{"id":7794,"date":"2025-07-15T11:57:58","date_gmt":"2025-07-15T18:57:58","guid":{"rendered":"https:\/\/dornsife.usc.edu\/mathematics\/?page_id=7794"},"modified":"2025-08-05T20:19:07","modified_gmt":"2025-08-06T03:19:07","slug":"math-040-basic-mathematical-skills-2025","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/mathematics\/math-040-basic-mathematical-skills-2025\/","title":{"rendered":"MATH 040 \u2013 Basic Mathematical Skills 2025"},"content":{"rendered":"\n\n \n \n\n\n\n\n\n\n\n
\n\n \n \n
\n\n \n

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

Basic Algebra with Applications (6th edition) by Zaigralin<\/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\n\n\n\n
Sections<\/strong><\/td>\nTopics<\/strong><\/td>\nLectures<\/strong><\/td>\n<\/tr>\n
1.1 – 1.5<\/td>\nReal numbers and their properties<\/td>\n2<\/td>\n<\/tr>\n
1.7 – 1.8<\/td>\nAddition and multiplication of fractions<\/td>\n2<\/td>\n<\/tr>\n
1.9<\/td>\nWord problems<\/td>\n1<\/td>\n<\/tr>\n
2.1 – 2.3<\/td>\nSolving linear equations<\/td>\n3<\/td>\n<\/tr>\n
2.4 – 2.5<\/td>\nPercents and units<\/td>\n2<\/td>\n<\/tr>\n
2.6<\/td>\nLinear inequalities<\/td>\n1<\/td>\n<\/tr>\n
3.1 – 3.7<\/td>\nGraphing lines<\/td>\n6<\/td>\n<\/tr>\n
4.1 – 4.4<\/td>\nSystems of linear equations<\/td>\n5<\/td>\n<\/tr>\n
5.1 – 5.2, 5.8<\/td>\nInteger exponents<\/td>\n3<\/td>\n<\/tr>\n
6.1 – 6.4<\/td>\nFactoring quadratic equations<\/td>\n5<\/td>\n<\/tr>\n
8.1 – 8.4<\/td>\nSquare roots<\/td>\n3<\/td>\n<\/tr>\n
8.7<\/td>\nRational exponents<\/td>\n2<\/td>\n<\/tr>\n
9.2 – 9.4*<\/td>\nRoots of quadratic equations (*excluding complex numbers)<\/td>\n5<\/td>\n<\/tr>\n
<\/td>\nTotal<\/td>\n40<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

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

    \n
  • Section 1.6 on prime numbers<\/li>\n
  • Section 4.5 on graphs of linear inequalities<\/li>\n
  • Sections 5.3-5.7 on polynomials and their properties<\/li>\n
  • Section 6.8 on applications of factoring<\/li>\n
  • Section 8.6 on the distance formula<\/li>\n
  • Section 9.1 and parts of 9.2 and 9.3 relating to complex numbers<\/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\n\n\n<\/div>\n\n\n <\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":328,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-7794","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"\nMATH 040 \u2013 Basic Mathematical Skills 2025 - Department of Mathematics<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/dornsife.usc.edu\/mathematics\/math-040-basic-mathematical-skills-2025\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"MATH 040 \u2013 Basic Mathematical Skills 2025 - Department of Mathematics\" \/>\n<meta property=\"og:url\" content=\"https:\/\/dornsife.usc.edu\/mathematics\/math-040-basic-mathematical-skills-2025\/\" \/>\n<meta property=\"og:site_name\" content=\"Department of Mathematics\" \/>\n<meta property=\"article:modified_time\" content=\"2025-08-06T03:19:07+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/dornsife.usc.edu\/mathematics\/math-040-basic-mathematical-skills-2025\/\",\"url\":\"https:\/\/dornsife.usc.edu\/mathematics\/math-040-basic-mathematical-skills-2025\/\",\"name\":\"MATH 040 \u2013 Basic Mathematical Skills 2025 - 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