Howard Hughes Medical Institute
Population Dynamics
Will human population growth always be exponential, or will we find a limiting factor we can't avoid? Young scientists learn about both exponential and logistic growth models in various animal populations. They use case studies to...
Chapman University
Proof of L’Hospital’s Rule
Understanding how calculus formulas were derived connects learners to the idea that the study of mathematics is continuous and cumulative. Learners will also develop a deeper appreciation for the derivative's application in simplifying...
Curated OER
Indeterminate Forms and L'Hopital's Rule
In this limits activity, students use Taylor's Theorem to solve two short answer problems. They use L'Hopital's Rule to solve two short answer problems. Students read a two page lesson on limits.
Curated OER
Complex Analysis: Harmonic Functions
In this harmonic function worksheet, students explore harmonic functions and construct a harmonic conjugate. This three-page worksheet contains three problems, with explanations and examples.
Curated OER
Complex Analysis: Analyticity and Harmonic Functions
In this harmonic function instructional activity, students summarize the theorems on analyticity, differentiability and the Cauch-Rieman equation. They identify the characteristics of a harmonic function. This three-page instructional...
Curated OER
Exponential Models
Pupils fit a continuous change exponential model to U.S. population data and use the model to predict future population.
Curated OER
Limits and Their Properties
Students discuss the following topics of Calculus: The Tangent Line Problem, The Area Problem, and Exercises. They find limits graphically and numerically. Students write a mathematical autobiography, they write their earliest memories...
Curated OER
Trig Functions
In this trig functions worksheet, students solve and complete 24 different types of problems. First, they find the limits for each trig function given. Then, students find xso that the given infinities series converges. They also find...
Curated OER
Difference of Equations
In this difference of equations worksheet, students solve and complete 49 various types of problems. First, they obtain the solution of any linear homogeneous second order difference equation. Then, students apply the method of solution...
Rice University
Calculus Volume 1
Differentiate between calculus concepts. The beginning of a helpful calculus resource begins with a short review of functions and moves right into limits to define derivatives. The six-chapter resource continues with applications of...
Inside Mathematics
Quadratic (2009)
Functions require an input in order to get an output, which explains why the answer always has at least two parts. After only three multi-part questions, the teacher can analyze pupils' strengths and weaknesses when it comes to quadratic...
Curated OER
Worksheet 5 - Integration
In this integration worksheet, students evaluate the divergence or convergence of improper integrals. They explain limits of functions. In this one-page worksheet, students solve six multi-step problems.
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
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
2012 AP® Calculus AB Free-Response Questions
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...
College Board
2011 AP® Calculus AB Free-Response Questions
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...
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...
Curated OER
Review Questions for Midterm 2
In this review activity, students prove the intersection of finitely of sets, construct increasing functions, and identify characteristics of an open and closed set. This two-page activity contains seven problems.
Curated OER
Calculus Review Worksheet
In this review worksheet, students evaluate given limits. They evaluate graphs. This four-page worksheet contains 27 multi-step problems. Answers are provided on pages three and four.
Curated OER
Definition of the Derivative
Students find the derivatives of functions. In this finding the derivatives of functions activity, students use the definition of derivative to take the derivative of a function. Students discuss scenarios in which the derivative does...
Curated OER
Numerical Analysis: Successive Intervals
In this successive interval worksheet, students find the approximation of a root, using the Bisection Algorithm. They identify intervals, and use algebraic manipulation to identify functions that have a fixed point.
Curated OER
Review of Calculus BC I
In this review worksheet, students match a function to the proper description. they identify the domain of a function. Students determine the slope of an inverse function. They find the derivative of given equations. This two-page...
Curated OER
Graphing Trigonometric Functions
The student should be able to transfer his knowledge of graphing functions to graphing trigonometric functions. Student should be able to graph trigonometric functions, find amplitude, period, and frequency.
Curated OER
Algebra II: Exponential Functions
Students investigate, describe, and predict the effects of parameter changes on the graphs of exponential functions; describe limitations on the domains and ranges of these functions; and examine asymptotic behavior.