Course Syllabus for: APâ Calculus
Teacher: Ms. Aleta Kandle (Doss)
Phone Number: (503) 668-8011 ext. 7221
Email: aleta.kandle@ortrail.k12.or.us, (aleta.doss@ortrail.k12.or.us)
Course Description
This course is for those students who have successfully completed Pre-Calculus.
Students will become familiar with fundamental calculus concepts such as the derivative and the integral. Students will also discover a purpose for these concepts in and out of the field of mathematics. In the month of May students will have the opportunity to take the AP Calculus AB test.
Course Goals:
1) Students will become familiar and confident with the math related to the above description.
2) Students will discover how math can be useful and how it relates to applied
situations.
3) Students will become self motivated to want to succeed in math.
Major Topics Covered
Functions, derivatives, antiderivatives, numerical integration, definite and
indefinite integrals.
Course Outline
1st Semester
Chapter 1 Functions in Calculus (3 weeks)
1.1 Functions, Calculus style (2 days)
1.2 Graphs (1 day)
1.3 Machine Graphics (1 day)
1.4 What is a Function (2 days)
1.5 A Field Guide to Elementary Functions (2 days)
1.6 New Functions from Old (2 days)
1.7 Modeling with Elementary Functions (2 days)
Chapter 2 The Derivative (3 weeks)
2.1 Amount Functions and Rate Functions: The Idea of the Derivative (2 days)
2.2 Estimating Derivatives: A Closer Look (1day)
2.3 The Geometry of Derivatives (2 days)
2.4 The Geometry of Higher-Order Derivatives (1 day)
2.5 Average and Instantaneous Rates: Defining the Derivative (2 days)
2.6 Limits and Continuity (2 days)
2.7 Limits involving Infinity: New limits from old (2 days)
Chapter 3 Derivative of Elementary Functions (4 weeks)
3.1 Derivatives of Power Functions and Polynomials (2 days)
3.2 Using Derivative and Antiderivative Formulas (2 days)
3.3 Derivatives of Exponential and Logarithm Functions (2 days)
3.4 Derivatives of Trigonometric Functions (2 days)
3.5 New Derivatives from Old: The Product and Quotient Rules (2 days)
3.6 New Derivatives from Old: The Chain Rule (2 days)
3.7 Implicit Differentiation (2 days)
3.8 Inverse Trigonometric Functions and Their Derivatives (2 days)
Chapter 4 Applications of the Derivative (4 weeks)
4.1 Differential Equations and Their Solutions (2 days)
4.2 More Differential Equations: Modeling Growth (1 day)
4.3 Linear and Quadratic Approximation: Taylor Polynomials (2 days)
4.4 Newton’s Method: Finding Roots (1 day)
4.6 Optimization (2 days)
4.8 Related Rates (2 days)
4.10 Why Continuity Matters (1 day)
4.11 Why Differentiability Matters: The Mean Value Theorem (2 days)
2nd Semester
Chapter 5 The Integral (2½ weeks)
5.1 Areas and Integrals (2 days)
5.2 The Area Function (1 day)
5.3 The Fundamental Theorem of Calculus (2 days)
5.4 Approximating Sums: The Integral as a Limit (3 days)
5.5 Approximating Sums: Interpretations and Applications (1 day)
Chapter 6 Finding Antiderivatives (1 week)
6.1 Antiderivatives: The idea (1 day)
6.2 Antiderivatives by Substitution (2 days)
Chapter 9 More Antidifferentiation Techniques (2 weeks)
9.1 Integration by Parts (3 days)
9.3 Trigonometric Antiderivatives (2 days)
9.4 Miscellaneous Exercises (4 days)
Chapter 7 Numerical Integration (1½ weeks)
7.1 The Idea of Approximation (2 days)
Calculator Approximation and Integration (1 day)
7.2 More on Error: Left and Right Sums and the First Derivative (2 days)
7.3 Trapezoid Sums, Midpoint Sums, and Second Derivative (1 day)
7.4 Simpson’s Rule (1 day)
Chapter 8 Using the Definite Integral (2½ weeks)
8.1 Introduction (1 day)
8.2 Finding Volumes by Integration (4 days)
8.3 Arclength (1 day)
8.4 Work (2 days)
Prepare for AP Test (1 week)
Review concepts to be on the test including slope fields.
