Plainfield Public School District

Mathematics (Advance Placement Calculus) Curriculum Guide

APPLICATION OF DIFFERENTIATION: The Students will apply the differentiation process to find maxima and minima of a function, determine if the graphs represented by functions are increasing or decreasing and also concave up or down. They will also use Roll’s Theorem, and Mean Value Theorem to find the values of a function at a point and an interval. Students will also use Newton’s method to approximate the real zeros of a function.
CPI / Areas of Focus / Instructional Activities
(Students should know / Students should be able to do) / Assessment / Resources / Materials
  • 4.2.12 A3
  • 4.2.12 A4
  • 4.3.12 B1
  • 4.3.12 B2
4.3.12 B4
  • 4.5 A1
  • 4.5 A2
  • 4.5 C1
4.5 C6 / Students will apply differentiation to find maxima and minima of a function and a graph.
Define maxima and minima
Find relative maxima and minima and
Find absolute maxima and minima.
The extreme Value Theorem
Critical Points
Guideline for finding extrema /
  1. TEACHER OBSERVATION
  2. NOTE BOOK CHECK
  3. QUIZZES
  4. CPATER TESTS
  5. CLASS WORK
  6. HOMEWORK
  7. PROJECTS
GROUP PRESENTATION
1. Find the extrema of f(X)=3X - 4 X on the interval [-1, 2] /
  • Calculus book “CALCULUS of a SINGLE VARIABLE” 8th Edition by LARSON, HOSTETLER and EDWARDS.
  • Teacher’s Resource Guide
  • College Board, Advance Placement Program
  • Fast Track to Preparing For the AP Placement CalculusAB and BC Examinations.
  • Test Item File by Larson, et al

  • 4.2.12 A3
  • 4.2.12 A4
  • 4.3.12 B1
  • 4.3.12 B2
4.3.12 B4
  • 4.5 A1
  • 4.5 A2
  • 4.5 C1
4.5 C6 / ILLUSTRATE ROLLE’S THEOREM AND APPLY TO FIND A POINT IN THE INTERVAL OF A GRAPH.
THE MEAN VALUE THEOREM AND ITS APPLICATION.
FIND INSTANTANEOUS RATE OF CHANGE.
DEFINE INCREASING AND DECREASING FUNCTIONS
THE FIRST DERIVATIVE TEST AND ITS APPLICATION
GUIDELINES TO FIND INCREASING AND DECREASING FUNCTIONS. /
  1. TEACHER OBSERVATION
  2. NOTE BOOK CHECK
  3. QUIZZES
  4. CPATER TESTS
  5. CLASS WORK
  6. HOMEWORK
PROJECTS
GROUP PRESENTATION
1. Find the relative exrema of f(x) = 3 X - 4 Sinx. Cosx /
  • Calculus book “CALCULUS of a SINGLE VARIABLE” 8th Edition by LARSON, HOSTETLER and EDWARDS.
  • Teacher’s Resource Guide
  • College Board, Advance Placement Program
  • Fast Track to Preparing For the AP Placement CalculusAB and BC Examinations.
  • Test Item File by Larson, et al

  • 4.2.12 A3
  • 4.2.12 A4
  • 4.3.12 B1
  • 4.3.12 B2
4.3.12 B4
  • 4.5 A1
  • 4.5 A2
  • 4.5 C1
4.5 C6 / DEFINE CONCAVITY.
TEST AND DETERMINE CONCAVITY.
DEFINE AND FIND POINTS OF INFLECTION.
THE SECOND DERIVATIVE TEST
APPLY SECOND DERIVATIVE TEST TO FIND RELATIVE EXTREMA. /
  1. TEACHER OBSERVATION
  2. NOTE BOOK CHECK
  3. QUIZZES
  4. CPATER TESTS
  5. CLASS WORK
  6. HOMEWORK
PROJECTS
GROUP PRESENTATION
1. Determine the points of inflection and discuss the concavity of the graph of f(x)=X-4 X /
  • Calculus book “CALCULUS of a SINGLE VARIABLE” 8th Edition by LARSON, HOSTETLER and EDWARDS.
  • Teacher’s Resource Guide
  • College Board, Advance Placement Program
  • Fast Track to Preparing For the AP Placement CalculusAB and BC Examinations.
  • Test Item File by Larson, et al

  • 4.2.12 A3
  • 4.2.12 A4
  • 4.3.12 B1
  • 4.3.12 B2
4.3.12 B4
  • 4.5 A1
  • 4.5 A2
  • 4.5 C1
4.5 C6 / Master guidelines for analyzing the graph of a function.
Sketch the graph of a rational function.
Sketch the graph of a radical function.
Sketch the graph of a polynomial function.
Sketch the graph of a Trigonometric function.
Find minimum and maximum in real world – length, distance, area and volume.
Understand and apply Newton’s method to find real zeros of a function.
Define differentials
Calculate differentials.
Apply differentials to estimate relative error, propagated error. /
  1. TEACHER OBSERVATION
  2. NOTE BOOK CHECK
  3. QUIZZES
  4. CPATER TESTS
  5. CLASS WORK
  6. HOMEWORK
PROJECTS
GROUP PRESENTATION
1.Find the differential of the composite function Y= Sin3X.
2. The radius of a ball bearing is measured to be 0.7 inch. If the measurement is correct to within 0.01 inch, estimate the propagated error in the volume V of the ball bearing. /
  • Calculus book “CALCULUS of a SINGLE VARIABLE” 8th Edition by LARSON, HOSTETLER and EDWARDS.
  • Teacher’s Resource Guide
  • College Board, Advance Placement Program
  • Fast Track to Preparing For the AP Placement CalculusAB and BC Examinations.
  • Test Item File by Larson, et al