Final Review

An architect is designing a horse stable in the shape of a horseshoe. The figure shows the design in the coordinate plane. The architect wants to confirm that entrance A is congruent to entrance B. The line segment connecting the points (−8, 7) and (−6, 9) represents entrance A, and the line segment connecting the points (8, 7) and (6, 9) represents entrance B. Which of the following transformations can be used by the architect to map entrance A to entrance B to prove that the two entrances are congruent?

• A translation 12 units to the right

• A reflection about the y-axis

• A rotation 90° clockwise about the origin

• A dilation from the origin by a scale factor of 1

A town investigated whether to install a traffic light at a certain four-way intersection. Sensors were installed under the pavement at each entry to the intersection. The sensors were able to record the number of vehicles entering and exiting the intersection, which of the four roads were used, and the times of entry and exit of all vehicles using the intersection. Which of the following best describes the method used for collecting these data?

• Survey

• Experiment

• Simulation

• Observational study

Triangle ABC is the preimage of a transformation that consists of a reflection across x-axis followed by a reflection across the y-axis. Which of the triangles is the image of △ABC under this transformation?

• Triangle in Quadrant 1

• Triangle in Quadrant 2

• Triangle in Quadrant 4

• None of the triangles

The measure of one of the interior angles of an isosceles triangle is 76°. What could be the measure, in degrees, of one of the other interior angles of the triangle?

• 28

• 52

• 76

• 104

A power-generating windmill is being designed and will consist of a tower with three large blades that rotate on a central hub at the top of the tower. The height of the tower from the ground to the center of the hub where the 3 blades meet is 262 feet, and the length of the blades from the center of the hub to the tip of each blade is 148 feet. The tower is in the shape of a right circular cylinder that has a diameter of 40 feet, as shown in the figure. When one of the blades is extended straight up, what is the total height of the windmill from its bottom to the tip of the extended blade?

• 336 feet

• 370 feet

• 410 feet

• 450 feet

A power-generating windmill is being designed and will consist of a tower with three large blades that rotate on a central hub at the top of the tower. The height of the tower from the ground to the center of the hub where the 3 blades meet is 262 feet, and the length of the blades from the center of the hub to the tip of each blade is 148 feet. The tower is in the shape of a right circular cylinder that has a diameter of 40 feet, as shown in the figure. As the blades rotate they span an area and displace the air in that area. In 1/3 of a full rotation of one of the blades, which if the following is closest to the area, in square feet, that the blade spans?

• 6,000 square feet

• 23,000 square feet

• 69,000 square feet

• 92,000 square feet

A power-generating windmill is being designed and will consist of a tower with three large blades that rotate on a central hub at the top of the tower. The height of the tower from the ground to the center of the hub where the 3 blades meet is 262 feet, and the length of the blades from the center of the hub to the tip of each blade is 148 feet. The tower is in the shape of a right circular cylinder that has a diameter of 40 feet, as shown in the figure. The windmill's tower extends from the ground to the center of the hub. Which of the following is closest to the volume of the windmill's tower?

• 185,982 cubic feet

• 329,239 cubic feet

• 515,221 cubic feet

• 1,316,956 cubic feet

A 25-foot ladder is propped up against a wall. The ladder is placed 7 feet from the base of the wall and reaches 24 feet up the wall. Which of the following equations could be solved to find θ, the measure of the angle that the ladder makes with the ground?

• tan(θ) = 24/7

• tan(θ) = 24/25

• tan(θ) = 7/24

• tan(θ) = 7/25

Which of the following sequences of transformations in the xy-plane shown can be used to prove that ∠A and ∠B are congruent?

• Let ∠A be the preimage of a transformation consisting of a reflection across the x-axis and then a translation of the reflected image 5 units to the left such that the image of ∠A under the transformation coincides with ∠B.

• Let ∠A be the preimage of a transformation consisting of a reflection across the y-axis and then a translation of the reflected image 5 units down such that the image of ∠A under the transformation coincides with ∠B.

• Let ∠A be the preimage of a transformation consisting of a 90° rotation clockwise about the origin and then a translation of the rotated image 5 units to the left such that the image of ∠A under the transformation coincides with ∠B.

• Let ∠A be the preimage of a transformation consisting of a 90° rotation counterclockwise about the origin and then a translation of the rotated image 5 units down such that the image of ∠A under the transformation coincides with ∠B.

Mr. Gaspar assigned a homework project to the students in his statistics classes. Each submission earned an integer score between 40 and 99, inclusive. Mr. Gaspar wants to present a summary of the distribution of the submission scores, including the exact value of the median score, to his classes. Which of the following data displays should Mr. Gaspar use to accomplish his goal?

• Histogram

• Box plot

• Circle graph

• Stem-and-leaf plot