# Mathematics 23 June 2009

Mathematics 23 June 2009 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
MATHEMATICS B
Tuesday, June 23, 2009 — 1:15 to 4:15 p.m., only

1. The number of degrees equal to 5/9π radians is

• (1) 45
• (2) 90
• (3) 100
• (4) 900

2. The accompanying graph shows the curves of best fit for data points comparing temperature to altitude in four different regions, represented by the relations A, B, C, and D.

Which relation is not a function?

• (1) A
• (2) B
• (3) C
• (4) D

3. What is the value of

• (1) 1
• (2) 2
• (3) 3
• (4) 0

4. If sin x= 1a, a ≠ 0, which statement must be true?

• (1) csc x = a
• (2) csc x = – 1a
• (3) sec x = a
• (4) sec x = – 1a
Answer: (1) csc x = a

6. When the sum of −4 + 8i and 2 − 9i is graphed, in which quadrant does it lie?

• (1) I
• (2) II
• (3) III
• (4) IV

7. What is the solution of the inequality |2x − 5|<1?

• (1) x < 3
• (2) 2 < x < 3
• (3) x > −3
• (4) x ≤ 2 or x ≥ 3
Answer: (2) 2 < x < 3

8. Point A(1,0) is a point on the graph of the equation y = x2 − 4x + 3. When point A is reflected across the axis of symmetry, what are the coordinates of its image, point A′?

• (1) (−1,2)
• (2) (0,3)
• (3) (2,−1)
• (4) (3,0)

9. The accompanying diagram represents the biological process of cell division.

If this process continues, which expression best represents the number of cells at any time, t?

• (1) t + 2
• (2) 2t
• (3) t2
• (4) 2t

10. The roots of the equation x2 − 5x + 1 = 0 are

• (1) real, rational, and unequal
• (2) real, rational, and equal
• (3) real, irrational, and unequal
• (4) imaginary
Answer: (3) real, irrational, and unequal

11. Using a drawing program, a computer graphics designer constructs a circle on a coordinate plane on her computer screen. She determines that the equation of the circle’s graph is (x − 3)2 + (y + 2)2 = 36. She then dilates the circle with the transformation D3. After this transformation, what is the center of the new circle?

• (1) (6,−5)
• (2) (−6,5)
• (3) (9,−6)
• (4) (−9,6)

12. Which expression is equivalent to

13. The accompanying graph shows the average daily readership, in thousands, of the newspaper “El Diario La Prensa.”

Which type of function best represents this graph?

• (1) exponential
• (2) logarithmic
• (3) trigonometric
• (1) cos A
• (2) tan A
• (3) sin A
• (4)  ½ sin A

15. What is the solution set of the equation

• (1) { }
• (2) {2}
• (3) {−4,4}
• (4) {4}

16. What is the third term in the expansion of (2x − 3)5?

• (1) –1080x2
• (2) –720x3
• (3) 720x3
• (4) 1080x3

17. The accompanying table shows the scores on a classroom test.

What is the population standard deviation for this set of scores?

• (1) 10.2
• (2) 10.4
• (3) 25
• (4) 88

18. The manager of Stuart Siding Company found that the number of workers used to side a house varies inversely with the number of hours needed to finish the job. If four workers can side the house in 48 hours, how many hours will it take six workers working at the same speed to do the same job?

• (1) 32
• (2) 36
• (3) 42
• (4) 72
• (1) 1 − x
• (2) x − y
• (3) y
• (4) −y

20. The Sea Dragon, a pendulum ride at an amusement park, moves from  its central position at rest according to the trigonometric function P(t) = −10 sin (π 3t) ,where t represents time, in seconds. How many seconds does it take the pendulum to complete one full cycle?

• (1) 5
• (2) 6
• (3) 3
• (4) 10