ROSE TREE MEDIA SCHOOL DISTRICT
COURSE CURRICULUM
COURSE TITLE: / ADVANCED PLACEMENT CALCULUSGRADE LEVEL: / HIGH SCHOOL
CREATION DATE: /
November 2003
Essential Question, Concept or Theme: A. The Cartesian Plane and Functions / Approx. Time Allotment: /PA Standards: 2.1.11.A; 2.3.11.B; 2.5.11.B; 2.8.11.E, J, K, L, M, N, O, Q, S, T; 2.10.11.A; 2.10.11.B /
Benchmark/Skills / Assessment / Aligned Materials/
Resources/Technology / Instructional Strategies /
A. The Cartesian Plan & Functions
1) Determine intervals on the real line
2) Solve inequalities
3) Solve inequalities involving absolute values
4) Use the distance and midpoint formulas
5) Find equations of circles
6) Graph equations and determine intercept points, symmetry, roots, and points of intersection
7) Use graphs to form a mathematical model
8) Calculate the slope of a line and use it to write the equation of the line
9) Find parallel and perpendicular lines
10) Define a function and use correct function notation
11) Graph a function
12) Classify and combine functions
13) Evaluate trigonometric functions
14) Solve and simplify trigonometric identities
15) Solve trigonometric equations
16) Graph trigonometric functions / A. – I. One major test and/ or one to two quizzes per unit will be used as a minimum.
A. – I. Final Examination
A. – J. Project / Presentation
Optional forms of assessment:
Additional tests or quizzes, homework, projects, reading assignments, written papers, teacher observation of students’ work, oral assessment, group activities, boardwork, etc. / TEXT: Calculus with Integrated Geometry (6th edition)– Larson, Hostetler, and Edwards / Houghton Mifflin 1998
Teacher resource materials associated with the text
TI-83 Plus graphing calculators and overhead view screen
Videos (available in D109)
AP exam review software available on computers in A227 and also available for purchase for at home use.
Internet sites suggested for AP review. / Instructional strategies by the teacher will include:
A. – I. Lecture, demonstration, review, and graphing calculator activities
Optional instructional strategies may include but are not restricted to:
Videos, discovery learning, group work, jigsaw, or any variety of classroom activities as suggested by the Professional Development Coordinator.
Essential Question, Concept or Theme: A. The Cartesian Plane and Functions / Approx. Time Allotment: /
PA Standards: 2.1.11.A; 2.3.11.B; 2.5.11.B; 2.8.11.E, J, K, L, M, N, O, Q, S, T; 2.10.11.A; 2.10.11.B /
Adaptations/Inclusion Techniques / Enrichment Strategies / Remediation Strategies / Multicultural/Interdisciplinary
Connection /
Adaptations for students with special instructional needs will be met in accordance with each student’s Individual Educational Plan.
Adaptations may include extended time on tests and assignments (not more than twice the given amount), preferential seating, after school help, or modified homework assignments. / Students are encouraged to prepare for the AP examination. AP review software is available for purchase for student use at home. Students can also access previous AP exam questions on the AP website. This website includes the questions and answers as well as an explanation to the scores given for sample responses. / Students who are enrolled in AP Calculus that are not capable of the work load are encouraged move into the Regular Calculus course. Students in the Regular Calculus course that are not capable of the work load are encouraged to take the Introduction to Calculus course offered in the second semester. / Calculus lends itself to have many connections with Physics. There is however, no formal interdisciplinary curriculum at this time.
Essential Question, Concept or Theme: B. Limits and Their Properties / Approx. Time Allotment: /
PA Standards: 2.2.1.B; 2.4.11.A; 2.5.11.B /
Benchmark/Skills / Assessment / Aligned Materials/
Resources/Technology / Instructional Strategies /
B. Limits and Their Properties
1) Find limits using estimates
2) Construct a formal definition of a limit
3) Find a delta for a given epsilon using the definition of a limit (optional)
4) Apply the three-step strategy for finding limits
5) Know the properties of limits
6) Determine limits of algebraic and trigonometric functions
7) Use the cancellation technique to evaluate limits
8) Use the rationalization technique to evaluate limits
9) Apply the Squeeze Theorem
10) Evaluate indeterminate forms
11) Apply the definition of continuity
12) Test for continuity
13) Evaluate one-sided limits
14) Apply the Intermediate Value Theorem
15) Apply properties of continuity
16) Determine infinite limits from a graph
17) Find vertical asymptotes
18) Apply properties of infinite limits / A. – I. One major test and/ or one to two quizzes per unit will be used as a minimum.
