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AP Test Prep
College Board

2012 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
What's on the test? Released items provide insight into the AP Calculus test. The six items are split into two groups, two calculator items and four non-calculator items. Resources allow teachers to see what kinds of answers test takers...
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AP Test Prep
College Board

2011 AP® Calculus AB Free-Response Questions

For Students 10th - 12th
So this is the real test? The resource provides the free-response questions from the 2011 AP Calculus AB exam. The six questions are split into two sections, calculator and non-calculator items. Several resources give teachers...
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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

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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Worksheet
Curated OER

Finding the Limit: Piecewise Functions and Graphs

For Students 9th - Higher Ed
This pre-calculus worksheet is short, yet challenging. High schoolers calculate the limit of piecewise functions, rational functions, and graphs as x approaches a number from the positive or negative side. There are four questions.
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Lesson Plan
Curated OER

Introduction to Limits

For Teachers 9th - 12th
High schoolers practice using graphing calculators and spreadsheets as they explore numeric limits using sequences and functions. They complete a sequencing worksheet, and determine which sequence corresponds to story a story called...
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Worksheet
Curated OER

Limits at Infinity

For Students 11th - 12th
In this calculus worksheet, students solve problems dealing with limits at infinity. There are 22 questions with an answer key.
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AP Test Prep
1
1
Flipped Math

Calculus AB/BC Mid-Unit 1 Review: Limits

For Students 10th - 12th
Limit the amount one forgets about limits. A mid-unit review lesson has individuals complete a worksheet of problems on limits. They go over the meaning of limits, evaluate limits algebraically, use graphs and tables to find limits, and...
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AP Test Prep
1
1
Flipped Math

Calculus AB/BC End of Unit 1 Review: Limits and Continuity

For Students 10th - 12th
Test the limits of one's knowledge on continuity. The last of 18 installments in Unit 1 - Limits and Continuity is an end-of-unit review learning exercise. Individuals identify and classify discontinuities, investigate continuity at a...
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Interactive
CK-12 Foundation

One-Sided Limit Type: Limit Notation and Graphs

For Students 11th - Higher Ed
A one-sided limit is no less important than a two-sided limit. Young mathematicians use an interactive to match limit notation to graphs. The exercise requires interpreting how one-sided limits connect to features of graphs.
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Interactive
CK-12 Foundation

Evaluate Limits Using Graphs and Tables: Where Is That Limit?

For Students 11th - Higher Ed
Limits are made easy through graphs and tables. An easy-to-use interactive lets users change a function on a coordinate plane. They relate graphs and tables to the limit at a specific value.
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Interactive
CK-12 Foundation

One-Sided Limit Type: One-Sided Limits

For Students 11th - Higher Ed
Not everything that's one-sided is bad. A slider interactive aids learners in investigating one-sided limits from graphs. A set of challenge questions assesses their understanding of the relationship between one- and two-sided limits.
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Interactive
CK-12 Foundation

Infinite Limit Type: Evaluating Limits of Rational Functions

For Students 11th - Higher Ed Standards
Rational functions become less mysterious when you know about limits. Individuals use an interactive to move a rational function on a coordinate plane and to investigate function values for certain x-values. They see how the limit...
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Interactive
CK-12 Foundation

Evaluate Limits Using Graphs and Tables: Evaluate the Limits

For Students 11th - Higher Ed
Discontinuities in the graph? No worries. Pupils investigate the limit of a function given graphically using an interactive. The graph has removable and jump discontinuities.
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Interactive
CK-12 Foundation

Concept of Limit

For Students 11th - Higher Ed
There's no limit to how useful the resource can be. Scholars use a slider interactive to investigate limits from graphs. They take both one-sided and two-sided limits into consideration.
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Interactive
CK-12 Foundation

Concept of Limit: Limit Notation

For Students 11th - Higher Ed
Limits to infinity are simple to find if you can compare numerators and denominators. Users of the interactive drag expressions to match with their limit as x approaches infinity. A set of challenge questions assesses their groupings.
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Interactive
CK-12 Foundation

Infinite Limit Type: Asymptotes and End Behavior Question

For Students 11th - Higher Ed Standards
There are an infinite number of reasons to use the resource. Scholars drag vertical and horizontal lines to the graph of a rational function to identify all asymptotes. They investigate the connection between asymptotes and limits to...
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Lesson Plan
Shodor Education Foundation

InteGreat

For Teachers 9th - Higher Ed Standards
Hands-on investigation of Riemann sums becomes possible without intensive arithmetic gymnastics with this interactive lesson plan. Learners manipulate online graphing tools to develop and test theories about right, left, and midpoint...
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Worksheet
Curated OER

Calculus Worksheet: Limits of Functions (1)

For Students 11th - 12th
In this calculus worksheet, students determine the limit of the given functions.  The two page worksheet contains four problems.  Answers are provided. 
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Lesson Plan
Curated OER

Intuitive Approach to Limits

For Teachers 11th - Higher Ed
Students identify and comprehend the concept of limit in mathematics. They also view artistic works illustrating limits by M. C. Escher and apply techniques of one-sided limits to graphs of relations. Finally, students compute limits...
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AP Test Prep9:18
1
1
Flipped Math

Calculus AB/BC - Determining Limits Using Algebraic Properties

For Students 10th - 12th
Taking calculus doesn't mean one can forget all about algebra. Viewers of an educational video learn how to determine limits using algebraic properties. They apply basic operations to calculate limits and use substitution to find one-...
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AP Test Prep
College Board

2009 AP® Calculus BC Free-Response Questions Form B

For Students 10th - 12th
Let them eat cake. The free-response questions from an AP® Calculus BC exam cover several topics that include finding the area under a curve within the context of creating a birthday cake. Calculus concepts include finding rates of...
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AP Test Prep
College Board

2003 AP® Calculus BC Free-Response Questions Form B

For Students 10th - 12th
Be integral to the learners in the classroom. Pupils use integrals, differentiation, and limits to solve the free-response questions from an AP® Calculus BC exam. Items cover topics such as area under a curve, particle motion, average...
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AP Test Prep7:18
1
1
Flipped Math

Calculus AB/BC - Defining Limits and Using Limit Notation

For Students 10th - 12th
There's no limit to what one can learn about limits. The second of 18 videos in Unit 1 - Limits and Continuity focuses on understanding the basic concept of a limit. Pupils learn the definition of limits and see how to determine a limit...

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