Download the ap calculus exam - Hood River County School District

AP Calculus AB Syllabus – Mr. Tactay
COURSE OVERVIEW and PREREQUISITES
This course is designed for those students who have demonstrated mastery in algebra, geometry, trigonometry,
analytic geometry, and elementary functions. These functions include linear, polynomial, rational, exponential,
logarithmic, trigonometric, inverse trigonometric, and piecewise defined. In particular, before studying calculus,
students must be familiar with the properties, graphs, and the language of functions (domain and range, odd and
even, periodic, symmetry, zeros, intercepts, and so on). Students must also be familiar with the various techniques
and formulas for simplifying, factoring, and solving functions. In addition, it is expected for students to know the
values of the trigonometric functions of the numbers 0, 6 , 4 , 3 , 2 , and their multiples.
The major topics of study will include functions, limits, differential calculus, and integral calculus.
COURSE OBJECTIVE
The primary objective of this course will be to understand the underlying mathematics of calculus. That is, to
understand the geometrical and numerical meanings of each concept in conjunction with the algebraic processes
involved in the study of calculus. Throughout the year you will be asked to interpret, understand, and apply the
concepts and relationships of all major topics in four ways: geometrically (graphs), numerically (tables of data),
algebraically (formulas, functions, etc.), and verbally. The textbook and supplementary material will reinforce
this approach by encouraging the communication of solutions to problems both verbally and in written sentences.
The ability to do so will greatly determine your success on the AP Calculus Exam.
CONTACT INFORMATION
(541)386– 4500 ext.4651 or [email protected]
(541)399-1024
HOW TO GET HELP
You may receive help from Mr. Tactay before school starting from approximately 8:00 am, or during his Prep
Periods, 3 and 8, during lunch (arrange with Mr. Tactay first), or after school. The school website currently
contains my syllabus and assignment sheets. I will also try to include all handouts and grades on the website.
REQUIRED MATERIALS
It is your responsibility to come to class prepared. It is highly recommended that you have a 3-inch
BINDER and develop a system TO FILE YOUR HOMEWORK, QUIZZES, AND
TESTS.
TEXTBOOK and RESOURCE MATERIALS
Calculus. Deborah Hughes-Hallett, Andrew M. Gleason, et al. John Wiley & Sons, Inc. 2005. Fourth Edition.
Amsco’s AP* Calculus AB/BC: Preparing for the Advanced Placement Examinations. Maxine Lifshitz. Amsco
School Publications. 2004.
Master the AP* Calculus AB & BC Tests. W. Michael Kelly and Contributing Author, Mark Wilding.
Peterson’s, a division of Thomson Learning, Inc. 2002.
* AP is a registered trademark of the College Entrance Examination Board, which does not endorse these books.
GRADING
Classwork: Homework and Quizzes - These daily assignments are worth 15% of your overall grade.
Homework is worth 8 points (4 points for notes, 4 points for the actual work). Points for Quizzes will
vary.
Tests - Tests are worth 100 points each and will be 45% of your overall grade. They are curved according
to your potential to pass the AP Exam. That is, a 90 average on tests would correlate to a potential of
passing the AP Exam with a 3 score. An average in the upper 90’s would correlate to a 4. An average of
over a 100 would correlate to a 5. They will be taken on scheduled dates. If you miss a test, you must
make it up the day you return to class. NO EXCEPTIONS. You must make prior arrangements (before
the test, not on test day) with Mr. Tactay in order to take the test on a later date.
Final Exam – This makes up 40% of your overall Semester Grade.
There is NO RETESTING in this course.
Academic Honesty – Any cheating in any form, despite how small, will result in an automatic zero points.
LETTER GRADES
A 90% and above
B 80% - 89.94%
C 70% - 79.94%
D 60% - 69.94%
F
less than 60%
TEST TAKING & QUIZ BEHAVIOR
Nothing is allowed on the desks during tests or quizzes except for a calculator (when allowed) and a writing
utensil. Notes are not allowed. There will be absolutely NO FORM OF INTERACTION OR
COMMUNICATION – VERBAL OR NONVERBAL - UNTIL EVERYONE HAS COMPLETED THE
TEST. This includes talking, eye contact, passing notes, asking for pencil, paper, etc. If you need anything,
raise your hand and ask Mr. Tactay. Leave your seats only to sharpen you pencil or to hand in your tests.
