# 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

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)

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

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

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.

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

• (1) 7
• (2) 7√2
• (3) 7√3
• (4) 14

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

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)

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.

What is m∠θ?

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

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°

12. Two complex numbers are graphed below.

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

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

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

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

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

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.

What is the radius of the pool?

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

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

What is the value of (f ° f)(6)?

• (1) 1
• (2) 2
• (3) 0
• (4) –2

Mathematics 16 August 2005 Questions Answers Keys

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