Kevin Quattrin, EdD
Add text
  • Home
    • Myers-Briggs Personality Types
    • Valuable Links
    • Interesting Books
    • Taking Notes for Yourself
    • Summary Sheet Rubrics
    • Test Anxiety
    • Dr Q's MCQ Tips
  • AP Calculus BC
    • BC Calc Tests
    • BC Calculus Syllabus
    • BC Calculus Objectives
    • BC Calculus Enduring Understandings and Essential Questions
  • The Readable Calculus (BC version)
    • Readable Calculus Screen Casts (BC Version)
    • The Readable Calculus (BC version) Odd Solutions
  • AP Calculus AB
    • AP Calculus AB Tests
    • AP Calculus AB Course Syllabus
    • AP Calculus AB Objectives
    • AP Calculus AB Enduring Understandings
  • Calculus (non-AP)
    • Calculus (Non-AP) Tests
    • Calculus Course Syllabus
    • Calculus Objectives
    • Calculus (AB and non-AP) Enduring Understandings
  • The Readable Calculus (AB and Non-AP version)
    • Readable Calculus Screen Casts (Non-AP Version)
    • The Readable Calculus (Non-AP version) Odd Solutions
  • PreCalculus (Seniors)
    • PreCalc (Sr) Tests
    • PreCalc (Sr) Syllabus
    • PreCalc (Sr) Objectives
  • Honors PreCalculus
    • Honors PreCalc Tests
    • Honors PreCalculus Syllabus
    • Honors PreCalc Objectives
    • Honors PreCalc Enduring Understandings and Essential Questions
  • PreCalculus Accelerated
    • PreCalc Acc Tests
    • PreCalculus Acc Syllabus
    • PreCalc Acc Enduring Understandings and Essential Questions
  • The PreCalculus Text
    • The PreCalculus Text Screencasts
    • The PreCalculus Text -- Odd Solutions
  • Dr. Quattrin's Biography
  • PSAT & SAT Prep
    • Heart of Algebra Screen Casts
    • Problem Solving and Data Analysis Screen Casts
    • Passport to Advanced Math Screen Casts
    • Additional Topics in Math Screen Casts
Unit Knowledge and Skills (Performance Objectives)

Unit I.        Derivatives


By the end of this unit, the student will be able to:
·            Use the Power Rule and Exponential Rules to find Derivatives.
·            Find the Derivative of Composite Functions.
·            Find Derivatives involving Trig, Trig Inverse, and Logarithmic Functions.
·            Use the equation of a tangent line to approximate function values.
·            Use Euler’s Method to approximate a numerical solution to a differential equation at a given point.
·            Find the Derivative of a product or quotient of two functions.
·            Find higher order derivatives.
·            Take derivatives of relations implicitly.
·            Use implicit differentiation to find higher order derivatives.
·            Determine when it is appropriate to use logarithmic differentiation.
·            Use logarithmic differentiation to take the derivatives of complicated functions.
·            Solve related rates problems.

Unit II        Anti-Derivatives


By the end of this unit, the student will be able to:
·            Find the anti-derivative of a polynomial.
·            Integrate functions involving Transcendental operations.
·            Use Integration to solve rectilinear motion problems.
·            Use the integration by substitution to integrate composite expressions.
·            Use the Integration by Substitution to integrate integrands involving Sine and Cosine.
·            Use the Integration by Substitution to integrate integrands involving Secant and Tangent or Cosecant and Cotangent.
·            Given a separable differential equation, find the general solution.
·            Given a separable differential equation and an initial condition, find a particular solution.
·            Given a differential equation, sketch its slope field.
·            Given a slope field, sketch a particular solution curve.
·            Given a slope field, determine the family of functions to which the solution curves belong.
·            Given a slope field, determine the differential equation that it represents.

Unit III      Applications of the Derivative


By the end of this unit, the student will be able to:
·            Find critical values and extreme values for functions.
·            Use the 1st and 2nd derivative tests to identify maxima vs. minima.
·            Find Points of Inflection and Intervals of Concavity.
·            Sketch the graph of a function using information from its first and/or second  derivatives.
·            Sketch the graph of a first and/or second derivative from the graph of a function.
·            Solve optimization problems.
·            Use the derivative to make conclusions about motion.
·            Relate the position, velocity, and acceleration functions.
·            Sketch the graphs of parametric equations. 
·            Eliminate the parameter of parametric equations.
·            Interpret information in the graph of a derivative in terms of the graph of the “original” function.
·            Use the graph of a function to answer questions concerning maximums, minimums, and intervals of increasing and decreasing
·            Use the graph of a function to answer questions concerning points of inflection and intervals of concavity.
·            Use the graph of a function to answer questions concerning the area under a curve.