CONSEQUENCES: Inappropriate behavior during tests will result in lunch time detention or an automatic
ZERO on the test.
TEST TIME LIMIT: You are to complete your tests or quizzes in the allotted time. You will be given the
entire class period to complete your tests. YOU WILL NOT BE ALLOWED TO TURN IN AN
UNFINISHED TEST AND COME BACK LATER TO FINISH IT.
CHAPTER TESTS & FINAL EXAM
Every question on the chapter tests will be an AP style question. The first semester is devoted to mastering
the multiple choice portion of the AP Exam, while the second semester will be devoted to mastering the
free response portion. Each chapter test will include material from previous tests. The Final Exam will be
equivalent to the entire multiple choice portion of the AP Exam. Similarly, the last chapter test in the
second semester before the actual AP Exam will be comparable to the free response portion.
There will be about a month remaining after the AP Exam. An additional chapter will be covered at that
time. That chapter test will only have material from that chapter and will take the place of the final exam.
THE AP CALCULUS EXAM
The AP Calculus Exam is on Tuesday, May 9, 2017. This is an A-Day. All topics, problems, and examples
ill represent the type of knowledge, skill, and understanding you will need to be successful on the AP
Calculus Exam. This exam, as well as all other AP Exams, will give you a score ranging from 1 to 5. A
score of at least a 3 is considered passing by most colleges.
AP Exam 2017
Approximate cost and deadline dates.
Regular Registration: $94 per exam, ($55 per exam if on free/reduced lunch): Deadline March 10, 2017
Late Registration: $149/exam, ($55 per exam if on free/reduced lunch): Deadline March 17, 2017
AP Pre-Administration Sessions: Must attend one of the two sessions usually scheduled in late April.
Students who have school related conflicts may choose to test late (sports contests) or if a student registers
for two exams on the same day and time. ($139/exam)
If you have any questions, then contact Ms. Bentley, guidance counselor.
TARDY POLICY
This policy is for the entire semester and will start over for the second semester.
First four tardies: no consequence.
Fifth and every tardy thereafter: a discipline referral will be given for each tardy.
LEAVING CLASS
You must use the pass to leave class. IT IS SCHOOL POLICY THAT YOU STAY IN THE CLASSROOM
THROUGHOUT THE ENTIRE PERIOD. LEAVE FOR EMERGENCIES ONLY.
Leaving for more than 5 minutes will result in a discipline referral.
Only one person may leave.
CELL PHONES, and OTHER TECHNOLOGY IN CLASS
You may not use Cell Phones, and other technology, during the beginning of class, during the lecture, during
quizzes, or during tests. They must be put away, OUT OF SIGHT, and TURNED OFF completely. You
may use them DURING WORK TIME ONLY. However, you may only use your Cell Phone to listen to
music. You may not text, play games, watch videos, be on any form of social media (Facebook, Snapchat,
Instagram, etc.), make calls, etc. Using them in class inappropriately will result in IMMEDIATE
CONFISCATION and given back at the end of class. To avoid potential use of unwanted technology, it is
recommended to keep BOTH HANDS ABOVE YOUR DESK AT ALL TIMES.
If there is FREE TIME at the end of class, then you may use your cell phone with no restrictions.
CALCULATOR USE IN CLASS
Graphing calculators are recommended to help understand and verify mathematical concepts. However, they
should be used for mathematical purposes only. Any non-mathematical purposes (such as games, writing
notes, drawing, or just typing in numbers or words so they run down your screen) will result in confiscation
of your calculator. It will be returned at the end of the period.
Below are things that you need to know for your graphing calculator that will help you to become more
successful.
1. Inputting functions into y=.
2. All keys involved in graphing a function. ie all the information under the keys "window", "zoom",
"trace", and "graph."
Especially:
- Know how to change the window.
- Know how to solve an equation looking at the graph. ie use "zero" or “intersect” under the key "Calc."
- Know how to solve a system of equations of two graphs. ie use the "intersect" under the key "Calc."
- Know how to "Zoom In" and "Zoom Out" on a graph
3. All keys involved in creating a table of values of a function. ie the keys "table set" and "table."
Especially:
- Know how to create a table using a constant change in x.
- Know how to create a table by "asking" what x is.
4. Understand the information in "Mode," especially the fact that most trigonometric problems require the
calculator to be in radian mode.