Chapter 10 Improper Integrals (1 week)*
10.1 When is an Integral Improper (2 days)
10.2 Detecting Convergence, Estimating Limits (1 day)
10.4 l’Hopital’s Rule: Comparing Rates (2 days)
Prepare for AP Test
Review concepts to be on the test including slope fields.
Texts
Calculus from Graphical, Numerical, and Symbolic Points of View. Ostebee and Zorn. Saunders College Publishing, 1997.
Materials Needed by Students
Each day the student will need to bring the following items:
a.) Book
b.) Pencil
c.) Paper
d.) Calculator (Graphing calculator required, Ti 83/84 recommended)
Academic/Behavioral Expectations
1.) Come to class each day prepared to learn.
2.) Respect yourself and others.
3.) Ask questions when they arise.
Make-up Test/Work:
It is your responsibility to make-up the work you have missed. Please get all make-up work from me, a classmate, or check the assignment list before you leave or on the day you return to school. If you know ahead of time that you will be absent for a test, please notify me so that you can schedule a time to retake it outside of class time.
Grading Procedure:
Your grade for this class will be determined by:
80% tests, projects, and work samples on which students may not use notes/assignments
20% homework quizzes and quizzes on which students may use notes/assignments
Scale:
100-90% A
89-80% B
79-70% C
69-60% D
59-0% F
Homework is the most important method for students to acquire math skill and hence will be a major facet of this course. Answer are available (in the back of the textbook or included in most handouts) for student to check each assignment. Students are responsible to correct assignments and seek assistance when needed. Each Wednesday a homework quiz, or a quiz on which students may use notes and assignments, will be given.
Unit Test:
For each unit we will review one day, test, review foundational concepts and correct our tests. If students are absent for test they will need to take it outside of class time.
Test Retakes:
Students may retake assessments after completing the retake form which includes:
1) A parent and student signature
2) Complete all assignments and additional review for retake.
3) A plan of how to study for future exams.
4) Arranging a time with their teacher to retake an exam OUTSIDE of class time.
***All retake assessments must be completed prior to the next unit test. If a student would like multiple assessments, he or she must schedule their time carefully to plan the moments needed to review and take each. He or she must frequently communicate with their teacher to complete all retake assessments prior to the next exam.
***All tests, retests and alternative assessments must stay in the classroom in individual student folders. Students may review and correct their work within the room.
*** Communication with your teacher is vital when a student(s) needs assistance understanding the current material. After school help from your teacher or other classmates or tutors may be needed frequently. Students must complete and correct all their assignments and seek assistance when needed.
***Except for meetings your teacher is available to help you before and after school daily. You are welcome to schedule ahead or you may simply drop by.
School Wide Policy:
Tardies: 0-10 minutes unexcused
10 minutes- end of class: absence unexcused
Tardy Response.
