# Geometry 12 August 2015

Geometry 12 August 2015 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY (Common Core)
Wednesday, August 12, 2015 — 8:30 to 11:30 a.m., only
Student Name:_________________________________________________________
School Name: _________________________________________________________

1. A parallelogram must be a rectangle when its

• (1) diagonals are perpendicular
• (2) diagonals are congruent
• (3) opposite sides are parallel
• (4) opposite sides are congruent
Answer: (2) diagonals are congruent

2. If ΔA’B’C’ is the image of ΔABC, under which transformation will the triangles not be congruent?

• (1) reflection over the x-axis
• (2) translation to the left 5 and down 4
• (3) dilation centered at the origin with scale factor 2
• (4) rotation of 270° counterclockwise about the origin
Answer: (3) dilation centered at the origin with scale factor 2

3. If the rectangle below is continuously rotated about side w, which solid figure is formed? • (1) pyramid
• (2) rectangular prism
• (3) cone
• (4) cylinder
Answer: (4) cylinder

4. Which expression is always equivalent to sin x when 0°< x <90°?

• (1) cos (90° – x)
• (2) cos (45° – x)
• (3) cos (2x)
• (4) cos x
Answer: (1) cos (90° – x)

5. In the diagram below, a square is graphed in the coordinate plane. A reflection over which line does not carry the square onto itself?

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

6. The image of ΔABC after a dilation of scale factor k centered at point A is ΔADE, as shown in the diagram below. Which statement is always true? Answer: (4)

7. A sequence of transformations maps rectangle ABCD onto rectangle A”B”C”D”, as shown in the diagram below Which sequence of transformations maps ABCD onto ABCD and then maps ABCD onto A’B’C’D’?

• (1) a reflection followed by a rotation
• (2) a reflection followed by a translation
• (3) a translation followed by a rotation
• (4) a translation followed by a reflection
Answer: (1) a reflection followed by a rotation If m∠R = 124°, what is m∠AFD?

• (1) 124°
• (2) 112°
• (3) 68°
• (4) 56°
Answer: (3) 68°

9. If x² + 4x + y² – 6y – 12 = 0 is the equation of a circle, the length of the radius is

• (1) 25
• (2) 16
• (3) 5
• (4) 4
Answer: (3) 5  • (1) y = –23x + 5
• (2) y = – 23x – 3
• (3) y = 3 ⁄2x + 7
• (4) y = 3 ⁄2x – 8
Answer: (1) y = –23x + 5

11. Linda is designing a circular piece of stained glass with a diameter of 7 inches. She is going to sketch a square inside the circular region.

To the nearest tenth of an inch, the largest possible length of a side of the square is

• (1) 3.5
• (2) 4.9
• (3) 5.0
• (4) 6.9
Answer: (2) 4.9  • (1) 6.4
• (2) 8
• (3) 12.5
• (4) 16
Answer: (3) 12.5

13. In the diagram below, which single transformation was used to map triangle A onto triangle B? • (1) line reflection
• (2) rotation
• (3) dilation
• (4) translation
Answer: (2) rotation

14. In the diagram below, ΔDEF is the image of ΔABC after a clockwise  rotation of 180º and a dilation where AB = 3, BC = 5.5, AC = 4.5, DE = 6, FD = 9, and EF = 11. Which relationship must always be true? Answer: (4)

15. In the diagram below, quadrilateral ABCD is inscribed in circle P. What is m∠ADC?

• (1) 70º
• (2) 72º
• (3) 108º
• (4) 110º
Answer: (3) 108º

16. A hemispherical tank is filled with water and has a diameter of 10 feet. If water weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank, to the nearest pound?

• (1) 16,336
• (2) 32,673
• (3) 130,690
• (4) 261,381
Answer: (3) 108º

17. In the diagram below, ΔABC ∼ΔADE. Which measurements are justified by this similarity?

• (1) AD = 3, AB = 6, AE = 4, and AC = 12
• (2) AD = 5, AB = 8, AE = 7, and AC = 10
• (3) AD = 3, AB = 9, AE = 5, and AC = 10
• (4) AD = 2, AB = 6, AE = 5, and AC = 15
Answer: (4) AD = 2, AB = 6, AE = 5, and AC = 15  What is the area of the sector formed by angle FOH?

• (1) 2π
• (2) 3 ⁄2π
• (3) 6π
• (4) 24π
Answer: (3) 6π Given ΔAEC ∼ ΔBED, which equation is true?  Answer: (2)

20. A triangle is dilated by a scale factor of 3 with the center of dilation at the origin. Which statement is true?

• (1) The area of the image is nine times the area of the original triangle.
• (2) The perimeter of the image is nine times the perimeter of the original triangle.
• (3) The slope of any side of the image is three times the slope of the corresponding side of the original triangle.
• (4) The measure of each angle in the image is three times the measure of the corresponding angle of the original triangle.
Answer: (1) The area of the image is nine times the area of the original triangle.

Geometry 12 August 2015 Questions Answers Keys

 Geometry Examination Question  Scoring Key and Rating Guide

See also:

0 comments… add one

Leave a Comment