BC Calculus Exams & Quizzes

This page provides FREE OF CHARGE a set of BC Calculus exams and quizzes as a resource for Teachers (see table below).


For purchase are:
 
BC Calc Exam Answers: Download
Full set of Answer Keys as a download.  Only $44.95		   
BC Calc Exams: Paper
Full set of Exams in printed form.  Only $24.95 + $5 shipping 		   
BC Calc Exam Answers: Paper
Full set of Exam Answer Keys in printed form.  Only $54.95 + $5 shipping 		   

 

Do you want the BC Calculus Solutions in combination with other MasterMathMentor products?  Click here for our comprehensive price list.
             

OVERVIEW:

Over the years, I have developed many exams and of course, they change from time to time. I am not one of those teachers who allow the students to see their exams for just a few minutes. I believe that because they will be taking the A.P. exam, they need to have these exams from which to study.


My exams take several forms: quizzes, exams, and take-home exams. Quizzes and exams differ in terms of quantity of problems, time given, and point value. Take-home exams are what they seem to be – students are given the exam, take it home to complete, and bring it back the next day. I take a risk when giving such an exam – the risk being that students will talk about the problems and get help on problems they cannot do. Students are warned of the consequences of blatantly copying from someone else. But, between you and me, I am not tremendously upset if students end up talking and even arguing about problems. The fact that they are discussing calculus is, to me, a positive sign, and the point value of a take-home exam is not so great that it will dramatically improve the average of a student. I am fully aware of the dangers of a take-home exam but there is not way I can stop students from talking. I give these exams infrequently, mostly to gain a bit of time (an in-class exam takes up an entire day), but I also like to give students a way to raise their averages a bit.


I am one of those teachers who return exams immediately and students appreciate the quick feedback. I look at an exam as a learning experience and a way for them to gauge how well students have mastered information. Still, going over exams can take a great deal of time, time that is at a premium in an A.P. course. To that end, I give a solution key to the students for every exam. We will still go over problems that the class in general had trouble with but students are asked to compare their exams to the solution key to understand their errors. The solution key is just that – not just a set of answers but the process used to solve each problem.


Occasionally, I will give a practice test a day or two before in similar format to the actual exam. Students use this to determine whether or not they understand the material.


Whether or not I give a practice test, the quizzes and exams are quite similar to the manual the students have. There are few tricks nor problems asking students to be clever. I want the students to be able to do the basic problems in calculus, finding limits, derivatives, indefinite, and definite integrals as well as the basic applications of each.  My course usually ends one month before the A.P. exam and we spend that month reviewing old released exams and many previous free response problems. It is during that times when we look at the “clever” concepts – the concepts that I rarely test during the school year. Students who have the basic concepts of calculus down do well with these difficult problems and do well in the A.P. exam as their scores indicate (see the About Us) page to view these scores.


You are free to use any or all of these exams. You are also free to white-out the website at the bottom of each page. You can come up with the answers yourself or purchase the full set of solutions yourself.

 

And, as of February 25, 2011 these exams have been updated and 11 problems similar to free response questions in past AP exams have been added. I suggest that you take the time to re-download the exams and if you ordered the solutions, I will have gotten in touch with you to provide you with the links.

 

DOWNLOAD BC CALC EXAMS - FREE!

 

Topic
Content
(file size: 212KB)
Algebraic (linear only) problems where epsilon is given and delta is found. Non linear problems are done via calculator.
(file size: 924 KB)
BC Calculus involves some reviewing ate first. I combine transformations. Continuity, differentiability, basic limits with the major thrust – l’Hopital’s rule,
(file size: 644 KB)
Marginals are tested as well as Newton’s method (without calculator) and estimation with differentials.
(file size: 184 KB)
Left, right, midpoint rectangles are tested along with the trapezoidal rule and Simpson’s method.

04a. Riemann SUM AP Type - NEW!

