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1. AD // CB and cut by transversal AB. AC ⊥ CB. AB = 10, ∠DAB = 35°. Which of the following expressions could be used to determine the length of AC?
A. 10 cos55° B. 10 sin55° C. 10 cos35° D. 10 tan35°
E. 10 cot35°
2. What is the area, in square inches, of the circle that is circumscribed about an equilateral triangle that has a perimeter of 36 inches?
A. 18π ≈ 56.55
B. 27π ≈ 84.82
C. 36π ≈ 113.10
D. 48π ≈ 150.80
E. 56π ≈ 175.93
3. The apothem (drawn from the center, perpendicular to a side) of a regular hexagon has a length of 6. What is the perimeter of the hexagon?
A. 2√3 ≈ 3.46
B. 4√3 ≈ 6.93
C. 8√3 ≈ 13.86
D. 12√3 ≈ 20.78
E. 24√3 ≈ 41.57
4. Trapezoid ABCD is inscribed in circle P. If AB ≌ BC ≌ CD and AP = 12, what is the measure of the median of the trapezoid?
A. 6 B. 12 C. 18 D. 24 E. 30
5. First rotate the triangle bounded by the vertices (0, 0), (0, 5), (4, 0) about the origin 180°. Then, reflect the resulting image across the x-axis. What quadrant contains the final image of the triangle after both transformations?
A. quadrant I B. quadrant II C. quadrant III
D. quadrant IV
E. None of them
6. Theorem: A triangle has at most one obtuse angle. Eduardo is proving the theorem above by contradiction. He began by assuming that in ΔABC, ∠A and ∠B are both obtuse. Which theorem will Eduardo use to reach a contradiction?
A. If two angles of a triangle are equal, the sides opposite the angles are equal.
B. If two supplementary angles are equal, the angles each measure 90°.
C. The largest angle in a triangle is opposite the longest side.
D. The sum of the measures of the angles of a triangle is 180°.
E. In a triangle, the sum of any two sides is longer than the third side and the difference of any two sides is shorter than the third side.
Two lines in a plane always intersect in exactly one point.
7. Which of the following best describes a counterexample to the assertion above?
A. coplanar lines
B. parallel lines
C. perpendicular lines
D. intersecting lines
E. any two opposite sieds in a polygon
8. Which triangles must be similar?
A. two obtuse triangles
B. two scalene triangles with congruent bases
C. two right triangles
D. two isosceles triangles with congruent vertex angles
E. two acute triangles
9. Water flows into a container at a constant rate. The equation w = 4t + 10 shows how the amount of water, w, in gallons, in the container relates to the amount of time, t, in minutes, since the water began to flow. What does the 10 in the equation represent?
A. the gallons of water already in the container
B. the rate at which the water flows into the container
C. the gallons of water needed to fill the container
D. the minutes needed to fill the container
E. None of them
10. The diagram above shows a construction of cube blocks. What is the view of the right side?
E. none of them
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