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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Exponents Question with Solutions
Last week I posted the laws of exponents that can be useful to know for standardized tests such as the ACT and SAT. You can see that post here: Laws of Exponents
Here are the laws once again for your convenience.
These should be memorized by students that are trying to get a perfect math score. I also mentioned that exponent problems can usually be solved by methods other than using the algebraic rules, but by using algebra you will solve them very, very quickly, giving you time to move on to other questions and to check your answers.
Last week, I had this level 5 exponents problem for you to solve:
Level 5 Exponents Question
If y = 7x, then which of the following expressions is equivalent to 49x − 7x+2 for all positive integer values of x?
A) y²
B) y² − y
C) y² − 7y
D) y² − 49y
Let’s look at two different ways to solve this problem.
Algebraic Solution
Let’s solve this algebraically using the exponent laws.
49x – 7x+2= (7²)x −7x72 = (7x)² − 49(7x) = y² – 49y
In the first equality we rewrote 49 as 7² and used the third law in our list to rewrite 7x+2 as 7x7². In the second equality we simply rewrote 7² as 49. Finally, in the third equality we replaced 7x by y twice.
This is choice D.
Solution by Picking Numbers
And here is an alternative solution using the strategy of “picking numbers”.
Let’s choose a value for x, say x = 2.
Then we have:
y = 7² = 49, and 49x − 7x+2 = 49² − 74 = 0.
Put a nice, big, dark circle around 0. Make it obvious that this is the value you are expecting to be your solution. Now substitute y = 49 into each answer choice:
A) y² = 49² = 2401
B) y² − y = 49² − 49 = 2401 – 49 = 2352
C) y² − 7y = 49² – 7*49 = 2401 – 343 = 2058
D) y² − 49y = 49² – 49*49 = 2401 – 2401 = 0
Since A, B, and C are incorrect, we can eliminate them. Therefore the answer choice is D.
As you can see the method of picking numbers is more time consuming than the algebraic method, but you will get the right answer as long as you are careful.
Whichever method you choose, you should try to check your answer with a different method if possible. If you can only solve the problem by picking numbers, then at least pick different numbers when you are “checking.”
And don’t forget to check out the Get 800 collection of test prep books.
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Laws of Exponents
Students seem to have a lot of trouble remembering the basic rules of exponents. On standardized tests such as the ACT and SAT, you can often do problems involving exponents by using some basic strategies that avoid using these rules altogether. Using the exponent laws, however, usually leads to the quickest solutions. Students that are trying to get a perfect ACT or SAT math score will want to become more proficient in using these laws of exponents. Here is a basic review.
Now let’s try a level 5 question involving exponents.
Level 5 Exponents Question
If y = 7x, then which of the following expressions is equivalent to 49x − 7x+2 for all positive integer values of x?
A) y²
B) y² − y
C) y² − 7y
D) y² − 49y
You can see solutions to this problem here: Level 5 Exponents Question with Solutions
And don’t forget to check out the Get 800 collection of test prep books.
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Solving Quadratic Equations
by Completing the Square
Before we learn how to solve quadratic equations by completing the square, let’s go over how to solve the problem given to you two weeks ago.
Solution to Problem from Two Weeks Ago
Two weeks ago we went over how to solve simple quadratic equations using the square root property. To review that material click the following link: The Square Root Property on the SAT
I also promised to provide a solution to the following question:
(x – 3)2 = 2
What is the solution set of the above equation?
(A) {1, 5}
(B) {3 + √2}
(C) {3 – √2, 3 + √2}
(D) The equation has no solutions.
Solution: When we apply the square root property we get
x – 3 = ±√2.
We then add 3 to each side of this last equation to get the two solutions
x = 3±√2.
This is choice (C).
Completing the Square
Before we solve a quadratic equation by completing the square you may want to review the procedure of completing the square itself. You can find a detailed explanation of that procedure here: Completing the Square on the SAT
Solving Quadratic Equations by Completing the Square
A quadratic equation has the form ax2 + bx + c = 0.
Let’s use an example to show how to solve such an equation by completing the square.
Example: In the quadratic equation x2 – 2x – 15 = 0, find the positive solution for x.
Solution by completing the square: We first add 15 to each side of the given equation to get
x2 – 2x = 15.
We now take half of –2, which is –1, and square this number to get 1. We then add 1 to each side of the equation to get
x2 – 2x + 1 = 16.
This is equivalent to
(x – 1)2 = 16.
We now apply the square root property to get
x – 1 = ±4.
So x = 1 ± 4. This yields the two solutions 1 + 4 = 5, and 1 – 4 = –3. Since we want the positive solution for x, the answer is 5.
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320 ACT Math Problems – Second Edition
Today I would like to announce that the second edition of 320 ACT Math Problems arranged by Topic and Difficulty Level is on sale on Amazon for only $5.57 for the next few hours.
The sale officially end at 3 PM (sometimes Amazon allows the sale to run longer, sometimes they don’t) 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 ACT Math Problems – Second Edition
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 (February 2, 2016).
