SAT Math: Challenging Problems #2

Here are five more challenging SAT Math problems.  Give each of them a try and let me know what you think!  The answers appear at the bottom of this post.

1)  On the number line below, the distance between each of the tick marks is the same.  What is the value of x?

Challenge 2-1

(Note:  This is a “grid-in” problem.  You need to supply your own answer.)

2)  In circle O, the diameter AB has a length of 12 inches.  If / ABC has measure 60 degrees, what is the total area, in square inches, of the shaded regions?

Challenge 2-2

(A) 18\pi - 18
(B) 18\pi - 18\sqrt{3}
(C) 36\pi - 18\sqrt{3}
(D) 36\pi - 36\sqrt{3}
(E) 72\pi - 18\sqrt{3}

3)  In the diagram below, the line makes an angle of 30 degrees with the x-axis and the line passes through the origin.  Which of the following could be the coordinates of Point P?

Challenge 2-3

(A)  (4, 3)
(B)  (5, 3)
(C)  (3\sqrt{3}, 3)
(D)  (4, 4\sqrt{3})
(E)  (6, 3)

4)  In the semicircle below, Point N is the point that has the least y-coordinate.  Point M has the least x-coordinate and Point P has the greatest x-coordinate.  What are the coordinates of Point N?

Challenge 2-4

(A)  (-2aa)
(B)  (-2a, -2a)
(C)  (-1/2a, –a)
(D)  (-a, -2a)
(E)  (-a, -3a)

5)  In the figure below, the circles are all congruent and tangent.  All lines that contain the centers of two of the circles would be either horizontal or vertical.  The total area of the circles is 100 pi.  What is the area of the shaded region?

Challenge 2-5

(A) 25 - 10\pi
(B) 50 - 10\pi
(C) 100 - 10\pi
(D) 100 - 25\pi
(E) 100 - 50\pi

If you have questions about these problems or anything else to do with the SAT, leave a comment below or send me an email at .

1)  1.5 or 3/2
2)  (B)
3)  (C)
4)  (D)
5)  (D)

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