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Lesson 8
216
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ARCO
■ SAT II Subject Tests
32. The correct answer is (C). sin
2
x + cos
2
x = 1 for all values of x, including 4 
θ.
33. The correct answer is (E). One way to solve this problem is to figure out what mathematical opera-
tions would be needed in g(x) to produce x from 3x – 2. First, you need x rather than 3x, so the
function would have to include dividing 3x by 3. And you don’t want –2 in the final result, so it should
also include adding 2 to the result of f(x). The expression that describes this procedure is
And we confirm that this is correct by performing this on f(x):
Alternatively, you could substitute the result of performing f(x) on x into each answer choice until you
find one that produces the value x:
(A)
3(3x – 2) + 2 = 9x – 6 + 2 = 9x – 4 Wrong!
(B)
2 – 3(3x – 2) = 2 – 9x + 6 = 8 – 9x Wrong!
(C)
Wrong!
(D)
Wrong!
(E)
Correct!
An even easier approach is to assign a value for x. Let x = 2. Then f(x) = 3(2) – 2 = 4. Now use the
result of f(x), 4, in the choices. The one that generates the value 2 (which is x) is the winner:
(A)
3(4) + 2 = 14 Wrong!
(B)
2 – 3(4) = –10 Wrong!
(C)
Wrong!
(D)
Wrong!
(E)
Correct!
34. The correct answer is (D). There are two insights required to handle this problem. First, 
∆BEG is
similar to 
∆BCA, and ∆BEF is similar to ∆BCD. This means that the ratio area ∆BEF:area ∆BEG is
the same as the ratio area of 
∆BCD:area ∆BCA. So if we find the first ratio, we also have the
second. Second, side BG, because it is perpendicular to side GE, is an altitude of triangle BEG and
of triangle BEF:

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