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 = 2
^{x} - (2) y = x
^{2}+ 2 - (3) y = 2
^{−x} - (4) 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?

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

- (1) b
^{2}– a - (2) b
^{2}+ a - (3) b – a
- (4) b + a

**4. What is the total number of points of intersection of the graphs of the equations xy = 12 and y = – x ^{2} + 3?**

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

**5. The expression i^{25} is equivalent to**

- (1) 1
- (2) –1
- (3)
*i* - (4) –
*i*

**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

**9. What is the value of b in the equation 4^{2b – }^{3} = 8^{1– }^{b}?**

**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 }

**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

**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

**13. Which is a true statement about the graph of the equation y = x ^{2} – 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.

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

- (1) x
^{2}+ 6x − 10 = 0 - (2) x
^{2}+ 6x + 8 = 0 - (3) x
^{2}− 6x + 10 = 0 - (4) x
^{2}− 6x − 8 = 0

**15. What is the amplitude of the function shown in the accompanying graph?**

- (1) 1.5
- (2) 2
- (3) 6
- (4) 12

**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

**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}/_{C}^{2}**

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

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

**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)

**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.

**Mathematics 26 January 2007 Questions Answers Keys**

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