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

Print Your Name: ______________________________________________________

Print Your School’s Name: ________________________________________________

 

1. Which equation best represents the accompanying graph?

Mathematics 26 January 2007
  • (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.

Mathematics 26 January 2007

Based on the measures shown in the diagram, which equation can be used to find x, the distance from point A to point S?

Mathematics 26 January 2007
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 
Mathematics 26 January 2007
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
Mathematics 26 January 2007
Answer: (1)

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

Mathematics 26 January 2007
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.

Mathematics 26 January 2007

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?

Mathematics 26 January 2007
  • (1) 1.5
  • (2) 2
  • (3) 6
  • (4) 12
Answer: (2) 2 

16. Which equation represents the circle shown in the accompanying graph?

Mathematics 26 January 2007
  • (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)?

Mathematics 26 January 2007
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 23 June 2009Mathematics Examination Question
Mathematics 23 June 2009Scoring Key and Rating Guide

 

See also: 

0 comments… add one

Leave a Comment