Unit IV       Integrals

By the end of this unit, the student will be able to:
·            Find approximations of integrals using different rectangles.
·            Use proper notation when dealing with integral approximation. 
·            Differentiate integral expressions with the variable in the boundary
·            Evaluate Definite Integrals
·            Find the average value of a continuous function over a given interval
·            Evaluate definite integrals using the Fundamental Theorem of Calculus.
·            Evaluate definite integrals applying the Substitution Rule, when appropriate.
·            Use proper notation when evaluating these integrals.
·            Relate definite integrals to area under a curve.
·            Understand the difference between displacement and total distance.
·            Extend that idea to understanding the difference between the two concepts in other contexts.
·            Analyze the interplay between rates and accumulation in context.


Unit V        Limits


By the end of this unit, the student will be able to:
·            Evaluate one-sided limits graphically, numerically, and algebraically.
·            Evaluate two-sided limits in terms of one-sided limits.
·            Prove continuity or discontinuity of a given function.
·            Interpret Vertical Asymptotes in terms of one-sided limits.
·            Determine if a function is differentiable or not.
·            Demonstrate understanding of the connections and differences between differentiability and continuity.  
·            Evaluate Limits algebraically.
·            Evaluate Limits using L’Hopital’s Rule.
·            Recognize and evaluate Limits which are derivatives.
·            Use the nDeriv function on the calculator to find numerical derivatives.
·            Evaluate Limits at infinity.
·            Interpret Limits at infinity in terms of end behavior of the graph.
·            Evaluate Type I Improper Integrals.
·            Determine convergence or divergence of a Type II Improper Integral.



Unit VI       Numerical Sequences and Series

By the end of this unit, the student will be able to:

·            Identify Sequences and Series
·            Find Partial Sums of a given Series.
·            Find the terms, partial sums, infinite sums, or n in a geometric sequence.
·            Determine the convergence or divergence of a sequence.
·            Determine the divergence of a series.
·            Use the Comparison Tests to check for convergence or divergence.
·            Use the Integral Test to check for convergence or divergence.
·            Use the Ratio and Nth Root Tests to check for convergence or divergence.
·            Use the Alternating Series Test to check for convergence or divergence.



Unit VII     Applications of the Integral

By the end of this unit, the student will be able to:
·            Find the area of the region between two curves.
·            Find the volume of a solid rotated when a region is rotated about a given axis
·            Find the volume of a solid rotated when a region is rotated about a given line
·            Find the volume of a solid with given cross sections.
·            Find the arc length of a function in Cartesian mode between to points.



Unit VIII    Techniques of Integration

By the end of this unit, the student will be able to:
·            Identify integrals where Integration by Parts is appropriate.
·            Apply the Integration by Parts method.
·            Integrate radical integrands using trig substitution.
·            Determine the appropriate technique to apply to a rational integral.
·            Determine the appropriate technique to apply to a rational integral.
·            Apply the Partial Fractions technique. 
·            Recognize the carrying capacity in a logistic growth setting.
·            Determine when the maximum growth rate in a logistic growth setting.
·            Know the solution to a logistic differential equation.
·            Apply Partial Fractions to the proper type of integral.
·            Apply Partial Fractions to integrals with Quadratic factors.
·            Determine the correct technique to use and perform the integration.



Unit IX       Parametric and Polar Coordinates

By the end of this unit, the student will be able to:
·            Graph relations in parametric mode.
·            Eliminate the parameter to identify the function form of a parametric.
·            Find the slope of a tangent line to a curve in parametric mode.
·            Find the concavity of a curve in parametric mode.
·            Find the arc length of a curve in parametric mode.
·            Find the position of an object in motion in two dimensions from its velocity.
·            Find the arc length of a curve expressed in parametric mode.
·            Graph curves in polar form.
·            Recognize certain polar equations as having particular graphs.
·            Determine and interpret intervals of increasing or decreasing of a polar curve.
·            Find slopes of lines tangent to polar curves.
·            Find the arc length of a shape describe in polar coordinates.
·            Find the area of a shape described in polar coordinates.



Unit X        Power Series

By the end of this unit, the student will be able to:
·            Create a Taylor polynomial from give numerical derivatives.
·            Identify numerical derivatives from a given Taylor or Maclaurin polynomial.
·            Use a Taylor or Maclaurin polynomial to approximate function values.
·            Create new series from a Taylor or Maclaurin polynomial.
·            Show that the error involved in an approximation of a function value is below a given amount.
·            Create a new series from a known series.
·            Find whether a given numerical series converges or diverges.
·            Find the Radius of Convergence for a given series.
·            Find the Interval of Convergence for a given series.



 

 
Proudly powered by Weebly