Slip-Sliding Away (8/11/22)
Should baseball players slide into first-base rather than running straight through? That question is answered using AP calculus AB. A neat little study that includes a sample AP free response question based on that problem including solution and suggested grading. Free.
Slip-Sliding Away download
Calculus from 33,000 Feet (7/28/22)
Based on the book Infinite Powers by Steven Strogatz, I wrote an addendum to the AB Calculus manual. This is meant for students to read after they completed the AP exam. It looks at calculus as a forest rather than a bunch of trees involving formulas and theorems. I liken it to reading a book, watching a movie, or viewing a sports event when you need to know the result. But then you want to reread or rewatch it to see all the detail that you may have missed. It is not meant for the student just wanting to get a high grade but those who are truly interested in calculus.
Calculus from 33,000 Feet is now part of the AP manual as a free addendum and consists of 4 parts that can be downloaded from the AB Calculus page or below. They will take about 30 seconds to download.
AB Calculus Manual
. Limits and the Infinity Guideline
. Derivatives as a Measure of Change
. Infinitesimals and Differentials - Smaller than Smallest
. Integrals as an Accumulation of Change
Everyone is playing WORDLE, the wonderful word game now on the New York Times website. Students can now try their hand at DIGITLE. This easy-to-play game uses digits (and sometimes letters) and puzzle answers are based on the answers to math questions. Just like the real game, students enter their answers and are told which characters are correct and in the correct position. DIGITLE is completely free to play and students can play it on their phones and share their results with others.
AB Calculus with 32 puzzles, each with 6 questions covering the entire range of the course is complete. BC Calculus with 15 puzzles along with the SAT/ACT version with 20 puzzles are complete as well. AP Statistics is ongoing with new puzzles added every few days.
Try it. You will be addicted. Click on the links below to get puzzles.
DIGITLE AB Calc DIGITLE BC Calc DIGITLE SAT/ACT
DIGITLE AP Statistics (In Progress)
Once students have solved the math problems, they use the link below to play DIGITLE.
Nuclear Containment (6/23/21)
MMM's Escape Room
Before the pandemic, Escape rooms were all the rage. A group of friends would go into some venue, pay some money, and get locked in a room with clues about how to escape. Some of them even had themes to them - like a haunted house or a gangster hideout.
I decided to create an escape room based on mathematics. It is called Nuclear Containment. Students and their friends tour a nuclear energy facility when one of the technicians runs amuck, threatening to flood the immediate area with radiation. It is up to the students, working together, to determine a code that will be input to a computer that will stop the destruction. And to do that, they have to solve clues that are given in terms of math problems. There are 16 clues in all, each containing 5 or 6 math problems. All problems must be solved correctly to get the next clue. And once all the clues have been solved, some ingenuity will be needed to create the special code.
Nuclear Containment is available in AB Calculus, BC Calculus, AP Statistics, Precalculus, and SAT math. It is available as separate games or together. The game is free although there is a charge for the worked out solutions. It requires either Microsoft Excel or Google Sheets (if you have a Gmail account, you have Google sheets). Nuclear Containment is a wonderful way to get students working together again after over a year of learning on their own. Available now.
Click Here to download and get more information:
Super Free Response Questions (2/15/21)
To really test all aspects of a typical free response problem situation, we have developed super free-response questions with not the usual 4 sub-parts but around 15. They test every conceivable question that can be asked so students have a sense of what they know and don't know. Included are student versions, solution versions, and a YouTube video for each question that describes in detail the nuances of solving these problems. All completely free. They are complete: 6 in AB and 4 in BC. Click the link for more details.
Let Me Help Teach Your AP Calculus Class!
YouTube Videos (8/1/2020)
In the largest project MMM has ever tackled, we are providing free YouTube videos for the entire AB Calculus AB and BC manuals that go hand-in-hand with the classwork sections. These videos has me teaching the material, explaining the concepts, and doing most of the example problems. This is being done to help teachers teach virtually because of COVID-19.
We are not doing this to replace teachers. That will never happen. But these videos will give support to teachers. It allows them to have students initially taught how to take derivatives and integrals and tackle all sorts of calculus problems, while leaving their teachers to go over homework problems and reinforce what the videos emphasize.
All the videos in the Essentials and Non-Essentials section of the manual are complete in both AB and BC. Get more information on this exciting project by clicking the links below.
