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AP Test Prep
College Board

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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AP Test Prep
College Board

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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AP Test Prep
College Board

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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AP Test Prep
College Board

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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AP Test Prep
College Board

2017 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Pupils use the six released free-response questions from an AP Calculus BC exam to prepare for their own exam. The questions cover a range of topics from the BC curriculum, with half of the items coming strictly from AB material and the...
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Handout
Curated OER

Series Review Sheet

For Students 9th - 12th Standards
Save an infinite amount of time and enjoy this pre-made series formula guide. Arithmetic and geometric formulas are all included as well as Pascal's Triangle and examples of how the Binomial Theorem expands. 
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Lesson Plan
Curated OER

Hop To It!

For Teachers 4th - 5th
Students determine patterns. In this mathematics lesson, students act out a skit, play a sequence game, and complete patterns. Students use problems solving skills.
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Instructional Video22:11
2
2
Flipped Math

Series

For Students 9th - 12th Standards
Add it all together. Pupils learn how Gauss was able to add the numbers from 1 to 100 so quickly and arrive at a formula to find the sum of a given number of terms of an arithmetic series. Scholars learn the formula to find the sum for a...
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eBook
Rice University

Precalculus

For Students 11th - Higher Ed Standards
Take a step beyond Algebra 2. Learners use the eBook to learn concepts from the typical Precalculus course. Content starts off with a short review of functions in general and moves on to the basic functions, finishing up with more...
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eBook
Rice University

Intermediate Algebra

For Students 9th - 12th Standards
Algebra concepts are all wrapped up in one nice bow. The resource combines all the concepts typically found in Algebra I and Algebra II courses in one eBook. The topics covered begin with solving linear equations and move to linear...
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AP Test Prep
College Board

Approximation

For Teachers 10th - 12th
Sometimes close enough is appropriate. A curriculum document for AP® Calculus examines the importance of providing approximation questions throughout the course. It looks at approximating derivative values, approximating definite...
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AP Test Prep
College Board

AP® Calculus: Special Focus - Infinite Series

For Teachers 10th - 12th
Read a series to develop an understanding of series. The special focus professional development on infinite series consists of eight articles. Articles contain information strictly for teachers along with aspects to incorporate into the...
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Activity
101 Questions

Super Stairs

For Teachers 9th - 12th Standards
Keep your classes climbing in the right direction. Young mathematicians collect data from a video presentation. Using their data, they build an arithmetic sequence and use it to make predictions.
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Activity
101 Questions

Pixel Pattern

For Teachers 9th - 12th Standards
Any vintage video game users in the room? Young scholars use a video presentation to analyze patterns in pixel arrangements. By writing an arithmetic sequence, they make predictions about the size of the image.
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Activity
Pleasantville Public School

Summer Reading Project

For Teachers 3rd - 4th Standards
Summer means sun, fun, and a good book! Boost scholars' enthusiasm and proficiency in reading with a summer project of their choice—a book jacket, collage, or shoe box diorama. A variety of titles and authors from every genre offers...
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Lesson Plan
West Contra Costa Unified School District

Arithmetic Series

For Teachers 9th - 12th
Fall for a series. Learners determine how to find out how far a skydiver falls in the first 20 seconds. The Algebra II lesson introduces the idea of adding up the terms of an arithmetic sequence. Pupils learn how to use Sigma notation to...
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Interactive
CK-12 Foundation

Arithmetic Series Sums: Adding Arithmetic Sums

For Students 11th - Higher Ed
Sum up the shortcuts. The interactive allows pupils to discover a shortcut in finding a partial sum of an arithmetic series. Learners use the shortcut to find other sums and to verify the process.
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Interactive
CK-12 Foundation

Sequence of Partial Sums: Partial Sums

For Students 11th - Higher Ed
Have some fun building squares out of triangles. Pupils investigate the partial sums of odd numbers. Using the sum of the first four odd numbers, learners see that it can be rewritten as a sum containing a triangular number. Simplifying...
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Interactive
CK-12 Foundation

Sum Notation and Properties of Sigma: Cracking the Code

For Students 11th - Higher Ed
Help your class develop an understanding of sigma notation. Pupils match the sigma notation with the sums. Using the expanded sums, learners evaluate the summations. The scholars move on to prove a property of sums.
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Lesson Plan
Virginia Department of Education

Arithmetic and Geometric Sequences and Series

For Students 9th - 12th Standards
Examine the importance of sequence and series through contextual situations. Here, learners partake in a five-day unit that begins with the basics of arithmetic and geometric sequences and series. As it progresses, pupils apply the...
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Lesson Plan
EngageNY

An Application of Linear Equations

For Teachers 8th Standards
Just how far will the Facebook post go? Lead a discussion on how to manipulate the sum of a geometric series to figure out a formula to find the sum at any step. The plan contains an alternative to the discussion with more accessible...
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Lesson Plan
TryEngineering

Recursion: Smaller Sibling Pyramids

For Teachers 3rd - 6th Standards
Get siblings to do your work. Scholars learn how to perform summations of arithmetic sequences in an innovative lesson. They use iterations, smaller siblings (tail-end recursion), and the divide-and-conquer approach.
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Lesson Plan
EngageNY

The Mathematics Behind a Structured Savings Plan

For Teachers 10th - 12th Standards
Make your money work for you. Future economists learn how to apply sigma notation and how to calculate the sum of a finite geometric series. The skill is essential in determining the future value of a structured savings plan with...
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Handout
Curated OER

Math Handbook: Calculus

For Students 10th - 12th
If only there was a reference that listed all the formulas covered in calculus. Luckily, there is. This comprehensive 197-page handbook provides formulas and explanations for all topics in AP Calculus or in a standard college calculus...