# AP Exam Date: Tuesday, May 9, 2017

# AP Exam Time: 8:00 am

# AP Exam Location: First Baptist Church

**Remember, if it’s pink it’s a link!**

## #1: No Put Downs!

## #2: No Sleeping!

## #3: Technology is a TOOL, not a TOY!

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**Text number: 81010**

**Text message: @apcalcuu**

**Grade Weighting: **

**Quizzes: 20%**

**Tests: 40%**

**Final Exam: 20%**

**AP Prep****: 20%**

**The following reviews will be due weekly as part of your AP Prep grade.**

**Exam Review #1 ** Due Date: Wednesday 1/11

**Exam Review #2** (#’s 1 – 10 only) Due Date: Wednesday 1/18

**Exam Review #3** (#’s 1 – 10 only) Due Date: Wednesday 1/25

**Exam Review #4** (#’s 1 – 10 only) Due Date: Wednesday 2/1

**Exam Review #5** (#’s 1 – 10 only) Due Date: Wednesday 2/8

**Exam Review #6** (#’s 1 – 10 only) Due Date: Wednesday 2/15

**Exam Review #7 ** (#’s 1 – 10 only) Due Date: Wednesday 2/22

USATestprep Assignment (AP Prep – Limits Review: **Code: PEKOWUDUNO**) Due Date: Wednesday 3/1

USATestprep Assignment (AP Prep – Continuity & Related Theorems: **Code: WOMATUCERU**) Due Date: Wednesday 3/8

USATestprep Assignment (AP Prep – Derivatives: **Code: JENENETOLU**) Due Date: Wednesday 3/15

USATestprep Assignment (AP Prep – Applications of the Derivative: **Code: RANUPUWAZE**) Due Date: Wednesday 3/22

USATestprep Assignment (AP Prep – Integrals **Code: REFEZEBOHU**) Due Date: Wednesday 3/29

USATestprep Assignment (AP Prep – Applications of Integration )Due Date: Wednesday 4/5

USATestprep Assignment (Mini AB Final Part 1) Due Date: Wednesday 4/19

USATestprep Assignment (Mini AB Final Part 2) Due Date: Wednesday 4/26

**Techniques of Integration**

**Content Vocabulary**

**Integrable Function** – A function for which the definite integral exists. Piecewise

continuous functions are integrable, and so are many functions that are not piecewise continuous.

**Antiderivative of a Function** – A function that has a given function as its derivative.

**Integral of a Function** – The result of either a definite integral or an indefinite integral.

**Indefinite integral** – The family of functions that have a given function as a common derivative. The indefinite integral of *f*(*x*) is written ∫* f*(*x*) *dx*.

**Fundamental Theorem of Calculus (FTC)** – The theorem that establishes the connection between derivatives, antiderivatives, and definite integrals.

**Integrand **– The function being integrated in either a definite or indefinite integral.

**Definite integral **– An integral which is evaluated over an interval. A definite integral is written . Definite integrals are used to find the area between the graph of a function and the *x*-axis. There are many other applications.

**Limits of Integration** – For the definite integral , the bounds (or limits) of integration are *a* and *b*.

**U Substitution** – An integration method that essentially involves using the chain rule in reverse.

**Integration by Parts** – A formula used to integrate the product of two functions.

**Partial Fractions** – The process of writing any proper rational expression as a sum of proper rational expressions.

**Trigonometric Substitution** – A method for computing integrals often used when the integrand contains expressions of the form *a*2 – *x*2, *a*2 + *x*2, or *x*2 – *a*2.

