Mathematics 27 January 2009 Questions Answer Keys

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

REGENTS HIGH SCHOOL EXAMINATION

MATHEMATICS B

Tuesday, January 27, 2009 — 9:15 a.m. to 12:15 p.m., only

Print Your Name: ______________________________________________________

Print Your School’s Name:_________________________________________________

**1. The parabola shown in the accompanying diagram undergoes a reflection in the y-axis.**

What will be the coordinates of the turning point after the reflection?

- (1) (3,−1)
- (2) (3,1)
- (3) (−3,1)
- (4) (−3,−1)

**3. If the probability that the Islanders will beat the Rangers in a game is ^{2} ⁄_{5} , which expression represents the probability that the Islanders will win exactly four out of seven games in a series against the Rangers?**

**4. What is the solution of the inequality x ^{2} − x − 6 < 0?**

- (1) −3 < x < −2
- (2) −2 < x < 3
- (3) 1 < x < 6
- (4) −3 < x < 2

**5. Which expression is equivalent to i ^{5}^{5}?**

- (1) 1
- (2) −1
- (3) i
- (4) −i

**6. What is the translation that maps the function f(x) = x ^{2} − 1 onto the function g(x) = x^{2} + 1?**

- (1) T
_{0,2 } - (2) T
_{0,1 } - (3) T
_{1,–1 } - (4) T
_{–1,1}

**7. The height of a swimmer’s dive off a 10-foot platform into a diving pool is modeled by the equation y = 2x ^{2} − 12x + 10, where x represents the number of seconds since the swimmer left the diving board and y represents the number of feet above or below the water’s surface. What is the farthest depth below the water’s surface that the swimmer**

- (1) 6 feet
- (2) 8 feet
- (3) 10 feet
- (4) 12 feet

**8. The accompanying diagram shows two intersecting paths within a circular garden.**

What is the length of the portion of the path marked x?

- (1) 8¹⁄
_{3} - (2) 11
- (3) 3
- (4) 12

**9. If f(x) = 3x − 5 and g(x) = x − 9, which expression is equivalent to (f ο g)(x)?**

- (1) 4x − 14
- (2) 3x − 14
- (3) 3x − 32
- (4) 3x
− 32x + 45^{2}

**10. A central angle of a circular garden measures 2.5 radians and intercepts an arc of 20 feet. What is the radius of the garden?**

- (1) 8 ft
- (2) 50 ft
- (3) 100 ft
- (4) 125 ft

**12. A graphic designer is drawing a pattern of four concentric circles on the coordinate plane. The center of the circles is located at (−2,1). The smallest circle has a radius of 1 unit. If the radius of each of the circles is one unit greater than the largest circle within it, what would be the equation of the fourth circle?**

- (1) (x − 2)
+ (y + 1)^{2}= 4^{2} - (2) (x + 2)
+ (y − 1)^{2}= 4^{2} - (3) (x − 2)
+ (y + 1)^{2}= 16^{2} - (4) (x + 2)
+ (y − 1)^{2}= 16^{2}

**13. Carol notices that the number of customers who visit her coffee shop varies inversely with the average daily temperature. Yesterday, the average temperature was 40° and she had 160 customers. If today’s average temperature is 25°, how many customers should she expect?**

- (1) 100
- (2) 145
- (3) 256
- (4) 1,000

**14. Given the relation A: {(3,2), (5,3), (6,2), (7,4)} Which statement is true?**

- (1) Both A and A,
^{–1 }are functions. - (2) Neither A nor A
^{–1}is a function. - (3) Only A is a function.
- (4) Only A
^{–1}is a function.

**15. The expression cotθ • secθ is equivalent to**

**16. If z _{1} = −3 + 2i and z_{2} = 4 − 3i, in which quadrant does the graph of (z_{2} − z_{1}) lie?**

- (1) I
- (2) II
- (3) III
- (4) IV

**17. Which graph represents the equation 9x ^{2} = 36 − 4y^{2}?**

**18. The accompanying graph illustrates the presence of a certain strain of bacteria at various pH levels.**

What is the range of this set of data?

- (1) 5 ≤ x ≤ 9
- (2) 5 ≤ x ≤ 70
- (3) 0 ≤ y ≤ 70
- (4) 5 ≤ y ≤ 70

**19. Juan has been told to write a quadratic equation where the sum of the roots is equal to −3 and the product of the roots is equal to −9. Which equation meets these requirements?**

- (1) x
^{2}+ 3x + 9 = 0 - (2) x
^{2}− 12x + 27 = 0 - (3) 2x
^{2}+ 6x − 18 = 0 - (4) (x + 3)(x + 9) = 0

**Mathematics 27 January 2009 Questions Answers Keys**

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