Calculus Conundrums 


Do you know what a Rube Goldberg machine is? It is a contraption or apparatus that uses a chain reaction to accomplish a very simple task in a complicated manner.  For instance, look at the cartoon to the right.  For Fanucci to get his cat treats, he pulls the rope which releases a ball which goes down the ramp and falls into the tube. The ball hits the switch which extends the punching bag into the target which shakes the bag of cat treats which fall down the chute and into Fanucci's mouth (and the ball goes to the bottom of the tube and attaches to the elevator which takes it back up to the top of the ramp).


Calculus Conundrums operates along the same principal. It is a series of quizzes, each with 9 open-ended calulus questions. The answer to any question becomes an input to the next question.


For instance, suppose question 1 asks for the derivative of 5x2 + 7x - 1 at x = -1.  If the answer to this question is A, question 2 might ask the speed of a particle traveling along the x-axis whose position is t cos (At) - sin (At) at t = A.  Obviously you can't get question 2 correct unless you know the value of A.


So in order for a student to get the 9th problem correct, he/she must get the 8th problem correct. And thus get the 7th problem correct. And so forth - like a Rube Goldberg machine.


Calculus Conundrums will initially be distributed as a subscription. If you are a member of MasterMathMentor, you will automatically receive the student version of Calculus Conundrums every two weeks according to the table below. Each exam is comprised of 9 questions which follows the order in our AP® Calculus Manual. Each question does not require any information which is taught further in the course meaning you can give these exams along the way.


The problems are of medium difficulty. Most problems are relative straightforward, have numerical answers, and test the basic concepts of the AP® curriculum. A student who eventually gets every problem correct is destined to to well in the AP® exam. The quizzes were built for even weaker students to achieve success.


The Calculus Conundrum student versions are free. The solutions are available for purchase.  With the solutions (that show all the necessary work to solve the problems), you receive a smart Excel spreadsheet that will use colors to indicate whether an answer is correct, incorrect, or not attempted. You are free to send this spreadsheet to students so they can do problems at home.  You also receive the AB student version as two separate quizzes - one for derivatives and one for integrals, each giving a Rube Goldberg machine with 54 questions. So rather than giving these quizzes every couple of weeks, teachers can give them when completing the derivative section and integral section, making it terrific for practicing for the AP® exam.



Calculus Conundrums Solutions

Calculus Conundrums AB Solutions:

Web Download Version

This purchase will provide you with Calculus Conundrums AB Soutions as downloadable files (PDF format - 13 mb and Excel file - 1 mb).

Only $23.95

Calculus Conundrums BC Solutions:

Web Download Version

(Not yet available)

This purchase will provide you with Calculus Conundrums BC Soutions as downloadable files (PDF format - 13 mb and Excel file - 1 mb).

Only $12.95

Calculus Conundrums AB/BC Solutions:

Web Download Version

(Not yet available)

This purchase will provide you with Calculus Acrostic AB and BC as downloadable files (PDF format - 12.5 mb).

Only $33.95


Free Student Versions


Below are the topics for each set of quizzes.  On the given date, teachers in the MMM community will receive an email with links to the quizzes. Also, the quizzes below will change to links and teachers can download them from here so there is no need to keep the original email.


Date AB Link and Topics BC Link and Topics

Quiz 1

   Limits - Graphical

   Limits - Algebraic

   Derivative Definition

Quiz 1

   L'Hospital's Rule

   Integration by Parts

   Partial Fractions


Quiz 2

   Differentiation Techniques

   Trig Differentiation

   Chain Rule

Quiz 2

   Improper Integrals

   Arc Length

   Euler's Method


Quiz 3

    Implicit Differentiation

    Transcendental Functions

    Derivatives of Inverses




Quiz 4

   Linear Approximations


   Related Rates

Quiz 3

   Logistic Growth

   Parametric Equations

   Polar Equations


Quiz 5

   Straight-Line Motion

   3 Important Theorems

   Function Analysis

Quiz 4

   Vector-Valued Functions

   Vectors and Motion

   Taylor Polynomials


Quiz 6

   Absolute Extrema


   L'Hospital's Rule


Quiz 7

   Indefinite Integrals


   Definite Integral as Area

Quiz 5

   Lagrange Error

   Series Convergence



Quiz 8

   Accumulation Function

   Riemann Sums

   Fundamental Theorem

Quiz 6

   Power Series

   Taylor & Maclaurin Series

   Manipulation of Series


Quiz 9

   Integrals & Substitution

   Integration w/Transcendentals

   Integration and Motion


Quiz 10

   Average Value and 2nd FT

   Inverse Trig Integrals



Quiz 11

   Volume of Revolutions

   Applications of Integration

   Slope Fields


Quiz 12

   Separable DEQs

   Exponential Growth

   Other Growth Models