If you are reading this in an email you received from me, do not click the link to sat.collegeboard.org below. Use the link to my website that is farther down on the email.
http://sat.collegeboard.org/practice/sat-question-of-the-day?questionId=20140314&oq=1 (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.)
To begin, I need to apologize. I think yesterday’s link to the SAT question was wrong. It took you to the previous day’s question. My mistake. Sorry.
The SAT staff’s explanation for today’s question is a good example of why I write my blog. They often do a wonderful job of doing the math questions the “math teacher way” but that is often a hard way to do the question. When you are taking the test, you will find there are much easier, quicker, and more accurate ways to do the questions. Please note that by the word “accurate,” I mean that it is not as simple to make silly mistakes. When doing questions the “math teacher way,” students often make common calculation errors. The test writers know what those errors are (as I did when I wrote test questions) and put those wrong answers as potential answers on the test which leads students to getting answers wrong.
Go ahead and read the SAT staff’s explanation for this question. Do you understand it? Could you have easily done it this way on test day? Would it have been quick for you? Would you have avoided thinking it was a positive slope? If your answers to these questions are “yes,” then that would have been a good way to do it. If not, let’s try my “substitute numbers for variables” strategy.
The answer is A. Instead of thinking about the coordinates (a,,0) and (0,2a), let’s substitute real numbers. Because a>0, let’s change the a to 2. Now we have (2,0) and (0,4). Draw a little grid and plot the two points. You can see that the line intersects the x-axis at 2 and the y-axis at 4. So, when you calculate the slope (change in y divided by change in x) and subtract 0-2, you get -2. When you subtract 4-0, you get 4. Then 4/-2 = -2. That’s answer A.
Was this easier? If so, I suggest you try using real numbers by substituting them for variables when they don’t give you numbers. You’ll have to remember to follow their rule. For example, in this case they told you y is twice as big as x (2a and a respectively). You could have used 6 and 3 or 786 and 393! Any pair of numbers would be okay as long as the y value is twice the x value. Remember my mantra: “The world of math is a world of patterns!” Antonio remembered it and he tells me that’s why he got into Princeton.
One final thing to learn from this question—common elements. Notice that there are 4 integer answers (all but Answer B). Eliminate B because it is an oddball. Three answers (the majority) are negative; eliminate the positive. Three answers don’t use a in them; eliminate the ones that do. That leaves you with the right answer, A! It has all the common elements: it is negative, has no a, and is an integer.
VERY IMPORTANT: this doesn’t always work. It is not the best way to do the problems. But on the SAT you need to guess after you’ve eliminated one answer. In this question, you probably realize that the slope is 2 something (2, -2, 2a, or -2a) because the change in y has to be twice the change in x because y = 2a and x = a. You’ve eliminated one answer, B) -1/2, Now you have to guess at the other four answers. Using “common elements” increases your chances of being correct BUT it isn’t a “slam dunk.”
The ACT has no guessing penalty and so you never leave a blank. Anytime you are guessing on the ACT, use common elements when you can. It will improve your odds and score!
I wonder if the ACT folks have something new for us this morning.
ACT Question of the Day: Use your “back” button to return to my website after reading the ACT Question of the Day.
Fantastic. The ACT folks have given us a question that gives me a chance to explain one of my other favorite guessing strategies!
Let’s begin by doing the “English teacher thing” which is the best way to do the question.
The answer is D. The underlined sentence is entirely superfluous. (Of course, when this question originally appeared on the test, it was about a “century ago.” Now it is closer to a century and a quarter; so, the writer’s math stinks!) In either case, we don’t need to be told how long ago it was because the previous sentence tells us Bessie was born in 1893. So, just OMIT the underlined material and move on to the next question.
Now let’s turn our attention to guessing. I’ve counted how often “NO CHANGE” and “OMIT” answers were correct on several released, actual ACT tests. Based on probability, you would expect them to be correct 25% of the time but that wasn’t the case in my research. “NO CHANGE” was correct less often than 25% and “OMIT” was correct more often than 25% of the time. Like “common elements,” that I described above, this information about the ACT English Test doesn’t always work; it simply improves your odds. If you aren’t sure what answer to choose randomly or after you’ve eliminated an answer or two, if “NO CHANGE” is among the remaining answers, avoid it. If “OMIT” is among the remaining answers, pick it.
Of course, these two guessing strategies, “common elements” and “NO CHANGE/OMIT” aren’t exactly techniques the SAT and ACT folks are going to tell you! That’s why you and all your friends should be reading my blog. Spread the word.
I’m working on a blog that will explain how to get the most from my free website. Stay tuned and you’ll see it soon.
Bob Alexander, the “SAT and ACT Wizard”