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AP/Advanced Calculus Part 1
Course Length: 1 Semester
Has Textbook: Yes

AP/Advanced Calculus Part 1 teaches a balanced approach to problem solving, using analytical, algebraic, numerical, graphical, and verbal/written methods of representing problems. This course begins with a brief review of linear, polynomial, exponential, parametric, logarithmic, and trigonometric functions. Students will study all topics associated with limits and continuity. Student will also study derivatives of a variety of functions (i.e., polynomial, trigonometric and inverse trigonometric, exponential, and logarithmic), as well as learn how to apply the chain rule and implicit differentiation. The course closes with a study of extreme values and the Mean Value Theorem. 

This course meets the Advanced Placement criteria required by the College Board.

*Note: AP/Advanced Calculus Parts 1 and 2 are required for the AP Calculus AB exam.

It is recommended that students successfully complete Pre-Calculus or equivalent course work before enrolling in this course. Successful completion of both Part 1 and Part 2 of this course is required for students to earn the AP designation. 

Course Objectives

Unit 1: Essential Content and Skills      

  • Identify the relationships between parallel lines, perpendicular lines, and slopes.      
  • Analyze exponential growth and decay, parametric equations, logarithms, and trigonometric functions.    
  • Estimate a limit and identify different ways that a limit can fail to exist.      
  • Locate and verify end behavior models for various functions.       
  • Identify vertical and horizontal asymptotes.      
  • State the intervals upon which a given function is continuous.  
  • Apply the Intermediate Value Theorem.

Unit 2: Essential Content and Skills

  • Discover derivatives and how f’(a) might fail to exist.      
  • Analyze how differentiability implies local linearity.      
  • Discover rules for differentiation: positive integer powers, multiples, sums and differences, products and quotients, and negative integer powers of x.
  • Calculate higher order derivatives.      
  • Examine instantaneous rate of change.    

Unit 3: Essential Content and Skills

  • Find the derivatives of trigonometric functions.  
  • Discover simple harmonic motion.      
  • Analyze jerk, a sudden change in acceleration.      
  • Examine the derivative of a composite function.      
  • Apply the chain rule.  
  • Use implicit differentiation to find derivatives of higher order.      
  • Find derivatives by using the Power Rule for rational powers of x.  

Unit 4: Essential Content and Skills

  • Find derivatives of the inverse trigonometric functions.
  • Discover the derivatives of ex, ax, ln x, and loga x.      
  • Locate absolute (global) values of functions.      
  • Find local (relative) extreme values.      
  • Examine the Mean Value Theorem.      
  • Analyze increasing and decreasing functions.   

Course Materials

  • Calculus Graphical, Numerical, Algebraic (textbook, practice book, and CD)

**NCAA approved