# MAT-194 Objectives

## MAT-194 College Algebra for STEM

### I. Review Objectives

Students should be proficient with these concepts. As such, only a short amount of time in class will be spent reviewing them.

• Classify real numbers
• Use properties of real numbers
• Use properties of negatives
• Add, subtract, multiply, and divide fractions
• Graph numbers on the real line.
• Work with set and interval notation
• Find and use absolute values of real numbers
• Simplify expressions using the laws of exponents
• Write numbers in scientific notation
• Multiply algebraic expressions
• Use the Special Product Formulas
• Factor out common factors
• Factor trinomials
• Solve linear equations in one variable
• Solve power equations
• Solve for one variable in terms of others
• Graph ordered pairs in the coordinate plane
• Graph equations by plotting points
• Graph equations by intercept method
• Find the slope of a line
• Find the point‐slope form of the equation of a line
• Find the slope‐intercept form of the equation of a line
• Find equations of horizontal and vertical lines
• Solve a system of two linear equations in two variables by graphing.
• Solve a system of two linear equations in two variables using the substitution and elimination methods.
• Use systems of two linear equations to solve applied problems.

### II. Primary Objectives

These are the course – level objectives.

• Simplify expressions involving rational exponents.
• Express radicals using rational exponents.
• Rationalize a denominator
• Factor Difference of Squares, Difference of Cubes, and Sum of Cubes
• Find the domain of a rational expression
• Simplify rational expressions
• Multiply and divide rational expressions
• Add and subtract rational expressions
• Simplify complex fractions
• Rationalize a denominator or numerator
• Solve problems related to uniform motion
• Solve quadratic equations by factoring, by completing the square and using quadratic formula
• Solve basic polynomial equations, equations involving radicals, and equations of quadratic type
• Define a complex number
• Add and subtract complex numbers
• Find complex roots of quadratic equations
• Multiply and divide complex numbers
• Solve applied problems modeled with these equations.
• Solve linear and quadratic inequalities
• Solve absolute value equations and absolute value inequalities
• Find the length of a line segment.
• Find the midpoint of a line segment.
• Identify equation of a circle
• Graph circles in a coordinate plane
• Use a graphing calculator to graph equations
• Find equations for parallel and perpendicular lines
• Model with linear equations: interpret slope as a rate of change
• Find equations for direct variation
• Find equations for inverse variation
• Find equations for joint variation
• Use these concepts to solve applied problems involving variation
• Define a function
• Recognize functions in the real world
• Define domain and range of a function
• Represent functions verbally, algebraically, graphically, and numerically
• Graph functions by plotting points and by using a graphing utility
• Graph piecewise defined functions
• Use the vertical line test to identify functions
• Determine whether an equation defines a function
• Find the domain and range of a function from a graph
• Find where a function is increasing or decreasing from a graph
• Find local maxima and minima of functions from a graph
• Find the average rate of change of a function
• Interpret average rate of change in real‐world situations
• Recognize that a function with constant average rate of change is linear
• Shift graphs vertically and horizontally
• Stretch or shrink graphs vertically or horizontally
• Determine whether a function is odd or even
• Find the sum or difference of two functions and the corresponding domain.
• Find the product or quotient of two functions and the corresponding domain.
• Find the composition of two functions
• Find the domain of a composite function.
• Determine whether a function is one‐to‐one
• Find the inverse function of a one‐two‐one function
• Express quadratic function in standard form and graph the function
• Apply quadratic function to real world problems
• Use synthetic division to divide polynomials
• Use the Remainder Theorem to find values of polynomials
• Define a rational function
• Define and graph exponential functions
• Evaluate and graph the natural exponential function
• Use exponential functions to solve application problems
• Define a logarithmic function: in logarithmic form and its equivalent exponential form
• Graph logarithmic functions
• Convert between exponential and logarithmic forms.
• Define the various properties of logarithms.
• Use the properties of logarithms to expand a log expression, and vice versa.
• Use the Change of Base Formula
• Solve exponential equations algebraically and graphically on the calculator.
• Solve logarithmic equations algebraically and graphically on the calculator.
• Solve applied problems involving exponential and logarithmic equations
• Solve systems of linear equations in three variables.
• Use systems of three equations to solve applied problems.
• Solve systems of equations using matrices.
• Evaluate determinants of square matrices.
• Use Cramer’s rule to solve systems of equations.
• Graph systems of linear inequalities.
• Use linear programming to solve applied problems.
• Decompose rational expressions in to partial fractions in the following cases.
• Denominator contains distinct linear factors.
• Denominator contains repeated linear factors.
• Denominator contains irreducible quadratic factors, none of which is repeated.
• Denominator has a repeated irreducible quadratic factor.
• Define an ellipse
• Graph ellipses centered at the origin and away from the origin
• Define a hyperbola
• Graph hyperbolas centered at the origin and away from the origin
• Define a parabola
• Graph parabolas centered at the origin and away from the origin
• Solve applied problems involving conic sections

### Student Learning Outcomes

After completing this course, the students will know and be able to:

• Demonstrate mastery of mathematical notation and terminology used in this course.
• Demonstrate knowledge of the fundamental principles including the laws and theorems relevant to course objectives.
• Demonstrate ability to apply concepts to model and solve real‐life problems using linear, polynomial, rational, root, exponential and logarithmic equations, and linear programming.
• Demonstrate a clear understanding of concepts of functions, including domain, range, operations, compositions and inverses.
• Demonstrate skills to graph functions and conic sections.
• Demonstrate knowledge, competencies, and thought process to support further study, such as precalculus and beyond.