College Board
2017 AP® Calculus AB Free-Response Questions
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...
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...
College Board
2018 AP® Calculus AB Free-Response Questions
Pupils interact with six released questions from the 2018 AP Calculus AB exam. Teachers use the additional materials to determine where the class is in terms of readiness for the exam to help provide additional instruction as needed.
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...
Curated OER
Properties of the Definite Integrals
In this math instructional activity, students investigate the properties of definite integrals. Then they apply the properties and compare sets of two integrals to each other.
Curated OER
The Fundamental Theorem of Calculus and Properties of the Definite Integral
Students discuss the importance of fundamental theorems in math. In this calculus lesson, students define the fundamental theorem of calculus and discuss why it is so important they understand it. They work problems to model how this...
Curated OER
Integrals with Secant Powers of Secant Tangent
Twelfth graders integrate trig functions with even powers. In this calculus lesson plan, 12th graders apply their knowledge of trig functions to help them integrate tangents and secants containing even exponents. They integrate the...
Curated OER
Integration By Parts
in this math worksheet, students read the example for the product rule. Then they apply the rule individually or in groups to the following integrals.
Curated OER
Basic Calculus II: Quiz 7
In this improper integrals worksheet, students explain the reasons each of three integrals may be considered improper. They evaluate each by determining if it converges to a number or diverges.
Curated OER
Basic Calculus II: Numerical Integration
In this numerical integration worksheet, students approximate the value of an integral using the methods taught in the class. They use left-hand Riemann sums, right-hand Riemann sums, the midpoint method and the trapezoidal rule.
Curated OER
Basic Calculus II: Fundamental Theorem of Calculus
In this fundamental theorem instructional activity, students find the antiderivative of a function. This two page instructional activity contains five multi-step problems.
Curated OER
Basic Calculus II: Quiz 8
In this infinite series worksheet, students use comparisons to determine convergence for improper integrals. They use the integral test for infinite series. Students state the reasons they believe a given integral is converging or...
Curated OER
Little Red Corvette
Learners investigate the acceleration of a car. In this acceleration of a car instructional activity, students make a scatter plot of corvette acceleration data. Learners find a model to fit the data by taking the integral of...
Curated OER
Basic Calculus II: Techniques of Integration
For this differentiation worksheet, students select from a list of differentiation rules which one they have to use to find the derivative of the given equation. They evaluate one integral exactly.
Curated OER
Applying the Fundamental Theorem of Calculus
In this fundamental theorem learning exercise, students identify the anti-derivative and write equations as an explicit function. This two-page learning exercise contains two multi-step problems.
Mathematics Vision Project
Quadratic Equations
Through a variety of physical and theoretical situations, learners are led through the development of some of the deepest concepts in high school mathematics. Complex numbers, the fundamental theorem of algebra and rational exponents...
Curated OER
Using Riemann Sums
In the Riemann sums instructional activity, students use Riemann sums to estimate the area under a curve. They calculate intervals and subintervals. Students create a graph picturing the intervals. This seven-page instructional...
Curated OER
Lab 2: Euler's Method and Riemann's Sums
In this Euler's Method and Riemann's Sum activity, students identify the best situation in which to use Euler's Method and Riemann's Sum. They identify the initial value of a problem and use the accumulation formula to determine the...
Curated OER
Worksheet 28 - Spring 1996
For this math worksheet, students examine the graph in polar coordinates of r = f(θ). Then they sketch a graph of the modified functions indicated.
Curated OER
Worksheet 10
In this math activity, students examine the concepts of upper division mathematics. They include linear operator, homogeneous, characteristic equation, fundamental solution set (solution basis), principle of superposition, Wronskian,...
Trinity College Dublin
History of Mathematics: Bonaventura Cavalieri (1598 1647)
A biography of Cavalieri that includes information on his principle or "indivisibles." From a 1904 text by W. W. Rouse Ball.