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40. The correct answer is (C). [0] A reflection in the line x = –y maps a point P with coordinates (x,y)
onto point P
′ with coordinates (–y, –x).
(x,y)
(–y, –x)
A (–1,–2)
→ A′ (2,1)
B (0,4)
→ B′ (–4,0)
C (3,–1)
→ C′ (1,–3)
41. The correct answer is (C). [0] You can answer this question either by applying the information pro-
vided in the explanation for question 28, above, or by visualizing the graph of the sine and cosine
functions:

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Mathematics Level IC/IIC Subject Tests
245
ARCO
■ SAT II Subject Tests
w w w . p e t e r s o n s . c o m / a r c o
42. The correct answer is (C). [–] The general form of the equation of a circle is:
(x – h)
2
+ (y – k)
2
= r
2
where (h,k) is the center of the circle and r its radius. The circle described in the question stem has a
radius of 2 and its center at (2, –1):
If a line of the form x = k (a vertical line) is tangent to this circle, it passes through point (0, –1) or (4, –1).
43. The correct answer is (D). [0] The graph intersects the y–axis where x = 0:
y = 2 cos 2(0) + 2
y = 2 cos 0 + 2
Since cos 0 = 1:
y = 2(1) + 2 = 4
44. The correct answer is (D). [–] According to the Binomial Theorem, the last term in the expansion
of a binomial having the form (a + b)
n
is b
n
. So the last term of this expansion will be (3y)
4
= 81y
4
.
45. The correct answer is (C). [–] Since a die has six faces, the chance that any one of those faces will be
exposed is 1 out of 6. With two dice, the chance that any two faces will both be exposed is 1/6 
× 1/6 = 1/36.
There are, however, three combinations that total 4: 1 + 3, 2 + 2, and 3 + 1. Thus, the chance that a 4 will
appear is 3/36 = 1/12.