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 = 6^x
(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)

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?