Geometry 13 August 2013

Geometry 13 August 2013 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY (2005 Standard)
Tuesday, August 13, 2013 — 8:30 to 11:30 a.m., only
Student Name:_________________________________________________________
School Name: _________________________________________________________

Which statement can not always be proven?

Answer: (2)  
  • (1) 35
  • (2) 55
  • (3) 70
  • (4) 110
Answer: (1) 35 

3. Given the statement: 

One is a prime number.

What is the negation and the truth value of the negation?

  • (1) One is not a prime number; true
  • (2) One is not a prime number; false
  • (3) One is a composite number; true
  • (4) One is a composite number; false
Answer: (1) One is not a prime number; true 

4. Triangle ABC has the coordinates A(1,2), B(5,2), and C(5,5). Triangle ABC is rotated 180° about the origin to form triangle ABC. Triangle ABC is

  • (1) acute
  • (2) isosceles
  • (3) obtuse
  • (4) right
Answer: (4) right 

5. What is an equation of the circle with center (- 5,4) and a radius of 7?

  • (1) (x – 5)² + (y + 4)² = 14
  • (2) (x – 5)² + (y + 4)² = 49
  • (3) (x + 5)² + (y – 4)² = 14
  • (4) (x + 5)² + (y – 4)² = 49
Answer: (4) (x + 5)² + (y – 4)² = 49 

6. In ΔABC, ∠A ≅ ∠B and ∠C is an obtuse angle. Which statement is true?

Answer: (2)  
  • (1) 6
  • (2) 2
  • (3) 3
  • (4) 9
Answer: (3) 3 
  • (1) straight
  • (2) obtuse
  • (3) acute
  • (4) right
Answer: (4) right 
Answer: (3)  

If m∠CAB = x + 40, m∠ACB = 3x + 10, and m∠CBD = 6x, what is m∠CAB?

  • (1) 13
  • (2) 25
  • (3) 53
  • (4) 65
Answer: (4) 65 
  • (1) 10
  • (2) 12
  • (3) 14
  • (4) 16
Answer: (2) 12 

12. What is the equation of circle O shown in the diagram below?

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

13. The diagram below shows the construction of line m, parallel to line ℓ, through point P.

Which theorem was used to justify this construction?

  • (1) If two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel.
  • (2) If two lines are cut by a transversal and the interior angles on the same side are supplementary, the lines are parallel.
  • (3) If two lines are perpendicular to the same line, they are parallel.
  • (4) If two lines are cut by a transversal and the corresponding angles are congruent, they are parallel.
Answer: (4) If two lines are cut by a transversal and the corresponding angles are congruent, they are parallel. 

14. The lateral area of a right circular cone is equal to 120π cm². If the base of the cone has a diameter of 24 cm, what is the length of the slant height, in centimeters?

  • (1) 2.5
  • (2) 5
  • (3) 10
  • (4) 15.7
Answer: (3) 10 

15. A student wrote the following equations:

3y + 6 = 2x
2y – 3x = 6

The lines represented by these equations are

  • (1) parallel
  • (2) the same line
  • (3) perpendicular
  • (4) intersecting, but not perpendicular
Answer: (4) intersecting, but not perpendicular 

16. In a coordinate plane, the locus of points 5 units from the x-axis is the

  • (1) lines x 5 and x -5
  • (2) lines y 5 and y -5
  • (3) line x 5, only
  • (4) line y 5, only
Answer: (2) lines y 5 and y -5 

17. The sides of a triangle are 8, 12, and 15. The longest side of a similar triangle is 18. What is the ratio of the perimeter of the smaller triangle to the perimeter of the larger triangle?

  • (1) 2:3
  • (2) 4:9
  • (3) 5:6
  • (4) 25:36
Answer: (3) 5:6 

18. Lines m and n are in plane A. What is the converse of the statement  “If lines m and n are parallel, then lines m and n do not intersect”?

  • (1) If lines m and n are not parallel, then lines m and n intersect.
  • (2) If lines m and n are not parallel, then lines m and n do not intersect.
  • (3) If lines m and n intersect, then lines m and n are not parallel.
  • (4) If lines m and n do not intersect, then lines m and n are parallel.
Answer: (4) If lines m and n do not intersect, then lines m and n are parallel. 

19. When the system of equations y + 2 = (x – 4)² and 2x + y – 6 =0 is solved graphically, the solution is

  • (1) (-4,-2) and (-2,2)
  • (2) (4,-2) and (2,2)
  • (3) (-4,2) and (-6,6)
  • (4) (4,2) and (6,6)
Answer: (2) (4,-2) and (2,2) 
  • (1) 5
  • (2) 13
  • (3) 16
  • (4) 32
Answer: (3) 16 

Geometry 13 August 2013 Questions Answers Keys

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