 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 straigh tforward, 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

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 9/5/19 Limits - Graphical    Limits - Algebraic    Derivative Definition L'Hospital's Rule    Integration by Parts    Partial Fractions 9/19/19 Differentiation Techniques    Trig Differentiation    Chain Rule Improper Integrals    Arc Length    Euler's Method 10/3/19 Implicit Differentiation     Transcendental Functions     Derivatives of Inverses 10/17/19 Linear Approximations    Continuity/Differentiation    Related Rates Logistic Growth    Parametric Equations    Polar Equations 10/31/19 Straight-Line Motion    3 Important Theorems    Function Analysis Vector-Valued Functions    Vectors and Motion    Taylor Polynomials 11/14/19 Absolute Extrema    Optimization    L'Hospital's Rule 12/12/19 Indefinite Integrals    u-Substitution    Definite Integral as Area Infinite Series    Series Convergence    Error Bounds 1/2/20 Accumulation Function    Riemann Sums    Fundamental Theorem Power Series    Taylor & Maclaurin Series    Manipulation of Series 1/16/20 Integrals & Substitution    Integration w/Transcendentals    Integration and Motion 1/30/20 Average Value and 2nd FT    Inverse Trig Integrals    Area 2/13/20 Volume of Revolutions    Applications of Integration    Slope Fields 2/27/20 Separable DEQs    Exponential Growth    Other Growth Models

Calculus Conundrums Solutions