Mathematics 16 August 2005

Mathematics 16 August 2005 Questions Answer Keys

The University of the State of New York
Regents High School Examination
Mathematics B
Tuesday, August 16, 2005 — 8:30 to 11:30 a.m., only

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1. What is the turning point, or vertex, of the parabola whose equation is y  = 3x2 + 6x – 1?

  • (1) (1,8) (3)
  • (2) (–1,–4)
  • (–3,8)
  • (4) (3,44)
Answer: (2) (–1,–4)

2. The growth of bacteria in a dish is modeled by the function f(t) = 2t/3For which value of t is f(t) = 32?

  • (1) 8
  • (2) 2
  • (3) 15
  • (4) 16
Answer: (3) 15

3. The graphs below show the average annual precipitation received at different latitudes on Earth. Which graph is a translated cosine curve?

Mathematics 16 August 2005
Answer: (4)

4. The accompanying diagram shows two cables of equal length supporting a pole. Both cables are 14 meters long, and they are anchored to points in the ground that are 14 meters apart.

Mathematics 16 August 2005

What is the exact height of the pole, in meters?

  • (1) 7
  • (2) 7√2
  • (3) 7√3
  • (4) 14
Answer: (3) 7√3 
Mathematics 16 August 2005
Answer: (4) 
Mathematics 16 August 2005
Answer: (1) 

7. When expressed as a monomial in terms of i, 2√– 32 – 5√–8 is equivalent to

  • (1) 2√2i
  • (2) 2i√2
  • (3) −2i√2
  • (4) 18i √2
Answer: (3) −2i√2

8. The image of the origin under a certain translation is the point (2,–6). The image of point (–3,–2) under the same translation is the point

  • (1) (–6,12)
  • (2) (–5,4)
  • (3) (– 3/2, 1/3)
  • (4) (–1,–8)
Answer: (4) (–1,–8) 

9. The solution of |2x – 3|< 5 is

  • (1) x < –1 or x > 4
  • (2) –1 < x < 4
  • (3) x > –1
  • (4) x < 4
Answer: (2) –1 < x < 4 

10. In the accompanying diagram of a unit circle, the ordered pair (– 3/2, – 1/2) represents the point where the terminal side of θ intersects the unit circle.

Mathematics 16 August 2005

What is m∠θ?

  • (1) 210
  • (2) 225
  • (3) 233
  • (4) 240
Answer: (1) 210 

11 Two straight roads intersect at an angle whose measure is 125°. Which expression is equivalent to the cosine of this angle?

  • (1) cos 35°
  • (2) –cos 35°
  • (3) cos 55°
  • (4) –cos 55°
Answer: (4) –cos 55° 

12. Two complex numbers are graphed below.

Mathematics 16 August 2005

What is the sum of w and u, expressed in standard complex number form?

  • (1) 7 + 3i
  • (2) 3 + 7i
  • (3) 5 + 7i
  • (4) –5 + 3i
Answer: (2) 3 + 7i 
Mathematics 16 August 2005
Answer: (3)

14. A certain radio wave travels in a path represented by the equation  = 5 sin 2x. What is the period of this wave?

  • (1) 5
  • (2) 2
  • (3) π
  • (4) 2π
Answer: (3) π 

15. The mean score on a normally distributed exam is 42 with a standard deviation of 12.1. Which score would be expected to occur less than 5% of the time?

  • (1) 25
  • (2) 32
  • (3) 60
  • (4) 67
Answer: (4) 67 

16. For which positive value of m will the equation 4x2 + mx + 9 = 0 have roots that are real, equal, and rational?

  • (1) 12
  • (2) 9
  • (3) 3
  • (4) 4
Answer: (1) 12 

17. An object orbiting a planet travels in a path represented by the equation 3(y + 1)2 + 5(x + 4)2 = 15. In which type of pattern does the object travel?

  • (1) hyperbola
  • (2) ellipse
  • (3) circle
  • (4) parabola
Answer: (2) ellipse

18. Kimi wants to determine the radius of a circular pool without getting wet. She is located at point K, which is 4 feet from the pool and 12 feet from the point of tangency, as shown in the accompanying diagram.

Mathematics 16 August 2005

What is the radius of the pool?

  • (1) 16 ft
  • (2) 20 ft
  • (3) 32 ft
  • (4) 4√10 ft
Answer: (1) 16 ft

19. What is the total number of distinct triangles that can be constructed if AC = 13, BC = 8, and m∠A = 36?

  • (1) 1
  • (2) 2
  • (3) 3
  • (4) 0
Answer: (2) 2 

20. The accompanying graph is a sketch of the function y = f(x) over the interval 0 ≤ x ≤ 7.

Mathematics 16 August 2005

What is the value of (f ° f)(6)?

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

 

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