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) T_0,2
(3) r_{y = 2}
(4) R_0,90

Answer: (2) T_0,2

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 R_90° ° 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?