# Mathematics 16 August 2007

Mathematics 16 August 2007 Questions Answer Keys

The University of the State of New York
Regents High School Examination
Mathematics B
Thursday, August 16, 2007 — 8:30 to 11:30 a.m., only

Print Your Name: ______________________________________________________

Print Your School’s Name: ________________________________________________ Answer: (2)

2. The expression 3i(2i2 − 5i) is equivalent to

• (1) 15 − 6i
• (2) 15 − 5i
• (3) −15 − 5i
• (4) −1 + 0i
Answer: (1) 15 − 6i

3. If csc θ = −2, what is the value of sin θ?

• (1) −2
• (2) 2
• (3) −½
• (4) ½
Answer: (3) −½

4. What is 235°, expressed in radian measure? Answer: (4)

5. The flight paths of two Thunderbird jets are plotted on a Cartesian coordinate plane, and the equations of the jets’ flight paths are represented by y = 2x + 3 and y = 0.5x . The best approximation of the intersection of the flight paths is

• (1) (−1.72,3.3)
• (2) (0,1)
• (3) (−1.50,2.82)
• (4) (−2,−1)
Answer: (1) (−1.72,3.3) • (1) +1
• (2) −1
• (3) 1 − a
• (4) −(1 − a)
Answer: (3) 1 − a

7. Which equation represents the function shown in the accompanying graph? • (1) f(x) = |x| + 1
• (2) f(x) = |x| − 1
• (3) f(x) = |x + 1|
• (4) f(x) = |x − 1|
Answer: (1) f(x) = |x| + 1

8. A meteorologist drew the accompanying graph to show the changes in relative humidity during a 24-hour period in New York City What is the range of this set of data?

• (1) 0 ≤ y ≤ 24
• (2) 0 ≤ x ≤ 24
• (3) 30 ≤ y ≤ 80
• (4) 30 ≤ x ≤ 80
Answer: (3) 30 ≤ y ≤ 80 Answer: (2)

10. Which type of function could be used to model the data shown in the accompanying graph? • (1) exponential
• (2) quadratic
• (3) trigonometric
• (4) linear
Answer: (1)

11. Under a dilation with respect to the origin, the image of P(−15,6) is P′(−5,2). What is the constant of dilation?

• (1) −4
• (2) 1/3
• (3) 3
• (4) 10
Answer: (2) 1/3

12. Which graph has an inverse that is a function? Answer: (4)

13. What is the solution set of the inequality x2 + 4x − 5 < 0?

• (1) {x|x < −1 or x > 5}
• (2) {x|x < −5 or x > 1}
• (3) {x| −1 < x < 5}
• (4) {x| −5 < x < 1}
Answer: (4) {x| −5 < x < 1}

14. The graph of which function is symmetric with respect to the graph of the line y = x?

• (1) y = 1/x
• (2) y = x2
• (3) y = x3
• (4) y = log x
Answer: (1) y = 1/x

15. The coordinates of ΔJRB are J(1,−2), R(−3,6), and B(4,5). What are the coordinates of the vertices of its image after the transformation T2,−1 ° ry-axis?

• (1) (3,1), (−1,−7), (6,−6)
• (2) (3,−3), (−1,5), (6,4)
• (3) (1,−3), (5,5), (−2,4)
• (4) (−1,−2), (3,6), (−4,5)
Answer: (3) (1,−3), (5,5), (−2,4) Answer: (4) − 1 − √3

17. The accompanying graph represents a portion of a sound wave Which equation best represents this graph?

• (1) y = 2 sin 1/x
• (2) y = 2 sin 1/x = 2
• (3) y = 2 sin 2x
• (4) y = 2 sin 2x = 2
Answer: (4) y = 2 sin 2x = 2

18. Which equation has the complex number 4 − 3i as a root?

• (1) x2 + 6x − 25 = 0
• (2) x2 − 6x + 25 = 0
• (3) x2 + 8x − 25 = 0
• (4) x2 − 8x + 25 = 0
Answer: (4) x2 − 8x + 25 = 0

20. If log2 a = log3 a, what is the value of a?

• (1) 1
• (2) 2
• (3) 3
• (4) 4
Answer: (1) 1

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