(file size: 687 KB)

 An AP Type problem that emphasizes the midpoint and trapezoidal rule as well as the meaning of these approximations.
(file size: 1500 KB)
Given a piecewise curve, students are asked to find definite integrals between various values utilizing geometric formulas. Also, examine the accumulation function based on this graph. Answers included.
(file size: 684 KB)
Same as above but without answers.
(file size: 200 KB)
Disk, washers, shells, arc length and surface area are tested.

07a. Area Volume AP Type  - NEW!

(file size: 128 KB)

 An area/volume function using a natural log function. Calculators permitted.
(file size: 1 MB)
A 27-question multiple choice exam testing all concepts up through volume, arc length, and surface area
(file size: 76 KB)
Work problems are hard for students so these are tested separately.
(file size: 448 KB)
This exam tests not only work but fluid force and center of mass. Answers included.
(file size: 184 KB)
Same as above but without answers.
(file size: 372 KB)
Much of this material is a review from AB calculus but it is vital that students be able to take derivatives and integrals using the ln function and exponentials.
12a. Differential Eq. AP Type - NEW! A related rates problem that turns into a DEQ problem.
(file size: 340 KB)
u-substitution, integration by parts, powers of sines and cosines, partial fractions and improper integrals are tested.
13a. Integration Techniques AP Type - NEW! A problem with the major work being integration by parts.
13b. Integration Techniques AP Type - NEW! An area/volume problem using u-substitution and also improper integrals.
(file size: 364 KB)
Students must make and interpret slope fields, use Euler’s Method to estimate numerical solutions to DEQ’s and solve a logistic growth problem.
14a. Slope Field Euler's Method AP Type - NEW! A slope field/Euler's Method problem that asks students to remember local linearity and concavity.
(file size: 1.9 MB)
Time to put all it all together with a big exam. This is a 37 question multiple choice exam testing all concepts through logistic growth. Two sections, one with calculator and one without.
(file size: 368 KB)
A small quiz testing knowledge of derivatives and integrals using inverse trig functions as well as finding the derivative of an inverse relation at a given point.
(file size: 180 KB)
Parametric equations, points of tangency, horizontal and vertical tangents, arc length and surface area of revolution.
(file size: 176KB)
5 problems each having 4 variations is good for a take-home quiz on polar equations. Horizontal and vertical tangents, arc length, and surface area of revolution are tested. Calculators needed.
18a. Polar Equations AP Type - NEW! Derivatives of polar curves along with area. Students better know sine and cosine of special angles.
(file size: 484 KB)
Vector addition, dot products, vector-valued functions, derivatives and integrals and velocity and acceleration.
19a. Vectors AP Type - NEW! A motion problem along a curve. Speed, acceleration, and position need to be computed. Calculators allowed.
(file size: 164 KB)
4 problems asking students to generate Maclaurin or Taylor polynomial approximations of functions and determine the error in using such.
20a. Taylor Polynomials AP Type - NEW! Students are given a Taylor polynomial for f and asked to find derivatives. The second derovative test will be needed for local etrema and the dreaded Lagrange error needs to be computed.
(file size: 440 KB)
Series is a big topic so I have a test that tests about half of it – convergence and divergence of sequences and series using some basic tests..
(file size: 1.1 MB)
This tests convergence and divergence using all tests. Answers are included although there are more than one way to prove convergence for many of them. Answers included.
(file size: 424 KB)
Same as above but without answers.

23a. Series AP Type - NEW!

 

 A typical AP type problem involving finding the interval of convergence. Also the second derivative test is used.
23b. Series AP Type - NEW! This AP type problem uses manipulation of the Taylor seies for cos(x), finding general terms, and convergence interval.

 
 
Do you want the BC Calculus Solutions in combination with other MasterMathMentor products?  Click here for our comprehensive price list.
             
 
Also check out our Calculus Clue Game - a great way to prepare for the AP Exam or 
end of the year final exam.   Click here for details.