Mathematics 16 August 2006

Mathematics 16 August 2006 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
MATHEMATICS B
Wednesday, August 16, 2006 — 8:30 to 11:30 a.m., only
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Answer: (3)  

2. What is the solution of the equation √2x – 3 – 3 = 6 ?

  • (1) 42
  • (2) 39
  • (3) 3
  • (4) 6
Answer: (1) 42 

3. What is the minimum point of the graph of the equation y = 2x2 + 8x + 9?

  • (1) (2,33)
  • (2) (2,17)
  • (3) (–2,–15)
  • (4) (–2,1)
Answer: (4) (–2,1) 

4. If x is a positive acute angle and cos x = 34 , what is the exact value of sin x?

  • (1) 35
  • (2) √134
  • (3) 35
  • (4) 45
Answer: (2) √134 

5. Which equation does not represent a function?

  • (1) x = π
  • (2) y = 4
  • (3) y = | x|
  • (4) y = x2 + 5x
Answer: (2) √134 
  • (1) 12 − √3
  • (2) 6 – 2√3
  • (3) 4 − 2√3
  • (4) 2 + √3
Answer: (2) 6 – 2√3 

7. The function y = 2x is equivalent to

  • (1) x = y log 2
  • (2) x = log2y
  • (3) y = x log 2
  • (4) y = log2x
Answer: (2) x = log2y 
Answer: (3)  

9. A designer who is planning to install an elliptical mirror is laying out the design on a coordinate grid. Which equation could represent the elliptical mirror?

  • (1) x2 = 144 + 36y2
  • (2) x2 + y2 = 144
  • (3) x2 + 4y2 = 144
  • (4) y = 4y2 + 144
Answer: (3) x2 + 4y2 = 144 

10. A solution set of the equation 5 sin θ + 3 = 3 contains all multiples of

  • (1) 45°
  • (2) 90°
  • (3) 135°
  • (4) 180°
Answer: (4) 180° 

11. What is the total number of points of intersection for the graphs of the equations y = x2 and y = –x2?

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

12. For which equation is the sum of the roots equal to the product of the roots?

  • (1) x2 + x + 1 = 0
  • (2) x2 + 3x – 6 = 0
  • (3) x2 – 8x – 4 = 0
  • (4) x2 – 4x + 4 = 0
Answer: (4) x2 – 4x + 4 = 0  

13. If the perimeter of an equilateral triangle is 18, the length of the altitude of this triangle is

  • (1) 6
  • (2) 6√3
  • (3) 3
  • (4) 3√3

Answer: (4) 3√3  

Answer: (2)   

15. What is the period of the graph of the equation y = 2 sin  13 x = 2 ?

  • (1) 23π
  • (2) 2π
  • (3) 6π
  • (4) 2
Answer: (3) 6π 

16. What is the solution set of the equation  | x2 – 2x | = 3x – 6? 

  • (1) {2,±3}
  • (2) {2}
  • (3) {±3}
  • (4) {2,3}
Answer: (4) {2,3} 
  • (1) 2 ⁄sin θ
  • (2) 2 cos θ
  • (3) 2 cot θ
  • (4) 2 tan θ
Answer: (3) 2 cot θ 

18. The accompanying diagram shows unit circle O, with radius OB = 1.

Which line segment has a length equivalent to cos θ?

Answer: (4)  
Answer: (2)  

20. Which graph represents a quadratic function with a negative discriminant?

Answer: (4)  

Mathematics 16 August 2006 Questions Answers Keys

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