AB Manual YouTube Videos
BC Manual YouTube Videos
Here is my YouTube channel:
COVID-19 SUPPORT FOR TEACHERS AND STUDENTS
I was both concerned and fascinated about COVID-19 when it was just a small story about an outbreak in China in early 2020. Both, because teaching calculus has allowed me to understand the frightening power of exponential growth. As the outbreak grew larger and larger, attacked the world and then the U.S. and turned our way of living on its head, I decided that the best use of my quarantine time was to help teachers. These are the people who are tasked with preparing students for the AP Calculus or AP Statistics exam, despite not even finishing the teaching part of the course and never seeing the students face to face.
In the past 40 days, I have written 20 free response questions and 160 true/false questions in calculus and statistics, all covering topics that will be tested, all with a grading spreadsheet, all with solutions, and all completely free.
I am not on the front lines helping those amazing people in hospitals, in supermarkets, food banks, and keeping order. But I am doing my part to help the teachers and students, many of whom are at a loss right now. Please download any and all of the material below with my compliments and please stay safe. We will get through this.
Practice AP Stat True/False Exam (4/24/20)
In my attempt to communicate directly with students to help them prepare for the revised AP Statistics exam which will be administered on May 22, I have put together a free 50-problem stat true/false exam in which the questions are intended to be answered in a minute or less. Included is a grading Excel spreadsheet which will allow students to track their strengths and weakness. Click on the link for information.
Practice AB and BC True/False Exam (4/13/20)
In my attempt to communicate directly with students to help them prepare for the revised AP Calculus exam which will be administered on May 12, I have put together a free 60-problem AB true/false exam in which the questions are intended to be answered in a minute or less. Included is a grading Excel spreadsheet which will allow students to track their strengths and weakness. Just added: the free BC exam is 50 questions and is now available. Click on the link for information.
Revised AP Exam Review (3/23/20)
With much of the world in lockdown, the College Board is electing now to revise the AP exam. I think that this is ultimately a good move as it will keep you and the students busy and give them a reason to go on in this very depressing and scary moment. I have been hard at work in constructing sample questions that hopefully will be similar to the types of questions that will be asked. And it is all free, solutions as well. My way of adding to the community effort to support each other. Both AB and BC are now available. Click on the link to see the wealth of materials you are now offered.
Flattening the Curve (3/18/20)
The world has changed radically because of the coronavirus with many of us self-quarantining and school is cancelled, maybe for quite awhile. We are told to practice social distancing for the purpose of "flattening the curve." What does that really mean? We look at the concept in terms of normal bell-shaped curves. Download a document that looks at flattening the curve for students with different mathematical backgrounds. The statistics student will approach it from their study of normal distributions while the calculus student will tackle it with generating equations to describe the growth of the virus and using integrals and derivatives. There are 10 problems which compare the virus growth in countries that don't social distance as opposed to those who do. For teachers who are providing on-line learning, this document allows you to review basic concepts from AP stat and AP calc while having the student understand why it is so important to stay at home. Completely free. Click on the link to download and feel free to share it with students.
Looking at Coronavirus Mathematically (2/1/20)
A rare mathematical analysis of a world crisis as it happens before our eyes. If you have students who are taking precalculus or above, they can understand this article that will be constantly updated as the number of virus case increases in China. There is also a section that investigates a mathematical variable (R0) describing the spread of infectious diseases like Coronavirus. Also, I take a look at the number of recovery cases as well as deaths. Late in the study, there is a necessity to use a piecewise function to describe the growth. I now look at the cases outside of Mainland China. Click on the link to download. (Updated 3/107/20)
A separate document now focuses on the effect coronavirus is having in the United States. lick on the link to download. (Updated 3/10/20)
Addition to AB Calculus Manual (12/15/19)
In the Non-Essential section of the AB Calculus manual (student and solution), we added two pages in the study of differentials. It shows how differentials can be used to develop the product and power rule. Go to the AB Calculus page and you can download the student versions (this affects the page number of this file and the review file). If you purchased solutions, contact me at email@example.com and I will send you links.
Optical Illusions (10/10/19)
New to MasterMathMentor is a set of 64 optical illusions presented in Powerpoint documents. They are perfect for filling in that last couple of minutes of a class when you finish the lesson early. Kids will be mesmerized by them and the genius it took to discover them. Best of all, they are free to all. Click on the link for more information and the download links.
Dorian and Me (9/4/19)
See how I sweated out the coming of Hurricane Dorian in South Florida ... by constructing a calculus problem that dealt with its closest possible approach to my home. Show it to your students for them to understand how calculus can be used to solve real-life problems and make perhaps life-saving decisions. Cick on the link.
Calculus Conundrums (8/1/19)
Calculus Condundrums is a set of
9-question open-ended quizzes covering all topics in the AB and BC calculus curriculums in order. The kicker is that you cannot move onto the next question until you answer the current question. Question n + 1 depends on the answer from question n, so like a Rube Goldberg machine, all questions must be answered perfectly. With the questions covering the basics, even weaker students will enjoy this.