Take a look at my product page to see all of my books: Get 800 Product Page
Note that based on customer feedback I have made just a few changes from the first edition. A few modifications have been made to some of the harder problems, and some additional solutions have been added.
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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The Square Root Property
Before we learn about the square root property, let’s go over how to solve the problem given to you last week.
Solution to Last Week’s Problem
In last week’s post we went over how to complete the square on an expression of the form
x2 + bx
You can see that post here: Completing the Square
I also promised to provide a solution to the following question:
If the method of completing the square is used to rewrite the expression above in the form (x – h)2 + k, then what is the value of h – k ?
Solution: We divide –8 by 2 to get –4, and then square this number to get 16. So we add and subtract 16 to the given expression to get
x2 – 8x = x2 – 8x + 16 – 16 = (x – 4)2 – 16
So h = 4, k = –16, and therefore h – k = 4 –(–16) = 4 + 16 = 20.
The Square Root Property
The square root property says that if x2 = a2, then x = ±a.
Example 1: The equation x2 = 9 has the two solutions
x = 3 and x = –3.
Important note: Using the square root property is different from taking a square root. We apply the square root property to an equation of the form x2 = a2 to get two solutions, whereas when we take the positive square root of a number we get just one answer.
For example when we take the positive square root of 9 we get 3, but when we apply the square root property to the equation x2 = 9, we have seen that we get the two solutions x = 3 and x = –3.
Example 2:
(x – 3)2 = 2
What is the solution set of the above equation?
(A) {1, 5}
(B) {3 + √2}
(C) {3 – √2, 3 + √2}
(D) The equation has no solutions.
I will provide you with the solution to this problem next week. In the meantime feel free to try this problem yourself and post your own solution in the comments.
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Completing the Square
Today I would like to discuss the method of completing the square. This is a technique with many useful applications. In particular, there are several types of problems on the revised SAT where this technique can be used.
We complete the square on an expression of the form
x2 + bx
To complete the square we simply take half of b, and then square the result. In other words we get (b/2)2.
The expression x2 + bx + (b/2)2 is always a perfect square. In fact,
x2 + bx + (b/2)2 = (x + b/2)2
Example 1: Let’s complete the square in the expression x2 + 6x.
Well half of 6 is 3, and when we square 3 we get 9. So the new expression is x2 + 6x + 9 which factors as (x + 3)2.
Important notes: (1) When we complete the square we usually get an expression that is not equal to the original expression. For example,
x2 + 6x ≠ x2 + 6x + 9.
(2) The coefficient of x2 must be 1 before we complete the square. So, for example, we cannot complete the square on the expression
2x2 + 32x.
But we can first factor out the 2 to get 2(x2 + 16x), and then complete the square on the expression x2 + 16x to get
2(x2 + 16x + 64).
Note that we increased the expression by 2 ⋅ 64 = 128 .
Example 2:
If the method of completing the square is used to rewrite the expression above in the form (x – h)2 + k, then what is the value of h – k ?
I will provide you with the solution to this problem next week. In the meantime feel free to try this problem yourself and post your own solution in the comments.
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28 New SAT Math Lessons – Beginner Course
Today I would like to announce the release of 28 New SAT Math Lessons to Improve Your Score in One Month – Beginner Course.
The paperback is now on sale on Amazon for only $5.29. 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.
The promotion has ended. Thanks to all of you that participated. I will still honor the incentive given below until the end of this month (January 31, 2016).
Click the following link to get to the book’s Amazon page: 28 New SAT Math Lessons – Beginner
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 (January 11, 2016 January 31, 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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SEVEN SAT Math Prep Books For The Price of THREE
Due to the popularity of my seven book bundle for the current SAT I am making a brand new seven book bundle available for the revised SAT. This new bundle also includes two books for the SAT math subject tests.
For a price of only $87, you will receive digital downloads of the following books as PDF files:
• 28 New SAT Math Lessons – Beginner Course
• 28 New SAT Math Lessons – Intermediate Course
• 28 New SAT Math Lessons – Advanced Course
• The 32 Most Effective SAT Math Strategies
• New SAT Math Problems
• 320 SAT Math Subject Test Problems – Level 1
• 320 SAT Math Subject Test Problems – Level 2
As an additional bonus you will receive two Challenge Sets each consisting of 16 challenging math problems to help raise your level of mathematical maturity.
Note that if you were to buy each of these books separately the total price would be $209.93. But by purchasing electronic copies now you will get all seven books for just $87. This is a 60% savings. To place your order simply click the following button.
For more information about these books click the following link:
Get 800 SAT Math 7 Book Bundle
If you have any questions or concerns please feel free to contact me at
And 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 – Intermediate Course
Today I would like to announce the release of 28 New SAT Math Lessons to Improve Your Score in One Month – Intermediate Course.
The paperback is now on sale on Amazon for only $6.22. 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 – Intermediate
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 21, 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 7 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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