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# 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

1. Evaluate algebraic expressions
1. Evaluate an expression for a given value of the variable
2. Apply the rules of exponents to simplify an expression
3. Apply the properties of real numbers to simplify an expression
4. Evaluate the value of a given expression with exponents
5. Recall and apply the order-of-operations rules
2. Solve multi-step linear equations and inequalities
1. Solve first degree equations and inequalities using the properties of equality and inequality
2. Solve linear equations and inequalities using the addition property of equality
3. Solve linear equations and inequalities using the multiplication property of equality
4. Classify equations as identity, contradiction, or conditional
5. Solve linear equations for one variable in terms of other variables
3. Solve absolute value and fractional equations
1. Solve absolute value equations with one absolute value
2. Solve absolute value equations with multiple absolute values
4. Write models for verbal problems that produce first-degree equations and inequalities in one variable
1. Translate phrases and sentences written in words into their algebraic form
2. Write an equation to solve a given word problem
5. Construct the equation of a specified line
1. Define slope
2. Determine the slope, given two points, and given the equation of the line
3. Construct an equation for a line given the slope and the y-intercept
4. Construct an equation of a line given the slope with a point that is not the y-intercept
5. Construct an equation for a line given two points
6. Determine the slope of a line parallel to a given line
7. Determine the slope of a line perpendicular to a given line.
6.  Graph a linear equation/inequality in two variables
1. Plot a given ordered pair of rational numbers on a graph
2. Name the coordinates, given a point on a graph
3. Determine ordered pairs which satisfy a given linear equation
4. State the x-intercept and y-intercept for a linear equation
5. Graph a linear equation/inequality on a coordinate plane
7. Construct functions incorporating function notation
1. Define a function
2. Determine the domain and range of a variety of functions
3. Construct a graph of functions including linear functions, quadratic functions, square root functions, and absolute value functions
4. Evaluate a given function
8. Solve systems of linear equations
1. Label lines as parallel, intersecting, or coinciding when given systems of two simultaneous equations
2. Solve system of equations by graphing method
3. Make use of the elimination method to solve system
4. Make use of the substitution method to solve system
9. Model the basic arithmetic operations with polynomials
1. Classify polynomials according to number of terms
2. Perform arithmetic operations with polynomials
10. Factor polynomials
1. Remove the greatest common monomial factor
2. Factor by grouping
3. Factor a trinomial which is the product of two binomials with integral coefficients
4. Factor a binomial which is the difference of two squares
5. Factor a binomial which is the difference or sum of two cubes
11. Analyze rational expressions
1. Identify whether an algebraic expression is rational or irrational
2. Determine whether two rational expressions are equivalent
3. State the restrictions on the variables in a given rational expression
4. Express the sum or difference of two rational expressions in simplest form
5. Express the product or quotient of two rational expressions in simplest form
6. Solve equations containing rational expressions
2. Rationalize a denominator
3. Perform basic arithmetic operations of algebraic square roots in simplest terms
4. Select between which two integers a square root of a number lies
13. Utilize basic arithmetic operations with expressions containing rational exponents or radicals
1. Relate the square root of a negative number and a complex number
2. Demonstrate the basic arithmetic operations with expressions containing complex numbers
3. Use the rules of exponents to simplify expressions containing rational exponents
4. Demonstrate the basic arithmetic operations with expressions containing rational exponents and radical expressions
5. Convert an expression from radical to exponential notation and vice versa
6. Make use of the properties of radicals to simplify radical expressions
14. Solve second degree equations involving multiple step transformations.
1. Solve second degree equations by factoring and by using the quadratic formula
2. Solve second degree equations by the square root method