Question 1:

The trapezoid in the figure above has an area of 34 square inches and an altitude h of 4 inches. What is the sum of its parallel sides?
a + b = 14 inches

a + b = 15 inches

a + b = 16 inches

a + b = 17 inches

Question 2:

If O is the center of circle C in the figure above, which of the following numbers is closer to the ratio between the area of the circle and the area of the isosceles triangle ABC?
2.7

3.1

3.3

3.5

Question 3: What is the area of the parallelogram shown on the coordinate plane below?

24

36

40

52

Question 4: If the parallelogram from the previous problem is translated 1 unit left, what is the area of the parallelogram that is part of the second quadrant?

7

8

11

12

Question 5: In the figure below, right triangles ABC and ADE are similar. Which of the following relations must be true?

AB/AC = AE/AD

AB/AC = AD/AE

AB/AC = AC/AB

AC/AE = ED/CB






Question 6: The piece of cardboard shown below has the shape of a square with the sides equal to 3 inches. A student cuts the four corners of the square. The right triangles cut have legs equal to 1 inch. What is the area of the remaining cardboard?



5 square inches

6 square inches

7 square inches

8 square inches

Question 7: Is the remaining cardboard of problem 6 a regular polygon?
yes

no

Question 8: What percentage of the area of the triangle below is shadowed? All triangles are equilateral.


50%

60%

62.5%

65.5%



A circle of center O is inscribed in a right isosceles triangle, ABC as seen in the figure above. If side BC is tangent to the circle in point T and the radius of the circle is r, which of the following approximates best the length of the segment AT?
1.5r

2r

2.25r

2.41r

Question 10: If the radius of sphere S₁ is r₁, the radius of sphere S₂ is r₂ and r₁ = 2r₂, what is the ratio of the volumes of the two spheres, S₁/S₂ ?
1/8

1/2

2

8

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