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Geometry
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Posttest
 
This test is meant to be taken after you've finished studying this Power Tactics book. This test will tell you how well you've mastered the material and what topics you still need to review.
 

1.    If the perimeter of square WXYZ is two times the perimeter of square abcd, and the perimeter of abcd is 8, then what is the length of side WX?
(A) 1
(B) 2
(C) 4
(D) 6
(E) 8
2.    What is the value of 2x?
(A) 46
(B) 69
(C) 92
(D) 134
(E) 180
3.    If a = 60, then what is the value of b?
(A) 10
(B) 25
(C) 30
(D) 45
(E) 60
4.    What is the length of side ac?
(A) 8
(B) 7
(C) 6
(D) 5
(E) It cannot be determined from the information given
5.    The two legs of a right triangle have lengths of x and 3y, and the hypotenuse has a length of x + 2y. In terms of y, what is the value of x?
(A) 5y
(B) 4y
(C)
(D)
(E)
6.    Grace wants to cut a piece of paper to create a lidless box with a volume of 200 cubic units. She plans to cut out a square from each corner of a rectangular piece of paper, then fold the sides up to create this box. If the original dimensions of the uncut piece of paper are 18 by 13, then what is the perimeter of one of the squares she will need to cut?
(A) 3
(B) 4
(C) 8
(D) 12
(E) 16
7.    In the figure above, WOYZ is a square. X is the midpoint of side WO, and the perimeter of square WOYZ is 32. What is the area of the circle?
(A) 8π
(B) 12π
(C) 16π
(D) 20π
(E) 32π
8.    Triangle OAB is inscribed in circle O. If the length of side AB is 10, and the value of each side is an integer, what is the smallest possible sum of sides OA and OB?

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9.    In the figure above, point h has the coordinates (4,2) and point g has the coordinates (–4, –4). What is the length of line segment gh?


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10.    The base of a cylindrical tube has a radius of 3 inches. Jim fills up part of the tube with water. If the total volume of water in the tube is 108π, how many inches up the side of the tube does the water reach?

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