MAT 099  Combined Algebra Credits: 5 Lecture Hours: 5 Lab Hours: 0 Practicum Hours: 0 Work Experience: 0 Course Type: Coll Prep This course will prepare the student for college algebra or equivalent course work. Topics include properties of real numbers, linear equations and inequalities, graphs of polynomial functions, exponents, factoring, system of equations and inequalities, polynomial and rational expressions, radicals, complex numbers, and quadratic equations.
Prerequisite: Minimum ALEKS score of 10% or MAT 045 with a C or higher or MAT 064 with a C or higher.
Competencies
 Evaluate algebraic expressions
 Evaluate an expression for a given value of the variable
 Apply the rules of exponents to simplify an expression
 Apply the properties of real numbers to simplify an expression
 Evaluate the value of a given expression with exponents
 Recall and apply the orderofoperations rules
 Solve multistep linear equations and inequalities
 Solve first degree equations and inequalities using the properties of equality and inequality
 Solve linear equations and inequalities using the addition property of equality
 Solve linear equations and inequalities using the multiplication property of equality
 Classify equations as identity, contradiction, or conditional
 Solve linear equations for one variable in terms of other variables
 Solve absolute value and fractional equations
 Solve absolute value equations with one absolute value
 Solve absolute value equations with multiple absolute values
 Write models for verbal problems that produce firstdegree equations and inequalities in one variable
 Translate phrases and sentences written in words into their algebraic form
 Write an equation to solve a given word problem
 Construct the equation of a specified line
 Define slope
 Determine the slope, given two points, and given the equation of the line
 Construct an equation for a line given the slope and the yintercept
 Construct an equation of a line given the slope with a point that is not the yintercept
 Construct an equation for a line given two points
 Determine the slope of a line parallel to a given line
 Determine the slope of a line perpendicular to a given line.
 Graph a linear equation/inequality in two variables
 Plot a given ordered pair of rational numbers on a graph
 Name the coordinates, given a point on a graph
 Determine ordered pairs which satisfy a given linear equation
 State the xintercept and yintercept for a linear equation
 Graph a linear equation/inequality on a coordinate plane
 Construct functions incorporating function notation
 Define a function
 Determine the domain and range of a variety of functions
 Construct a graph of functions including linear functions, quadratic functions, square root functions, and absolute value functions
 Evaluate a given function
 Solve systems of linear equations
 Label lines as parallel, intersecting, or coinciding when given systems of two simultaneous equations
 Solve system of equations by graphing method
 Make use of the elimination method to solve system
 Make use of the substitution method to solve system
 Model the basic arithmetic operations with polynomials
 Classify polynomials according to number of terms
 Perform arithmetic operations with polynomials
 Factor polynomials
 Remove the greatest common monomial factor
 Factor by grouping
 Factor a trinomial which is the product of two binomials with integral coefficients
 Factor a binomial which is the difference of two squares
 Factor a binomial which is the difference or sum of two cubes
 Analyze rational expressions
 Identify whether an algebraic expression is rational or irrational
 Determine whether two rational expressions are equivalent
 State the restrictions on the variables in a given rational expression
 Express the sum or difference of two rational expressions in simplest form
 Express the product or quotient of two rational expressions in simplest form
 Solve equations containing rational expressions
 Inspect radical expressions
 Simplify a single radical
 Rationalize a denominator
 Perform basic arithmetic operations of algebraic square roots in simplest terms
 Select between which two integers a square root of a number lies
 Utilize basic arithmetic operations with expressions containing rational exponents or radicals
 Relate the square root of a negative number and a complex number
 Demonstrate the basic arithmetic operations with expressions containing complex numbers
 Use the rules of exponents to simplify expressions containing rational exponents
 Demonstrate the basic arithmetic operations with expressions containing rational exponents and radical expressions
 Convert an expression from radical to exponential notation and vice versa
 Make use of the properties of radicals to simplify radical expressions
 Solve second degree equations involving multiple step transformations.
 Solve second degree equations by factoring and by using the quadratic formula
 Solve second degree equations by the square root method
 Solve radical equations
 Solve radical equations with one radical
 Solve radical equations with multiple radicals
Competencies Revised Date: AY2023
Add to Portfolio (opens a new window)
