MAT-099 Objectives
MAT-099 Intermediate Algebra
Course Description
This course is a continuation of MAT-097, Foundations of Algebra. Topics in this course include polynomial arithmetic, introduction to functions, factoring, roots and radicals, rational expressions, absolute value inequalities, quadratic equations and the quadratic formula, and solving applied problems. This course does not satisfy degree requirements. PREREQUISITE: Grade of C or better in MAT-097, Foundations of Algebra or placement. Course may require an additional lab hour. Credit hours: 3.0.
Learning Outcomes
- Rewrite expressions by understanding and applying the concepts of combining like terms, the distributive property, and factoring
- Write equivalent forms of equations and inequalities and solve them with fluency
- Apply knowledge of a variety of types of equations, including linear, quadratic, rational, and radical equations, to solve real world problems
Instructional Objectives
POLYNOMIALS
- Define and identify: monomial, binomial, polynomial
- State the degree of a term, the degree of a polynomial, and write a polynomial in descending powers of a variable
- Find the sum and difference of two polynomials
- Multiply a polynomial by a monomial or a binomial
- Divide a polynomial by a monomial
- Use long division to divide a polynomial by a binomial
FUNCTIONS - Understand the concepts of relation and function
- Decide whether an equation defines a function
- Use function notation
- Apply the function concept in applications and graphing
FACTORING - Define and identify: factor, common factor, greatest common factor
- Factor out the greatest common factor from a polynomial
- Factor by grouping
- Factor the difference of two squares as a sum and difference of binomials
- Factor the sum and difference of cubes
- Factor a perfect square trinomial as the square of a binomial
- Factor a trinomial into two binomial factors
- Factor binomials and trinomials completely
INEQUALITIES - Solve linear inequalities, including compound linear inequalities
- Graph the solution set of a linear inequality
- Use interval notation to describe the solution set of a linear inequality
- Solve equations and inequalities involving absolute value
- Solve linear inequalities in two variables and graph their solution sets
RATIONAL EXPRESSIONS - Define a rational expression
- Find the values of the variable for which a rational expression is undefined
- Write rational expressions in lowest terms
- Multiply and divide rational expressions
- Add and subtract rational expressions
- Simplify a complex fraction involving rational expressions
- Solve equations involving rational expressions
- Solve applied problems using equations involving rational expressions
RADICALS - Find roots of real numbers
- Decide whether a given root is rational, irrational, or not a real number
- Use the Pythagorean Theorem
- Simplify radical expressions
- Convert between radical expressions and expressions using rational exponents
- Add and subtract radical expressions
- Multiply and divide radical expressions
- Rationalize the denominator of a radical expression
- Find values for which a radical expression is undefined
- Solve equations involving radical expressions
QUADRATIC EQUATIONS - Solve quadratic equations by factoring
- Solve quadratic equations by the square root property
- Solve quadratic equations by completing the square
- Solve quadratic equations using the quadratic formula
- Graph quadratic equations
- Solve applied problems using quadratic equations