500 New SAT Math Problems
Just 19.99 on Amazon

Hi everyone! The latest edition of 500 New SAT Math Problems is now available in paperback from Amazon. This edition just has been modified from the previous edition to account for the changes on the Digital SAT.

The paperback is now on sale on Amazon for only $19.99. Note that once the sale ends (by the end of today), the price of this book will go up to $42.99. 

The promotion has ended. Thanks to everyone who participated. The book is now available at its regular price here: 500 New SAT Math Problems

If you have any questions, feel free to contact me at steve@SATPrepGet800.com 

Thank you all for your continued support!

A Trick For Free Two Day Shipping

I would like to finish this post with a little trick you can use to get free 2 day shipping on any of the books you decide to purchase without making any additional purchases. If you have never used Amazon Prime you can sign up for a free month using the following link.

Sign Up For Amazon Prime For Free

If you have already had a free trial of Amazon Prime you can simply open up a new Amazon account to get a new free trial. It just takes a few minutes! You will need to use a different email address than the one you usually use.

This next part is very important! After you finish your transaction, go to your Account, select “Manage my prime membership,” and turn off the recurring billing. This way in a month’s time Amazon will not start charging you for the service.

After shutting off the recurring billing you will still continue to receive the benefit of free 2 day shipping for one month. This means that as long as you use this new Amazon account for your purchases you can do all of your shopping on Amazon for the next month without having to worry about placing minimum orders to get free shipping.

Just be aware that certain products from outside sellers do not always qualify for free shipping, so please always check over your bill carefully before you check out.

Well I hope you decide to take advantage of this very special offer, or at the very least I hope you will benefit from my Amazon “free 2 day shipping trick.” Here is the link one more time:

Sign Up For Amazon Prime For Free

If you think your friends might be interested in this special offer, please share it with them on Facebook:

Thank you all for your continued support!

AP Calculus AB Related Rates Problem with Solution

Yesterday I posted a Level 4 related rates problem for the AP Calculus AB exam (although this problem is a pretty standard Calculus problem that you may come across in any Calculus course). You can see that post here: AP Calculus AB Problem – Related Rates

Today I would like to provide a full explanation for this problem. Here is the problem one more time:

The radius of a spherical balloon is decreasing at a constant rate of 0.5 centimeters per second. At the instant when the volume V becomes 288π cubic centimeters, what is the rate of decrease, in square centimeters per second, of the surface area of the balloon?

(A) 24π
(B) 48π
(C) 64π
(D) 72π

Solution: Recall that the volume of a sphere with radius r is

V = 4/3 πr³,

and the surface area of a sphere with radius r is

S = 4πr².

We are given that  dr/dt = –0.5, and we are being asked to find  dS/dt  when V = 288π.

First note that when V = 288π, we have

288π = 4/3 πr³
3/4 ⋅ 288π = πr³
216 = r³
6 = r

Now,

dS/dt = 8πr ⋅ dr/dt = 8πr(–0.5) = –4πr.
dS/dt (at r = 6) = –4π(6) = –24π.

So the surface area of the balloon is decreasing at a rate of 24π cm²/sec. Therefore, the answer is choice (A).

Notes: (1) Observe that one can get the formula for the surface area of a sphere by differentiating the formula for the volume of a sphere. This is just a little trick that can be used to reduce the number of formulas to memorize.

(2) Remember that the word rate generally indicates a derivative. “Increasing at a rate of” indicates a positive derivative, and “decreasing at a rate of” indicates a negative derivative.

(3) A radius is a length and is therefore measured in single units (in this case centimeters). Area (and in particular, surface area) is measured in square units. Volume is measured in cubic units.

The type of units being mentioned usually gives a big hint as to what measurement is being given or asked for.

(4) This is a related rates problem. In a related rates problem we differentiate the independent and dependent variables with respect to a new variable, usually named t, for time.

(5) A related rates problem can be pictured as a dynamic (moving) process that gets fixed at a specific moment in time.

For this problem we can picture a sphere shaped balloon deflating. We then freeze time at the moment when the volume is 288π cm³.

At this moment in time we want to know what the rate of decrease of the surface area is. The word “rate” indicates that we want the derivative of surface area with respect to time,  dS/dt.

Don’t forget to apply the chain rule when differentiating the right hand side. In this case, the derivative of r is  dr/dt.

More AP Calculus Problems with Explanations

If you are preparing for one of the AP Calculus exams, you may want to take a look at one of the following books.

