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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28 ACT Math Lessons – Beginner Course
Now Half Price
Today I would like to announce the release of 28 ACT Math Lessons to Improve Your Score in One Month – Beginner Course.
The paperback is now on sale on Amazon for 50% off. Click the following link to get to the book’s Amazon page: 28 ACT Math Lessons – Beginner
The sale has ended. Thank you to all who participated.
Check out my other ACT math books here: Get 800 ACT Math Books
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
Thank you all for your continued support!
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28 ACT Math Lessons – Intermediate CourseNow Half Price
Today I would like to announce the release of 28 ACT Math Lessons to Improve Your Score in One Month – Intermediate Course.
The paperback is now on sale on Amazon for 50% off. Click the following link to get to the book’s Amazon page: 28 ACT Math Lessons – Intermediate
Visit my website to see all of my other books: Get 800 Books
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
Thank you all for your continued support!
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Hard Functions Problem
with Solutions for the SAT
Today I will give several solutions to the problem I posted yesterday. Use this link to see the question: Hard Function Problem for the SAT
This problem is from the book 28 SAT Math Lessons – Advanced Course. Here is the problem one more time, followed by three methods of solution.
Level 5 Functions
For which of the following functions is it true that f(-x) = f(x) for all values of x ?
A) f(x) = x2 + 5
B) f(x) = x2 + 5x
C) f(x) = x3 + 5x
D) f(x) = x3 + 5
Solution by picking numbers: Let’s choose a value for x, say x = 2. We compute f(-2) and f(2) for each answer choice.
f(-2) f(2)
A) 9 9
B) -6 14
C) -18 18
D) -3 13
Since choices (B), (C), and (D) do not match up, we can eliminate them. The answer is therefore choice (A).
Important note: (A) is not the correct answer simply because both computations gave the same answer. It is correct because all 3 of the other choices did not work. You absolutely must check all four choices!
* Quick solution: We are looking for an even function. Each answer choice is a polynomial. Therefore, the answer is the one with only even powers of x. This is choice (A) (remember that 5 = 5x0 ).
Note: See the following post for more information on this method: Even and Odd Functions
Graphical solution: Begin putting each of the four answer choices into your graphing calculator (starting with choice (B) or (C)), and choose the one that is symmetrical with respect to the y-axis. This is choice (A).
Note: Again, see this post for more information: Even and Odd Functions
More SAT and ACT Math Problems with Explanations
If you are preparing for the SAT, ACT, or an SAT math subject test, you may want to take a look at the Get 800 collection of test prep books.
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Hard Functions Problem for the SAT
Today I would like to give a hard functions problem from the book 28 SAT Math Lessons – Advanced Course. I will provide a full explanation for this problem tomorrow. Feel free to leave your own solutions in the comments.
Level 5 Functions
For which of the following functions is it true that f(-x) = f(x) for all values of x ?
A) f(x) = x2 + 5
B) f(x) = x2 + 5x
C) f(x) = x3 + 5x
D) f(x) = x3 + 5
If you’re having trouble getting started, you may want to read the following post: Even and Odd Functions
More SAT and ACT Math Problems with Explanations
If you are preparing for the SAT, ACT, or an SAT math subject test, you may want to take a look at the Get 800 collection of test prep books.
And if you liked this article, please share it with your Facebook friends:
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320 SAT Chemistry Subject Test Problems
Today I would like to announce the release of 320 SAT Chemistry Subject Test Problems arranged by Topic and Difficulty Level.
The paperback is now on sale on Amazon. Click the following link to get to the book’s Amazon page: 320 SAT Chemistry Subject Test Problems
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 of my other books (except for 28 ACT Math Lessons, which is not available as a PDF). 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, February 16, 2017.
You can forward your Amazon confirmation to
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
Thank you all for your continued support!
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28 ACT Math Lessons – Advanced CourseNow Half Price
Today I would like to announce the release of 28 ACT Math Lessons to Improve Your Score in One Month – Advanced Course.
The paperback is now on sale on Amazon for 50% off. Click the following link to get to the book’s Amazon page: 28 ACT Math Lessons – Advanced
Take a look at my product page to see all of my other 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
Thank you all for your continued support!
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Hard Statistics Problem with Solution
Today I would like to give a solution to yesterday’s statistics problem. Before reading the solution, you may want to review the following article: Changing Averages to Sums
Here is the problem once again, followed by a solution.
Level 5 Statistics
Suppose that the average (arithmetic mean) of a, b, and c is h, the average of b, c, and d is j, the average of c, d, and e is k, and the average of d, e, and f is m. What is the value of (a + c) – (d + f ) ?
