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 = 3x ^{2} + 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) = 2 ^{t/3}For 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√2
*i* - (2) 2
*i*√2 - (3) −2
*i*√2 - (4) 18
*i*√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

**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 + 3
*i* - (2) 3 + 7
*i* - (3) 5 + 7
*i* - (4) –5 + 3
*i*

**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 4x ^{2} + 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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