91勛圖

Revised 08/2021

MDE 60 - Intermediate Algebra (3 CR.)

Course Description

Covers topics in algebra. 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.
  • Apply learned concepts and success skills toward continued progress in MTH 161 with corequisite.

Algebra

  • Solve first degree equations using the Addition Property and the Multiplication Property of Equality.
  • Solve first degree equations in one variable with the variable on both sides of the equal sign.
  • Solve formulas using the Addition Property and the Multiplication Property of Equality.
  • Solve first degree inequalities in one variable stating the solution using inequality and interval notation.
  • Solve first degree inequalities in one variable and graph the solution on a real number line.

Graphing and Equations

  • Find the equation of the line passing through two ordered pairs.
  • Graph equations of lines, including horizontal lines, vertical lines, and lines in slope-intercept form.
  • Graph a linear inequality in two variables.
  • Find the slope of a line given two points on the line.
  • Find the slope of a line given its equation in general or slope-intercept form.
  • Write an equation of a line in slope-intercept form given the slope and the y-intercept.
  • Write an equation of a line in slope-intercept form given the slope and a point on the line.
  • Write an equation of a line in slope-intercept form given two points on the line.
  • Evaluate y = f(x) for specific values of x.
  • Given the graph of y = f(x), evaluate f(x) for specific values of x.
  • Given the graph of y = f(x), find x for specific values of f(x).
  • Given the equation of y = f(x), find x for specific values of f(x).

Exponents

  • Use the product rule to simplify expressions containing exponents.
  • Use the quotient rule to simplify expressions containing exponents.
  • Use the power rule to simplify expressions containing exponents.
  • Use and apply negative exponents.
  • Multiple two monomials.
  • Divide two monomials.
  • Evaluate expressions containing products, quotients, power of a power, and negative exponents.
  • Multiply/divide numbers in scientific notation.

Radicals

  • Convert between square root and 𝑎1/2
  • Convert between nth root and 𝑎1/𝑛
  • Calculate square roots and nth roots via calculator.
  • Simplify using the properties of rational exponents.
  • Simplify radicals by using the multiplication property of radicals.
  • Combine and simplify like radicals.
  • Multiply and simplify radicals.
  • Simplify radicals by rationalizing a denominator with one or two terms.
  • Solve radical equations.

Polynomials

  • Identify an expression as a monomial, binomial, trinomial, or polynomial.
  • Add, subtract, multiply and divide monomials using the rules of exponents.
  • Add, subtract, and multiply polynomials.
  • Divide polynomials using long division.
  • Divide polynomials using synthetic division.
  • Find the greatest common factor from a list of terms.
  • Factor a polynomial by finding the greatest common factor.
  • Factor a polynomial by grouping.
  • Factor trinomials of the form 𝑥2 + 𝑏𝑥 + 𝑐.
  • Factor trinomials of the form 𝑎𝑥2 + 𝑏𝑥 + 𝑐, 𝑎 ≠ 1.
  • Factor a difference of squares.
  • Factor a sum of two cubes.
  • Factor a difference of two cubes.
  • Solve polynomial equations using factoring techniques.

Complex Numbers

  • Define 𝑖 = √−1
  • Define imaginary numbers (e.g. √−25).
  • Simplify square roots of negative numbers using the imaginary unit.
  • Add, subtract, multiply complex numbers.

Quadratics

  • Describe the roots of a quadratic based upon the discriminant in all cases.
  • Find the roots of quadratic equations of the form 𝑎𝑥2 + 𝑐 = 0.
  • Find the roots of quadratic equations of the form 𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0.
  • Determine whether the parabola opens upward or downward.
  • Use completing the square to write a quadratic expression in the form𝑎(𝑥 − ℎ)2 + 𝑘.
  • Find the vertex of a quadratic equation 𝑦 = 𝑎𝑥2 + 𝑏𝑥 + 𝑐.
  • Determine the axis of symmetry for a parabola.
  • Graph a parabola using intercepts, vertex, and axis of symmetry.

Rational Functions and Expressions

  • Find the x-values for which a rational expression is undefined.
  • Simplify a rational algebraic expression.
  • Perform addition and subtraction of rational algebraic expressions having like denominators.
  • Perform addition and subtraction of rational algebraic expressions having unlike denominators.
  • Perform multiplication and division of rational algebraic expressions with common factors.
  • Perform multiplication and division of rational algebraic expressions without common factors. fy 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