A) h – j + k – m
B) 3(h – j + k – m)
C) 3/4 (h – j + k – m)
D) 3(h + j + k + m)
E) 3/4 (h + j + k + m)
Solution by changing averages to sums: We have
a + b + c = 3h
b + c + d = 3j
c + d + e = 3k
d + e + f = 3m
We subtract the second equation from the first equation to get
a – d = 3h – 3j
We subtract the fourth equation from the third equation to get
c – f = 3k – 3m
We now add these last two equations to get
a – d + c – f = 3h – 3j + 3k – 3m
This is equivalent to choice B.
More SAT and ACT Math Problems with Explanations
If you are preparing for the SAT, ACT, or an SAT math subject test, you may want to take a look at the Get 800 collection of test prep books.
And if you liked this article, please share it with your Facebook friends:
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Hard Statistics Problem
Today I would like to give a hard statistics problem from the book 320 SAT Math Subject Test Problems – Level 2. I will provide a full explanation for this problem tomorrow. Feel free to leave your own solutions in the comments.
Level 5 Statistics
Suppose that the average (arithmetic mean) of a, b, and c is h, the average of b, c, and d is j, the average of c, d, and e is k, and the average of d, e, and f is m. What is the value of (a + c) – (d + f ) ?
A) h – j + k – m
B) 3(h – j + k – m)
C) 3/4 (h – j + k – m)
D) 3(h + j + k + m)
E) 3/4 (h + j + k + m)
More SAT and ACT Math Problems with Explanations
If you are preparing for the SAT, ACT, or an SAT math subject test, you may want to take a look at the Get 800 collection of test prep books.
And if you liked this article, please share it with your Facebook friends:
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SAT Exponential Growth Problem with Solution
Today I would like to give a solution to the SAT exponential growth problem presented in this post: Exponential Growth and Decay
Here is the problem once again, followed by a solution.
Level 4 SAT Exponential Growth
On January 1, 2015, a family living on an island releases their two pet rabbits into the wild. Due to the short gestation period of rabbits, and the fact that the rabbits have no natural predators on this island, the rabbit population doubles each month. If P represents the rabbit population years after January 1, 2015, then which of the following equations best models the rabbit population on this island over time?
A) P = 2t/12 + 1
B) P = 2t + 1
C) P = 212t
D) P = 212t + 1
Solution using the exponential growth model formula: As seen in example (4) from this post, a quantity that continually doubles over a fixed time period can be modeled by the exponential function P = a(2)t/d where a is the quantity at time t = 0, and d is the doubling time in years. In this case, there are initially 2 rabbits, so that a = 2, and the doubling time is every month, or every 1/12 year.
It follows that P = 2(2)t ÷ 1/12 = 2(2)12t = 21212t = 21 + 12t = 212t + 1, choice (D).
Notes: (1) For a review of the laws of exponents used here, see the following post: Laws of Exponents
(2) For additional methods for solving this problem, you may want to take a look at 28 New SAT Math Lessons – Advanced Course
More SAT and ACT Math Problems with Explanations
If you are preparing for the SAT or ACT, you may want to take a look at the Get 800 collection of test prep books.
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Exponential Growth and Decay
The current version of the SAT gives problems on exponential growth and decay. Here are the basics that you should know if you want to get a perfect SAT score:
A general exponential function has the form f(t) = a(1 + r)ct, where a = f(0) is the initial amount and r is the growth rate. If r > 0, then we have exponential growth and if r < 0 we have exponential decay.
Examples: (1) The exponential function f(t) = 300(2)t can be used to model a population with a growth rate of 1 = 100% each year that begins with 300 specimens. The growth rate of 100% tells us that the population doubles each year.
(2) The exponential function f(t) = 50(3)2t can be used to model a population with a growth rate of 2 = 200% every 6 months that begins with 50 specimens. The growth rate of 200% tells us that the population triples. Since c = 2, the tripling occurs every 1/2 year or 6 months.
(3) The exponential function f(t) = 120(0.75)t/3 can be used to model a substance which is decaying at a rate of 1 – 0.75 = 0.25 = 25% every 3 years. The initial amount of the substance might be 120 grams. Since c = 1/3, the 25% decay occurs every 3 years.
(4) A quantity that continually doubles over a fixed time period can be modeled by the exponential function f(t) = a(2)t/d where a is the quantity at time t = 0, and d is the doubling time in years.
Now try the following SAT math problem. I will post a solution after Thanksgiving, but feel free to post your own solutions in the comments meanwhile.
Level 4 SAT Exponential Growth
On January 1, 2015, a family living on an island releases their two pet rabbits into the wild. Due to the short gestation period of rabbits, and the fact that the rabbits have no natural predators on this island, the rabbit population doubles each month. If P represents the rabbit population years after January 1, 2015, then which of the following equations best models the rabbit population on this island over time?
A) P = 2t/12 + 1
B) P = 2t + 1
C) P = 212t
D) P = 212t + 1
More SAT and ACT Math Problems with Explanations
If you are preparing for the SAT or ACT, you may want to take a look at the Get 800 collection of test prep books.
And if you liked this article, please share it with your Facebook friends:
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