Geometry 17 June 2016 Questions Answer Keys

**The University of the State of New York**

REGENTS HIGH SCHOOL EXAMINATION

GEOMETRY (Common Core)

Friday, June 17, 2016 — 1:15 to 4:15 p.m., only

Student Name:_________________________________________________________

School Name: _________________________________________________________

**1. A student has a rectangular postcard that he folds in half lengthwise. Next, he rotates it continuously about the folded edge. Which three dimensional object below is generated by this rotation?**

**2. A three-inch line segment is dilated by a scale factor of 6 and centered at its midpoint. What is the length of its image?**

- (1) 9 inches
- (2) 2 inches
- (3) 15 inches
- (4) 18 inches

**3. Kevin’s work for deriving the equation of a circle is shown below.**

x² + 4x – (y² – 20)

STEP 1 x² +4x = – y² + 20

STEP 2 x² + 4x + 4 = – y² + 20 – 4

STEP 3 (x + 2)² = – y² + 20 – 4

STEP 4 (x + 2)² = y² = 16

In which step did he make an error in his work?

- (1) Step 1
- (2) Step 2
- (3) Step 3
- (4) Step 4

- (1) a translation of two units down
- (2) a reflection over the x-axis
- (3) a reflection over the y-axis
- (4) a clockwise rotation of 90° about the origin

**5. Using the information given below, which set of triangles can not be proven similar?**

**6. A company is creating an object from a wooden cube with an edge length of 8.5 cm. A right circular cone with a diameter of 8 cm and an altitude of 8 cm will be cut out of the cube. Which expression represents the volume of the remaining wood?**

- (1) (8.5)³ – π(8)²(8)
- (2) (8.5)³ – π(4)²(8)
- (3) (8.5)³ – ¹⁄
_{3}π(8)²(8) - (4) (8.5)³ – ¹⁄
_{3}π(4)²(8)

**7. Two right triangles must be congruent if**

- (1) an acute angle in each triangle is congruent
- (2) the lengths of the hypotenuses are equal
- (3) the corresponding legs are congruent
- (4) the areas are equal

**8. Which sequence of transformations will map ABC onto A’B’C’?**

- (1) reflection and translation
- (2) rotation and reflection
- (3) translation and dilation
- (4) dilation and rotation

Which statement must always be true?

- (1) ∠BAC ≅ ∠BOC
- (2) m∠BAC = ½ m∠BOC
- (3) ΔBAC and ΔBOC are isosceles.
- (4) The area of ΔBAC is twice the area of ΔBOC.

**11. A 20-foot support post leans against a wall, making a 70° angle with the ground. To the nearest tenth of a foot, how far up the wall will the support post reach?**

- (1) 6.8
- (2) 6.9
- (3) 18.7
- (4) 18.8

- (1) y + 1 =
^{4}⁄_{3}^{ }(x + 3) - (2) y + 1 = – ¾ (x + 3)
- (3) y – 6 =
^{4}⁄_{3}(x – 8) - (4) y – 6 = – ¾ (x – 8)

If SU = h, UT = 12, and RT = 42, which value of h will make ΔRST a right triangle with ∠RST as a right angle?

- (1) 6√3
- (2) 6√10
- (3) 6√14
- (4) 6√35

**14. In the diagram below, ΔABC has vertices A(4,5), B(2,1), and C(7,3).**

**15. In the diagram below, ΔERM ∼ ΔJTM.**

Which statement is always true?

**16. On the set of axes below, rectangle ABCD can be proven congruent to rectangle KLMN using which transformation?**

- (1) rotation
- (2) translation
- (3) reflection over the x-axis
- (4) reflection over the y-axis

- (1) 10
- (2) 12
- (3) 17
- (4) 22.5

**18. Seawater contains approximately 1.2 ounces of salt per liter on average. How many gallons of seawater, to the nearest tenth of a gallon, would contain 1 pound of salt?**

- (1) 3.3
- (2) 3.5
- (3) 4.7
- (4) 13.3

**20. A hemispherical water tank has an inside diameter of 10 feet. If water has a density of 62.4 pounds per cubic foot, what is the weight of the water in a full tank, to the nearest pound?**

- (1) 16,336
- (2) 32,673
- (3) 130,690
- (4) 261,381

**Geometry 17 June 2016 Questions Answers Keys**

Geometry Examination Question |

Scoring Key and Rating Guide |

**See also: **