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.