{"id":3403,"date":"2023-06-09T13:37:41","date_gmt":"2023-06-09T20:37:41","guid":{"rendered":"https:\/\/dornsife.usc.edu\/mathematics\/?page_id=3403"},"modified":"2023-11-13T12:43:19","modified_gmt":"2023-11-13T20:43:19","slug":"math-040-basic-mathematical-skills","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/mathematics\/math-040-basic-mathematical-skills\/","title":{"rendered":"MATH 040 – Basic Mathematical Skills"},"content":{"rendered":"\n\n \n \n\n\n\n\n\n\n\n
\n\n \n \n
\n\n \n

REQUIRED TEXTBOOK<\/strong><\/p>\n

Intermediate Algebra by Elayn Martin-Gay (7th edition); ISBN-13: 978-0134196176<\/a><\/p>\n

 <\/p>\n

SECTION COVERAGE<\/strong><\/p>\n

The following table lists the minimum<\/em> set of topics to be included in this course.\u00a0 The number of lectures listed for each chapter is only a suggestion and will vary across instructors and semesters.<\/p>\n

There are typically 42-43 lecture days in a semester, so lecture periods are available for exams.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Sections<\/strong><\/td>\nTopics<\/strong><\/td>\nLectures<\/strong><\/td>\n<\/tr>\n
1.2 – 1.4<\/td>\nAlgebraic expressions<\/td>\n3<\/td>\n<\/tr>\n
2.1, 2.3 – 2.7<\/td>\nLinear equations and linear inequalities<\/td>\n5<\/td>\n<\/tr>\n
3.1 – 3.4, 3.7<\/td>\nIntroduction to functions and graphs<\/td>\n6<\/td>\n<\/tr>\n
4.1 – 4.3<\/td>\nSystems of equations<\/td>\n5<\/td>\n<\/tr>\n
5.1 – 5.2, 7.1-7.2<\/td>\nExponents, rational exponents and radicals<\/td>\n5<\/td>\n<\/tr>\n
5.3 – 5.4<\/td>\nIntroduction to polynomials<\/td>\n2<\/td>\n<\/tr>\n
8.1 – 8.2, 8.5<\/td>\nQuadratic functions and graphs<\/td>\n5<\/td>\n<\/tr>\n
<\/td>\nOptional topics<\/td>\n4<\/td>\n<\/tr>\n
<\/td>\nIntegrated review<\/td>\n3<\/td>\n<\/tr>\n
<\/td>\nTotal<\/td>\n38<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

OPTIONAL TOPICS (time permitting)<\/strong><\/p>\n

    \n
  • Section 7.7, introduction to complex numbers<\/li>\n
  • Section 8.6, more on quadratic functions, maximums and minimums<\/li>\n
  • Sections 9.3-9.6, basics on exponential and logarithmic functions<\/li>\n
  • Other outside topics, readings, videos, or materials the instructor deems relevant<\/li>\n<\/ul>\n

     <\/p>\n

    MEASURABLE OBJECTIVES<\/strong><\/p>\n

     <\/p>\n

    Real Numbers and Algebraic Expressions:<\/p>\n

      \n
    • Identify different types of numbers, including real numbers, integers, rationals, and irrationals.<\/li>\n
    • Determine absolute values and negatives of numbers.<\/li>\n
    • Translate word problems into algebraic expressions.<\/li>\n
    • Evaluate and simplify algebraic expressions.<\/li>\n<\/ul>\n

      Equations and Inequalities:<\/p>\n

        \n
      • Rearrange formulas to isolate a specified variable.<\/li>\n
      • Solve linear equations with one variable.<\/li>\n
      • Solve linear inequalities with one variable and represent the solution set in interval notation.<\/li>\n
      • Solve compound inequalities.<\/li>\n
      • Solve equations and inequalities involving absolute values.<\/li>\n<\/ul>\n

        Functions, Coordinate Systems and graphs:<\/p>\n

          \n
        • Plot ordered pairs on coordinate systems.<\/li>\n
        • Determine the domain and range of relations or functions.<\/li>\n
        • Identify functions using the vertical line test.<\/li>\n
        • Write linear equations in function format and graph linear functions.<\/li>\n
        • Express linear functions in slope-intercept form and compute slope, x-intercept, and y-intercept.<\/li>\n
        • Graph vertical and horizontal lines.<\/li>\n
        • Graph linear inequalities and represent the intersection or union of two inequalities.<\/li>\n<\/ul>\n

          System of equations:<\/p>\n

            \n
          • Solve systems of equations with two variables, visualize the solution by plotting the two lines in the
            \nsystem.<\/li>\n
          • Solve systems of equations with three variables.<\/li>\n<\/ul>\n

            Exponents, Scientific Notation, and Radicals:<\/p>\n

              \n
            • Simplify exponents using product and quotient rules, zero exponent, and negative exponent.<\/li>\n
            • Utilize scientific notation.<\/li>\n
            • Simplify radical expressions.<\/li>\n<\/ul>\n

              Polynomials and Quadratic Functions:<\/p>\n

                \n
              • Identify polynomial terms and determine the degrees of terms and polynomials.<\/li>\n
              • Multiply two polynomials.<\/li>\n
              • Solve quadratic equations by completing the square and using the quadratic formula.<\/li>\n
              • Understand the basics of graphing quadratic functions.<\/li>\n<\/ul>\n

                Exponential and Logarithmic Functions (optional):<\/p>\n

                  \n
                • Graph exponential functions and solve problems modeled by exponential equations.<\/li>\n
                • Identify, graph logarithmic functions and use the properties of logarithms.<\/li>\n<\/ul>\n

                   <\/p>\n

                   <\/p>\n

                   <\/p>\n

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