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
• 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
• 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.