And if you liked this article, please share it with your Facebook friends:

AP Calculus AB – Related Rates 

Students that are taking AP Calculus (or any Calculus course) usually find related rates word problems to be difficult. The concept however is really not so hard to understand. The idea is that you have two or more quantities that are changing with time, and those two quantities are related in some way. In a Precalculus problem, we would explore the relationship between those two quantities. But in a Calculus problem we explore the relationship between the rates at which those quantities are changing.

Let’s try a typical AP Calculus AB related rates problem (note that any Calculus AB problem can also appear on the BC exam). I will provide a full explanation for this problem tomorrow. In the meantime, feel free to leave your own solutions in the comments.

Level 4 Related Rates Problem

The radius of a spherical balloon is decreasing at a constant rate of 0.5 centimeters per second. At the instant when the volume V becomes 288π cubic centimeters, what is the rate of decrease, in square centimeters per second, of the surface area of the balloon?

(A) 24π
(B) 48π
(C) 64π
(D) 72π

More AP Calculus Problems with Explanations

If you are preparing for one of the AP Calculus exams, you may want to take a look at one of the following books.

And if you liked this article, please share it with your Facebook friends:

AP Calculus BC Exam Changes

The AP Calculus exams are going through a few small changes, and so I have been updating my AP Calculus prep books to account for these changes. The revised version of the book for the BC exam is now ready. Here is a link to the book’s Amazon page: 320 AP Calculus BC Problems

The following changes are being made to the AP Calculus BC exam beginning with the 2016-2017 academic year:

1. Multiple choice questions will have only 4 answer choices instead of 5.
2. The distribution of multiple choice questions will be modified slightly as follows: The “no calculator allowed” portion (Part A) will now consist of 30 questions (up from 28) and you will have 60 minutes (up from 55). The “calculator required” portion (Part B) will now consist of 15 questions (down from 17) and you will have 45 minutes (down from 50).
3. The following topics will be added: limit comparison test, absolute and conditional convergence, and the alternating series error bound.

My New AP Calculus Social Media Accounts

Don’t forget to like my new AP Calculus Facebook page, and follow my new AP Calculus Twitter account.

If you think your friends might be interested in this information, please share it with them on Facebook:

Thank you all for your continued support!

320 AP Calculus BC Problems – New Edition

Today I would like to announce the release of the second edition of  320 AP Calculus BC Problems arranged by Topic and Difficulty Level.

The paperback is now on sale on Amazon for only $5.74.

This sale will run for just a few hours, and once the sale ends the price will go up to $34.99. If you want to take advantage of the sale price I strongly recommend you purchase the book right away.

Click the following link to get to the book’s Amazon page: 320 AP Calculus BC Problems, 2nd Edition

Note that this book is for preparing for the May 2017 exam.

As an additional incentive to purchase this book today, I will also give you an additional book for FREE as a downloadable PDF file. You can choose ANY of my other books. So if you would like a different book, go ahead and purchase this one (as soon as it is available), forward me your Amazon confirmation email (to steve@SATPrepGet800.com) and let me know which of my books you would like for free. You will be provided with a link to download your additional free book. This offer is available until the end of today (June 20, 2016).

You can choose any book on my product page.

AP Calculus BC Exam Changes

i created new editions of my AP Calculus books because the AP Calculus exams are going through a few small changes. My new editions have been created to reflect these changes.

The following changes are being made to the AP Calculus BC exam beginning with the 2016-2017 academic year:

1. Multiple choice questions will have only 4 answer choices instead of 5.
2. The distribution of multiple choice questions will be modified slightly as follows: The “no calculator allowed” portion (Part A) will now consist of 30 questions (up from 28) and you will have 60 minutes (up from 55). The “calculator required” portion (Part B) will now consist of 15 questions (down from 17) and you will have 45 minutes (down from 50).
3. The following topics will be added: limit comparison test, absolute and conditional convergence, and the alternating series error bound.

A Trick For Free Two Day Shipping

I would like to finish this post with a little trick you can use to get free 2 day shipping on any of the books you decide to purchase without making any additional purchases. If you have never used Amazon Prime you can sign up for a free month using the following link.

Sign Up For Amazon Prime For Free

If you have already had a free trial of Amazon Prime you can simply open up a new Amazon account to get a new free trial. It just takes a few minutes! You will need to use a different email address than the one you usually use.

