(A).3261
(B).5
?.6467
(D).7598
(E).9238
If you didn’t take a moment to think about this problem, you might just rush into it wielding your calculator, calculating the cosine and sine functions, squaring them each and then adding them together, etc. But take a closer look: cos2(3 63°) + sin2(3 63°) is a trigonometric identity. More specifically, it’s a Pythagorean identity: sin2q + cos2q = 1 for any angle q. So, the expression {cos2(3 63°) + sin2(3 63°)} 4/2 simplifies to 14 /2 = 1/2 = .5. B is correct. Calculator-Useless Questions Even if you wanted to, you wouldn’t be able to use your calculator on calculator-useless problems. For the most part, problems involving algebraic manipulation or problems lacking actual numerical values would fall under this category. You should be able to easily identify problems that can’t be solved with a calculator. Quite often, the answers for these questions will be variables rather than numbers. Take a look at the following example:
(x + y – 1)(x + y + 1) =
(A)(x + y)2
(B)(x + y)2 – 1
?x2 – y2
(D)x2 + x – y + y2 + 1
(E)x2 + y2 + 1
This question tests you on an algebraic topic—that is, it asks you how to find the product of two polynomials—and requires knowledge of algebraic principles rather than calculator acumen. You’re asked to manipulate variables, not produce a specific value. A calculator would be of no use here. To solve this problem, you need to notice that the two polynomials are in the format of a Difference of Two Squares: (a + b)(a – b) = a2 – b2. In our case, a = x + y and b = 1. As a result, (x + y – 1)(x + y + 1) = (x + y)2 – 1. B is correct. Don't Immediately Use Your Calculator The fact that the test contains all four of these question types means that you shouldn't get trigger-happy with your calculator. Just because you've got an awesome shiny hammer doesn't mean you should try to use it to pound in thumbtacks. Using your calculator to try to answer every question on the test would be just as unhelpful. Instead of reaching instinctively for your calculator, first take a brief look at each question and understand exactly what it's asking you to do. That short pause will save you a 美国GREat deal of time later on. For example, what if you came upon the question:
If (3, y) is a point on the graph of f(x) = , then what is y?
(A)–3
(B)–1.45
?0
(D).182
(E)4.87
A trigger-happy calculator user might immediately plug in 3 for x. But the student who takes a moment to think about the problem will probably see that the calculation would be much simpler if the function was simplified first. To start, factor 11 out of the denominator: Then, factor the numerator to its simplest form: The (x – 4) cancels out, and the function becomes f(x) = (x – 1) 11. At this point you could shift to the calculator and calculate f(x) = (3 – 1) 11 = 2/ 11 = .182, which is answer D. If you were very comfortable with math, however, you would see that you don't even have to work out this final calculation. 2 11 can't work out to any answer other than D, since you know that 2 11 isn't a negative number (like answers A and B), won’t be equal to zero (answer C), and also won't be 美国GREater than 1 (answer英语作文
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