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!
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Improve Your Math Score by Teaching Math to Others
This week I would like to share an approach to improving your own math score on standardized tests such as the SAT and ACT by helping other students to improve their score. Every student I tutor is encouraged to pass along their knowledge to other students as there are many benefits for both students.
I believe that if you want to take yourself to the next level without too much effort, simply teach what you already know to someone else. Helping someone else to learn something new requires a much deeper understanding of the underlying material than simply having superficial knowledge of the subject matter. By engaging with someone else with less understanding than you, you will find that you often have to be creative with your explanations in order to get the other person to acquire a complete understanding of what you are trying to teach. This will force you to think about the subject matter in different ways. A nice side effect of this process is an overall improvement in both your current knowledge and your critical reasoning skills.
This is especially useful for ACT and SAT preparation and also mathematics in general where it often helps to solve problems by thinking “outside the box.” By helping others to understand how to solve problems you will be forced to review the tips, tricks and techniques that you already know. This will help you to internalize them more quickly so that you will be able to more easily identify problems where a specific strategy will be useful, and you will become more adept at using them.
Ways To Help Others
There are several ways to help others:
- You can find students in your school (or elsewhere) whose current score levels are below yours and offer to tutor them in a formal setting.
- You can let other students know that whenever they are stuck on a math problem, they should see you, and you will be happy to do your best to provide a solution for them.
- You can answer questions on forums where students post ACT, SAT, and general math questions.
Benefits Of Helping Others
And now here are some of the benefits of helping others to improve in math:
- You will be forced to review material that you have already learned.
- You will be more likely to internalize strategies that you are familiar with so that they’re application becomes faster and more reliable.
- You will begin developing a deeper understanding of the underlying mathematics leading to a higher level of mathematical maturity.
- You will improve your problem solving and critical reasoning skills at a faster rate than by simply learning new material.
- You will be providing a service to others by helping them improve their grades and standardized test scores.
So get out there and offer your tutoring services to someone who needs your help. You will be providing an invaluable service to another person. They will certainly be grateful for your help.
Of course, this applies not only to improving your math scores but to anything in life that you want to perform well in: be it college, sports, or even just playing video games!
And what about the fact that primarily you’re actually helping yourself to get into your college of choice? Well, we’ll keep that as our little secret.
And for daily SAT/ACT/GRE preparation, take a look at the Get 800 collection of test prep books.
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Revised SAT Math Problem with Solution
Today I would like to provide you with a sample question and solution for the revised SAT. This one is a Level 2 Problem Solving question.
Level 2 Problem Solving
A chemist has a supply of 5.2 liter bottles of a certain solvent that must be shipped to a central warehouse. The warehouse can accept the solvent at the rate of 3 hectoliters per minute for a maximum of 8 hours per day. If 1 hectoliter equals 100 liters, what is the maximum number of bottles that the warehouse could receive from the chemist each day.
(A) 461
(B) 462
(C) 27,692
(D) 83,200
Solution: The warehouse can receive 3 ∙ 60 ∙ 8 hectoliters of the solvent per day, or equivalently, 1440 ∙ 100 = 144,000 liters of the solvent per day. Therefore the number of bottles that can be accepted each day is 144,000/5.2 which is approximately 27,692.30769. The maximum number of bottles that the warehouse can accept in one day is therefore 27,692, choice (C).
Notes: (1) Since there are 60 minutes in an hour, “3 hectoliters per minute” is the same as 3 ∙ 60 = 180 hectoliters per hour.
Similarly, since the warehouse can accept the solvent for a maximum of 8 hours per day, “180 hectoliters per hour” is equivalent to a maximum of 180 ∙ 8 = 1440 hectoliters per day.
(2) In the above solution we combined the two conversions given in note 1 into a single conversion: “3 hectoliters per minute” is equivalent to a maximum of 3 ∙ 60 ∙ 8 = 1440 hectoliters per day.
(3) Since 1 hectoliter equals 100 liters, we can convert hectoliters to liters by multiplying by 100. So 1440 hectoliters is equal to 1440 ∙ 100 = 144,000 liters.
(4) We can convert between hectoliters and liters more formally by setting up a ratio. The two things being compared are “liters” and “hectoliters.”
liters 100 x
hectoliters 1 1440
Now draw in the division symbols and equal sign, cross multiply and divide the corresponding ratio to find the unknown quantity x.
100/1 = x/1440
1x = 100 ∙ 1440
x = 144,000
(5) Instead of converting 1440 hectoliters to 144,000 liters, and then dividing by 5.2, we can instead convert 5.2 liters to hectoliters, and then divide 1440/.052, giving the same answer of 27,692, choice (C).
