Mrs



AP Calculus BC Syllabus 2015-2016

Mrs. Meyer South 226

@MeyerMathWO Txt: @360460 to meyers@ (616)738-6953

81010

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WHAT YOU’LL NEED:

• A CALCULATOR!!!!! (TI-83+ or comparable calculator is required for this course)

• Pencil, eraser, lined paper, graph paper

• 3 different colored highlighters

• 3 ring binder

• 2 packages of 5-tab dividers

• 2

PRIMARY TEXTBOOK:

Finney, Ross L., Franklin D. Demana, Bert K. Waits, and Daniel Kennedy. Calculus: Graphical, Numerical, Algebraic: AP Edition. Boston: Pearson Prentice Hall, 2007.

ONLINE RESOURCES:

Our textbook has very little online support. Instead, we will be utilizing Moodle and other sites for help!

Equation solving –

Concepts –

Homework questions – moodle.

Enrollment key: apcalculusbc

Practice AP Material: apcentral.

ADDITIONAL INFORMATION

If students do not have computer access at home, there are many options. Computer labs are available during certain school hours and students may use the computers in the libraries at lunch and after school in AAL. There is an additional student computer in the back of my classroom that you may use before and after school as well.

CLASSROOM DYNAMICS:

Throughout their coursework, students will use the “Rule of Four” for problem solving. Students will be asked to solve problems algebraically or analytically, support our results graphically and numerically (with and without a calculator), and then interpret the results in the context of the original problem verbally and in writing. Students will use technology to enhance and support their proofs and problem solving techniques, but will also recognize that the calculator itself does not give a proof of a concept.

EXTRA HELP!:

• First thing; you need to let me know!

• Sign up, next to my door, for seminar.

• See me to set up a time after school (

• After School Assistance Lab (AAL)!

• Come in before school.

Class Grade (80% of Final Grade)

Tests (70% of Class Grade) & Quizzes (25% of Class Grade)

There will be one test at the end of each chapter, although some chapters may be broken into smaller unit tests. Likewise, there will be one/two quizzes per chapter. If you are absent on the day of a test/quiz, be prepared to take it on the day you return or after school in AAL. Missing a test/quiz is a big deal, and an assigned AAL might not be convenient for you. Remember that when missing one. A retake, Form B, of any test is available to students who complete the correctives assignment and make arrangements with the teacher.

Homework (5% of Class Grade)

Students can expect homework every day! It is crucial to complete the assignment and show all steps, thoughts and ideas you used. There is a difference between “doing your homework” and “doing your homework well”.

Exam (20% of Final Grade)

Both semesters will culminate with a Final Exam over all topics covered throughout the semester.

CLASSROOM EXPECTATIONS:

1. Be on time to class.

2. Come to class prepared with your own textbook, calculator, pencil, notebook, and homework.

3. Respect other students, the teacher, and the classroom.

4. Participate in class discussions and activities (there will be lots of these!).

5. Please refrain from eating or drinking in the classroom (only water bottles are allowed).

General Pacing Guidelines:

**Note: Pacing for each unit is approximate. Adjustments may need to be made!

Unit 1: Prerequisites for Calculus (10 days)

• Basic Elementary Functions (linear, power, exponential, logarithmic, trigonometric, inverse trigonometric

• Parametric equations

• Using the graphing calculator to find regression lines and investigate features of basic functions

Unit 2: Limits and Continuity (9 days)

• Limits (at a point, at infinity, infinite limits, properties of limits, one-sided limits)

• Continuity (of a function, at a point)

• Intermediate Value Theorem

• Tangent line to a curve

• Normal lines

• Slope of a curve at a point

Unit 3: Derivatives (18 days)

• Definition of f’.

• Derivatives at a point (using nDeriv on calculator and by hand)

• Relating graphs of f, f’, and f’’.

• Differentiability (when f(a) fails to exist)

• Rules for Differentiation: Sum, Product, Quotient, and Chain Rule

• Implicit Differentiation

• Derivatives of trigonometric, inverse trigonometric, exponential, and logarithmic functions.

Unit 4: Applications of Derivatives (15 days)

• Local and extreme values

• Mean Value Theorem

• Connecting graphs of functions with their derivatives

• Using the derivative to find: critical points, where the function is increasing/decreasing, points of inflection, and where a function is concave up/down.

• Modeling and Optimization problems

• Linearization (using the tangent lines to approximate function values)

• Newton’s Method

• Absolute, Relative, and Percentage Change

• Related Rates

Unit 5: The Definite Integral (12 days)

• Rectangular Approximation Method (RAM)

• Riemann Sums (left, right and midpoint approximations)

• Finding an antiderivative (with and without a calculator)

• Using a definite integral to find area, volume, and average value

• Fundamental Theorem of Calculus (parts 1 and 2)

• Approximating a definite integral using the Trapezoid Rule, Simpson’s Rule and Error Analysis.

