Algebra

Link of the Day

One of the previous essay questions asked on the SAT reads, “Is there always another explanation or another point of view?”  Rather than talking loosely about your own opinion, use a specific example from current events to back up your opinion.  For example, read this article about an incident that occurred in a London art gallery.  This current event could serve as an excellent example for other broad SAT questions as well.  Can you find themes in this article that could relate it to other questions about feelings, originality, creativity, change, authority, respect, and courage?  Which facts would you need to memorize to be able to write knowledgeably about this current event?

10/9 Algebra

Read the following SAT test question and then select the correct answer. 

Read each question carefully.  Then identify the bottom line and assess your options for finding it.  Choose the most efficient method to attack the problem.  Before selecting your answer, loop back to make sure that you solved for the bottom line; you do not want to give the answer for x when your problem asks for something else entirely!

If x + y = 3 and x – y = 5, then x² - y² =

Bottom Line:  x² - y² = ?

Assess your options: For this problem, noting your bottom line can save you a lot of time!  Most people are going to solve for x and y, but your bottom line is really x² - y².  You do not need to know what x and y equal to solve this problem.  If you solve for your bottom line rather than solving for x and y, you can save time on this problem and have more time for other problems during your SAT test.

Attack the problem:  x² - y² is one of three key quadratic equations that you should have memorized.  It shows up on your Knowsys Formula chart as a² - b² = (a + b)(a – b).  If you have this memorized, you know that x² - y² = (x + y)(x – y).  You have already been given the values for both (x + y) and (x – y) in the question!  All you have to do is plug them in.  Then you have x² - y² = (x + y)(x – y) = (3)(5).  Your answer is 15. 

Loop back:  This is the process that you just used:  x² - y² = (x + y)(x – y) = (3)(5) = 15.  You solved for the bottom line, so you are ready to look down at your answer choices.

(A) 4

(B) 8

(C) 15

(D) 16

(E) 64

The correct answer is (C).

On sat.collegeboard.org, 62% of the responses were correct.

For more help with math, visit www.myknowsys.com!