Mathematics 20 June 2003 Questions Answer Keys

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

REGENTS HIGH SCHOOL EXAMINATION

MATHEMATICS B

Friday, June 20, 2003 — 1:15 to 4:15 p.m., only

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**1. For which value of x is y = log x undefined?**

- (1) 0
- (2)
^{1}⁄_{10} - (3) π
- (4) 1.483

**2. If sin θ > 0 and sec θ < 0, in which quadrant does the terminal side of angle lie?**

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

**3. What is the value of x in the equation 81 ^{x+2 } = 27^{5x+4 }?**

**4. The relationship between voltage, E, current, I, and resistance, Z, is given by the equation E = IZ. If a circuit has a current I = 3 + 2i and a resistance Z = 2 – i, what is the voltage of this circuit?**

- (1) 8 + i
- (2) 8 + 7i
- (3) 4 + i
- (4) 4 – i

**6. What are the coordinates of point P, the image of point (3,–4) after a reflection in the line y = x?**

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

**7. The roots of the equation ax ^{2} + 4x = –2 are real, rational, and equal when a has a value of**

- (1) 1
- (2) 2
- (3) 3
- (4) 4

**8. Two objects are 2.4 × 10 ^{20} centimeters apart. A message from one object travels to the other at a rate of 1.2 × 10^{5} centimeters per second. How many seconds does it take the message to travel from one object to the other?**

- (1) 1.2 × 10
^{15} - (2) 2.0 × 10
^{4} - (3) 2.0 × 10
^{15} - (4) 2.88 × 10
^{25}

**9. If f(x) = cos x, which graph represents f(x) under the composition r _{y-axis} ° r_{x-axis }?**

**10. Which diagram represents a relation in which each member of the domain corresponds to only one member of its range?**

**11. The accompanying diagram represents the elliptical path of a ride at an amusement park.**

Which equation represents this path?

**13. Which transformation is an opposite isometry?**

- (1) dilation
- (2) line reflection
- (3) rotation of 90°
- (4) translation

**14. Which equation is represented by the accompanying graph?**

- (1) y =|x|– 3
- (2) y = (x – 3)2 + 1
- (3) y = |x + 3| – 1
- (4) y = |x – 3| + 1

**15. What is the value of i ^{99} – i^{3}?**

- (1) 1
- (2) i
^{96} - (3) –i
- (4) 0

- (1) 8
- (2) –8
- (3) 25
- (4) –25

**18. What is the solution set of the inequality |3 – 2x| ≥ 4?**

**19. What value of x in the interval 0° ≤ x ≤ 180° satisfies the equation √3 tan x + 1 = 0?**

- (1) –30°
- (2) 30°
- (3) 60°
- (4) 150°

Which statement would not be used to prove ΔABC ≅ ΔDEF?

- (1) SSS ≅ SSS
- (2) SAS ≅ SAS
- (3) AAS ≅ AAS
- (4) HL ≅ HL

**Mathematics 20 June 2003 Questions Answers Keys**

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