• Analyzing antiderivatives graphically

General Pacing Guidelines:

**Note: Pacing for each unit is approximate. Adjustments may need to be made!

Unit 1: Prerequisites for Calculus (10 days)

• Basic Elementary Functions (linear, power, exponential, logarithmic, trigonometric, inverse trigonometric

• Parametric equations

• Using the graphing calculator to find regression lines and investigate features of basic functions

Unit 2: Limits and Continuity (9 days)

• Limits (at a point, at infinity, infinite limits, properties of limits, one-sided limits)

• Continuity (of a function, at a point)

• Intermediate Value Theorem

• Tangent line to a curve

• Normal lines

• Slope of a curve at a point

Unit 3: Derivatives (18 days)

• Definition of f’.

• Derivatives at a point (using nDeriv on calculator and by hand)

• Relating graphs of f, f’, and f’’.

• Differentiability (when f(a) fails to exist)

• Rules for Differentiation: Sum, Product, Quotient, and Chain Rule

• Implicit Differentiation

• Derivatives of trigonometric, inverse trigonometric, exponential, and logarithmic functions.

General Pacing Guidelines, Continued:

Unit 6: Differential Equations and Mathematical Modeling (13 days)

• Slope Fields

• Euler’s Method

• Antidifferentiation by substitution, by parts, and by partial fractions

• Antiderivatives and the indefinite integral

• Separable differential equations

• Exponential growth and decay

• Logistic Growth

Unit 7: Applications of Definite Integrals (12 days)

• Definite integrals – as net change (motion on a line, consumption over time)

• Area between two curves

• Integrating with respect to y.

• Volumes (using geometric cross sections, disks, cylinders, and cylindrical shells)

• Length of a Curve

• Surface Area of a solid of revolution

• Work and Fluid Force

Unit 8: Sequences, L’Hopital’s Rule, and Improper Integrals (13 days)

• Arithmetic and Geometric Sequences (graphing and finding limits)

• Indeterminate forms and L’Hopital’s Rule

• Relative rates of growth

• Improper integrals (re-visit partial fractions)

• Convergence and Divergence testing

Unit 9: Infinite Series (16 days)

• Geometric Series

• Taylor and Maclaurin Series

• Power series: Term by term differentiation and integration to find power series of new functions

• Taylor Polynomials

• Remainder Estimation Theorem

• Lagrange form of the remainder

• Tests for convergence and divergence (nth term test, direct comparison test, ratio test, integral test, limit comparison test, and alternating series test (Leibniz)

• Radius of convergence

• Interval of convergence

Unit 10: Parametric, Vector, and Polar Functions (12 days)

• Parametric Functions:

o Derivative at a point

o Slope and Concavity

o Second derivatives

o Arc Length

o Surface area of a solid of revolution

• Vector Functions:

o Vector operations

o Angle between two vectors

o Scalar products

o Describing motion in the plane

o Velocity, acceleration, and speed

o Displacement and distance traveled

• Polar Functions:

o Polar coordinates (converting between rectangular and polar)

o Slope

o Horizontal and Vertical tangent lines

o Area enclosed by two polar curves

o Length of a polar curve

Tips to avoid ‘burn out’ in your AP classes:

1. Realize that the actual test that will earn you credit is usually in the beginning of May.

2. Attend class every day!

3. Do the readings and homework… no matter what.

4. Take notes on everything, including lectures and readings/outside materials.

5. Be sure to ASK FOR HELP!

6. When the AP test comes, don’t sweat it!

Purpose of the Graphing Calculator on AP Calculus Exams:

1. Plot a graph of a function within an arbitrary viewing window.

2. Find the zeros of a function (to solve an equation numerically).

3. Numerically calculate the derivative of a function.

4. Numerically calculate the value of a definite integral.

Characteristics of a great AP student:

1. Motivated and dedicated to school work.

2. Committed to homework and extra reading/research.

3. Responsible: able to multitask, to prioritize activities, to make deadlines.

4. Prepared and organized.

5. Beyond proficient in reading and writing.

6. Commitment to hard work!

7. Willingness to try.

Pre-requisites for AP Calculus BC

1. Successful completion of Algebra 1, Geometry, Algebra 2, and Advanced Math (Pre-calculus).

2. Basic understanding of elementary functions including, but not limited to: linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise defined.

3. Familiarity with properties of functions, the algebra of functions, and the graphs of functions.

4. Understand the language of functions (domain, range, even, odd, periodic, symmetry, zeros, intercepts, and so on).

5. Know the trigonometric functions of the numbers [pic], and their multiples.

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