If you liked this article, please share it with your Facebook friends:
For daily SAT preparation, take a look at the Get 800 collection of SAT math prep books.
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320 GRE Math Problems
320 GRE Math Problems arranged by Topic and Difficulty Level is now available on Amazon. Click the following link to get to the book’s Amazon page: 320 GRE Math Problems
As an additional incentive to purchase this book today, I will also give you another 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 book. This offer is available until the end of the month (April 30, 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!
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320 GRE Math Problems
Today I would like to announce my new math prep book for the GRE: 320 GRE Math Problems arranged by Topic and Difficulty Level
This book will be released on Amazon in about a week at a promotional price of about $5.00.
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 that you get on the email notification list.
To be added to the notification list, simply 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 being notified of this special offer, please share it with them on Facebook:
Thank you all for your continued support!
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Vocabulary Builder
Today I would like to announce the new Get 800 book: Vocabulary Builder.
The paperback is now on sale on Amazon for only $5.25.
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: Vocabulary Builder
As an extra incentive to buy this book from Amazon I want to offer you an additional book for FREE as a downloadable PDF file. You can choose ANY book from the Get 800 collection. 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 book. This offer is available until April 6, 2016.
You can forward your Amazon confirmation email to
Take a look at my product page to see all of my books: Get 800 Product Page
Note that this book essentially has the same content has SAT Vocabulary Book. We’ve decided to rebrand it because although it is no longer relevant for the new SAT, it is still a wonderful book for building vocabulary.
A Trick For Free Two Day Shipping
Here is 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
Thank you all for your continued support!
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1. Attempting too many questions.
Students have been trained since they were very young that they need to answer every question that is on a test. For most in-class exams this is good advice. On standardized tests however this advice can be very bad. Attempting to answer too many questions on the SAT is guaranteed to lower your score. Here are some of the negative effects of trying to answer too many questions:
- Precious time is wasted attempting problems that are too hard.
- Students spend less time on easier problems, thus making careless errors.
- Test taking anxiety is much higher because the student has too many questions to get to in very little time. This leads to more careless errors.
In many cases simply by reducing the number of questions that you answer on the exam your score can go up 40 points or more. This may seem unlikely but if you think about it for a moment it makes perfect sense. If you eliminate just two careless errors per math section (1 multiple choice question and 1 grid in per section), you add 4 points to your raw score. This translates roughly to 40 points on the SAT.
So how many questions should you be answering? There is no absolute answer to this, but here is a general guideline. There are two math sections on the SAT – one where a calculator is allowed and one where a calculator is not allowed. The calculator section has 30 multiple choice (mc) questions and 8 free response (grid in) questions. The non-calculator section has 15 multiple choice (mc) questions and 5 free response (grid in) questions.
You should first make sure that you know what you got on your last SAT practice test, actual SAT, or actual PSAT (whichever you took last). What follows is a general goal you should go for when taking the exam.
This is just a general guideline. Of course it can be fine tuned. As a simple example, if you are particularly strong at heart of algebra problems, but very weak at geometry problems, then you may want to try every heart of algebra problem no matter where it appears, and you may want to reduce the number of geometry problems you attempt.
One important thing. There is no guessing penalty on the current version of the SAT. So although you may not be attempting to solve some of the problems, you should still fill in an answer for every single question. Before time is up make sure to bubble in random guesses for the problems you did not attempt.
2. Not checking answers.
Many students feel a terrible amount of time pressure when taking their SAT. One of the primary causes of this is attempting too many questions, as stated above. Students therefore tend to rush through questions without checking over their work. This results in a significant number of careless errors.
The fact is that if you’re taking the test correctly, there is no need to rush through anything. You should be able to do each problem, and check it over quickly before moving on. Use the strategies that I teach you to get through problems quickly, but don’t rush through the actual mechanics of doing the problem.
Furthermore, you should always use at least five minutes at the end of the test for going back and checking over your earlier work. Remember, if you catch just two careless errors per section, your score will go up approximately 40 points.
3. Getting hung up on one question.
Students often have the misconception that if they abandon a problem, all the time that they have put into it has been wasted. Nothing could be further from the truth. In fact, sometimes leaving a problem temporarily is the best thing you can do to solve that problem. I can’t tell you how many times I have abandoned a problem to do something else, and then all of a sudden many minutes later the answer came to me without me even consciously thinking about it.
Even if this doesn’t happen, coming back to a problem later with fresh eyes is often very helpful. Your mind will not forget all the work you have already done on that problem.
