http://sat.collegeboard.org/practice/sat-question-of-the-day?src=R&questionId=20130212 (This link takes you to today’s question. If you use my archive, you will see the question related to my SAT explanation for that date.)
The answer is A. As usual the SAT math staff do a fine job of showing you a way to do this question that will keep you math teacher happy and you should take a look at it. However, there is a simpler Wizard technique to use that is faster and less prone to introducing a simple math mistake on a Saturday morning when you are in a hurry and wish you were doing sleeping late! My LNHS students learned about it last night: Change the abstract to the concrete.
They give you a and 2a instead of corresponding, respective values for x and y coordinates on a line. Then they tell you a>1 and to figure out the slope of the line. This is a “World of Math is a World of Patterns” question: just make stuff up that follows their rules. Let a be 2 since 2 is greater than 1. Now you have the coordinates (1,0) and (0,2). Draw a simple coordinate using those points and then draw the line l that passes through them. Well, it sure goes down hill so it is negative. You can see that in goes down or the “rise” is actually a “fall” or a negative rise (change in y two units) while the change is x is 1 unit or run equal 1. Rise/run is -2/1 or -1, Answer A.
By substituting numbers for the variables using their rules, we now have concrete numbers to use and now have real values to do this question. It is much easier to do and certainly is less prone to errors. Shazaam!!
Hey, LNHS students, didn’t I tell you so? The SAT folks even cooperated with a question this morning that supports the Wizard’s strategy. Very nice.
I wonder what the ACT test writers have prepared for us to start off this fine Tuesday.
http://www.act.org/qotd/ (The ACT staff does not put a date on their questions so if you click on an archived blog, you’ll get today’s question and the old explanation. Sorry. The SAT staff has dated their questions; so, the archive is helpful. The ACT folks simply don’t do that.)
The answer is J. The ACT answer isn’t bad; it helps answer this question but this particular question isn’t going to be on the test and it takes a lot of time to use their explanation. But what can you learn from this question to use on future questions? Wizard’s students have the “Wizard’s Checklist.” Among other things, they know to use the “ADD?” rule. (Watch the free YouTube video on the home page.) F, G, and H all violate the “add.” rule. Throw them out. Getting the answer is easy. Move on to the next question.
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