# Mathematics 27 January 2006

Mathematics 27 January 2006 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
MATHEMATICS B
Friday, January 27, 2006 — 9:15 a.m. to 12:15 p.m., only
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1. What is the value of • (1) 70
• (2) 130
• (3) 470
• (4) 530
Answer: (3) 470

2. The effect of pH on the action of a certain enzyme is shown on the accompanying graph. What is the domain of this function?

• (1) 4 ≤ x ≤ 13
• (2) 4 ≤ y ≤ 13
• (3) x ≥ 0
• (4) y ≥ 0
Answer: (1) 4 ≤ x ≤ 13

3. Which graph shows that soil permeability varies inversely to runoff? Answer: (1)

4. On a standardized test, a score of 86 falls exactly 1.5 standard deviations below the mean. If the standard deviation for the test is 2, what is the mean score for this test?

• (1) 84
• (2) 84.5
• (3) 87.5
• (4) 89
Answer: (4) 89

5. Which transformation of the graph of y = x2 would result in the graph of y = x2 + 2?

• (1) D2
• (2) T0,2
• (3) ry = 2
• (4) R0,90
Answer: (2) T0,2

6. A sound wave is modeled by the curve y = 3 sin 4x. What is the period of this curve?

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

7. If √2x – 1 + 2 = 5 , then x is equal to

• (1) 1
• (2) 2
• (3) 5
• (4) 4
Answer: (3) 5

8. The expression (1 + cos x)(1 – cos x) is equivalent to

• (1) 1
• (2) sec2 x
• (3) sin2 x
• (4) csc2 x
Answer: (3) sin2 x Answer: (2)

10. What is the solution of the inequality |y + 8| > 3?

• (1) y > –5 or y < –11
• (2) y > –5
• (3) –11 < y < –5
• (4) –5 < y < 11
Answer: (1) y > –5 or y < –11 Answer: (3)

12. In physics class, Eva noticed the pattern shown in the accompanying diagram on an oscilloscope. Which equation best represents the pattern shown on this oscilloscope? Answer: (1) Answer: (2)

14. The roots of the equation 2x2 – 5 = 0 are

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

15. What is the radian measure of the angle formed by the hands of a clock at 2:00 p.m.?

• (1) π/2
• (2) π/3
• (3) π/4
• (4) π/6
Answer: (2) π/3

16. If θ is an angle in standard position and P(–3,4) is a point on the terminal side of θ, what is the value of sin θ?

• (1) 3/5
• (2) – 3/5
• (3) 4/5
• (4) – 4/5
Answer: (3) 4/5 Answer: (4)

18. What are the coordinates of point A′, the image of point A(–4,1) after the composite transformation R90° ° r y=x where the origin is the center of rotation?

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

19. The accompanying diagram shows a 24-foot ladder leaning against a building. A steel brace extends from the ladder to the point where the building meets the ground. The brace forms a right angle with the ladder. If the steel brace is connected to the ladder at a point that is 10 feet from the foot of the ladder, which equation can be used to find the length, x, of the steel brace? Answer: (1)

20. The center of a circle represented by the equation (x – 2)2 + (y + 3)2 = 100 is located in Quadrant

• (1) I
• (2) II
• (3) III
• (4) IV
Answer: (4) IV

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