So when is it time to move on? After you’ve been working on a question for about 1 minute you should make a decision. If you understand the question and think that you can get the answer in another 30 seconds or so, continue to work on the problem. If you still don’t know how to do the problem or you’re using a strategy that is going to take a long time, mark it off and come back to it later if you have time.
Always feel free to take a guess, but you still want to leave open the possibility of coming back to it later. Remember that every problem is worth the same amount. Don’t sacrifice problems that you may be able to do by getting hung up on a problem that is too hard for you.
Make sure that you are wearing a watch on test day. This will help you with your pacing.
4. Going with the first instinct on hard questions.
A standard piece of test-taking advice is to always go with your first instinct. In general this is good advice, but on standardized tests this advice is terrible.
The problem is that the more difficult SAT questions are specifically designed to trick you. This means that if you go with your first instinct, you are probably falling right into the trap that was laid out for you. On high numbered math questions on the SAT you should actually eliminate a choice if your intuition leads you to that answer too quickly. If you have a proper justification for why that particular answer is correct, then of course you can choose that answer. Otherwise however you should take a guess from the other choices.
5. Performing complicated computations.
It is never necessary to do messy algebra or perform tedious and complicated computations. If you find yourself doing this often, it means that you do not know some basic SAT test-taking strategies.
6. Taking the test without knowing the directions and given geometric formulas by heart.
Although I advise you not to rush through questions, you shouldn’t be wasting your time either. The last thing that you want to be doing during the test is reading the directions. They are always the same. Learn them ahead of time.
A more common mistake than that is walking into the test without knowing the geometric formulas that are given to you on the front of each math section. There aren’t that many. Just memorize them. It is a waste of time to be flipping back and forth.
The more advanced student may want to memorize additional formulas to save time while taking the test. Visit the following page for details: SAT Math Formulas
7. Overusing their calculator.
Sometimes I see students typing away on their calculators without taking any break. What they are usually doing here is wasting time. Your calculator is a tool that is there for you to speed up computations. It is not there to solve the problem for you. If you are taking the test right, you shouldn’t be using your calculator all that much.
That said, make sure that you do use your calculator for arithmetical computations (on the section where a calculator is allowed). This is usually quicker than doing computations by hand or in your head, and you’re less likely to make a careless error.
Finally, make sure that you know how to input things into your calculator correctly. Many students mess up their order of operations when using calculators, especially using parentheses correctly.
Remember that as a general rule numerators, denominators and exponents should all be in parentheses when using your calculator.
A complete list of things you should know how to do with your calculator can be found here: Graphing Calculator Features You Should Know for the SAT/ACT
8. Rounding or truncating decimals too soon on grid ins.
When gridding in an answer all four slots must be used unless the answer terminates before this. I see students get answers wrong all the time because they rounded an answer to soon. If your calculator displays 2.111111111 for the final answer, then your answer will be marked wrong if you grid in 2.1. You must grid in 2.11.
9. Being nervous for no reason.
Some students get test-taking anxiety, and some more than others. This is just a fact we have to deal with. There are many techniques you can use to alleviate test-taking anxiety such as meditation and other techniques of the mind.
There are some reasons for nervousness that can easily be avoided. For example, reducing the number of questions that you expect yourself to answer can go a long way in making you less nervous. When you come to a problem that is giving you a lot of trouble simply move on to the next one. You don’t need to answer all of them.
Another way to battle nervousness is through confidence. Spend at least 3 months before the exam preparing about 10 to 20 minutes each day. Learn all of the basic strategies that I teach, and make sure to practice some problems that are right at your ability level.
Although getting answers correct does not improve your score (only learning from your mistakes improves your score), getting some answers correct will instill confidence. This will ensure that you don’t decrease your score.
If you are a nervous test taker, then you may want to check out the following article I’ve written: Eliminating Test Taking Anxiety
10. Running out of steam.
The SAT is a long test. Many students lose too much endurance and start performing poorly towards the end of the exam. All you need to do to combat this is to be prepared for it. Try to do at least 2 full practice tests before the actual exam. Struggle through that length of time so you can feel it before it matters.
Get 800 Test Prep Books
If you like the information in this article, you may want to check out the Get 800 collection of test prep books.
Please share this information with your Facebook friends:
All the best…
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Can You Be Accused Of Cheating
If You Show Significant Improvement
on Your SAT or ACT?
Who would ever think that a student could be punished for their hard work? But the sad truth is that it happens. Most students do not even consider the possibility that they will be accused of cheating on a standardized test because they performed so well. But this situation does occur.
