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#### Calculus AB/BC - Determining Concavity of Functions over Their Domains

For Students 10th - 12th
Time to take a second look at derivatives finding concavity. While watching the video, learners find out the definition of concavity. Individuals see how to determine whether an interval is concave up or concave down using graphs and the...
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#### Civic Knowledge and Action: Voter Registration

For Teachers 10th - 12th Standards
What does the data say? Using provided voter data from the 2016 presidential election, scholars describe the data and identify questions they could answer by analyzing it. Learners then construct tables and use them to determine whether...
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#### Calculus AB/BC - Derivatives of tan(x), cot(x), sec(x), and csc(x)

For Students 10th - 12th
Continue to differentiate the rest of the trigonometric functions. Pupils see the derivatives of the other four trigonometric functions and begin to memorize the rules. Learners see examples that show that the calculus portion of a...
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#### Calculus AB/BC - The Quotient Rule

For Students 10th - 12th
Some differentiation rules are just better to memorize. The ninth lesson in a unit of 11 presents the quotient rule to pupils for them to memorize. Learners use the quotient rule to determine the derivative of two quotients after seeing...
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#### Calculus AB/BC - The Product Rule

For Students 10th - 12th
There's more to derivatives of multiplication than simply the product of the derivatives. A helpful video gives learners the product rule of finding the derivative of the product of two functions. Pupils find the derivatives of functions...
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#### Calculus AB/BC - Derivatives of cos(x), sin(x), e^x, and ln(x)

For Students 10th - 12th
The shortcuts are not just for polynomial functions. Pupils learn the derivatives of the two basic trigonometric functions, cosine and sine. The video provides the derivatives for exponential and logarithmic functions. Learners work...
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#### Calculus AB/BC - Derivative Rules: Constant, Sum, Difference, and ​Constant Multiple

For Students 10th - 12th
Use derivatives to find equations of lines. Pupils learn more rules to use as shortcuts to find derivatives. Using the rules, they find the equations of the tangent line and the normal line at a given point. Scholars then apply the new...
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#### Calculus AB/BC - The Power Rule

For Students 10th - 12th
There has to be a quicker way. Pupils learn the power rule that allows for a shortcut to take the derivative of terms to a power. Using the newly found rule, scholars find the slope of the tangent line to a function at a given x value....
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#### Calculus AB/BC - Connecting Differentiability and Continuity

For Students 10th - 12th
Despite what you thought, you can differentiate between continuity and differentiability. Using a short lesson, pupils learn how differentiability and continuity relate to each other. It provides three descriptions of when a function is...
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#### Calculus AB/BC - Estimating Derivatives of a Function at a Point

For Students 10th - 12th
It seems like it should be about three. Pupils learn to get an estimate of the derivative of a function at a point by using the derivative functionality of their graphing calculators. They take that information to determine the equation...
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#### Calculus AB/BC - Defining the Derivative of a Function and Using Derivative Notation

For Students 10th - 12th
Pupils learn how to find the derivative of a function by applying the definition using limits. Learners understand that the derivative provides the slope of the tangent line and use that information to find the equation of the tangent...
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#### Calculus AB/BC - Average and Instantaneous Rate of Change

For Students 10th - 12th
Ramp up the average rate of change—instantly. Learners use their knowledge of the formula to find the average rate of change to find the instantaneous rate of change. The presenter shows pupils an interactive that demonstrates finding...
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For Teachers 9th - 12th Standards
How high will it fly? Pairs build straw rockets and launch them at different angles and determine the height and horizontal distance of the flight path. Teams make conjectures about how the angle affects the measured distances and use...
Performance
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#### Projectile Motion and Quadratic Functions

For Teachers 9th - 12th Standards
Model the flight of a ball. Small groups collect time data for how long it takes to toss a ball between two people. The teacher leads a discussion about projectile motion to get the class thinking about how to calculate the equation of...
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#### 2009 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Dive into the exam review. Pupils use questions, including one about diving into a pool, to prepare for the AP® Calculus BC exam. Items include contextual and non-contextual questions with contextual examples requiring a calculator....
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#### 2007 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Provide a review for the exam so individuals don't tank. AP® provides the free-response questions for teachers to use to help their pupils prepare for the exam. The six BC questions from 2007 include regions bounded by functions, water...
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#### 2009 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
What was one of the big takeaways from 2009? By reviewing the released AP® Calculus free-response questions, pupils and teachers realize that performing mathematics is not all there is to doing well on the exam. Several items require...
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#### 2007 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Grow your knowledge of Calculus AB. Items released from the 2007 AP® Calculus AB exam provide information to teachers about the importance of particular topics. Pupils use the questions to gain an understanding of ways the exam assesses...
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#### 2006 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
Develop more than just a topical approach to the exam. The six free-response questions from 2006 reveal how the AP exam assesses topics. By using the questions, pupils practice topics such as velocity, sketch slope fields, solving...
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#### 2015 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
How will the exam ask this question? The free-response questions from the 2015 AP Calculus BC exam demonstrate how questions appear on the test. Using the questions, pupils gain experience answering similar inquiries to what they see on...
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#### 2013 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Apply the skills to problems to ace the AP test. Free-response questions require scholars to take calculus skills and apply them to situations. Pupils use the questions to see how those situations appear on an upcoming exam. Teacher use...
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#### 2016 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
The split is 50-50. Released free-response questions from the 2016 AP Calculus BC show that half the questions are from the AB portion of the course and the others are from the BC portion. Teachers and pupils use the items to prepare and...
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#### 2018 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Don't just rely on the textbook. Released items from the AP Calculus BC provide pupils and teachers insight on how topics appear on the exam. The six items are divided into calculator and non-calculator sets with half of them also...
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#### 2017 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
What is the answer to this question? Pupils use six questions to practice for the AP Calculus AB test. The review questions are divided in two sections, calculator and non-calculator. Additional resources allow teachers to determine how...