# Mathematics 26 January 2007

Mathematics 26 January 2007 Questions Answer Keys

The University of the State of New York
Regents High School Examination
Mathematics B
Thursday, June 14, 2007 — 1:15 to 4:15 p.m., only

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1. Which equation best represents the accompanying graph? • (1) y = 2x
• (2) y = x2 + 2
• (3) y = 2−x
• (4) y = −2x
Answer: (3) y = 2−x

2. The accompanying diagram shows the approximate linear distances traveled by a sailboat during a race. The sailboat started at point S, traveled to points E and A, respectively, and ended at point S. Based on the measures shown in the diagram, which equation can be used to find x, the distance from point A to point S? Answer: (2)

3. If √x − a = b, x > a, which expression is equivalent to x?

• (1) b2 – a
• (2) b2 + a
• (3) b –  a
• (4) b + a
Answer: (2)

4. What is the total number of points of intersection of the graphs of the equations xy = 12 and y = – x2 + 3?

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

5. The expression i25 is equivalent to

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

7. The term “snowstorms of note” applies to all snowfalls over 6 inches. The snowfall amounts for snowstorms of note in Utica, New York, over a four-year period are as follows: 7.1, 9.2, 8.0, 6.1, 14.4, 8.5, 6.1, 6.8, 7.7, 21.5, 6.7, 9.0, 8.4, 7.0, 11.5, 14.1, 9.5, 8.6

What are the mean and population standard deviation for these data, to the nearest hundredth?

• (1) mean = 9.46; standard deviation = 3.74
• (2) mean = 9.46; standard deviation = 3.85
• (3) mean = 9.45; standard deviation = 3.74
• (4) mean = 9.45; standard deviation = 3.85
Answer: (1) mean = 9.46; standard deviation = 3.74 Answer: (1)

9. What is the value of b in the equation 42b – 3 = 81– b? Answer: (3)

10. What is the solution set of the inequality | 2x – 1 | < 9?

• (1) {x | –4 < x < 5 }
• (2) {x | x < –4 or x > 5 }
• (3) { x | x < 5 }
• (4) { x | x < –4 }
Answer: (1) {x | –4 < x < 5 }

11. Which transformation could be used to make the graph of the equation y = sin x coincide with the graph of the equation y = cos x?

• (1) translation
• (2) rotation
• (3) dilation
• (4) point reflection
Answer: (1) translation

12. Data collected during an experiment are shown in the accompanying graph. What is the range of this set of data?

• (1) 2.5 ≤ y ≤ 9.5
• (2) 2.5 ≤ x ≤ 9.5
• (3) 0 ≤ y ≤ 100
• (4) 1 ≤ x ≤ 10
Answer: (3) 0 ≤ y ≤ 100

13. Which is a true statement about the graph of the equation y = x2 – 7x – 60?

• (1) It is tangent to the x-axis.
• (2) It does not intersect the x-axis.
• (3) It intersects the x-axis in two distinct points that have irrational coordinates.
• (4) It intersects the x-axis in two distinct points that have rational coordinates.
Answer: (4) It intersects the x-axis in two distinct points that have rational coordinates.

14. Which quadratic equation has the roots 3 + i and 3 − i?

• (1) x2 + 6x − 10 = 0
• (2) x2 + 6x + 8 = 0
• (3) x2 − 6x + 10 = 0
• (4) x2 − 6x − 8 = 0
Answer: (3) x2 − 6x + 10 = 0

15. What is the amplitude of the function shown in the accompanying graph? • (1) 1.5
• (2) 2
• (3) 6
• (4) 12
Answer: (2) 2

16. Which equation represents the circle shown in the accompanying graph? • (1) (x – 1)2 – (y + 2)2 = 9
• (2) (x – 1)2 + (y + 2)2 = 9
• (3) (x + 1)2 – (y – 2)2 = 9
• (4) (x + 1)2 + (y – 2)2 = 9
Answer: (2) (x – 1)2 + (y + 2)2 = 9

17. A black hole is a region in space where objects seem to disappear. A formula used in the study of black holes is the Schwarzschild formula, R = 2GM/C2

Based on the laws of logarithms, log R can be represented by

• (1) 2 log G + log M – log 2c
• (2) log 2G + log M – log 2c
• (3) log 2 + log G + log M – 2 log c
• (4) 2 log GM – 2 log c
Answer: (3) log 2 + log G + log M – 2 log c

18. In the unit circle shown in the accompanying diagram, what are the coordinates of (x,y)? Answer: (1)

19. Which transformation represents a dilation?

• (1) (8,4) → (11,7)
• (2) (8,4) → (–8,4)
• (3) (8,4) → (–4,–8)
• (4) (8,4) → (4,2)
Answer: (4) (8,4) → (4,2)

20. In ΔABC, m∠A = 30, a = 14, and b = 20. Which type of angle is ∠B?

• (1) It must be an acute angle.
• (2) It must be a right angle.
• (3) It must be an obtuse angle.
• (4) It may be either an acute angle or an obtuse angle.
Answer: (4) It may be either an acute angle or an obtuse angle.

Mathematics 26 January 2007 Questions Answers Keys Mathematics Examination Question Scoring Key and Rating Guide

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