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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Hard System of Equations Problem for the Revised SAT
Last week I gave you a Level 5 problem about systems of equations for the revised SAT to try. Today I will provide a solution. If you have not yet attempted the problem go back and take a look at it first so you can try it on your own. Here is the link: Hard Problem for the Revised SAT
Level 5 – System of Equations
Here is the problem once again followed by solutions:
3x + 9y = 11
cx + dy = 55
In the system of equations above, c and d are constants. If the system has infinitely many solutions, what is the value of c/d ?
Solution: The system of equations
3x + 9y = 11
cx + dy = 55
has infinitely many solutions if 3/c = 9/d = 11/55. In particular, we must have 3/c = 9/d, or equivalently c/d = 3/9 = 1/3 or .333.
Note: The general form of an equation of a line is ax + by = c where a, b, and c are real numbers. More information about this type of equation can be found in the books below.
Feel free to add your own solutions to the comments.
More Hard SAT Math Practice Problems
For many more SAT math problems like these, each with several fully explained solutions, check out my SAT math books for the revised SAT. If you received above a 600 on the PSAT take a look at
28 New SAT Math Lessons to Improve Your Score in One Month.
Everyone else should consider
New SAT Math Problems arranged by Topic and Difficulty Level.
Click on the pictures below for more information about these books.
If you think your friends would like to see this, please share:
Speak to you soon!
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Hard SAT Math Question – System of Equations
Today I would like to provide a hard SAT math question. This question is for the revised SAT beginning March 2016.
Level 5 – System of Equations
3x + 9y = 11
cx + dy = 55
In the system of equations above, c and d are constants. If the system has infinitely many solutions, what is the value of c/d ?
Please feel free to post your solutions or attempted solutions in the comments below and we can discuss the best way to solve the problem. I will post solutions to this problem next week.
More SAT Math Practice Problems
For many more SAT math problems like these, each with several fully explained solutions, check out my SAT math books for the revised SAT. If you received above a 600 on the PSAT take a look at
28 New SAT Math Lessons to Improve Your Score in One Month.
Everyone else should consider
New SAT Math Problems arranged by Topic and Difficulty Level.
Click on the pictures below for more information about these books.
If you think your friends would like to try this problem, please share:
Speak to you soon!
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28 New SAT Math Lessons – Advanced Course
Today I would like to announce the release of 28 New SAT Math Lessons to Improve Your Score in One Month – Advanced Course.
The paperback is now on sale on Amazon for only $7.54. This sale may run for just a few hours (until 12 PM), 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: 28 New SAT Math Lessons – Advanced
If you would like to check the book out before making a purchase you can download a free sample here: 28 Advanced Free Sample
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 today (December 4, 2015).
Take a look at my product page to see all of my books: Get 800 Product Page
I am also making the following promotion available until December 30, 2015: if you buy any 3 of my books in paperback, you get all 6 of the following SAT math prep books for free.
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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28 New SAT Math Lessons – Advanced Course
Last week I posted a question from my new book 28 New SAT Math Lessons – Advanced Course. Today I will provide a solution to that question. And now here is last week’s question with a solution.
Level 5 Passport to Advanced Math
For a polynomial p(x), the value of p(–3) is 5. Which of the following must be true about p(x) ?
(A) x – 8 is a factor of p(x).
(B) x + 5 is a factor of p(x).
(C) x – 5 is a factor of p(x).
(D) The remainder when p(x) is divided by x + 3 is 5.
This problem can be solved in just a few seconds if you know the remainder theorem. This theorem says that for a polynomial p, p(r) = a if and only if the remainder when p(x) is divided by x – r is a.
To apply the remainder theorem to this questions, since p(–3) = 5, by the remainder theorem , the remainder when p(x) is divided by x + 3 is 5, choice (D).
If you found this post useful, please share it with your Facebook friends:
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28 New SAT Math Lessons – Advanced Course
Hello everybody. I have been working overtime every single day for the last several months to get the most up to date material to you for the revised SAT as quickly as possible. I am pleased to announce that I will be releasing the new edition of my best selling SAT math book, the Advanced Course from my 28 SAT Math Lessons series in just a few short weeks.
