The SAT Prep Black Book(126)

I would start off by simplifying the expression on the left-hand side of the equation, dividing by n/n and ‘eliminating’ an n from the top of first fraction and the bottom of the second fraction. Then it’s a little easier to see that the whole thing could be combined to this:

n/(n2 - 1)

(Notice that (n - 1) can be multiplied by (n + 1) to create the difference of squares (n2 - 1). This is something we’d want to be able to do in our heads, without needing to foil it out manually.)

So now our equation looks like this:

n/(n2 - 1) = 5/k

This means that n corresponds to 5, and (n2 - 1) corresponds to k.

If n is 5, then (n2 - 1) is 24, so the answer is (C).

In our wrong answers, we see the value of n, which helps reassure us that we attacked the question correctly, because it suggests that the College Board is hoping some test-takers will correctly realize that n is 5 but then forget the question was asking for k. We also see a series that goes 24, 25, 26, which might seem odd at first, because normally we’d expect the right answer to be in the middle of a series like that. But there’s a certain logic to it here, because in order to arrive at 24 we have to square 5 and subtract 1; in this case, the wrong answers reflect squaring 5 and adding 1, and squaring 5 while forgetting to add or subtract. We can see there’s a certain symmetry the College Board is going for here, in trying to give test-takers a variety of ways to mess this question up. And that can reassure us that squaring 5 and then subtracting 1 was, indeed, the right way to go.





Conclusion


We’ve just looked at a whole bunch of SAT Math questions, and we never really broke a sweat! We did this by sticking to our simple process, and by looking for quick and easy answers. As we saw, the hardest part of each problem was the setup. The actual calculations didn’t present much of a problem, as long as we had our basic concepts in order.

On the next page, you’ll see a brief, one-page summary of the main ideas to keep in mind on the SAT Math section. After that, we’ll dive into the SAT Writing section. You’ll see that the Writing section, like the SAT Math section, is a lot easier to attack if you’re familiar with a core set of basic principles.





Video Demonstrations


If you’d like to see videos of some sample solutions like the ones in this book, please visit http://www.SATprepVideos.com. A selection of free videos is available for readers of this book.





SAT Math Quick Summary


This is a one-page summary of the major relevant concepts. Use it to evaluate your comprehension or jog your memory. For a more in-depth treatment of these ideas, see the rest of the section.



The Big Secret: SAT Math tests very simple things in very strange ways.

The concepts in the SAT Math section must be limited because of standardization. No trig or advanced stats—just arithmetic, algebra, and geometry. Refer to the SAT Math Toolbox if necessary.

Focus on the definitions and properties of the concepts in each question, not on formulas.

All SAT Math is “easy,” and each question can be done in 30 seconds or less if you find the fastest solution. If your solution is very complicated, you’re probably doing the question wrong.

Look for shortcuts, things that cancel out, equivalent terms, etc. Leave expressions as fractions and radicals, instead of decimals, for easier canceling and substitution.

Diagrams are assumed to be to scale unless the question says otherwise. Taking a close look can often help to eliminate wrong answers or even point to the right one without doing any math.

Diagrams that aren't drawn to scale often yield important information if you redraw them to scale.

Every question contains all the information you need to answer it (unless “not enough information” is an answer choice, in which case there may not be enough information), even if it doesn't seem like that. If you understand every word in the question, then you know enough to mark the right answer.

Some common wrong answer patterns include choices that are:

ohalf or double the right answer

oin a series with the right answer

oa number that you have to find “on the way” to the answer

osimilar in appearance to the right answer

I recommend a step-by-step process called the Math Path for questions that are hard to figure out:

oRead the question carefully and consider the words. This is the most important step.

oConsider any diagrams—scale, missing dimensions, etc.

oConsider answer choices (if there are any)—relationships with each other and with question.

oWhat areas of math are involved? What can the SAT test in those areas? (Math Toolbox.)

oIn light of steps 1 - 4, look for a solution that would take 30 seconds or less, ideally.

oSolve the problem.