[Math Center]



In the figure above, the diameter of the circle is [latex]10[latex].

Quantity A Quantity B
The area of quadrilateral [latex]ABCD[latex] [latex]40[latex]


2. pikachu(1)For the rectangular solid below, find the following.

(a) Surface area of the solid
(b) Length of diagonal [latex]AB[latex]


3. A circle is inscribed in a square with sides of length [latex]5[latex].

Quantity A Quantity B
The circumference of the circle [latex]15[latex]


4. Eight points are equally spaced on a circle. If [latex]4[latex] of the [latex]8[latex] points are to be chosen at random, what is the probability that a quadrilateral having the [latex]4[latex] points chosen as vertices will be a square? 

(A) [latex]\frac{ 1 }{ 70 }[latex]
(B) [latex]\frac{ 1 }{ 35 }[latex]
(C) [latex]\frac{ 1 }{ 7 }[latex]
(D) [latex]\frac{ 1 }{ 4 }[latex]
(E) [latex]\frac{ 1 }{ 2 }[latex]


5. pikachu(1)A flat rectangular picture, represented by the unshaded region in the figure above, is mounted in a flat rectangular frame, represented by the shaded region. The frame is [latex]1[latex] inch wide on all sides. For what value of [latex]x[latex], in inches, is the area of the frame equal to the area of the picture? 

(A) [latex]4[latex] 
(B) [latex]5[latex] 
(C) [latex]6[latex] 
(D) [latex]7[latex] 
(E) [latex]8[latex]


6. In the figure, [latex]ABCD[latex] is a square, and [latex]BC[latex] is tangent to the circle with radius [latex]3[latex]. [latex]P[latex] is the point of intersection of the line [latex]OC[latex] and the circle. If [latex]PC = 2[latex], then what is the area of square [latex]ABCD[latex] ?

pikachu(1)(A) [latex]9[latex]
(B) [latex]13[latex]
(C) [latex]16[latex]
(D) [latex]18[latex]
(E) [latex]25[latex]


7. In the figure, [latex]ABCD[latex] and [latex]ABEC[latex] are parallelograms. The area of the quadrilateral [latex]ABED[latex] is [latex]6[latex]. What is the area of the parallelogram [latex]ABCD[latex] ?

pikachu(1)(A) [latex]2[latex]
(B) [latex]4[latex]
(C) [latex]4.5[latex]
(D) [latex]5[latex]
(E) [latex]6[latex]


8. In the figure, if [latex]y = 60[latex], then what is the value of [latex]z[latex] ?

pikachu(1)(A) [latex]20[latex]
(B) [latex]30[latex]
(C) [latex]55[latex]
(D) [latex]75[latex]
(E) [latex]90[latex]


9. In the figure, [latex]P[latex] and [latex]Q[latex] are centers of the two circles of radius [latex]3[latex] and [latex]4[latex], respectively. [latex]A[latex] and [latex]B[latex] are the points at which a common tangent touches each circle.


Quantity A Quantity B
[latex]AB[latex] [latex]PQ[latex]


10. In the figure, what is the area of ∆[latex]ABC[latex] if [latex]EC/CD = 3[latex] ?

pikachu(1)(A) [latex]12[latex]
(B) [latex]24[latex]
(C) [latex]81[latex]
(D) [latex]121.5[latex]
(E) [latex]143[latex]


11. In the figure above, point [latex]O[latex] is the center of the circle, points [latex]A[latex] and [latex]C[latex] are located on the circle, and line segment [latex]BC[latex] is tangent to the circle. If the area of triangle [latex]OBC[latex] is [latex]24[latex], what is the length of [latex]AB[latex]?


(A) [latex]2[latex]
(B) [latex]4[latex]
(C) [latex]6[latex]
(D) [latex]8[latex]
(E) [latex]10[latex]


12. In the figure, ∆[latex]ABC[latex] is inscribed in the circle. The triangle does not contain the center of the circle [latex]O[latex].

Quantity A Quantity B
[latex]x[latex] [latex]90[latex]


13. pikachu(1)

Quantity A Quantity B
The area of the square [latex]50[latex]



14.  In the [latex]7[latex]-inch square above, another square is inscribed. What fraction of the larger square is shaded?


(A) [latex]3/12[latex]
(B) [latex]24/49[latex]
(C) [latex]1/2[latex]
(D) [latex]25/49[latex]
(E) [latex]7/12[latex]



Quantity A Quantity B
[latex]a+g+f[latex] [latex]e+b+h[latex]




1 D
2 (a) 208 (b) [latex]3\sqrt { 17 }[latex]
3 A
4 B
5 C
6 C
7 B
8 B
9 B
10 D
11 B
12 A
13 A
14 B
15 A