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
- Add and subtract polynomials
- 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
- Solve problems about interest, about areas and lengths, about mixtures and concentrations
- 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 radicals
- 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
- Model with quadratic equations
- 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.