MAT-192 Objectives

MAT-192 College Algebra

I. Review Objectives

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

  • Classify real numbers
  • Use properties of real numbers
  • Add, subtract, multiply, and divide fractions
  • Graph numbers on the real line
  • Use inequality symbols
  • Find and use absolute values of real numbers
  • Use exponential notation
  • Simplify expressions using laws of exponents
  • Evaluate and simplify algebraic expressions
  • Plot points in the rectangular coordinate system
  • Graph equations in the rectangular coordinate system
  • Find the slope of a line given its equation or graph
  • Interpret slope as a rate of change to solve applied problems
  • Find the slope-intercept form of the equation of a line given its slope and one point
  • Use point-slope form to find the equation of a line containing two given points
  • Identify lines as parallel, perpendicular, or neither, given their slopes
  • Find the slope-intercept form of the equation of a line parallel or perpendicular to a given line
  • Write a linear equation in standard form
  • Recognize equations of horizontal and vertical lines and identify the slope of each (zero or undefined)
  • Solve linear equations
  • Recognize identities, conditional equations, and inconsistent equations
  • Solve applied problems using linear equations
  • Simplify expressions with integral exponents
  • Convert between decimal and scientific notations
  • Perform computations with scientific notation
  • Determine whether a given ordered pair is a solution to a system of two equations
  • Solve systems of two linear equations using the methods of graphing,
  • substitution, and elimination
  • Identify a system of two linear equations as consistent (independent), inconsistent, or dependent
  • Solve applied problems using systems of linear equations (investments,mixtures, business, and uniform motion)
  • Divide polynomials using long division

II. Primary Objectives

These are the course-level objectives.

  • Model data using the slope-intercept form of the equation of a line
  • Use scientific notation to solve problems
  • Find the domain and range of a relation
  • Determine whether a relation is a function, given a set of points or a graph (vertical line test)
  • Evaluate a function
  • Graph functions by plotting points
  • Identify the domain and range of a function from its graph
  • Solve linear inequalities and express their solution sets using interval notation
  • Graph solution sets of linear inequalities on the number line
  • Recognize inequalities with no real solutions or all real numbers as solutions
  • Solve applied problems using linear inequalities
  • Find the intersection and union of two sets
  • Solve compound inequalities involving “and” (intersections) or “or” (unions)
  • Interpret and use set notation
  • Solve absolute value equations
  • Solve absolute value inequalities
  • Recognize absolute value inequalities with no solution or all real numbers as solutions
  • Use mathematical models involving linear inequalities
  • Graph a system of linear inequalities
  • Evaluate polynomial functions
  • Add, subtract, and multiply polynomials
  • Factor out the greatest common factor (GCF) of a polynomial
  • Factor polynomials by grouping
  • Factor a trinomial of the form ax2  bx  c
  • Factor the difference of two squares
  • Factor perfect square trinomials
  • Factor the sum and difference of two cubes
  • Use a general strategy for factoring polynomials completely
  • Solve higher-degree polynomial equations by factoring
  • Solve problems using polynomial equations (e.g., motion)
  • Evaluate rational functions
  • Find the domain of a rational function
  • Simplify rational expressions
  • Multiply and divide rational expressions
  • Add and subtract rational expressions with like or unlike denominators
  • Simplify complex fractions
  • Solve equations with rational expressions
  • Solve applied problems using rational function models (average cost), and
  • rational equations (motion and work)
  • Solve direct, inverse, joint, and combined variation problems
  • Define even and odd roots of real numbers
  • Evaluate radical functions
  • Find the domain of a radical function
  • Simplify radical expressions (including those involving rationalizing denominators)
  • Simplify expressions with rational exponents
  • Simplify radical expressions using rational exponents
  • Solve radical equations
  • Use radical function models to solve applied problems
  • Express square roots of negative numbers in terms of i.
  • Add, subtract, multiply, and divide complex numbers
  • Solve quadratic equations using factoring, the square root property, completing the square, and the quadratic formula.
  • Solve applied problems using quadratic equations
  • Recognize characteristics of parabolas
  • Graph parabolas in the form y = ax2  bx  c
  • Determine the minimum or maximum value of a quadratic function
  • Evaluate exponential functions
  • Graph exponential functions
  • Use compound interest formulas
  • Find the inverse of a function algebraically
  • Use the horizontal line test to determine if a function has an inverse function
  • Change a function from exponential to logarithmic form and vice-versa
  • Evaluate logarithms
  • Find the domain of a logarithmic function
  • Use like bases to solve exponential equations
  • Solve an equation with a single logarithm
  • Find the distance between two points
  • Find the midpoint of a line segment
  • Write the standard form of the equation of a circle and sketch its graph
  • Give the center and radius of a circle whose equation is in standard form and sketch its graph
  • Convert the general form of a circle’s equation to standard form

Student Learning Outcomes

After completing this course, students will 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 objective concepts.
  • Demonstrate ability to apply concepts to model and solve real-life problems using linear, polynomial, rational, and root equations.
  • Demonstrate a clear understanding of concepts of functions, including domain, range, operations, and inverses.
  • Demonstrate skills to graph functions, parabolas, and circles.