AP Calculus Projects and Assessments

This is a poster project whereby students create 3-dimensional models of physical objects by using cross sections. Students determine what functions to use for their base regions and the cross sections. They use a spreadsheet to calculate the Riemann sum for their objects and compare their calculations to their integral values. Students have a lot of fun with this project and they get very creative. I recommend that you allow at least 3 weeks for the project and require them to submit their

This assessment (2 versions) contains 11 free response problems (some with parts) and 1 multiple choice question along with answer keys that show step-by-step solutions (where appropriate) with suggested point distributions. Tests are in both PDF and Word form, keys are in PDF form. The tests assess: - Sketching a graph from descriptions of discontinuities - Evaluating limits from graphs and a piecewise function - Sketching a graph from limits - Using limit properties to evaluate limits - Using

This is a poster project for optimization. It's a great way for students to demonstrate what they've learned. Shown are posters that students have made. They were to find a 3-dimensional object (usually a cylinder), take a picture of it, measure its dimensions, and either minimize its surface area or maximize its volume. Attached are the project description and specifications, as well as a scoring sheet. Files are both in MS Word and pdf format.

The Integral Review Quiz contains 3 free response problems (one with 8 parts) along with answer keys that show step-by-step solutions (where appropriate) with suggested point distributions. Quizzes are in both PDF and Word form, keys are in PDF form. The Integral Review Quiz assesses: - Evaluating definite and indefinite integrals using u-substitution and algebraic simplification - Evaluating an integral for a piecewise function The Volume Review Quiz contains 5 free response problems along

The Derivatives Quiz 1 (4 versions) contains 6 free response problems (some with parts) along with answer keys that show step-by-step solutions (where appropriate) with suggested point distributions. Quizzes are in both PDF and Word form, keys are in PDF form. The quizzes assess: - Using the definition of the derivative to differentiate (no shortcuts) - Using the derivative to write the equation of a tangent line at a given point - Using the derivative to write the equation of horizontal tange

These handouts consist of 3 review worksheets and one notes packet, and include answer keys. Files are in both PDF and Word form, keys are in PDF form. The review worksheets cover: - Using the definition of the derivative to find derivatives (no shortcuts) - Finding horizontal tangent using derivatives - Finding equations of tangent lines at given x values - Finding points where the tangent line is normal (perpendicular) - Sketching the derivative given a piecewise graph - Motion problems that

These quizzes help determine if students are prepared for AP Calculus AB at the beginning of the school year. If students were given a summer packet, this is a great way to assess their basic skills. Quizzes are in both PDF and Word form, keys are in PDF form. The Algebra Review Quizzes (2 versions) contain 12 free response problems along with answer keys that show step-by-step solutions with suggested point distributions. The quizzes assess: - Simplifying a complex fraction - Rewriting a ration

This assessment (2 versions) contains 10 free response problems (some with parts) with answer keys that show step-by-step solutions (where appropriate) with suggested point distributions. Tests are in both PDF and Word form, keys are in PDF form. The tests assess: - Finding the derivative using derivative rules (power rule, log rule, exponential rule, product rule, chain rule) - Finding the second derivative using derivative rules - Sketching the graph of the derivative given a piecewise graph

This handout consists of 3 problems with an answer key. Files are in both PDF and Word form, key is in PDF form. The handout provides piecewise graphs of derivative functions and requires students to graph the antiderivative function, given an initial condition.

These worksheets (2 versions) each contain 3 problems where students must sketch a piecewise graph from a given set of conditions (limits and a function value). This gives students practice with determining vertical and horizontal asymptotes, removable discontinuities, and jump discontinuities from limit descriptions. Worksheets are in both PDF and Word form, keys are in PDF form.

This assessment (2 versions) contains 9 free response problems (one with 9 parts) with answer keys that show step-by-step solutions (where appropriate) with suggested point distributions. Tests are in both PDF and Word form, keys are in PDF form. The tests assess: - Evaluating direct and indirect integrals with some requiring algebraic simplification and u-substitution and one involving a piecewise function - Evaluating an integral using a graph - Finding the area of a bounded region - Finding

The Derivatives Quiz 4 (4 versions) contains 4 free response problems (one with 7 parts) along with answer keys that show step-by-step solutions (where appropriate) with suggested point distributions. Quizzes are in both PDF and Word form, keys are in PDF form. The quizzes assess: - Using derivative rules to find derivatives (power rule, product rule, quotient rule, multiple uses of chain rule, log rules, exponential rules, trig rules, inverse trig rules) - Using the derivative to write the eq

The Derivatives Quiz 3 (4 versions) contains 3 free response problems (one with 12 parts) along with answer keys that show step-by-step solutions (where appropriate) with suggested point distributions. Quizzes are in both PDF and Word form, keys are in PDF form. The quizzes assess: - Using derivative rules to find derivatives (power rule, product rule, quotient rule, multiple uses of chain rule, log rules, exponential rules, trig rules) - Using the derivative to write the equation of a tangent

The Derivatives Quiz 2 (4 versions) contains 7 free response problems (some with parts) along with answer keys that show step-by-step solutions (where appropriate) with suggested point distributions. Quizzes are in both PDF and Word form, keys are in PDF form. The quizzes assess: - Finding displacement, velocity, acceleration, when a particle stops, moves right/left, speeds up, slows down from the particle function - Using the derivative to find where a tangent line is perpendicular to a given

The Limits Review Quizzes (4 versions) contain 10 free response problems along with answer keys that show step-by-step solutions (where appropriate) with suggested point distributions. Quizzes are in both PDF and Word form, keys are in PDF form. The quizzes assess: - Determining eight limits using algebraic simplification, end behavior reasoning, and numerical analysis - Sketching a piecewise graph and finding limits - Sketching a graph from limits

The Differential Equations and Slope Fields Quiz (2 versions) contains 4 free response problems (some with parts) along with answer keys that show step-by-step solutions (where appropriate) with suggested point distributions. Quizzes are in both PDF and Word form, keys are in PDF form. The quizzes assess: - Finding particular solutions to differential equations - Drawing slope fields - Establishing a relationship between an amount and its rate, solving for a particular solution, and then usin

The Integral Quiz (2 versions) contains 4 free response problems (one with 6 parts) along with answer keys that show step-by-step solutions (where appropriate) with suggested point distributions. Quizzes are in both PDF and Word form, keys are in PDF form. The quizzes assess: - Evaluating direct and indirect integrals using algebraic simplification, power rule with linear "inside" function, trig, and natural logs (no u-substitution required) - Sketching and finding a bounded area - Sketching

The Critical Points Quiz (2 versions) contains 2 free response problems (one with 8 parts) along with answer keys that show step-by-step solutions (where appropriate) with suggested point distributions. Quizzes are in both PDF and Word form, keys are in PDF form. The quizzes assess: - Finding maxima/minima, intervals of increase/decrease, inflection points, intervals of concave up/down, and sketching a graph of the function - Sketching the graph of f(x) given a graph of its derivative