Calculus Conundrums is our new subscription and everyone who is a member of MasterMathMentor will receive the free student versions every two weeks starting September 5. But for those who cannot wait, the quizzes, solutions, and grading spreadsheet are available now. For more information, click on the link.
AP® Calculus College Board Standards (7/30/2019)
For teachers with administrations insisting that their AP® Calculus courses be aligned to the new College Board Standards published in 2019, here is the documentation to show this alignment.
AB Standards: BC Standards:
Free Response Question Database (4/20/19)
For those teachers who frequent the AP® Central website (https://apcentral.collegeboard.org), we have put together a database of free-response questions since the year 1998. It classifies the calculus topics of every question (AB and BC) so that teachers can find free-response problems that cover specific techniques. Available in Excel or PDF. Completely free. Clck on the link to check it out.
Our new matrices unit, which will eventually be included as one of our extra topics in precalculus, is available. This 47-page document covers the basics of matrix operations. It contains some very interesting applications that are not usually taught at the high school level but gives students insight as to why matrices are important. Instructiosn on using the calculator are also included. Its format is the same as our popular precalculus and calulus manuals: classwork and homework. Solution versions also include 2 exams. This is perfect as an add-on to precalculus or as a 2-week topic after the AP exam in calculus or precalc. Click on the link for more information.
Test Your Strength - SAT® and ACT® (2/18/19)
Similar to the popular Test Your Strength series in AP® Calculus, AP Statistics, and now precalculus, TYS for the SAT® and ACT® exam measures 24 student skill levels areas in algebra, geometry, trigonometry, and probability/statistics by use of a 72-question multiple-choice exam. An impressive printout tells students where to focus their studies for the upcoming SAT® and ACT® exams. This can be purchased by teachers with a SAT ®or ACT® Rreview course or individual student. Requires Microsoft Excel. Click on the SAT link or ACT link for more information.
Our new probability unit, which will eventually be included as one of our extra topics in precalculus, is available. This 99-page document covers everything that a course in probability should: counting, permutations and combinations, combinational and conditional probability, expected value, as well as different types of distributions. Its format is the same as our popular precalculus and calulus manuals: classwork and homework. Solution versions also include 3 exams. This is perfect as an add-on to precalculus or as a month-long topic after the AP exam in calculus or precalc. Click on the link for more information.
Test Your Strength Precalculus (12/1/18)
Test your Strength has been very successful for AB and BC Calculus as well as AP® Statistics. Our latest edition of it is a companion piece to RU Ready for AP® Calculus. It is meant to be given to students prior to them starting AP calc in order to give them a detailed report on the precalculus areas in which they are weak. In that way, they have the summer to reinforce those skills and walk into AP® calculus secure in the knowledge that their algebra skills are strong. Check it out by clicking on this link.
Calculus Acrostic (8/1/18)
Our subscription for the year is an acrostic game. In 2017/2018, we did a crossword puzzle game that gave students typical AP free response questions. This year's game focuses on multiple-choice. It can be used throughout the year as students solve clues to spell out a quote about calculus or mathematics. There are 3 different acrostics: derivatives, integral, and BC. Teachers enrolled as MMM members will automatically receive new clues every 3 weeks. It will be fun and challenging to play and a smart Excel spreadsheet can be used to give instant feedback. More information can be found by clicking on the link.
A Summer Math Problem
Did you ever have a dream about math? I do occasionally. I had this dream the other night that involved math calculations and I have no idea whether I was trying to do the calculations while alseep or in that limbo land.
The dream involved me running a workshop at a school some morning. For some reason, the particpants were only men. A similar workshop was run in another room for women. In both workshops, everyone was required to shake hands. In the afternoon, both groups got together and all the men shook hands with all the women.
For some reason in the dream, I was interested in whether there were more total handshakes in the morning or in the afternoon. Strange thing to dream about!
I tried to calculate whether there were group sizes when the total morning handshakes and afternoon handshakes were the same. I couldn't find any, but then, I was sort of asleep. It wasn't until I got up and 4 hours later, the dream came to me when I biking. I came home and put together a problem about it.
So concerning the number of handshakes, which is correct? More importantly, can you prove your answer?
(A) There are always more handshakes in the morning.
(B) There are always more handshakes in the afternoon.
(C) There are no group sizes where the number of morning handshakes and afternoon handshakes are the same.
(D) There is a finite number of group sizes where the number of morning handshakes and afternoon handshakes are the same.
(E) There is an infinite number of group sizes where the number of morning handshakes and afternoon handshakes are the same.