0-2 Warning
3 Call home
4+ Long form
Calculus Assignments
1.1 p10 1-6
1.1 p10 7,9,11,14,18,19
1.2 &1.3 p21 3-9,36,37, p34 2a,3a,8,19
1.3 p26 1-3,6-8,13-17,22,28,32-34,40,45
1.4 p26 18-21,41,42,48a,53abc
1.5 p65 1-4,9-11,17-19,23-28,35
1.6 p78 1,3-9,15-19
1.6 p79 27-28,35,37-39,41,44,47-49,57,58
1.7 p90 Labs 3,5; 1ab,3a-e,5a-c
1.8 read
review study guide
Test 1
2.1 p105 1-7,10,11,13,17,27
2.2 p114 1-3,7,10a,b,12,14,16
2.3 p127 1,3,4,6-8,19,22-24
2.3 p127 2,5,9-11,20,26,30
2.4 p135 2,3,4a-d,6-8,13,19
2.5 p148 1-5average only
2.5 p148 7abd,10,14ab,16
2.1-2.5 Worksheet , 12
2.6 p160 1-11,29,31,39,45
2.6 p160 17-27,33,40,41,50-52,61-63
2.7 p173 1,2,3abcf
2.7 p173 5-7,15,19,25,28abf
Worksheet chapter 2
Review
Test 2
3.1 p191 1-3,8,31,35,36,40,41,90
3.1 p191 21-26,32,33,34ac,38,58,59,73ab,78,84
3.2 p197 1,4,10,11,23,24
3.3 p206 1-14
3.3 p206 15,31-50,52,66,77a-d,71,98-102
3.4 p213 1,2,5,6,9-13,15,16,17,19 (optional 21,25,29,46,47,52)
3.4 worksheet
3.1-3.4 worksheet #20
Quiz 3.1-3.4
3.5 p221 1-3,5-7,9,12-36 (multiples of 3)
3.5 p221 10-37 every 3rd, 41,50,55
3.6 p230 1,12-23
3.6 p230 3-11odd,25-39odd,50-53,64,65
3.7 p236 1,2,5,6,9-14
3.8 p245 1-10,13-16,42,44
3.8 p245 19-24,26,19-33
Review p230 24-40 even,41
Test 3
4.1 p254 2-7,11
4.1 p254 8-10,12,14,15,19
4.2 p264 1-4,7-9
4.3 p277 1-3,8,15a
4.3 p277 16,17,19a-c,24a,c
Puzzlers #28
4.4 p286 1-4
4.4 p286 10,11,13
Worksheet 4.1-4.4 #30
4.6 p303 1,4,5
4.6 p303 6,8,12,17
4.8 p314 1-4
4.8 p314 6,15,19
4.10 p330 1-3, 11,12
4.11 p338 2,6,7
Review
Test 4
Final
AP Calculus Homework Assignments
Semester 2
Chapter 5
Pg 352 #s 1, 2a ,4ab ,5a-f ,6
Pg 352 #s 8, 15a-c, 24, 31, 45, 54
Pg 363 #s 2, 6, 7a ,8, 11a-g
Pg 373 #s 1-4
Pg 373 #s 6, 7, 9, 10, 13,
Pg 384 #s 1
Pg 384 #s 2-3, 5, 7, 9, 11, 15
Pg 394 #s 1-3, 5-10, 12, 14-16
Review Worksheet 5.1-5.6
Chapter 6
Pg 245 #s 19-24, 26, 29-35, 40, 41(Inverse Trig.) Pg 404 #s 1-18
Pg 411 #s 1-7
Pg 411 #s 8-14, 16, 22-27
Worksheet
Chapter 9
Pg 499 #s 1-9, 13
Pg 499 #s 16-20, 23-26, 35, 37ab
Pg 516 #s 2-6, 9, 17,18
Pg 516 #s 10, 11, 13, 15, 26, 28, 32a
Pg 517 #s 1-5, 9, 11, 13, 17, 19, 21, 23, 29, 33, 35, 37, 41
Pg 518 #s 47, 49, 55, 57, 63, 65, 67, 71, 75, 79
Worksheet – Integrals and Approximation on Calculator
Practice Test 1
Chapter 8
Pg 458 #s 3, 6
Pg 463 #s 1-4
Pg 463 #s 6-8 (rotate about the x-axis)
Pg 463 #s 5, 6, 8-10
Pg 464 #s 12-15, 18, 19, 21
Pg 469 #s 2, 3b, 5, 6 (by calculator), 10a
Pg 476 #s 2, 4-6
Worksheet 8.1-8.4
Practice Test 2
Practice Test 3
Sandy High School
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