This next part is very important! After you finish your transaction, go to your Account, select “Manage my prime membership,” and turn off the recurring billing. This way in a month’s time Amazon will not start charging you for the service.

After shutting off the recurring billing you will still continue to receive the benefit of free 2 day shipping for one month. This means that as long as you use this new Amazon account for your purchases you can do all of your shopping on Amazon for the next month without having to worry about placing minimum orders to get free shipping.

Just be aware that certain products from outside sellers do not always qualify for free shipping, so please always check over your bill carefully before you check out.

Well I hope you decide to take advantage of this very special offer, or at the very least I hope you will benefit from my Amazon “free 2 day shipping trick.” Here is the link one more time:

Sign Up For Amazon Prime For Free

If you think your friends might be interested in this special offer, please share it with them on Facebook:

Thank you all for your continued support!

Recognizing Blocks

Today, let’s discuss a math strategy I like to call “Recognizing Blocks.” This is a strategy that can sometimes be used on standardized tests such as the ACT, SAT, GRE, and AP Calculus exams.

First, let me give my definition of a block: A block is an algebraic expression that appears more than once in a given problem.

Very often in math problems on standardized tests a block can be treated just like a variable. In particular, blocks should usually not be manipulated—treat them as a single unit.

This is simple in theory. Let’s first try it with a basic algebra  problem:

Example 1

If 3x – 5y = 7 , what is the value of 6(3x − 5y) ?

(A) 50
(B) 42
(C) 36
(D) 30
(E) 4

In this example there is a block of 3x – 5y. Let’s look at the following seemingly easier problem:

If a = 7, what is the value of 6a?

The answer to this problem is (6)(7) = 42.

But this is essentially the same problem as the one we were given. We just replaced the block by the variable a. So the answer to the original question is also 42, choice (B).

You can be really sharp by doing this problem in your head in just a few seconds: (6)(7) = 42. choice (B).

Easy, right?

Here is a more difficult problem for you:

Example 2

If b = 7(u + v + x + y +z)/5, then in terms of b what is the average (arithmetic mean) of u, v, x, y, and z?

(A) b/35
(B) b/7
(C) b/5
(D) 5b
(E) 7b

In this example there is a block of a = (u + v + x + y + z)/5 which is precisely the average of u, v, x, y, and z. So solving this problem is the same as solving the following equation for a.

b = 7a

To solve this equation for a we will simply divide both of the sides by 7 to get a = b/7, choice (B).

These problems as relatively straightforward to solve as long as you treat all blocks as variables and do not try to manipulate them.

More Problems Involving Blocks

If you are preparing for the ACT, SAT, GRE, or another standardized test, you may want to take a look at the Get 800 collection of test prep books. Click on the picture below for more information.

And if you liked this article, please share it with your Facebook friends:

320 AP Calculus AB Problems – Just $5.69

Today I would like to announce the release of the second edition of 320 AP Calculus AB Problems arranged by Topic and Difficulty Level. This new edition reflects the changes that will be implemented for the exam being given next May.

The paperback is now on sale on Amazon for only $5.69.

This sale may last for only a few hours, and once the sale ends the price will go up to $34.99. Amazon will automatically raise the price once a predetermined number of copies has been sold. If you want to take advantage of the sale price I strongly recommend you purchase the book now.

Click the following link to get to the book’s Amazon page: 320 AP Calculus AB Problems

As an additional incentive to buy this book, I would like to give you an additional books for FREE as a downloadable PDF file. You can choose ANY of my other books. So if you would like a different book, go ahead and purchase this one, forward me your Amazon confirmation email (to steve@SATPrepGet800.com) and let me know which of my books you would like for free. You will be provided with a link to download your additional free book. This offer is available until the end of today (June 13, 2016).

Take a look at my product page to see all of my books: Get 800 Product Page

AP Calculus AB Exam Changes

The AP Calculus exams are going through a few small changes, and so I have been updating my AP Calculus prep books to account for these changes. The revised version of the book for the AB exam is just about ready, and so today I thought I would focus on the AB exam.

The following changes are being made to the AP Calculus AB exam beginning with the 2016-2017 academic year:

1. Multiple choice questions will have only 4 answer choices instead of 5.
2. The distribution of multiple choice questions will be modified slightly as follows: The “no calculator allowed” portion (Part A) will now consist of 30 questions (up from 28) and you will have 60 minutes (up from 55). The “calculator required” portion (Part B) will now consist of 15 questions (down from 17) and you will have 45 minutes (down from 50).
3. One new topic has been added: L’Hôpital’s rule*

* Note that there have always been problems on the AP Calculus AB exam where L’Hôpital’s rule could be used. The difference now is that problems may show up where L’Hôpital’s rule must be used. This is a very minor addition to the exam.

