# Mathematics 27 January 2009

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

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 25 , 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 x2 − x − 6 < 0?

• (1) −3 < x < −2
• (2) −2 < x < 3
• (3) 1 < x < 6
• (4) −3 < x < 2
Answer: (2) −2 < x < 3

5. Which expression is equivalent to i55?

• (1) 1
• (2) −1
• (3) i
• (4) −i
Answer: (2) −2 < x < 3

6. What is the translation that maps the function f(x) = x2 − 1 onto the function g(x) = x2 + 1?

• (1) T0,2
• (2) T0,1
• (3) T1,–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 = 2x2 − 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) 3x2 − 32x + 45

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)2 + (y + 1)2 = 4
• (2) (x + 2)2 + (y − 1)2 = 4
• (3) (x − 2)2 + (y + 1)2 = 16
• (4) (x + 2)2 + (y − 1)2 = 16
Answer: (4) (x + 2)2 + (y − 1)2 = 16

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.
Answer: (3) Only A is a function.

15. The expression cotθ • secθ is equivalent to

16. If z1 = −3 + 2i and z2 = 4 − 3i, in which quadrant does the graph of (z2 − z1) lie?

• (1) I
• (2) II
• (3) III
• (4) IV

17. Which graph represents the equation 9x2 = 36 − 4y2?

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
Answer: (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) x2 + 3x + 9 = 0
• (2) x2 − 12x + 27 = 0
• (3) 2x2 + 6x − 18 = 0
• (4) (x + 3)(x + 9) = 0
Answer: (3) 2x2 + 6x − 18 = 0