Get on the Notification List
If you are interested in this book, then I strongly suggest you get on my notification list as I will be releasing the book at a very low promotional price for the first few hours of its release. To get on the list simply send an email to
with the words “Notify Me” in the subject line.
Get a FREE Sample
If you would like to also get an idea of what the new book will look like, then I am happy to provide you with a free sample consisting of 2 full lessons from the book. To get the free sample simply include the words “Free Sample” in the main body of the email. Please be patient as it may take up to 24 hours to get the sample to you. I anticipate that I will be fulfilling a lot of these requests.
It would be great if you could also provide some information about yourself in the email. For example, are you a student, a parent, a teacher, a tutor, or just someone that enjoys mathematics. What do you do for a living? What are your hobbies? And anything else you would like to share. I would genuinely like to learn about the people that are interested in my materials. This is of course optional however.
I’d like to finish this post with an additional problem right from the book (this one is not included in the free sample). Feel free to post your attempted solutions in the comments. I will provide my own solutions next week.
Level 5 Passport to Advanced Math
For a polynomial p(x), the value of p(–3) is 5. Which of the following must be true about p(x) ?
(A) x – 8 is a factor of p(x).
(B) x + 5 is a factor of p(x).
(C) x – 5 is a factor of p(x).
(D) The remainder when p(x) is divided by x + 3 is 5.
If you liked this post, please share it with your Facebook friends:
And don’t forget to check out my social media pages:
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555 Advanced Math Problems
Today I would like to announce the release of 555 Advanced Math Problems for Middle School Students.
The paperback is now on sale on Amazon for only $5.37. This sale may run for just a few hours (until 12 PM), and once the sale ends the price will go up to $30. 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: 555 Advanced 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 today (November 20, 2015).
Take a look at my product page to see all of my books: Get 800 Product Page
I am also making the following promotion available until November 30, 2015: if you buy any 3 of my books in paperback, you get all 6 of the following SAT math prep books for free.
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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Hard Problem Solving Question
Last week I gave you a Level 5 Problem Solving question for the revised SAT to try. Today I will provide a solution for this problem. If you have not yet attempted the problem go back and take a look at it first so you can try it on your own. Here is the link: Hard Problem Solving Question for the Revised SAT
Level 5 – Problem Solving
Here is the problem once again followed by a solution:
John, a United States resident, is on vacation in Spain and is trying to decide if he should use his own credit card from the U.S., or to purchase a prepaid credit card for 500 euros in Spain.
The bank that issues John’s U.S. credit card converts all purchase prices at the foreign exchange rate for that day, and an additional fee of 6% of the converted cost is applied before the bank posts the charge.
If John decides to purchase the prepaid card, he can use this card spending dollars at the exchange rate for that day with no fee, but he loses any money left unspent on the card.
Suppose that John does decide to buy the prepaid card. What is the least number of the 500 euros John must spend for the prepaid card to have been the cheaper option? Round your answer to the nearest whole number of euros.
Solution: If we let d be the cost of the 500 euro card in dollars, and we let e be John’s total purchases on the prepaid card in euros, we need
d < 1.06(d/500)e.
We can divide each side of this inequality by d to get 1 < e(1.06/500), and then multiply each side of this last equation by 500/1.06 to get 500/1.06 < e, or equivalently e > 471.698 .
So the least number of the 500 euros John must spend is 472.
For an even more detailed solution to this problem check out New SAT Math Problems arranged by Topic and Difficulty Level.
Feel free to add your own solutions to the comments.
More Hard SAT Math Practice Problems
For many more hard SAT math problems like these, each with several fully explained solutions, check out New SAT Math Problems arranged by Topic and Difficulty Level. Click on the picture below for more information about this book.
If you think your friends would like to try this problem, please share:
Speak to you soon!
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Hard Problem Solving Question
Today I would like to provide an example of a hard “problem solving” question that could show up on the revised SAT. You can use your calculator for this one.
