# Mathematics 14 June 2007

Mathematics 14 June 2007 Questions Answer Keys

The University of the State of New York
Regents High School Examination
Mathematics B
Thursday, June 14, 2007 — 1:15 to 4:15 p.m., only

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1. The accompanying graph represents the equation y = f(x).

Answer: (1)

2. During a single day at radio station WMZH, the probability that a particular song is played is .38. Which expression represents the probability that this song will be played on exactly 5 days out of 7 days?

• (1) 7C5(.38)2 (.62)5
• (2) 7C5 (.38)5 (.62)2
• (3) 7P5 (.38)5 (.62)2
• (4) 7C2(.38)5 (.62)2
Answer: (2) 7C5 (.38)5 (.62)2

3. Which equation is best represented by the accompanying graph?

• (1) y = 6x
• (2) y = 6x2
• (3) y = 6x + 1
• (4) y = −x2 + 1
Answer: (4) y = −x2 + 1

4. Jack is planting a triangular rose garden. The lengths of two sides of the plot are 8 feet and 12 feet, and the angle between them is 87°. Which expression could be used to find the area of this garden?

• (1) 8 • 12 • sin 87°
• (2) 8 • 12 • cos 87°
• (3) ½ • 8 • 12 • cos 87°
• (4) ½ • 8 • 12 • sin 87°
Answer: (4) ½ • 8 • 12 • sin 87°

5. What could be the approximate value of the correlation coefficient for the accompanying scatter plot?

• (1) −0.85
• (2) −0.16
• (3) 0.21
• (4) 0.90
Answer: (4) 0.90

6. What is one solution of the accompanying system of equations?

y = −x2 + 5
= −0.5x2 + 3

• (1) (3,5)
• (2) (0,5)
• (3) (−2,1)
• (4) (0,3)
Answer: (3) (−2,1)

7. Which inequality is represented by the accompanying graph?

• (1) |x + 2|> 5
• (2) |x + 3|≥ 2
• (3) |x − 1|≤ 5
• (4) |x − 5|≥ 2
Answer: (2) |x + 3|≥ 2

8. The volume of a soap bubble is represented by the equation V = 0.094√A3, where A represents the surface area of the bubble. Which expression is also equivalent to V?

Answer: (1)
Answer: (3)

10. A function, f, is defined by the set {(2,3), (4,7), (−1,5)}. If f is reflected in the line y = x, which point will be in the reflection?

• (1) (5,−1)
• (2) (−5,1)
• (3) (1,−5)
• (4) (−1,5)
Answer: (1) (5,−1)

11. Which equation is represented by the accompanying graph?

• (1) y = cos x
• (2) y = cos ½ x
• (3) y = cos 2x
• (4) y = ½ cos x
Answer: (1) y = cos x
Answer: (2)
Answer: (2)

14. The expression 1 + √2 + 3√3 is equivalent to

Answer: (4)

15. Which set of ordered pairs does not represent a function?

• (1) {(3,−2), (−2,3), (4,−1), (−1,4)}
• (2) {(3,−2), (3,−4), (4,−1), (4,−3)}
• (3) {(3,−2), (4,−3), (5,−4), (6,−5)}
• (4) {(3,−2), (5,−2), (4,−2), (−1,−2)}
Answer: (2) {(3,−2), (3,−4), (4,−1), (4,−3)}

16. Cerise waters her lawn with a sprinkler that sprays water in a circular pattern at a distance of 15 feet from the sprinkler. The sprinkler head rotates through an angle of 300°, as shown by the shaded area in the accompanying diagram.

What is the area of the lawn, to the nearest square foot, that receives water from this sprinkler?

• (1) 79
• (2) 94
• (3) 589
• (4) 707
Answer: (3) 589

17. Which number is the discriminant of a quadratic equation whose roots are real, unequal, and irrational?

• (1) 0
• (2) −5
• (3) 7
• (4) 4
Answer: (3) 7

18. The formula S = 20√t + 273 is used to determine the speed of sound, S, in meters per second, near Earth’s surface, where t is the surface temperature, in degrees Celsius. Which graph best represents this function?

Answer: (2)

19. If 2 + i and 2 − i are the roots of the equation x2 − 4x + c = 0, what is the value of c?

• (1) −5
• (2) 5
• (3) −4
• (4) 4
Answer: (2) 5
• (1) 1
• (2) sin A
• (3) sec A
• (4) csc A
Answer: (4) csc A

Mathematics 14 June 2007 Questions Answers Keys

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