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Calculus Part 1
LI.MAT.402012.1.CE
Course Length: 1 Semester
Has Textbook: Yes
Calculus Part 1 explores higher-level mathematics through analytical/algebraic, numerical, graphical, and verbal methods. Students will study functions, graphs, limits, differentiation, applications of derivatives, as well as exponential and logarithmic functions.
It is recommended that students successsfully complete Pre-Calculus or equivalent course work before enrolling in this course.


Course Objectives

 Unit 1: Essential Content and Skills

  • Use inequalities to model and solve real-life problems.
  • Break down expressions with exponents.
  • Use special products and factorization techniques to factor polynomials.
  • Solve rational expressions.
  • Find the x-intercepts and y-intercepts of equations.
  • Use the slope-intercept form of a linear equation to sketch graphs.
  • Use the point-slope form to write equations of lines.

Unit 2: Essential Content and Skills

  • Find limits of functions graphically and numerically.
  • Use the limit definition to find the derivatives of functions.
  • Describe the relationship between differentiability and continuity.
  • Apply the Power Rule to find the derivatives of functions.
  • Find the instantaneous rates of change of functions at points.
  • Use the Product Rule to find the derivatives of functions.
  • Apply the Quotient Rule to find the derivatives of functions.

Unit 3: Essential Content and Skills

  • Use the Chain Rule and General Power Rule to find derivatives.
  • Find higher-order derivatives.
  • Discover and use the position functions to determine the velocity and acceleration of moving objects.
  • Find derivatives implicitly.
  • Solve related-rate problems.
  • Use the First-Derivative Test to find the relative extrema of functions.
  • Discover the points of inflection of the graph of functions.

Unit 4: Essential Content and Skills

  • Find the differentials of functions.
  • Use differentials to approximate changes in functions.
  • Discover the derivatives of natural exponential functions.
  • Apply calculus to analyze the graphs of functions that involve the natural logarithmic function.
  • Find derivatives of exponential and logarithmic functions involving other bases.
  • Use exponential growth to model real-life situations.

Course Materials

  • Calculus: An Applied Approach (textbook)

*Available as an iText course

**NCAA approved