solving formulas for different variables; geometry vocabulary and formulas; applications
D. Linear Equations in Two Variables and Graphing in a Cartesian Coordinate System
Solutions of linear equations in two variables; intercepts; slope; graphing lines in a Cartesian coordinate system; parallel and perpendicular lines; Standard Form, Slope-Intercept Form, and Point-Slope Form; writing the equation of a line
E. Systems of Linear Equations
Consistent (Independent), Inconsistent, and Dependent Systems of linear equations in two variables; solving systems (simultaneous equations) using the Graphing Method, Substitution Method, and Addition/Elimination Method
F. Polynomials and Exponential Expressions
Simplifying exponential expressions involving products, quotients, raising powers and products to powers, and integer exponents; Scientific Notation; addition, subtraction, and multiplication of polynomials; division of polynomials by monomials
G. Factoring Polynomials Factoring out the monomial or binomial GCF of the terms of a polynomial; factoring 4-term polynomials by grouping; factoring trinomials of the forms x2 + bx + c or ax2 + bx + c by using the Trial Factors (Trial and Error) Method and by using the "ac Grouping Method"; factoring a Difference of Squares; solving quadratic equations using the Factoring Method
H. Radical Expressions, Quadratic Equations, the Pythagorean Theorem, and Rational Equations
Simplifying radical expressions with index 2 (square roots) to simplest radical form; addition, subtraction, multiplication, and division of radical expressions; rationalizing denominators; rational vs. irrational vs. imaginary/complex numbers; solving quadratic equations using the Factoring Method, the Square Root Method, and the Quadratic Formula; the Pythagorean Theorem; solving rational equations with monomial denominators; solving rational equations in the form of proportions
Effective Term: Fall 2015