New 8/2021
NOVA COLLEGE-WIDE COURSE CONTENT SUMMARY
MDE 60 – INTERMEDIATE ALGEBRA (3 CR.)
Course Description
Presents topics in algebra, including graphing, exponents, radicals, polynomials, rational functions, and complex
numbers. Lecture 3 hours. Total 3 hours per week.
General Course Purpose
The general purpose of this one-semester course is to help students develop a foundation in algebra skill
required for success in MTH 161 with MDE 61. Instructors are encouraged to employ a combination of direct
instruction, guided practice, and individualized support to prepare students for subsequent mathematics
coursework.
Course Prerequisites/Corequisites
Prerequisites: MDE 10 or equivalent, any three MTE units 1-9.
Course Objectives
Demonstrate comprehension of the major topics listed below. Apply learned concepts and success skills toward
continued progress in MTH 161 with co-requisite.
• Algebra
o Solve first degree equations using the Addition Property and the Multiplication Property of
Equality.
o Solve first degree equations in one variable with the variable on both sides of the equal sign.
o Solve formulas using the Addition Property and the Multiplication Property of Equality.
o Solve first degree inequalities in one variable stating the solution using inequality and interval
notation.
o Solve first degree inequalities in one variable and graph the solution on a real number line.
• Graphing and Equations
o Find the equation of the line passing through two ordered pairs.
o Graph equations of lines, including horizontal lines, vertical lines, and lines in slope-intercept
form.
o Graph a linear inequality in two variables.
o Find the slope of a line given two points on the line.
o Find the slope of a line given its equation in general or slope-intercept form.
o Write an equation of a line in slope-intercept form given the slope and the y-intercept.
o Write an equation of a line in slope-intercept form given the slope and a point on the line.
o Write an equation of a line in slope-intercept form given two points on the line.
o Evaluate y = f(x) for specific values of x.
o Given the graph of y = f(x), evaluate f(x) for specific values of x.
o Given the graph of y = f(x), find x for specific values of f(x).
o Given the equation of y = f(x), find x for specific values of f(x).
• Exponents
o Use the product rule to simplify expressions containing exponents.
o Use the quotient rule to simplify expressions containing exponents.
o Use the power rule to simplify expressions containing exponents.
o Use and apply negative exponents.
o Multiple two monomials.
o Divide two monomials.
o Evaluate expressions containing products, quotients, power of a power, and negative exponents.
o Multiply/divide numbers in scientific notation.
• Radicals
o Convert between square root and
forms.
o Convert between nth root and
forms.
o Calculate square roots and nth roots via calculator.
o Simplify using the properties of rational exponents.
o Simplify radicals by using the multiplication property of radicals.
o Combine and simplify like radicals.
o Multiply and simplify radicals.
o Simplify radicals by rationalizing a denominator with one or two terms.
o Solve radical equations.
• Polynomials
o Identify an expression as a monomial, binomial, trinomial, or polynomial.
o Add, subtract, multiply and divide monomials using the rules of exponents.
o Add, subtract, and multiply polynomials.
o Divide polynomials using long division.
o Divide polynomials using synthetic division.
o Find the greatest common factor from a list of terms.
o Factor a polynomial by finding the greatest common factor.
o Factor a polynomial by grouping.
o Factor trinomials of the form
.
o Factor trinomials of the form
, .
o Factor a difference of squares.
o Factor a sum of two cubes.
o Factor a difference of two cubes.
o Solve polynomial equations using factoring techniques.
• Complex Numbers
o Define
o Define imaginary numbers (e.g.
).
o Simplify square roots of negative numbers using the imaginary unit.
o Add, subtract, multiply complex numbers.
• Quadratics
o Describe the roots of a quadratic based upon the discriminant in all cases.
o Find the roots of quadratic equations of the form
.
o Find the roots of quadratic equations of the form
.
o Determine whether the parabola opens upward or downward.
o Use completing the square to write a quadratic expression in the form
.
o Find the vertex of a quadratic equation
.
o Determine the axis of symmetry for a parabola.
o Graph a parabola using intercepts, vertex, and axis of symmetry.
• Rational Functions and Expressions
o Find the x-values for which a rational expression is undefined.
o Simplify a rational algebraic expression.
o Perform addition and subtraction of rational algebraic expressions having like denominators.
o Perform addition and subtraction of rational algebraic expressions having unlike denominators.
o Perform multiplication and division of rational algebraic expressions with common factors.
o Perform multiplication and division of rational algebraic expressions without common factors.
o Simplify complex fractions.
Major Topics to be Included
• Properties of exponents
• Polynomials
• Factoring
• Solving quadratics and Pythagorean theorem
• Complex numbers
• Graphing (lines and quadratics)
• Linear equations and inequalities
• Linear systems
• Functions
• Rational expressions and equations
• Radical expressions and equations