A. – I. Final Examination
A. – J. Project / Presentation
Optional forms of assessment:
Additional tests or quizzes, homework, projects, reading assignments, written papers, teacher observation of students’ work, oral assessment, group activities, boardwork, etc. / TEXT: Calculus with Integrated Geometry (6th edition)– Larson, Hostetler, and Edwards / Houghton Mifflin 1998
Teacher resource materials associated with the text
TI-83 Plus graphing calculators and overhead view screen
Videos (available in the Penncrest Math Office)
AP exam review software available on computers in A227 and also available for purchase for at home use.
Internet sites suggested for AP review. / Instructional strategies by the teacher will include:
A. – I. Lecture, demonstration, review, and graphing calculator activities
Optional instructional strategies may include but are not restricted to:
Videos, discovery learning, group work, jigsaw, or any variety of classroom activities as suggested by the Professional Development Coordinator.
Essential Question, Concept or Theme: B. Limits and Their Properties / Approx. Time Allotment: /
PA Standards: 2.2.1.B; 2.4.11.A; 2.5.11.B /
Adaptations/Inclusion Techniques / Enrichment Strategies / Remediation Strategies / Multicultural/Interdisciplinary
Connection /
Adaptations for students with special instructional needs will be met in accordance with each student’s Individual Educational Plan.
Adaptations may include extended time on tests and assignments (not more than twice the given amount), preferential seating, after school help, or modified homework assignments. / Students are encouraged to prepare for the AP examination. AP review software is available for purchase for student use at home. Students can also access previous AP exam questions on the AP website. This website includes the questions and answers as well as an explanation to the scores given for sample responses. / Students who are enrolled in AP Calculus that are not capable of the work load are encouraged move into the Regular Calculus course. Students in the Regular Calculus course that are not capable of the work load are encouraged to take the Introduction to Calculus course offered in the second semester. / Calculus lends itself to have many connections with Physics. There is however, no formal interdisciplinary curriculum at this time.
Essential Question, Concept or Theme: C. Differentiation / Approx. Time Allotment: /
PA Standards: 2.4.11.E /
Benchmark/Skills / Assessment / Aligned Materials/
Resources/Technology / Instructional Strategies /
C. Differentiation
1) Find tangent lines to graph of a nonlinear function
2) Define and apply the definition of the derivative
3) Examine the relationship of differentiability and continuity
4) Use derivatives to find velocity, acceleration, and other rates
5) Apply the following rules for derivatives: constant rule, power rule, constant multiple rule, sum and difference rules
6) Find derivatives of sine and cosine
7) Solve simple applications of the derivative
8) Find derivatives using the product and/ or quotient rules
9) Find derivatives of the rest of the trigonometric functions
10) Find higher order derivatives
11) Compose and decompose composite functions
12) Find derivatives using the chain rule and the general power rule
13) Simplify derivatives
14) Find derivatives of implicit and explicit functions
15) Solve related rate problems / A. – I. One major test and/ or one to two quizzes per unit will be used as a minimum.
A. – I. Final Examination
A. – J. Project / Presentation
Optional forms of assessment:
Additional tests or quizzes, homework, projects, reading assignments, written papers, teacher observation of students’ work, oral assessment, group activities, boardwork, etc. / TEXT: Calculus with Integrated Geometry (6th edition)– Larson, Hostetler, and Edwards / Houghton Mifflin 1998
Teacher resource materials associated with the text
TI-83 Plus graphing calculators and overhead view screen
Videos (available in the Penncrest Math Office)
AP exam review software available on computers in A227 and also available for purchase for at home use.
Internet sites suggested for AP review. / Instructional strategies by the teacher will include:
A. – I. Lecture, demonstration, review, and graphing calculator activities
Optional instructional strategies may include but are not restricted to:
Videos, discovery learning, group work, jigsaw, or any variety of classroom activities as suggested by the Professional Development Coordinator.
Essential Question, Concept or Theme: C. Differentiation / Approx. Time Allotment: /
PA Standards: 2.4.11.E /
Adaptations/Inclusion Techniques / Enrichment Strategies / Remediation Strategies / Multicultural/Interdisciplinary
Connection /
Adaptations for students with special instructional needs will be met in accordance with each student’s Individual Educational Plan.
Adaptations may include extended time on tests and assignments (not more than twice the given amount), preferential seating, after school help, or modified homework assignments. / Students are encouraged to prepare for the AP examination. AP review software is available for purchase for student use at home. Students can also access previous AP exam questions on the AP website. This website includes the questions and answers as well as an explanation to the scores given for sample responses. / Students who are enrolled in AP Calculus that are not capable of the work load are encouraged move into the Regular Calculus course. Students in the Regular Calculus course that are not capable of the work load are encouraged to take the Introduction to Calculus course offered in the second semester. / Calculus lends itself to have many connections with Physics. There is however, no formal interdisciplinary curriculum at this time.
