# Mathematics 15 June 2006

Mathematics 15 June 2006 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
MATHEMATICS B
Thursday, June 15, 2006 — 1:15 to 4:15 p.m., only
Print Your Name: ______________________________________________________
Print Your School’s Name:_________________________________________________

1. Each graph below represents a possible relationship between temperature and pressure. Which graph does not represent a function? Answer: (3) Answer: (1)  What is m∠DAY?

• (1) 90
• (2) 110
• (3) 130
• (4) 150
Answer: (2) 110

4. If x is a positive acute angle and sin x = ½ , what is sin 2x?

• (1) – ½
• (2)  ½
• (3) –√32
• (4)√32
Answer: (4)√32

5. The temperature generated by an electrical circuit is represented by t = f(m) = 0.3m2, where m is the number of moving parts. The resistance of the same circuit is represented by r = g(t) = 150 + 5t, where t is the temperature. What is the resistance in a circuit that has four moving parts?

• (1) 51
• (2) 156
• (3) 174
• (4) 8,670
Answer: (3) 174

6. If the equation x2 – kx – 36 = 0 has x = 12 as one root, what is the value of k?

• (1) 9
• (2) –9
• (3) 3
• (4) –3
Answer: (1) 9

7. The height, f(x), of a bouncing ball after x bounces is represented by f(x) = 80(0.5)x. How many times higher is the first bounce than the fourth bounce?

• (1) 8
• (2) 2
• (3) 16
• (4) 4
Answer: (1) 8

8. A radio transmitter sends a radio wave from the top of a 50-foot tower. The wave is represented by the accompanying graph.. What is the equation of this radio wave?

• (1) y = sin x
• (2) y = 1.5 sin x
• (3) y = sin 1.5x
• (4) y = 2 sin x
Answer: (2) y = 1.5 sin x

9. If tan θ = 2.7 and csc θ < 0, in which quadrant does θ lie?

• (1) I
• (2) II
• (3) III
• (4) IV
Answer: (3) III • (1) 1
• (2) –1
• (3) sin x
• (4) cos x
Answer: (1) 1

11. The graph of y = (x – 3)2 is shifted left 4 units and down 2 units. What is the axis of symmetry of the transformed graph?

• (1) x = –2
• (2) x = –1
• (3) x = 1
• (4) x = 7
Answer: (2) x = –1

12. The solution set of 2+2x = 2− 1 is

• (1) {1}
• (2) {–1}
• (3) {–1,1}
• (4) { }
Answer: (2) {–1}

13. Which transformation best describes the relationship between the functions f(x) = 2x and g(x) =(½)x?

• (1) reflection in the line y = x
• (2) reflection in the origin
• (3) reflection in the x-axis
• (4) reflection in the y-axis
Answer: (4) reflection in the y-axis

14. What is the multiplicative inverse of 3i?

• (1) –3i
• (2) –3
• (3) 13
• (4) –i3
Answer: (4) –i3

15. Mrs. Donahue made up a game to help her class learn about imaginary numbers. The winner will be the student whose expression is equivalent to –i. Which expression will win the game?

• (1) i46
• (2) i47
• (3) i48
• (4) i49
Answer: (2) i47

16. Which equation represents a hyperbola?

• (1) y2 = 16 – x2
• (2) y = 16 – x2
• (3) y = 16x2
• (4) y = 16x
Answer: (4) y = 16x

17. The solution set of which inequality is represented by the accompanying graph? • (1) |x – 2| > 7
• (2) |x – 2| < 7
• (3) |2 – x| > –7
• (4) |2 – x| < –7
Answer: (1) |x – 2| > 7

18. According to Boyle’s Law, the pressure, p, of a compressed gas is inversely proportional to the volume, v. If a pressure of 20 pounds per square inch exists when the volume of the gas is 500 cubic inches, what is the pressure when the gas is compressed to 400 cubic inches?

• (1) 16 lb/in2
• (2) 25 lb/in2
• (3) 40 lb/in2
• (4) 50 lb/in2
Answer: (2) 25 lb/in2

19. What is the fourth term in the expansion of (y – 1)7?

• (1) 35y4
• (2) 35y3
• (3) –35y4
• (4) –35y3
Answer: (3) –35y4

20. Sam needs to cut a triangle out of a sheet of paper. The only requirements that Sam must follow are that one of the angles must be 60°, the side opposite the 60° angle must be 40 centimeters, and one of the other sides must be 15 centimeters. How many different triangles can Sam make?

• (1) 1
• (2) 2
• (3) 3
• (4) 0
Answer: (1) 1

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