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More Lessons for the Regents High School Exam

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High School Math based on the topics required for the Regents Exam conducted by NYSED. The following are the worked solutions for the Geometry (Common Core) Regents High School Examination June 2015.

The following are questions for the past paper:

Regents High School Geometry June 2015 Exam (pdf).

Scroll down the page for the step by step solutions.

Geometry - June 2015 Regents - Questions and solutions 1 - 5

- Which object is formed when right triangle RST shown below is rotated around leg RS?
- The center of circle Q has coordinates (3,-2). If circle Q passes through R(7,1), what is the length of its diameter?
- In the diagram below, congruent figures 1, 2, and 3 are drawn.

Which sequence of transformations maps figure 1 onto figure 2 and then figure 2 onto figure 3?

(1) a reflection followed by a translation

(2) a rotation followed by a translation

(3) a translation followed by a reflection

(4) a translation followed by a rotation

Geometry - June 2015 Regents - Questions and solutions 6 - 10

7. A shipping container is in the shape of a right rectangular prism with a length of 12 feet, a width of 8.5 feet, and a height of 4 feet. The container is completely filled with contents that weigh, on average, 0.25 pound per cubic foot. What is the weight, in pounds, of the contents in the container?

9. Which equation represents a line that is perpendicular to the line represented by 2x - y = 7?

Geometry - June 2015 Regents - Questions and solutions 11 - 15

14. The equation of a circle is x^{2} + y^{2} + 6y = 7. What are the coordinates of the center and the length of the radius of the circle?

(1) center (0,3) and radius 4

(2) center (0,-3) and radius 4

(3) center (0,3) and radius 16

(4) center (0,-3) and radius 16

Geometry - June 2015 Regents - Questions and solutions 16 - 20

19. A gallon of paint will cover approximately 450 square feet. An artist computations. wants to paint all the outside surfaces of a cube measuring 12 feet on each edge. What is the least number of gallons of paint he must buy to paint the cube?

Geometry - June 2015 Regents - Questions and solutions 21 - 24

22. The line 3y = -2x + 8 is transformed by a dilation centered at the origin. Which linear equation could be its image? (1) 2x + 3y = 5

(2) 2x - 3y = 5

(3) 3x + 2y = 5

(4) 3x - 2y = 5

Geometry - June 2015 Regents - Questions and solutions 25 - 27

25. Use a compass and straightedge to construct an inscribed square in circle T shown below. [Leave all construction marks.]

28. The diagram below shows a ramp connecting the ground to a loading platform 4.5 feet above the ground. The ramp measures 11.75 feet from the ground to the top of the loading platform.

Geometry - June 2015 Regents - Questions and solutions 28 - 36

Question 28 starts at 37:40

28. The diagram below shows a ramp connecting the ground to a loading platform 4.5 feet above the ground. The ramp measures 11.75 feet from the ground to the top of the loading platform.

Determine and state, to the nearest degree, the angle of elevation formed by the ramp and the ground.

31. A flagpole casts a shadow 16.60 meters long. Tim stands at a distance of 12.45 meters from the base of the flagpole, such that the end of Tim’s shadow meets the end of the flagpole’s shadow. If Tim is 1.65 meters tall, determine and state the height of the flagpole to the nearest tenth of a meter.

34. In the diagram below, the line of sight from the park ranger station, P, to the lifeguard chair, L, on the beach of a lake is perpendicular to the path joining the campground, C, and the first aid station, F. The campground is 0.25 mile from the lifeguard chair. The straight paths from both the campground and first aid station to the park ranger station are perpendicular.

If the path from the park ranger station to the campground is 0.55 mile, determine and state, to the nearest hundredth of a mile, the distance between the park ranger station and the lifeguard chair.

Gerald believes the distance from the first aid station to the campground is at least 1.5 miles. Is Gerald correct? Justify your answer.

35. The water tower in the picture below is modeled by the two-dimensional figure beside it. The water tower is composed of a hemisphere, a cylinder, and a cone. Let C be the center of the hemisphere and let D be the center of the base of the cone.

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