# Mathematics 25 January 2008

Mathematics 25 January 2008 Questions Answer Keys

The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
MATHEMATICS B
Friday, January 25, 2008 — 9:15 a.m. to 12:15 p.m., only
Print Your Name: ______________________________________________________
Print Your School’s Name:_________________________________________________

1. Which equation is represented by the accompanying graph? • (1) y = 2x2 + 1
• (2) y = 2(x2 + 1)
• (3) y = x2
• (4) y = 2x2
Answer: (1) y = 2x2 + 1

2. What is the value of x in the equation √3 + x  − 5 =− 2  ?

• (1) 46
• (2) 12
• (3) 3
• (4) 6
Answer: (4) 6

3. Under a dilation where the center of dilation is the origin, the image of A(–2,–3) is A′(–6,–9). What are the coordinates of B′, the image of B(4,0) under the same dilation?

• (1) (–12,0)
• (2) (12,0)
• (3) (–4,0)
• (4) (4,0)
Answer: (2) (12,0)

4. Matthew is a fan of the Air Force’s Thunderbirds flying team and is designing a jacket patch for the team, as shown in the accompanying diagram. If P has the coordinates (a,b), what are the coordinates of Q, the reflection of P in the line y = x?

• (1) (a,b)
• (2) (b,a)
• (3) (–a,b)
• (4) (y,x)
Answer: (2) (b,a)

5. Sean tells prospective clients that the probability of rain at the dive location is .2 each day. Which expression can be used to calculate the probability that it will rain on exactly 5 days of the 7 days at the dive location?

• (1) 7C5(.2)5(.8)2
• (2) 7C5(.2)2(.8)5
• (3) 7C5(.5)(.7)
• (4) 7C2(.5)(.7)
Answer: (1) 7C5(.2)5(.8)2

6. Jack wants to plant a border of flowers in the shape of an arc along the edge of a circular walkway. If the circle has a radius of 5 yards and the angle subtended by the arc measures 1½ radians, what is the length, in yards, of the border?

• (1) 0.5
• (2) 2
• (3) 5
• (4) 7.5
Answer: (4) 7.5

7. Mayken collected data about the size of the honors classes in her school building. This set of data is shown in the accompanying table. Which statement about the range of this sample is true?

• (1) range = mean
• (2) range > mean
• (3) range < mean
• (4) range < standard deviation
Answer: (3) range < mean

8. The accompanying diagram shows a resultant force vector, R. Which diagram best represents the pair of component force vectors, A and B, that combined to produce the resultant force vector R? Answer: (1)

9. On a standardized test with a normal distribution, the mean was 64.3  and the standard deviation was 5.4. What is the best approximation of the percent of scores that fell between 61.6 and 75.1?

• (1) 38.2%
• (2) 66.8%
• (3) 68.2%
• (4) 95%
Answer: (2) 66.8%

10. A wave displayed by an oscilloscope is represented by the equation y = 3 sin x. What is the period of this function?

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

12. The accompanying tables define functions f and g. What is (g ° f )(3)?

• (1) 6
• (2) 2
• (3) 8
• (4) 4
Answer: (3) 8

13. A radioactive substance has an initial mass of 100 grams and its mass  halves every 4 years. Which expression shows the number of grams remaining after t years? Answer: (3)

14. In the accompanying diagram, line is perpendicular to line m at A, line k is perpendicular to line m at B, and lines , m, and k are in the same plane. Which statement is the first step in an indirect proof to prove that is parallel to k?

• (1) Assume that l , m, and k are not in the same plane.
• (2) Assume that l is perpendicular to k.
• (3) Assume that l is not perpendicular to m.
• (4) Assume that l is not parallel to k.
Answer: (4) Assume that l is not parallel to k.

15. Which method of collecting data would most likely result in an unbiased random sample?

• (1) selecting every third teenager leaving a movie theater to answer a survey about entertainment
• (2) placing a survey in a local newspaper to determine how people voted in the 2004 presidential election
• (3) selecting students by the last digit of their school ID number to participate in a survey about cafeteria food
• (4) surveying honor students taking Mathematics B to determine the average amount of time students in a school spend doing homework each night
Answer: (3) selecting students by the last digit of their school ID number to participate in a survey about cafeteria food

16. In the physics lab, Thelma determined the kinetic energy, KE, of an  object at various velocities, V, and found the linear correlation coefficient between KE and V to be +0.8. Which graph shows this relationship? Answer: (2)

17. Which equation has roots that are real, rational, and unequal?

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

18. The expression cos (π – x) is equivalent to

• (1) sin x
• (2) –sin x
• (3) cos x
• (4) –cos x
Answer: (4) –cos x

19. If logx 9 = −2, what is the value of x?

• (1) 81
• (2) 181
• (3) 3
• (4) 13
Answer: (4) 13

20. What is the coefficient of the fifth term in the expansion of (x + 1)8?

• (1) 8
• (2) 28
• (3) 56
• (4) 70
Answer: (4) 70

Mathematics 25 January 2008 Questions Answers Keys Mathematics Examination Question Scoring Key and Rating Guide

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