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# MAT 095 - Pre-College Algebra

5 Credits, 5 Contact Hours
5 lecture periods 0 lab periods

Basic and intermediate algebra concepts. Includes translating written statements into algebraic expressions, linear equations, linear inequalities, graphing, integer exponents, and polynomials. Also includes factoring, rational and radical expressions and equations, square roots, quadratic equations, functions, exponential and logarithmic expressions.

Prerequisite(s): Within the last three years: ICS 081  with an A, or MAT 086 with a B or better, or completion of module 22 in MAT 089A  or MAT 089B , or required score on the Mathematics assessment test. Course Learning Outcomes
1. Solve linear rate of change application problems.
2. Solve linear 2x2 system application problems.
3. Solve absolute value inequalities involving linear equations.
4. Solve rational equations with at least one factorable second-degree polynomial in the denominator.
5. Solve radical equations that result in a quadratic equation solvable by factoring.
6. Use the quadratic formula to solve quadratic equations that comes from an application problem.

Performance Objectives:
1. Find distance and midpoint between two points.
2. Calculate slopes of lines, determine equations of lines and graph lines.
3. Solve and graph linear inequalities and compound linear inequalities and graph in 1-D and 2-D.
4. Solve systems of two and three linear equations and interpret geometrically.
5. Solve absolute value equations and inequalities.
6. Factor polynomials and solve related equations.
7. Perform operations on square root expressions.
8. Solve quadratic equations by factoring, using the square root property, completing the square, and using the quadratic formula; interpret the discriminant; and graph quadratic equations.
9. Perform operations on rational expressions, and solve rational equations that yield quadratic equations.
10. Apply exponent rules to integer and rational exponents; convert between rational exponents and radical notation; and solve radical equations.
11. Evaluate exponential and logarithmic functions, convert between exponential and logarithmic forms, and graph exponential functions.
12. Define and identify functions, determine their domains, and use function notation.

Outline:
1. Distance and Midpoint Between Two Points
1. Distance calculations
2. Midpoint calculations
2. Lines in the Plane
1. Determine slopes of lines
2. Write the equation of a line
1. Given two points
2. Given a point and a slope
3. Give a point and a parallel or perpendicular line
3. Graph lines

D. Applications

1. Inequalities
1. Interval notation
2. Compound inequalities
3. Linear inequalities with two variables
4. Applications
2. Systems of Linear Equations
1. Graphical representation of systems with two variables
2. Elimination and substitution methods for two variables
3. Geometrical interpretation of consistent, and inconsistent systems
4. Applications for two variables
5. Algebraic solution of systems with three variables
6. Geometrical interpretation of consistent, inconsistent and independent systems of three variables
7. Applications for three variables
3. Absolute Value
1. Solve equations
2. Solve inequalities
4. Polynomials
1. Factoring
1. Grouping
2. Trinomials
3. Substitution methods
4. Difference of squares, and sum and difference of cubes
2. Solve equations by factoring
5. Square Roots and nth Roots
1. Evaluate
2. Simplify
3. Perform operations
1. Completing the square
2. Quadratic formula and the discriminant
4. Applications
7. Rational Expressions and Equations
1. Reduce and build
2. Basic operations (addition, subtraction, multiplication and division)
3. Simplify complex rational expressions
4. Solve rational equations including those involving quadratic equations
5. Applications
8. Radical and Exponential Expressions and Equations
1. Laws of exponents for integer exponents
2. Scientific notation
3. Conversion between rational exponents and radical notation
4. Laws of exponents for rational exponents
6. Rationalizing numerators and denominators
8. Applications
9. Exponents and Logarithms
1. Conversion between exponential and logarithmic forms
2. Evaluation of exponential and logarithmic functions
3. Graphing exponential functions
10. Functions
1. Definition
2. Identification
3. Notation
4. Domain

Effective Term:
Spring 2020