College Mathematics II

Course Description

This course continues the demonstration and examination of various basic algebra concepts that was begun in MTH 208: College Mathematics I. It assists in building skills for performing more complex mathematical operations and problem solving than in earlier courses. These concepts and skills should serve as a foundation for subsequent quantitative business coursework. Applications to real-world problems are emphasized throughout the course. Specific applications to disciplines such as statistics, accounting, finance, and economics are demonstrated and discussed. A variety of other applications, such as geometry, personal finance, science, and engineering, are also demonstrated and discussed.

Topics and Objectives

Math as a Language

• Develop problem-solving strategies for real-life problems.
• Differentiate the formats of expressions, equations, and functions.
• Explain basic mathematical operations as concepts and laws.
• Translate word problems into mathematical formulas.
• Establish algebra's relationship to quantitative business disciplines and real-world situations.
• Terms, Factors, Coefficients, Exponents, and Mathematical Operations of

Polynomials

• Categorize the four operations in terms of whole numbers, decimals, fractions, and variables.
• Relate the properties of addition and subtraction to those of multiplication and division.
• Identify a term in an algebraic expression.
• Identify a coefficient when adding and/or subtracting like terms.
• Identify a factor in an algebraic expression.
• Identify exponents when multiplying and/or dividing like factors.
• Classify operations into two groups: addition and subtraction, and multiplication and division.
• Recall the order of operations and demonstrate its consequences in simplifying expressions.
• Illustrate that 0 is a term of no significance and 1 is a factor of no significance.
• Identify like terms and common factors.

Operations with Polynomials

• Add and subtract polynomials.
• Generalize addition and subtraction of polynomials as putting the like terms together.
• Simplify polynomials using the concepts of combining like terms. Illustrate the concept of like terms in various situations, including fractional coefficients.
• Apply the concept of factors to multiplication and division of polynomials.
• Illustrate the concept of like factors (common factors) in various situations, including fractional exponents (radicals).
• Demonstrate the distributive property when multiplying or dividing two or more polynomials.

Factoring Polynomials

• Demonstrate that factoring a polynomial is the reverse of multiplying polynomials by using distributive property.
• Explain factoring by grouping, and factoring a trinomial by splitting the middle term.
• Factor complete squares

Operations with Radical and Rational Expressions

• Define the concepts of rational expressions containing variables.
• Factor polynomials to compute the LCD when simplifying rational expressions by addition and subtraction, and canceling the common factors when simplifying rational expressions by multiplication and division.
• Perform operations on rational expressions. (Show that, for rational expressions, the denominator cannot be 0; addition and subtraction need LCDs and that multiplication and division of rational expressions do not need LCDs.)
• Simplify radical expressions.
• Demonstrate that radicals are similar to exponentials and follow the same mathematical principles.

Solving Quadratic, Rational, and Radical Equations

• Solve quadratic equations by factoring, by using square-root property, and by using quadratic formula.
• Solve rational equations by converting each rational equation into a linear or a quadratic equation.
• Solve radical equations by raising each side to a power.

Graphs of Quadratic Functions

• Solve a quadratic equation to compute the intercepts of a quadratic function.
• Compute the axis and vertex of the graph of a quadratic function.
• Illustrate the graph of a quadratic function in terms of intercepts and axis.
• Draw the graph of a quadratic function.

Solving Quadratic and Rational Inequalities

• Solve quadratic and rational inequalities