Geometry 20 June 2014

Geometry 20 June 2014 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY (2005 Standard)
Friday, June 20, 2014 — 1:15 to 4:15 p.m., only
Student Name:________________________________________________________
School Name: _________________________________________________________

1. Plane P is parallel to plane Q. If plane P is perpendicular to line ℓ, then plane Q

  • (1) contains line ℓ
  • (2) is parallel to line ℓ
  • (3) is perpendicular to line ℓ
  • (4) intersects, but is not perpendicular to line ℓ
Answer: (3) is perpendicular to line ℓ

2. In the diagram below, quadrilateral ABCD has vertices A(- 5,1), B(6,- 1), C(3,5), and D(- 2,7).

  • (1) (1,3)
  • (2) (1,3)
  • (3) (1,4)
  • (4) (2,3)
Answer: (1) (1,3)
  • (1) 6
  • (2) 16
  • (3) 24
  • (4) 28
Answer: (2) 16

4. The measures of the angles of a triangle are in the ratio 2:3:4. In degrees, the measure of the largest angle of the triangle is

  • (1) 20
  • (2) 40
  • (3) 80
  • (4) 100
Answer: (3) 80

5. The diameter of the base of a right circular cylinder is 6 cm and  its height is 15 cm. In square centimeters, the lateral area of the cylinder is

  • (1) 180π
  • (2) 135π
  • (3) 90π
  • (4) 45π
Answer: (2) y + 2 = 2(x – 3)

6. When the system of equations y + 2x = x² and y = x is graphed on a set of axes, what is the total number of points of intersection?

  • (1) 1
  • (2) 2
  • (3) 3
  • (4) 0
Answer: (2) 2

7. The vertex angle of an isosceles triangle measures 15 degrees more than one of its base angles. How many degrees are there in a base angle of the triangle?

  • (1) 50
  • (2) 55
  • (3) 65
  • (4) 70
Answer: (2) 55

8. Circle O is graphed on the set of axes below. Which equation  represents circle O?

  • (1) (x + 1)² + (y – 3)² = 9
  • (2) (x – 1)² + (y + 3)² = 9
  • (3) (x + 1)² + (y – 3)² = 6
  • (4) (x – 1)² + (y + 3)² = 6
Answer: (1) (x + 1)² + (y – 3)² = 9
 

Which statement must always be true?

Answer: (3)  

10. In the diagram below, ΔAEC ≅ ΔBED.

Which statement is not always true?

Answer: (4)  
  • (1) 2√2
  • (2) 40
  • (3) 2√10
  • (4) 2√17
Answer: (3) 2√10

12. What are the truth values of the statement “Two is prime” and its negation?

  • (1) The statement is false and its negation is true.
  • (2) The statement is false and its negation is false.
  • (3) The statement is true and its negation is true.
  • (4) The statement is true and its negation is false.
Answer: (4) The statement is true and its negation is false.

13. A regular polygon has an exterior angle that measures 45°. How many sides does the polygon have?

  • (1) 10
  • (2) 8
  • (3) 6
  • (4) 4
Answer: (2) 8
 
  • (1) 8
  • (2) 16
  • (3) √44
  • (4) √136
Answer: (2) 16

15. If the surface area of a sphere is 144π square centimeters, what is the length of the diameter of the sphere, in centimeters?

  • (1) 36
  • (2) 18
  • (3) 12
  • (4) 6
Answer: (3) 12

16. Which numbers could represent the lengths of the sides of a triangle?

  • (1) 5, 9, 14
  • (2) 7, 7, 15
  • (3) 1, 2, 4
  • (4) 3, 6, 8
Answer: (4) 3, 6, 8

17. The equation of a line is 3y + 2x = 12. What is the slope of the line perpendicular to the given line?

  • (1) 2/3
  • (2) 3/2
  • (3) – 2/3
  • (4) – 3/2
Answer: (2) 3/2

18. In the diagram below, point K is in plane P

How many lines can be drawn through K, perpendicular to plane P ?

  • (1) 1
  • (2) 2
  • (3) 0
  • (4) an infinite number
Answer: (1) 1 

If m∠B = 123 and m∠D = 75, what is m∠C?

  • (1) 57
  • (2) 75
  • (3) 105
  • (4) 123
Answer: (2) y + 2 = 2(x – 3)

20. What is the equation of a line passing through the point (4,- 1) and parallel to the line whose equation is 2y – x = 8?

  • (1) y = ½x – 3
  • (2) y = ½x – 1
  • (3) y = – 2x + 7
  • (4) y = – 2x + 2
Answer: (1) y = ½x – 3 

Geometry 20 June 2014 Questions Answers Keys

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