Essential Question, Concept or Theme: D. Applications of Differentiation / Approx. Time Allotment: /
PA Standards: 2.8.11.E, K, S, T; 2.11.11.A, B /
Benchmark/Skills / Assessment / Aligned Materials/
Resources/Technology / Instructional Strategies /
D. Applications of Differentiation
1) Define and locate extrema
2) Define and apply Rolle’s Theorem and the Mean Value Theorem
3) Define and test for internals of increasing and decreasing
4) Apply the First Derivative Test
5) Test for concavity
6) Find the points of inflection
7) Apply the Second Derivative Test
8) Evaluate a limit at infinity
9) Determine horizontal and oblique asymptotes
10) Sketch functions using the curve sketching techniques
11) Applications of maximum and minimum problems
12) Use Newton’s Method to approximate the zeros of a function (individual study assignment)
13) Use the differential form to evaluate functions / A. – I. One major test and/ or one to two quizzes per unit will be used as a minimum.
A. – I. Final Examination
A. – J. Project / Presentation
Optional forms of assessment:
Additional tests or quizzes, homework, projects, reading assignments, written papers, teacher observation of students’ work, oral assessment, group activities, boardwork, etc. / TEXT: Calculus with Integrated Geometry (6th edition)– Larson, Hostetler, and Edwards / Houghton Mifflin 1998
Teacher resource materials associated with the text
TI-83 Plus graphing calculators and overhead view screen
Videos (available in the Penncrest Math Office)
AP exam review software available on computers in A227 and also available for purchase for at home use.
Internet sites suggested for AP review. / Instructional strategies by the teacher will include:
A. – I. Lecture, demonstration, review, and graphing calculator activities
Optional instructional strategies may include but are not restricted to:
Videos, discovery learning, group work, jigsaw, or any variety of classroom activities as suggested by the Professional Development Coordinator.
Essential Question, Concept or Theme: D. Applications of Differentiation / Approx. Time Allotment: /
PA Standards: 2.8.11.E, K, S, T; 2.11.11.A, B /
Adaptations/Inclusion Techniques / Enrichment Strategies / Remediation Strategies / Multicultural/Interdisciplinary
Connection /
Adaptations for students with special instructional needs will be met in accordance with each student’s Individual Educational Plan.
Adaptations may include extended time on tests and assignments (not more than twice the given amount), preferential seating, after school help, or modified homework assignments. / Students are encouraged to prepare for the AP examination. AP review software is available for purchase for student use at home. Students can also access previous AP exam questions on the AP website. This website includes the questions and answers as well as an explanation to the scores given for sample responses. / Students who are enrolled in AP Calculus that are not capable of the work load are encouraged move into the Regular Calculus course. Students in the Regular Calculus course that are not capable of the work load are encouraged to take the Introduction to Calculus course offered in the second semester. / Calculus lends itself to have many connections with Physics. There is however, no formal interdisciplinary curriculum at this time.
Essential Question, Concept or Theme: E. Integration / Approx. Time Allotment: /
PA Standards: 2.2.11.B, D, F; 2.4.11.E; 2.5.11.A; 2.11.11.D, E /
Benchmark/Skills / Assessment / Aligned Materials/
Resources/Technology / Instructional Strategies /
E. Integration
1) Evaluating sigma notation formulas
2) Find the area of a plane region using upper, lower, and midpoint sums
3) Find the area of a plane region using Riemann sums
4) Find the area of a plane region using the Trapezoid Rule and Simpson’s Rule
5) Define the anti-derivative
6) Apply basic integration rules
7) Find general and specific solutions of the integral
8) Define and evaluate definite integrals
9) State and apply the Fundamental Theorem of Calculus, Mean Value Theorem, and the Second Fundamental Theorem of Calculus
10) Evaluate integrals
11) Find the average value
12) Recognize special integration patterns
13) Integrate using substitution and/ or general power rule / A. – I. One major test and/ or one to two quizzes per unit will be used as a minimum.
A. – I. Final Examination
A. – J. Project / Presentation
Optional forms of assessment:
Additional tests or quizzes, homework, projects, reading assignments, written papers, teacher observation of students’ work, oral assessment, group activities, boardwork, etc. / TEXT: Calculus with Integrated Geometry (6th edition)– Larson, Hostetler, and Edwards / Houghton Mifflin 1998