A Trick For Free Two Day Shipping

I would like to finish this post with a little trick you can use to get free 2 day shipping on any of the books you decide to purchase without making any additional purchases. If you have never used Amazon Prime you can sign up for a free month using the following link.

Sign Up For Amazon Prime For Free

If you have already had a free trial of Amazon Prime you can simply open up a new Amazon account to get a new free trial. It just takes a few minutes! You will need to use a different email address than the one you usually use.

This next part is very important! After you finish your transaction, go to your Account, select “Manage my prime membership,” and turn off the recurring billing. This way in a month’s time Amazon will not start charging you for the service.

After shutting off the recurring billing you will still continue to receive the benefit of free 2 day shipping for one month. This means that as long as you use this new Amazon account for your purchases you can do all of your shopping on Amazon for the next month without having to worry about placing minimum orders to get free shipping.

Just be aware that certain products from outside sellers do not always qualify for free shipping, so please always check over your bill carefully before you check out.

Well I hope you decide to take advantage of this very special offer, or at the very least I hope you will benefit from my Amazon “free 2 day shipping trick.” Here is the link one more time:

Sign Up For Amazon Prime For Free

If you think your friends might be interested in this special offer, please share it with them on Facebook:

Thank you all for your continued support!

AP Calculus AB Exam Changes

The AP Calculus exams are going through a few small changes, and so I have been updating my AP Calculus prep books to account for these changes. The revised version of the book for the AB exam is now ready. Here is a link to the book’s Amazon page: 320 AP Calculus AB Problems

The following changes are being made to the AP Calculus AB exam beginning with the 2016-2017 academic year:

1. Multiple choice questions will have only 4 answer choices instead of 5.
2. The distribution of multiple choice questions will be modified slightly as follows: The “no calculator allowed” portion (Part A) will now consist of 30 questions (up from 28) and you will have 60 minutes (up from 55). The “calculator required” portion (Part B) will now consist of 15 questions (down from 17) and you will have 45 minutes (down from 50).
3. One new topic has been added: L’Hôpital’s rule*

* Note that there have always been problems on the AP Calculus AB exam where L’Hôpital’s rule could be used. The difference now is that problems may show up where L’Hôpital’s rule must be used. This is a very minor addition to the exam.

If you think your friends might be interested in this information, please share it with them on Facebook:

Thank you all for your continued support!

320 AP Calculus BC Problems – Just $4.57 for a Limited Time

Today I would like to announce that 320 AP Calculus BC Problems arranged by Topic and Difficulty Level is on sale today on Amazon for just $4.57.

This sale may last for only a few hours, and once the sale ends the price will go up to $34.99. Amazon will automatically raise the price once a predetermined number of copies has been sold. If you want to take advantage of the sale price I strongly recommend you purchase the book now.

Click the following link to get to the book’s Amazon page: 320 AP Calculus BC Problems

As an additional incentive to purchase this book today, I will also give you an additional book for FREE as a downloadable PDF file. You can choose ANY of my other books. So if you would like a different book, go ahead and purchase this one, forward me your Amazon confirmation email and let me know which of my books you would like for free. You will be provided with a link to download your additional free books. This offer is available until the end of today (March 5, 2016).

Take a look at my product page to see all of my books: Get 800 Product Page

A Trick For Free Two Day Shipping

I would like to finish this post with a little trick you can use to get free 2 day shipping on any of the books you decide to purchase without making any additional purchases. If you have never used Amazon Prime you can sign up for a free month using the following link.

Sign Up For Amazon Prime For Free

If you have already had a free trial of Amazon Prime you can simply open up a new Amazon account to get a new free trial. It just takes a few minutes! You will need to use a different email address than the one you usually use.

This next part is very important! After you finish your transaction, go to your Account, select “Manage my prime membership,” and turn off the recurring billing. This way in a month’s time Amazon will not start charging you for the service.

After shutting off the recurring billing you will still continue to receive the benefit of free 2 day shipping for one month. This means that as long as you use this new Amazon account for your purchases you can do all of your shopping on Amazon for the next month without having to worry about placing minimum orders to get free shipping.

Just be aware that certain products from outside sellers do not always qualify for free shipping, so please always check over your bill carefully before you check out.