5. Basic knowledge of typing in functions correctly.
Especially:
- functions with automatic parenthesis like sin(, cos(, and ln(.
- inputting exponents
- inputting fractions
6. Use the key "Sto" to store a value for X then evaluate the value of a function at that point.
ACTIVITIES and WRITING ASSIGNMENTS
The use of calculators to solve problems and verify answers will be ongoing throughout the course. However, separate activities
will be given to help conceptualize major ideas. Each activity below can be found in the course outline, denoted by *.
Group/Calculator Activity 1: Domain, Range, and Asymptotes
You will work in groups to predict the domain, range, and asymptotes of various functions, then verify using the calculator.
Group/Calculator Activity 2: Limits
You will work in groups to graphically and numerically evaluate limits using the calculator.
Calculator Activity 3: Zooming in to find the Derivative
You will zoom in at a point to find the derivative using a Difference Quotient. You will then verify using Math 8.
Writing Assignment 1:
The Derivative
You will explain the meaning of the derivative, relating the graphical meaning of slope to the formal definition of the derivative.
Group Activity 4: Tangent Line Approximations
You will work in groups to find equations of tangent lines numerically (from a table of values) and algebraically (using the
short-cuts) and use them to predict values.
Group/Calculator Activity 5: Optimization - Maximizing and Minimizing
You will work in groups to solve classic optimization problems. You will solve the problem first without the use of calculus by
creating a table, then verify using the graph. You will then solve the problem using calculus.
Group Activity 6: The Definite Integral and Distance Traveled
You will work in groups to find the distance between two locations in town. You will record data of your velocities for three
different cases – every two minutes, every minute, and then every 10 seconds. The definite integral using the trapezoid rule for
the three different cases will estimate the distance traveled.
Writing Assignment 2: The Definite Integral
You will explain the meaning of the definite integral, relating the graphical meaning of area to the notation of the definite integral.
AP CALCULUS LEARNING GOALS and COURSE OUTLINE
* denotes Group/Calculator activity
Chapter 1: Review - Functions and Graphs (2 to 3 weeks)
A. Simplify, Graph, and Analyze Basic Functions and their Graphs
1. Slope and Equation of lines
2. Exponential, Logarithmic Functions, and Polynomials
B. Understand the Properties and Language of Functions and Inverses
* 1. Domain, Range, and Asymptotes - Group/Calculator Activity 1
2. Graphs of Inverse Functions
C. Graph a Function from a Family of Functions - Translations, Reflections, and Amplitudes
D. Graph, Solve, and Apply Trigonometric Functions
1. Unit Circle and Graphing
2. Solving and Applications
E. Understand Properties of Limits and Evaluating Limits
1. The Concept of Limits for Finding Horizontal or Vertical Asymptotes
2. Left and Right Hand Limits
3. The Limit Definition for Continuity/Discontinuity
* 4. Analyzing Limits Approaching a Finite Number and Infinity Graphically and Numerically
- Group/Calculator Activity 2
F. Evaluate Limits using Algebraic Techniques
1. Limits Approaching a Finite Number
2. Limits Approaching Infinity
3. Limits of Piecewise Functions
G. Evaluate Limits using L’Hôpital’s Rule
H. Understand Removable and Jump (Essential) Discontinuity
1. Graphical Analysis of Discontinuity – show on the calculator how to recognize
2. The Algebraic Relationship of the Function and the Discontinuity
Chapter 2: Introduction to The Derivative (3 weeks)
A. Understand the Graphical Definition of The Derivative - Slope of the Tangent Line
1. Relationship between the Derivative and its Function
2. The Derivative as the Average Rate of Change
3. Difference Quotient
B. Using the Formal Definition of the Derivative
1. Recognize the Definition
* 2. Find the Derivative at a Point Using the Definition - Calculator Activity 3
C. Understand, Interpret, and Apply the Derivative
1. Instantaneous and Average Velocity
2. The Meaning Behind the Units and Notations of the Derivative
3. Estimate the Derivative from a Tables of x, y Values
D. Graph the Derivative of a Function
E. Find the Equation of a Tangent Line
1. Use the Calculator to Find Slope at a Point
