College Board
2016 AP® Calculus BC Free-Response Questions
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...
College Board
2018 AP® Calculus BC Free-Response Questions
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...
College Board
2014 AP® Calculus BC Free-Response Questions
How much of the material is really important? Pupils use the free-response questions from the 2014 AP Calculus BC exam to see how the questions appear. With the supporting material, teachers understand the topics that appear on the test...
College Board
2017 AP® Calculus BC Free-Response Questions
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...
College Board
2011 AP® Calculus BC Free-Response Questions Form B
Take a second look. Form B of the AP® Calculus BC free-response questions allow pupils and teachers to see another set of items. The six questions expand the set of items from the 2011 free-response questions. Form B items include a...
College Board
2010 AP® Calculus BC Free-Response Questions Form B
Keep moving along a curve. Two items in the set of released free-response questions from the 2010 AP® Calculus BC exam involve movement along a graph. One involves particle motion along a polar curve while the other uses a squirrel...
College Board
2009 AP® Calculus BC Free-Response Questions Form B
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...
College Board
2005 AP® Calculus BC Free-Response Questions Form B
Let's put it in context. Pupils use the AP® Calculus BC free-response questions to practice for the exam. Five of the six released items deal with mathematical problems, with one using a real-world situation. Learners use differentiation...
College Board
2002 AP® Calculus BC Free-Response Questions Form B
Though the items may be older, they still provide information. Released free-response items from the 2002 AP® Calculus BC exam provide teachers and pupils with information about how topics appear on the exam. Questions come from the AB...
College Board
2012 AP® Calculus BC Free-Response Questions
Get better prepared. Individuals use the six released AP® Calculus BC free-response questions to practice for the actual exam. The questions contain two calculator items and four non-calculator items. Topics include particle movement,...
College Board
AP® Calculus: Special Focus - Infinite Series
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...
CK-12 Foundation
Sums of Geometric Series
Geometric series either get bigger or approach a single number. So, how do you know which it is? An interactive presents three different geometric series with varying common ratios. With the aid of patterns, pupils determine values of r...
CK-12 Foundation
Limit of a Sequence: Finding the Limit of a Sequence (Part 4)
Take a look at another alternating sequence. The resource provides a graphical display of a sequence that alternates between two values. Pupils use the display to determine whether the sequence has a limit. Given a theory of limit,...
CK-12 Foundation
Limit of a Sequence: Finding the Limit of a Sequence (Part 3)
Limit the view of sequences on both sides of the axis. Learners explore an alternating sign sequence. Using a graphical display of the first 10 terms of the sequence, pupils determine the formula for the general term. they then use the...
CK-12 Foundation
Limit of a Sequence: Finding the Limit of a Sequence (Part 1)
Put a squeeze on a sequence. An interactive provides a graphical display of a sequence. Using the graph, learners determine the algebraic expression for the sequence. Pupils use the general definition of a limit of a sequence to find the...
University of Southern California
What Lives In The Ocean?
One of the most diverse environments on Earth is the ocean. Young scientists explore the living things found in the ocean during an exciting seven-lesson unit. Their study includes organisms from plankton to invertebrates and vertebrates...
Exploratorium
Touch the Spring
Concave mirrors and the images they produce are traditional topics in the physics classroom. This resource explains how to set up an investigation of them, and it provides you with the explanation of concepts.
Curated OER
NUMB3RS - Season 2 - "Convergence" - Air Hockey
Learn how to use a matrix to organize data to solve a problem. This activity uses wins and losses to rank players for an air hockey tournament they wish to have. After practicing some basic matrix operations the class could do the...
Curated OER
Worksheet 39 - Convergence or Divergence
In this convergence worksheet, students use given tests to determine the convergence or divergence of a series. This one-page worksheet contains 30 problems.
Curated OER
Worksheet 38 - Convergence or Divergence
In this convergence worksheet, pupils apply tests to determine the convergence or divergence of a series and identify the limit of a sequence of terms. This one-page worksheet contains four multi-step problems.
Curated OER
Worksheet 4 - function
In this function worksheet, students identify functions, express decimals as fractions and write decimals as a geometric series. This one-page worksheet contains six multi-step problems.
Curated OER
Worksheet 7 - Integral Test
In this integral test worksheet, students use the integral test to determine the upper and lower bounds for a given function. They identify the convergence of a series. This one-page worksheet contains four multi-step problems.
Curated OER
Introduction to Limits
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...
Curated OER
P-Series Handout
In this calculus worksheet, students are given 3 short-answer problems regarding p-series, convergence, and estimating convergent p-series.