Well I hope you decide to take advantage of this very special offer, or at the very least I hope you will benefit from my Amazon “free 2 day shipping trick.” Here is the link one more time:

Sign Up For Amazon Prime For Free

If you think your friends might be interested in this special offer, please share it with them on Facebook:

Thank you all for your continued support!

AP Calculus BC Exam Changes

The AP Calculus exams are going through a few small changes, and so I have been updating my AP Calculus prep books to account for these changes. The revised version of the book for the BC exam is just about ready, and so today I thought I would focus on the BC exam.

The following changes are being made to the AP Calculus BC exam beginning with the 2016-2017 academic year:

1. Multiple choice questions will have only 4 answer choices instead of 5.
2. The distribution of multiple choice questions will be modified slightly as follows: The “no calculator allowed” portion (Part A) will now consist of 30 questions (up from 28) and you will have 60 minutes (up from 55). The “calculator required” portion (Part B) will now consist of 15 questions (down from 17) and you will have 45 minutes (down from 50).
3. The following topics will be added: limit comparison test, absolute and conditional convergence, and the alternating series error bound.

New AP Calculus BC Problems

I am also happy to announce that New AP Calculus BC Problems arranged by Topic and Difficulty Level  will be available this week. This book will prepare you for the revised AP Calculus BC exam beginning with the 2016-2017 academic year. The first exam that will implement these changes will be in May 2017.

The book will be released on Amazon  at a promotional price of $5.69 for a few hours.

Once the sale ends the price will go up to $34.99. If you want to take advantage of the sale price I strongly recommend that you get on the notification list.

If you want to be added to my email notification list for this and future promotions, send an email to steve@SATPrepGet800.com with “Notify me” written in the subject line.

In the meantime, you can take a look at my product page to see all of the other books from the Get 800 collection: Get 800 Product Page

If you think your friends might be interested in this special offer, please share it with them on Facebook:

Thank you all for your continued support!

 

320 ACT Math Problems – Only $5.49 for a limited time

Today I would like to announce that the title of the ACT Prep Red Book has been changed to  320 ACT Math Problems arranged by Topic and Difficulty Level.

The paperback is now on sale on Amazon for only $5.49.

This sale may last for only a few hours, and once the sale ends the price will go up to $34.99. Amazon will automatically raise the price once a predetermined number of copies has been sold. If you want to take advantage of the sale price I strongly recommend you purchase the book now.

Click the following link to get to the book’s Amazon page: 320 ACT Math Problems

As an additional incentive to purchase this book today, I will also give you an additional book for FREE as a downloadable PDF file. You can choose ANY of my other books. So if you would like a different book, go ahead and purchase this one (as soon as it is available), forward me your Amazon confirmation email and let me know which of my books you would like for free. You will be provided with a link to download your additional free books. This offer is available until the end of today (March 2, 2015).

Take a look at my product page to see all of my books: Get 800 Product Page

You should also be aware that I am also making the following promotion available until the end of the month: if you buy any 3 of my books in paperback, you get all 6 of the following SAT math prep books for free. This promotion is available until March 31, 2015. Contact me at steve@SATPrepGet800.com for details.

 

A Trick For Free Two Day Shipping

I would like to finish this post with a little trick you can use to get free 2 day shipping on any of the books you decide to purchase without making any additional purchases. If you have never used Amazon Prime you can sign up for a free month using the following link.

Sign Up For Amazon Prime For Free

If you have already had a free trial of Amazon Prime you can simply open up a new Amazon account to get a new free trial. It just takes a few minutes! You will need to use a different email address than the one you usually use.

This next part is very important! After you finish your transaction, go to your Account, select “Manage my prime membership,” and turn off the recurring billing. This way in a month’s time Amazon will not start charging you for the service.

After shutting off the recurring billing you will still continue to receive the benefit of free 2 day shipping for one month. This means that as long as you use this new Amazon account for your purchases you can do all of your shopping on Amazon for the next month without having to worry about placing minimum orders to get free shipping.

Just be aware that certain products from outside sellers do not always qualify for free shipping, so please always check over your bill carefully before you check out.

Well I hope you decide to take advantage of this very special offer, or at the very least I hope you will benefit from my Amazon “free 2 day shipping trick.” Here is the link one more time:

Sign Up For Amazon Prime For Free

If you think your friends might be interested in this special offer, please share it with them on Facebook:

Thank you all for your continued support!