Level 5 – Problem Solving
John, a United States resident, is on vacation in Spain and is trying to decide if he should use his own credit card from the U.S., or to purchase a prepaid credit card for 500 euros in Spain.
The bank that issues John’s U.S. credit card converts all purchase prices at the foreign exchange rate for that day, and an additional fee of 6% of the converted cost is applied before the bank posts the charge.
If John decides to purchase the prepaid card, he can use this card spending dollars at the exchange rate for that day with no fee, but he loses any money left unspent on the card.
Suppose that John does decide to buy the prepaid card. What is the least number of the 500 euros John must spend for the prepaid card to have been the cheaper option? Round your answer to the nearest whole number of euros.
Please feel free to post your solutions or attempted solutions in the comments below and we can discuss the best way to solve the problem. I will post solutions to this problem next week.
More Hard SAT Math Practice Problems
For many more hard SAT math problems like these, each with several fully explained solutions, check out New SAT Math Problems arranged by Topic and Difficulty Level. Click on the picture below for more information about this book.
If you think your friends would like to try this problem, please share:
Speak to you soon!
What Will Your Math Score Be on the New SAT?
Lately many students have been asking me how they can figure out what their math score will be on the new SAT beginning March 2016. Although the College Board has 4 sample tests for the new SAT at their website, they do not provide any method for scoring these tests.
Free SAT Math Diagnostic Exam
As a solution to this problem I have created this 28 minute SAT Math Diagnostic Exam complete with a scoring guide so that you can now know approximately what you would score in math if you were to take the new SAT today. To download this diagnostic for free simply enter your email below and then press the “Download PDF” button:
If you have any trouble downloading your free exam, you can contact me at
If you think your friends might be interested in this free diagnostic exam, please share it with them on Facebook:
Thank you all for your continued support!
Hard Geometry Problem
Last week I gave you a Level 4 Geometry problem for the revised SAT to try. Today I will provide a solution for this problem. If you have not yet attempted the problem go back and take a look at it first so you can try it on your own. Here is the link: Hard Geometry Problem for the Revised SAT
Level 4 – Geometry
Here is the problem once again followed by a solution:
The head of a copper “hexagon head screw bolt” (one cross section of which is shown above) has the shape of a cylinder with a hole shaped like a regular hexagon. The cylindrical head is 2 cm thick with a base diameter of 3 cm. The hexagonal hole is only half the thickness of the entire head, and each side of a hexagonal cross section has a length of 1 cm. Given that the density of copper is 8.96 grams per cubic cm, and density is mass divided by volume, find the mass of the head to the nearest gram.
Solution: We first compute the volume of the head. There are two parts to the volume.
The bottom half of the head is a cylinder with height 2/2 = 1 cm and base radius 3/2. It follows that the volume is
V = πr2h = π(3/2)2(1) = 9π/4 cm3.
The top half of the head consists of the same cylinder as the bottom half, but this time we have to subtract off the volume of a hexagonal prism. The regular hexagonal face can be divided into 6 equilateral triangles, each with area
A = s2√3/4 = 12√3/4 = √3/4.
So the volume of the hexagonal prism is
V = Bh = (6√3/4)(1) = 3√3/2 cm3
and the volume of the top half of the head is
9π/4 – 3√3/2 cm3
It follows that the total volume of the head is
9π/4 + (9π/4 – 3√3/2) = 18π/4 – 3√3/2 = (9π – 3√3)/2 cm3.
Finally,
D = M/V → 8.96 = M / [(9π – 3√3)/2] → M = 8.96 ∙ (9π – 3√3)/2 ≈ 103.39 grams.
To the nearest gram, the answer is 103.
For an even more detailed solution to this problem check out New SAT Math Problems arranged by Topic and Difficulty Level.
Feel free to add your own solutions to the comments.
More Hard SAT Math Practice Problems
For many more hard SAT math problems like these, each with several fully explained solutions, check out New SAT Math Problems arranged by Topic and Difficulty Level. Click on the picture below for more information about this book.
If you think your friends would like to try this problem, please share:
Speak to you soon!