**Suggested Textbook Problems**

**Textbook Solutions**

**Chapter 7 Review Exercises Solutions **

**Differential Equations**

**Content Vocabulary**

**Differential Equation** – An equation showing a relationship between a function and its derivative(s).

**Euler’s Method** – a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value.

**Ordinary Differential Equation** – a differential equation containing one or more functions of one independent variable and its derivatives

**Logistic Differential Equation** – (sometimes called the Verhulst model or logistic growth curve) is a model of population growth

**Textbook Solutions**

**Infinite Series**

**Content Vocabulary**

**Sequence** – A list of numbers set apart by commas, such as 1, 3, 5, 7, . . .

**Bounded Sequence** – A sequence with terms that have an upper bound and a lower bound.

**Series **– The sum of the terms of a sequence.

**Alternating Series** – A series which alternates between positive and negative terms.

**Converge** – To approach a finite limit.

**Diverge** – To fail to approach a finite limit.

**Convergent Series** – An infinite series for which the sequence of partial sums converges.

**Divergent Series **– A series that does not converge.

**Convergent Sequence** – A sequence with a limit that is a real number.

**Divergent Sequence** – A sequence that does not converge.

**Limit Test for Divergence** – A convergence test that uses the fact that the terms of a convergent series must have a limit of zero.

**Integral Test** – A convergence test used for positive series with decreasing terms.

**Comparison Test** – A convergence test which compares the series under consideration to a known series. Essentially, the test determines whether a series is “better” than a “good” series or “worse” than a “bad” series. The “good” or “bad” series is often a p-series.

**Limit Comparison Test** – A convergence test often used when the terms of a series are rational functions. Essentially, the test determines whether a series is “about as good” as a “good” series or “about as bad” as a “bad” series. The “good” or “bad” series is often a p-series.

**Ratio Test** – A convergence test used when terms of a series contain factorials and/or nth powers.

**Root Test **– A convergence test used when series terms contain nth powers.

**Power Series** – A series which represents a function as a polynomial that goes on forever and has no highest power of *x*.

**Derivative of a Power Series** – The derivative of a function defined by a power series can be found by differentiating the series term-by-term.

**Remainder of a Series** – The difference between the nth partial sum and the sum of a series.

**Infinite Series** – A series that has no last term.

**Infinite Geometric Series** – An infinite series that is geometric. An infinite geometric series converges if its common ratio *r* satisfies –1 < *r* < 1. Otherwise it diverges.

**Interval of Convergence **– For a power series in one variable, the set of values of the variable for which the series converges. The interval of convergence may be as small as a single point or as large as the set of all real numbers.

**Nth Degree Taylor Polynomial **– An approximation of a function using terms from the function’s Taylor series. An nth degree Taylor polynomial uses all the Taylor series terms up to and including the term using the nth derivative.

**Nth Partial Sum** – The sum of the first *n* terms of an infinite series.

**P-Series** – A series of the form or , where *p* > 0. Often employed when using the comparison test and the limit comparison test.

**Taylor Series **– The power series in *x – a* for a function *f* .

**Maclaurin Series **– The power series in *x* for a function *f*(*x*).

**Taylor Series Remainder **– A quantity that measures how accurately a Taylor polynomial estimates the sum of a Taylor series.

**Suggested Textbook Problems**

**Textbook Solutions**

**Ch 10 Chapter Review Solutions**

**Parametric Equations**

**and**

**Polar Coordinates**

**Content Vocabulary**

**Parametric Equation** – A system of equations with more than one dependent variable. Often parametric equations are used to represent the position of a moving point.

**Parameter** – The independent variable or variables in a set of parametric equations.

**Parametrize** – To write in terms of parametric equations.

**Polar Coordinates** – A way to describe the location of a point on a plane. A point is given coordinates (*r*, θ). *r * is the distance from the point to the origin. θ is the angle measured counterclockwise from the polar axis to the segment connecting the point to the origin.

**Spiral** – A curve on a plane that turns endlessly outward or inward (or both). Spirals usually have polar equations.

**Lemniscate** – A curve usually expressed in polar coordinates that resembles a figure eight.

**Cardioid** – A curve that is somewhat heart shaped. A cardioid can be drawn by tracing the path of a point on a circle as the circle rolls around a fixed circle of the same radius. The equation is usually written in polar coordinates.

**Limacon** – A famliy of related curves usually expressed in polar coordinates. The cardioid is a special kind of limaçon.

**Polar Rose Curve** – A smooth curve with leaves arranged symmetrically about a common center.

**Arc Length** – The length of a curve or line.

**Suggested Textbook Problems**