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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Breakdown of the SAT Math Sections
Today I would like to tell you exactly what types of math problems to expect on the SAT. This information comes right from the College Board. The information I give here will probably be enough for most of you, but if you want more information right from the College Board, you can download the full document here: About the SAT Math Test
There are two math sections on the SAT: one where a calculator is allowed, and one where a calculator is not allowed. The following is a breakdown of the exact number of questions of each type that you can expect in each of these sections.
“Calculator Allowed” Section
Heart of Algebra: 11 questions, 29% of section
Geometry, Trigonometry, and Complex Numbers: 3 questions, 8% of section
Passport to Advanced Math: 7 questions, 18% of section
Problem Solving and Data Analysis: 17 questions, 45% of section
Total: 38 questions
“No Calculator” Section
Heart of Algebra: 8 questions, 40% of section
Geometry, Trigonometry, and Complex Numbers: 3 questions, 15% of section
Passport to Advanced Math: 9 questions, 45% of section
Problem Solving and Data Analysis: 0 questions, 0% of section
Total: 20 questions
If you are preparing for the SAT, you may want to check out this special deal on all 8 of my SAT math prep books:
Get Eight Books for the Price of Three
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Thank you all for your continued support!
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The Contrapositive
A statement of the form “if p, then q” is known as a conditional statement. An example of such a statement is “If you are a cat, then you have fur.” Another common way to say this is “All cats have fur.”
There are 3 other statements that often come up in association with a conditional statement. Let’s use the example above to illustrate.
Conditional: If you are a cat, then you have fur.
Converse: If you have fur, then you are a cat.
Inverse: If you are not a cat, then you do not have fur.
Contrapositive: If you do not have fur, then you are not a cat.
The most important thing to know for standardized tests such as the SHSAT is that the contrapositive is logically equivalent to the original conditional statement! The converse and inverse are not.
For example, suppose the conditional statement “All cats have fur” is true. You may want to rewrite this as “If you are a cat, then you have fur.” It follows that “If you do not have fur, then you are not a cat” is also true.
In particular, if you are given the statement “Skittles does not have fur,” you can infer “Skittles is not a cat.”
Note that neither the converse nor the inverse is logically equivalent to the original conditional statement, but they are equivalent to each other.
Example 1
All of Jim’s friends can ski.
If the statement above is true, which of the following statements must also be true?
(A) If John cannot ski, then he is not Jim’s friend
(B) If Jeff can ski, then he is not Jim’s friend.
(C) If Joseph can ski, then he is Jim’s friend.
(D) If James is Jim’s friend, then he cannot ski.
(E) If Jordan is not Jim’s friend, then he cannot ski.
Solution: The given statement can be written in conditional form as “If you are Jim’s friend, then you can ski.” The contrapositive of this statement is “If you cannot ski, then you are not Jim’s friend. Replacing “you” with “John” gives the correct answer as choice (A).
Example 2
If a beverage is listed in menu A, it is also listed in menu B.
If the statement above is true, which of the following statements must also be true?
(A) If a beverage is listed in menu B, it is also in menu A.
(B) If a beverage is not listed in menu A, it is not listed in menu B.
(C) If a beverage is not listed in menu B, it is not listed in menu A.
(D) If a beverage is not listed in menu B, it is in menu A.
(E) If a beverage is listed in menu B, it is not listed in menu A.
Solution: Simply observe that the statement in choice (C) is the contrapositive of the given statement. So the answer is choice (C).
Conclusion
If you understand how to identify the contrapositive of a conditional statement, then you will be able to easily get most logic questions correct that appear on standardized tests.
If you will be taking the ACT, you may want to check out my series of ACT math prep books:
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New SAT Verbal Prep Book
The New SAT Verbal Prep Book for Reading and Writing Mastery gives you the most effective tips, tricks and tactics from Get 800, a prep company of doctors dedicated to their students achieving their dream SAT scores.
