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SAMPLE PROBLEMS
Algebra
EXAMPLE:
If 
and if x 
=
3 – 2i, then x
2
=
(A)
3 – 12i
(B)
5 – 12i
(C)
9 – 12i
(D)
13 – 12i
(E)
13 – 15i
Solution:
x
2
= (3 – 2i)
2
= (3 – 2i)(3 – 2i) = 9 – 12i + 4i
2
Since 
, i
2
= –1. Therefore:
9 – 12i + 4i
2
= 9 – 12i + 4(–1) = 5 – 12i
So the correct answer is (B).
Plane Geometry
EXAMPLE:
In the following figure, if PQ is parallel to ST, then y =
(A)
20
(B)
40
(C)
50
(D)
60
(E)
80

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Mathematics Level IC/IIC Subject Tests
191
ARCO
■ SAT II Subject Tests
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Solution: Since the sum of the degree measures of the interior angles of a triangle is 180:
45 + 55 + PQR = 180
PQR = 180 – 100 = 80
Since PQR = x + x:
2x = 80
x = 40
Since PQ and ST are parallel, x = y, and y = 40.
So the correct answer is (B).
(NOTE: Level II does not test plane geometry per se, so this is a problem that might appear on Level I, but
would not appear on Level II.)
Coordinate Geometry
EXAMPLE:
Which of the lines in the above figure is the graph of y = –2?
(A) a
(B) b
(C) c
(D) d
(E) e
Solution: The graph of y = –2 is a horizontal line with y intercept –2. So the correct answer is (A).
Solid Geometry
EXAMPLE:
If a cube has edges of length 1, what is the distance from any vertex to the center of the cube?
(A)
(B)
(C) 1
(D)
(E)

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Lesson 8
192
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ARCO
■ SAT II Subject Tests
Solution: A figure will make the solution to the problem easier to understand:
The center of the cube lies on the hypotenuse of a right triangle formed by an edge of the cube, a diagonal
of the face of the cube, and the diagonal of the cube itself. The diagonal of the face of the cube forms a
right isosceles triangle:
Since the legs of the triangle have length 1, the hypotenuse has length 1 
× 
. Now we can calculate
the length of the diagonal of the cube using the Pythagorean Theorem:
Since the center of the cube lies at the midpoint of the diagonal of the cube, the distance from any vertex
to the center of the cube is 
. So the correct answer is (B).
Trigonometry
EXAMPLE:
sin
2
(2x) + cos
2
(2x) =
(A) 0
(B) 1
(C) 2
(D) 4
(E) 4 sin
2
x
2
cosx
2
The correct answer to this item is (B): “sin
2
A + cos
2
A = 1” is one of the Pythagorean Identities.

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Mathematics Level IC/IIC Subject Tests
193
ARCO
■ SAT II Subject Tests
w w w . p e t e r s o n s . c o m / a r c o