Yes it is in fact true. The College Board has accused students of cheating on their SAT based only on their score increases from one SAT to the next (or from a student’s PSAT to his/her SAT).
If you are accused of cheating on the SAT, the College Board will most likely cancel your scores and ask you to retake the test in a private setting.
Now nobody likes being accused of cheating, and nobody wants to retake a four hour exam. But that’s not even the worst part. By the time you are asked to retake the test it may have been a long while since you last prepared for the exam. You may not do as well simply because you are out of practice. You thought that this long, arduous test was finally over and now you have to go through the whole process again.
And by the way, this is not unique to the SAT. This happens with the ACT as well. I actually had a student that was already in college on a scholarship while the ACT was threatening to cancel her scores. The case went into arbitration. If the ACT had won, the student would have had to pay back all of her scholarship money. As the student’s ACT tutor I had to testify in her defense.
How can you protect yourself?
Well if you have spent a lot of time preparing properly for the SAT (or ACT) and you expect your score to go up several hundred points from the last time you took the test, you may want to take the following two precautions:
(1) Show additional work in your test booklet even if you do not need to.
(2) Try to be certain of your answers before you bubble them in so you do not produce too many erasure marks.
Yes I do realize that the test makers are not supposed to be looking at your work in your test booklet, and I also realize that there is not supposed to be a penalty for changing your answers after checking them over. But these two key pieces of “evidence” can be used against you in a hearing. Indeed, they have been used as evidence of cheating by prosecutors in the past.
Also, if you take the above two precautions, it is less likely that you will be accused of cheating to begin with. An extremely large score increase will possibly set off a flag that the test makers will want to investigate. But they may not immediately accuse you of cheating before looking over your results carefully. If they are convinced from your test booklet that you knew what you were doing, then you will most likely be left alone.
By the way, if you happen to use my test prep materials, you will probably notice that for many problems you do not need to show much work in your test booklet at all. Many of the techniques I teach are designed to solve problems very quickly and with little to no writing. Nonetheless, if you feel like your score is going to improve several hundred points from your last test, please show some work in your test booklet anyway.
One might then ask “Does spending extra time writing in the test booklet negate the positive effects of using my time-saving strategies to begin with?”
My answer is “no.” First of all, the advice in this article is only for students that believe they will go up at least 400 total points from their last SAT (by total points, I mean 400 points across all three sections – math, reading and writing). Second, if you happen to be one of these students, then your skill level has improved so much that it should not affect your score at all to scribble a little extra work in your test booklet.
So please continue to prepare, and do the best that you can when you take your test, but be a little extra cautious if you are expecting a very large score increase.
For your everyday preparation, you may want to take a look at the following books for the SAT and ACT.
If you liked this article, please share it with your Facebook friends:
I’ll see you next week!
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Informal Algebra
Suppose we are asked to solve for x in the following equation:
x + 3 = 8
In other words, we are being asked for a number such that when we add 3 to that number we get 8. It is not too hard to see that 5 + 3 = 8, so that x = 5.
I call the technique above solving this equation informally. In other words, when we solve algebraic equations informally we are solving for the variable very quickly in our heads. I sometimes call this performing “mental math.”
Algebra The Formal Way
We can also solve for x formally by subtracting 3 from each side of the equation:
x + 3 = 8
-3 -3
x = 5
In other words, when we solve an algebraic equation formally we are writing out all the steps – just as we would do it on a test in school.
To save time on the SAT you should practice solving equations informally as much as possible. And although informal skills should take precedence during your SAT prep, you should also practice solving equations formally – this will increase your mathematical skill level.
Another Example
Let’s try another one:
5x = 30
Informally, 5 times 6 is 30, so we see that x = 6.
Formally, we can divide each side of the equation by 5:
5x = 30
5 5
x = 6
A Harder Example
Now let’s get a little harder:
5x + 3 = 48
We can still do this informally. First let’s figure out what number plus 3 is 48. Well, 45 plus 3 is 48. So 5x is 45. So x must be 9.
Here is the formal solution:
5x + 3 = 48
-3 -3
5x = 45
5 5
x = 9
Exercise
Try this one on your own: 3x + 4 = 31
And feel free to post your explanations in the comments.
College Board Question
In the following video I solve Question 1 from Test 1, Section 3 in the College Board’s Official Study Guide using the methods from this article.
Get 800 Test Prep Books
If you like the information in this article, you may want to check out the Get 800 collection of test prep books.
Please share this information with your Facebook friends:
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The Complete College Planning Calendar
by Ashleigh Bell
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!
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