Click the following link to get to the book’s Amazon page: New SAT Verbal Prep Book
If you would like to take a look at a free sample of this book, click the following link: New SAT Verbal Free Sample
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
Please share this information with your Facebook friends:
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SHSAT Verbal Prep Book
If you or your child are planning to attend one of the specialized high schools in NYC, make sure to get your copy of the SHSAT Verbal Prep Book to Improve Your Score in Two Months.
Click the following link to get to the book’s Amazon page: SHSAT Verbal Prep Book
For more information on the specialized high schools you may want to take a look at the following page on the Department of Education’s website: Specialized High Schools
The material in this SHSAT prep book includes:
- 40 scrambled paragraphs
- 6 logical reasoning practice quizzes
- 15 reading passages
- Full explanations for all questions.
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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SHSAT Verbal Prep Book – Just $4.54 on Amazon
Today I would like to announce the release of SHSAT Verbal Prep Book to Improve Your Score in Two Months.
The paperback is now on sale on Amazon for only $4.54. 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: SHSAT Verbal Prep Book
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 (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 the end of today (May 23, 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
Thank you all for your continued support!
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Free Proctored Exam
Sullivan Tutorials, in cooperation with Get 800, are inviting you to Staten Island, NY to take a free proctored PSAT. The test will be available on
May 12th from 6:30 – 9:30 P.M OR May 15th from 1:00 P.M. – 4:00 P.M.
We will be testing students to see if they can make it into one our National Merit prep groups. There is no charge to take this proctored test and there is no obligation to sign up for a course. To save yourself a seat, please send an email to:
You will receive the testing location via email.
About Sullivan Tutorials
For the past 25 years, Sullivan Tutorials has been responsible for about 60% of all the National Merit Semi-Finalists and all but a few of the Finalists on Staten Island. Students are placed in groups of 5-6 students with similar math scores. Groups meet for math sessions in the home of one student and for verbal sessions in the home of another student in the group.
National Merit Students
Students that make it into one of the National Merit groups will start meeting on weekday evenings in mid-July. They will meet for two 3 hour verbal sessions and two 2 hour math sessions in July and August and then 2 hour sessions once a week right up to the PSAT in October. They will then take the PSAT in October, and the SAT in Nov, Dec and Jan.
This is a very difficult year as the SAT has changed radically. To see some of the major changes, take a look at this article I wrote a while back: Preview the Math Changes on the “New” SAT
In addition, here are some of the changes in SAT Verbal:
- The essay will be optional – individual institutions will decide if they require the essay.
- There will be a 65 minute reading section.
- There will be a 35 minute language and writing section.
- There will no longer be sentence completions.
- There will be a greater emphasis on the meaning of words in extended contexts, and on how word choice shapes meaning, tone and impact.
Other Students
Students who do not make into one of the National Merit groups may start preparing with Sullivan Tutorials in mid-August to take the November, December and January exams if they are fairly strong in math and have scores that are reasonably high. All other students will begin preparing in January and take the new May exam.
Meetings in May will start with a 15 minute Q & A for parents and then students will take a 2 hour and ten minute PSAT. These exams will be graded before the students leave. Parents can either have a consultation right then, or they can do so by phone during the week after the exam.
National Merit Information
There are three levels for the National Merit. The first is 201 pts and up which is Commended Student. This information goes to any two colleges that the student designates. The second and more important level is Semi-Finalist. The cut off for this varies between 215 and 219 in New York State. 218 is the most common number. Students who get this are considered elite – most colleges want these students for bragging rights. These students are informed in early September of their senior year that they are semi-finalists and they are given the opportunity to write an essay that is evaluated by a committee. The top 1000 students in America are then designated as Finalists. Scholarship money is attached to this designation. On the aegis of becoming a finalist, many students are eligible for full scholarships to some of their chosen schools.
Once again, to save yourself a seat for the proctored exam, please send an email to:
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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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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