2. Estimate the Equation of a Tangent Line from a Tables of x, y Values
E. Analyze the Graph of a Function to Determine Values of the First and Second Derivatives
1. Find Critical Points from the Graph of the Function
2. Understand the Relationship between the Intervals of Increase or Decrease of
the Function and the Values of the First Derivative
3. Understand the Relationship between the Intervals of Concave Up or Down of
the Function and the Values of the Second Derivative
4. Sketch the First Derivative from the Behavior of the Function
F. Estimate the Second Derivative from Tables of Values
* G. Writing Assignment 1: The Derivative
Chapter 3: Rules and Shortcuts of The Derivative (3 weeks)
A. Find the Derivative of Powers, Polynomials, and Exponents
B. Find the Derivative of Trigonometric Functions
C. Find the Derivative of Natural Logs
D. Find the Derivative of the Chain Rule
D. Find the Derivative using the Product and Quotient Rules
*E. Find the Equation of a Tangent Line Using the Rules and Shortcuts for Derivatives
- Group/Calculator Activity 4
F. Find the Derivative of an Implicit Function
Chapter 4: Using Derivatives to Understand the Behavior of the Parent Function (2 to 3 weeks)
A. Find the Critical Points of a Function Using the Short-Cuts of the Derivative
1. Use the First Derivative Test to find Local (relative) extrema
2. Classify Critical Points and Endpoints as Global (absolute) extrema
B. Analyze the Graphs and Values of the First and Second Derivatives
1. Finding Intervals of Increase or Decrease of the Parent Function
2. Finding Intervals of Concave Up or Down of the Parent Function
3. Use the Second Derivative Test to Find Extrema
4. Sketch the First Derivative from the Behavior of the Function
*C. Optimization - Use the Derivative and Critical Points to Solve Problems that Maximize or Minimize
Physical Measurements
- Group/Calculator Activity 5
D. Related Rates - Use Implicit Differentiation to Solve Problems Involving Rates of Change Over
Time
E. Use the Derivative to Solve Problems Involving Position, Velocity, and Acceleration of a Particle in
Motion or Projectiles
F. Understand Basic Derivative Theorems
1. The Extreme Value Theorem
2. Rolle’s Theorem
3. The Mean Value Theorem
Unit 5: The Definite Integral (3 weeks)
A. Understand the Graphical Definition of the Definite Integral
1. Approximate the Area Under a Curve Using Riemann Sums
a. Left- and Right-Hand Sums
b. Midpoint Rule
2. Approximate the Area Under Using the Trapezoid Rule
*B. Group Activity 6
C. Use the Short-Cuts to Find the Antiderivatives or Indefinite Integrals of Power Functions
D. Apply The Fundamental Theorem of Calculus
1. Calculate the Definite Integral
2. Interpret the Meaning of the Definite Integral of Rates
(eg. Velocity, Gallons per minute, Population per year, etc.)
3. Find the Area Under the Curve of a Function
a. Interpret that Area as the Total Change of its Antiderivative
b. Use that Area to Graph the Antiderivative
E. Use the Definite Integral to Find the Average Value of a Function
*F. Writing Assignment 2: The Definite Integral
Chapter 6: More on The Definite Integral (3 weeks)
A. Integrate Exponential, Natural Logarithmic, and Trigonometric Functions
B. Integrate by u-Substitution
C. Solve Differential Equations by Separation of Variables
D. Find the Area Between Two Functions
E. Find the Volumes of Solids of Revolution
1. Disk Method
2. Washer Method
F. Find the Volumes of Solids with Known Cross Sections Perpendicular to the x or y axes
Additional AP Topics of The Definite Integral and AP Exam Review (3 weeks)
A. Analyze Two Rate Functions Over a Given Interval
B. Sketch the Slope Fields of the Solutions of Differential Equations
C. Solve Problems Involving The Fundamental Theorem of Calculus: Part Two
1. Derivatives of Definite Integrals
2. The Accumulation Function
D. AP Exam Review
The AP Exam
Tuesday, May 9, 2017
Unit after the AP Exam : Miscellaneous Topics (3 weeks)
A. Limits of Trigonometric Functions
B. Derivatives of Inverse Trigonometric Functions
C. Graphing Functions Using First and Second Derivatives
D. Integration by Parts
E. More Definite Integral Applications
1. Income Stream
2. Density
3. Work
4. Pumping Water Problems
CLASSROOM EXPECTATIONS
1. Don't worry about the outcome of this (or any) class. Just do your best and learn as much as you can. If you get an
A or an F, an AP score of 5 or a 1, don’t stress over it too much. You all are awesome just for being here.