# 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

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

• (1) 42
• (2) 39
• (3) 3
• (4) 6

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)

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

5. Which equation does not represent a function?

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

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°

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

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

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

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

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

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

Which line segment has a length equivalent to cos θ?

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