Think about it. If you would like the answer, click on the following link.
If after reading through my solution, you have further insight into the problem, write me at firstname.lastname@example.org.
Answers to Calculus Manual 12/25/17
We have added answers to the AB and BC Calculus manuals. Teachers can give this to students who want to check homework answers. Purchasers of the AB and BC solution manuals were sent download links and new purchasers of solutions will automatically receive the answers as well. They are also available as a separate purchase.
Test Your Strength Stat (12/13/17)
50 question diagnostic multiple choice test that cover every aspect of the AP® Statistics exam. The student version of the exam is free and the solutions include an amazing Excel spreadsheet that will detail every statistics topic and the student understanding of it. This is a wonderful tool to give a couple of weeks before the AP® exam so students can see where their strength and weaknesses lie. Problems are broken down into topics in the 5 major sections of the AP® Stat curriculum and further broken down into whether problems are calculation oriented or more based on reading and terminology. This product is quite similar to the wildly successful Test Your Strength: AP® Calculus.
R.I.P. - Newton, the Calculus Cat
Newton has made a number of appearances in precalculus, calculus and statistics problems in my materials. Many students fell in love with his antics and in 2006, I decided to make him a part of the website. One of my former students Sam Tsui (now a huge YouTube singing star), drew him into our logo. And when I decided to have cartoons made for my products, Newton played a prominent role. He has been a biker, an archaeologist, and a teacher. He has dived into pools, helped a swami, joined a carnival, and hung from a catenary. He has left this world but he still lives in all these drawings. I won't soon forget him. He was my friend.
Change to Calculus Cache (10/1/17)
Because the AP® exam's multiple choice questions contain 4 choices, we have changed Calculus Cache so that all questions now have 4 choices. While the 5-choice version is available upon request, downloading the Calculus Cache student exam questions will get you the 4-choice version. Purchasers of the solutions in Word format can login and when they download the solutions, they will get the 4-choice version. They will also be contacted via email with the download links.
Across & Down (9/1/17)
Getting AP® Calculus - Across and Down is a crossword puzzle. However, the clues are calculus problems and the answers are numbers 0 - 9 and negative signs. It covers all aspects of AB calculus and the problems are more straightforward than the tricky AP® calculus type question. This is avalable as a subscription ... MasterMathMentor members will receive a new set of clues every week starting September 14. They will be in order of the AP® Calculus manual so you can give it to kids from day one of the course. Or you can give it at the end of the year as a review. It will work terrifically as a review for BC students as well. If you are a member of MasterMathMentor, you will receive it by email every Thursday starting in September. Or click on the link below to get the student downloads every week.
For more information, click on the link.
Clue game revision - 7/1/17
The calculus doesn't change but the suspects definitely do. In 2006, we had suspects like OJ Simpson, Paris Hilton, Usher, Kobe Bryant, Martha Stewart, Jack Nicholson, Michael Jordan, John Kerry, Donald Rumsfeld, Kate Winslett, Tony Soprano, Lance Armstrong, Nemo, George Foreman and Emiril Lagasse. What student would recognize these names today? The only remaining names from our original list is Tom Cruise, Bill Gates, and Hillary Clinton. So we revised the clue cards with more contemporary names in the news. Purchasers of the Clue game can email me at email@example.com and I will send you the revised clue cards.
Test Your Strength Calculus - 4/1/17
Test Your Strength is a 50-question multiple choice diagnostic exam that focuses on all aspects of the AP® curriculum. The student version is free and the solution version includes an amazing Excel spreadsheet template that quickly grades a student exam and provides a detailed report as to how the student performed in all questions as well as strength and weaknesses in all topics. There is an AB version as well as a BC version that includes both an AB/BC exam, similar to actual AP® exam, as well as a BC only exam that focuses as much as possible on strictly BC topics.
AB Test Your Strength
BC Test Your Strength
Ahead of the Curve
This free compendium of 32 mathematical curves with exotic names like conchoids, foliums, pearls, conchoids, cissoids, strophoids, and devil curves are subject to students calculus skills in finding tangent lines, areas, volumes, and arc lengths. Algebraic skills are challenged and students are encouraged to use this workbook in conjunction with a computer graphing app. Read more about it by clicking on the link.
SAT® Clue is completely new and represents the first material on MasterMathMentor.com not written by Stu. It was written by Dr. Sheldon Goldberg who has an extensive knowledge of the SAT Mathematics exam including the recent revisions to the exam. The game is like our popular Calculus Clue game but this one has students determining their future college, future profession, and future city residence by solving clues in the form of sample SAT® math problems. It is fun and instructive and the student version without solutions is available free of charge. Check it out by clicking on this link.