Problem 1 :
In rectangle PQRS above, arcs QT and RT are quarter circles with centers at P and S, respectively. If the radius of each quarter circle is 1, what is the area of the shaded region?
Problem 2 :
The cube shown above has edges of length 2, and A and B are midpoints of two of the edges. What is the length of AB (not shown) ?
A) √2 B) √3 C) √5 D) √6 E) √10
Problem 3 :
In the figure above, what is the value of c in terms of a and b?
A) a + 3b - 180 B) 2a + 2b - 180 C) 180 - a - b
D) 360 - a - b E) 360 - 2a - 3b
Problem 4 :
In right triangle ABC above, EF || AC, E and F is the midpoint of BC. What is the area of the shaded rectangular region?
A) 25 B ) 25√2 C) 50 D) 50√2 E) 100
Problem 5 :
Naomi makes silver jewelry. For one style of earnings she cuts wedges from a silver disk, as shown in the center of the disk. If the weight of each uncut disk is a uniformly distributed 2.5 grams, how many grams does each wedge weigh?
Problem 6 :
The flag shown is made of overlapping equilateral triangles ADF and BCE. Because ribbon is to be sewn around the entire outer edge, it is necessary to know the perimeter of the flag. If CD, DE, and EF each have length 10 inches, what is the length, in inches, of the perimeter shown in bold?
Problem 7 :
In the figure above, EBCD is a square and AE = 8. What is the area of EBCD?
Problem 8 :
In the figure above, PQST is a rectangle and URST is a square. PU = 5 and UT is a positive integer. If the area of PQST must be more than 10 but less than 30, what is one possible value of UT?
Problem 9 :
In the figure above, what is the area of the shaded square?
Problem 10 :
Five points, A, B, C, D, and E, lie on a line, not necessarily in that order. AB has a length of 24. Point C is the midpoint of AB, and point D is the midpoint of AC. If the distance between D and E is 5, what is one possible distance between A and E?
Problem 11 :
1) 2 - π/2
2) AB = √6
3) c = 360 - 2a - 3b
4) 50
5) 0.3 grams
6) 90
7) 192 square units.
8) possible value of x is 3.
9) 5 square units.
10) AE = 11
11) 9/4
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