Come back to www.coolrocketschool.org after you finish today’s math problem on the college board site. You can use this problem and the solution to learn to solve numerous other mathematics problems by spending five minutes here today.
First, go to www.collegeboard.com question of the day and solve the math problem. Look at the hint AND the solution. Look at the hint and the solution whether you are correct or not. Always look at the hint and the solution on the SAT site, as the hints and solutions are presented to address the way to solve the exact question as you will see them on the SAT test, with the solution explanations relating to what the question is designed to test. This visualization will come back to help you again and again. I can give you more help and strategies on this site that relate to other questions like this one. Combine my tutorial help with the actual question to help you to understand why this particular type of question is asked, and you can solve MANY others.
Please come back and note below exactly why the question and the answer is presented this way. You are being asked to show your aptitude for using what you know to solve something new. On the SAT, you are often 'detecting' a way to find the answer. Your aptitude can be racheted up by prediction strategies. Know what will be asked and how those questions are designed, and you can spend your time at the test actually finding the solution and checking your answer.
From the solution explanation to this problem, you can understand the following about other math problems on the SAT: If you connect what you know with what you need to know, you will reap more points solving problems on the SAT:
The most helpful step you could do with a problem like this one is to visualize it, by jotting it down with pencil and paper, and to notice as soon as possible that if you plug in numbers to make the bottom number (the number you are dividing into the top number) equal to zero, the number you use to make this value on the bottom equal zero will be the value of x that will NOT define y, as the top number divided by zero will not define y.
You are looking for a value of x that will make the denominator zero. Those numbers are 4 and -3. Positive 4 is not one of the answer choices, but negative 3 is. Therefore, -3 is the answer (B.)
1) Know what happens to signs, positive and negative, when you add, subtract, multiply, or divide (and how to assume the positive sign on positive numbers when operating with those numbers).
2) Plug in possible answers, as the numbers will be low enough to do so with or without a calculator, and the problems are about concepts rather than the actual calculations.
3) Visualize or to sketch the problem so you will see the type of answer you are looking to find.
4) Know facts about how zero affects other parts of a math problem, especially in terms of eliminating possibilities.
In learning about zero, pay some attention to the number line, as well as to the concept of zero as none. That is: Notice that there are instances when you are looking for the answer to be zero in order to find what another number is, and there are times when you will be expected to understand that there is distance between numbers, whether positive or negative: the absolute value.
5) Think about zero and absolute value in other types of problems. This will help in thinking about adding and subtracting positive and negative values.
Draw a number line left and right and up and down before beginning the math section. Put some increments on each side to use in considering positive and negative numbers and visualization.
For example, the weather forecaster says that today it is 5 degrees Fahrenheit, and tomorrow we are expecting the temperature to be -10 degrees Fahrenheit. How many degrees below freezing is this prediction if freezing is 32 degrees Fahrenheit? It is 42 degrees BELOW freezing because freezing is 32 degrees above the zero and -10 is ten more degrees below the zero.
Now, did the weather forecaster say that it would be 10 degrees below freezing (= +22 degrees) or ten degrees below zero? Or did the forecaster say the temperature will be 42 degrees below freezing (=-10 degrees Fahrenheit)?
6) Practice finding x or y when you have one or the other. Remember, the letters can be other symbols than ‘x’ or ‘y’--Call them other letters for practice; but do remember that some letters also indicate other things in the math section (i.e.,m for mode; a,b,c commonly used in the Pythagorean theorem problems).
You can ‘see’ that y is 4 in the same way I am asking you to ‘see’ what to do in this SAT problem today. But what if the numbers were bigger? Use this low number problem to see what you would do. If you know that x is 3 and x + y=7, then you plug in ‘3’ for x.
x+y=7
y=7-x (I do this by changing the signs of what I move across the equal sign, either way. If I had moved the 7 to the left of the equal sign, it would be -7. What is actually happening in the way I did it is that x is being subtracted from both sides of the equation.)
y=7-3
y=4
or
x+y=7
-7+y=-x
-7+y=-3
Y=-3+7
Y=4
If you do not get the answer, there are things to learn with this question and answer that will help you to do many others on the SAT. If you DO get the answer right, you need to notice some of the ways you can shorten the procedure on questions you understand so that you can check the answers quickly to make sure you answered the question asked. The most common way to miss problems that you do know how to do is to answer the wrong question. This is part of the way you are tested on the SAT.
In today’s problem, one of the answer choices is negative 4 (-4). One of the other possibilities that correctly answers the question is positive 4 (4). If you knew how to do this but did not check yourself, you could easily choose the wrong answer—even after all the work of doing the problem correctly. Learn strategies to check the work you know how to do and to get those points. Learn strategies to give your best shot on the ones you do not understand—by applying all that you do know to make a solid, quick guess. Then, move on. If you are totally lost, try to eliminate one or two answers.
Then, choose an answer from the remaining answers—unless you are completely mystified. In that case, weigh the odds and decide whether to skip it altogether. You are penalized ¼ of a point for every incorrect answer EXCEPT the math grid questions. Do learn to do the grid question style so that you can guess on every single one. There is absolutely no penalty on the grid in answers in mathematics. Don’t let them intimidate you!rocketcat&judiethcarolMay10,2010
