1.

In the ﬁgure above, the diameter of the circle is \(\)10\(\).

Quantity A |
Quantity B |

The area of quadrilateral \(\)ABCD\(\) | \(\)40\(\) |

2. For the rectangular solid below, ﬁnd the following.

(a) Surface area of the solid

(b) Length of diagonal \(\)AB\(\)

3. A circle is inscribed in a square with sides of length \(\)5\(\).

Quantity A |
Quantity B |

The circumference of the circle | \(\)15\(\) |

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

(A) \(\)\frac{ 1 }{ 70 }\(\)

(B) \(\)\frac{ 1 }{ 35 }\(\)

(C) \(\)\frac{ 1 }{ 7 }\(\)

(D) \(\)\frac{ 1 }{ 4 }\(\)

(E) \(\)\frac{ 1 }{ 2 }\(\)

5. 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 \(\)1\(\) inch wide on all sides. For what value of \(\)x\(\), in inches, is the area of the frame equal to the area of the picture?

(A) \(\)4\(\)

(B) \(\)5\(\)

(C) \(\)6\(\)

(D) \(\)7\(\)

(E) \(\)8\(\)

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

(A) \(\)9\(\)

(B) \(\)13\(\)

(C) \(\)16\(\)

(D) \(\)18\(\)

(E) \(\)25\(\)

7. In the figure, \(\)ABCD\(\) and \(\)ABEC\(\) are parallelograms. The area of the quadrilateral \(\)ABED\(\) is \(\)6\(\). What is the area of the parallelogram \(\)ABCD\(\) ?

(A) \(\)2\(\)

(B) \(\)4\(\)

(C) \(\)4.5\(\)

(D) \(\)5\(\)

(E) \(\)6\(\)

8. In the figure, if \(\)y = 60\(\), then what is the value of \(\)z\(\) ?

(A) \(\)20\(\)

(B) \(\)30\(\)

(C) \(\)55\(\)

(D) \(\)75\(\)

(E) \(\)90\(\)

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

Quantity A |
Quantity B |

\(\)AB\(\) | \(\)PQ\(\) |

10. In the figure, what is the area of ∆\(\)ABC\(\) if \(\)EC/CD = 3\(\) ?

(A) \(\)12\(\)

(B) \(\)24\(\)

(C) \(\)81\(\)

(D) \(\)121.5\(\)

(E) \(\)143\(\)

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

(A) \(\)2\(\)

(B) \(\)4\(\)

(C) \(\)6\(\)

(D) \(\)8\(\)

(E) \(\)10\(\)

12. In the figure, ∆\(\)ABC\(\) is inscribed in the circle. The triangle does not contain the center of the circle \(\)O\(\).

Quantity A |
Quantity B |

\(\)x\(\) | \(\)90\(\) |

Quantity A |
Quantity B |

The area of the square | \(\)50\(\) |

14. In the \(\)7\(\)-inch square above, another square is inscribed. What fraction of the larger square is shaded?

(A) \(\)3/12\(\)

(B) \(\)24/49\(\)

(C) \(\)1/2\(\)

(D) \(\)25/49\(\)

(E) \(\)7/12\(\)

15.

Quantity A |
Quantity B |

\(\)a+g+f\(\) | \(\)e+b+h\(\) |

##### Answers:

1 D

2 (a) 208 (b) \(\)3\sqrt { 17 }\(\)

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