Spring 2012 MA Exam 3: Mathematics Problems, Exams of Calculus

A set of mathematical problems from an exam held in spring 2012. The problems cover various topics including trigonometry, logarithms, and calculus. Students are required to approximate angles, find zeros of functions, and determine the domain of a composite function.

Typology: Exams

2012/2013

Uploaded on 02/14/2013

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MA 15900 EXAM 3 SPRING 2012
1
1. A builder wishes to construct a ramp that is 32 feet long. One end of the ramp will sit on the level
ground and the other end will be 7 feet above the level ground. Approximate the acute angle
between the ramp and the level ground to one decimal place.
1)
14.7°
2)
14.4°
3)
14.1°
4)
13.8°
5)
13.5°
6)
13.2°
7)
12.9°
8)
12.6°
9)
12.3°
2. If the angle
θ
is in standard position, which of the following is a pair of angles that are both
coterminal to
θ
?
θ
=580°
1)
760°, 400°
2)
40°, 760°
3)
4)
5)
940°,320°
6)
7)
8)
220°,320°
9)
220°, 940°
3. Find the zeros of f.
f(x)=x2e3x+xe3x30e3x
1)
30,6,5
2)
6,0,5
3)
6,1,5
4)
30,0
5)
30,1
6)
30
7)
0
8)
1
9) None of the above
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  1. A builder wishes to construct a ramp that is 32 feet long. One end of the ramp will sit on the level ground and the other end will be 7 feet above the level ground. Approximate the acute angle between the ramp and the level ground to one decimal place. 1) 14.7° 2) 14.4° 3) 14.1° 4) 13.8° 5) 13.5° 6) 13.2° 7) 12.9° 8) 12.6° 9) 12.3°
  2. If the angle θ is in standard position, which of the following is a pair of angles that are both coterminal to θ? θ = 580 ° 1)

220 °, 940 °

  1. Find the zeros of f. f ( x ) = x^2 e −^3 x^ + xe −^3 x^ − 30 e −^3 x

  1. None of the above
  1. Suppose $31, 000 is deposited in a savings account that has an interest rate of 5.7 % per year and the interest is compounded monthly. How much money will be in the account after 17 years? Round your answer to the nearest cent.

  1. None of the above
  1. Suppose that a certain language originally had N 0 basic words and that at time t , measured in millennia (1 millennium = 1000 years), the number N ( t ) of basic words that are still in common use is given by N ( t ) = N 0 (0.765) t

. Approximate the percentage of basic words lost every 200 years. 1)

  1. None of the above
  1. Solve the equation.

log 2 ( x + 6) + log 2 ( x − 1) = 3

  1. x = − 52 ± 12 61
  2. x = − 52 + 12 61
  3. x = − 52 ± 12 85
  4. x = − 52 + 12 85
  5. x = − 7 , 2
  6. x = (^158)
  7. x = (^92)
  8. x = (^32)
  9. None of the above
  1. Find the domain of gf , where f ( x ) = x + 2 x − 1 and g ( x ) = x − 5 x + 4 .

(− ∞, 25 ) ∪ (^25 , 1 ) ∪ ( 1 , 74 ) ∪ ( 74 ,∞)

(− ∞,− 4) ∪ (− 4, 25 ) ∪ (^25 , 74 ) ∪ ( 74 ,∞)

(− ∞,− 4) ∪ (− 4, 25 ) ∪ (^25 , 1 ) ∪ ( 1 ,∞)

(− ∞, 25 ) ∪ (^25 , 1 ) ∪ ( 1 ,∞)

(− ∞,− 4) ∪ (− 4, 25 ) ∪ (^25 ,∞)

(− ∞, 25 ) ∪ (^25 ,∞)

  1. Which of the following are true of the function f ( x ) = 2 x ? I. f has a y - intercept at ( 0 , 2 ) II. The graph of f is increasing on the interval (−∞, 0 ) III. The range of the function is (−∞, 0 ) ∪ ( 0 , ∞)
  1. I
  2. II
  3. III

I and II

I and III

II and III

I, II, and III

  1. Cannot be determined
  2. None of the above
  1. Determine the exact value of sin θ.

sin θ =

sin θ =

sin θ =

sin θ =

sin θ =

sin θ =

sin θ =

sin θ =

  1. None of the above
  1. Given f ( x ) = x 4
  • 5 x 2 − 36. Find all values of x such that f ( x ) > 0.
  1. (− ∞, − 3 ) ∪ (− 2 , 2 ) ∪ ( 3 , ∞)
  2. (− 3 , 2 ) ∪ ( 2 , 3 )
  3. (− 3 , ∞)
  4. (− ∞, − 9 ) ∪ ( 4 , ∞)
  5. (− 9 , 4 )
  6. (− 9 , ∞)
  7. (− ∞, − 2 ) ∪ ( 2 , ∞)
  8. (− 2 , 2 )
  9. (− 2 , ∞) θ 20 13
  1. Which of the following are true of the function f ( x ) = log 2 ( x + 4)? I. f has a y - intercept at (0,2). II. The graph of f has an asymptote y = 4. III. The range of f is

I

II

III

I and II

I and III

II and III

I, II, and III

  1. Cannot be determined
  2. None of the above

17. Find the exact values of all angles θ in the interval [ 0 , 2 π) that satisfy the following equation.

tan θ = − 1 3

5 π 6 , 7 π 6

π 6 , 7 π 6

2 π 3 , 5 π 3

2 π 3 , 4 π 3

5 π 6 , 11 π 6

π 3 , 4 π 3

π 3 , 2 π 3

7 π 6 , 11 π 6

  1. None of the above
  1. Which of the following are true of the function f ( x ) = − 7 sin(^12 x −^ π 3 )? I. The maximum value of the function f is 7 and occurs when

x =^ π

2 . II. The period of the function is

III. The phase shift of f is

2 π

I

II

III

I and II

I and III

II and III

I, II, and III

  1. Cannot be determined
  2. None of the above
  1. The power, P , supplied to a resistor is directly proportional to the square of the voltage, V , and is inversely proportional to the resistance, R. What is the effect on the power if the voltage is tripled and the resistance is reduced to one-fourth of R.
    1. The power decreases by a factor of 121 2 ) The power decreases by a factor of 361 3 ) The power decreases by a factor of (^34) 4 ) The power decreases by a factor of (^49) 5 ) The^ power^ increases^ by a^ factor^ of^12 6 ) The power increases by a factor of 36 7 ) The power increases by a factor of (^43) 8 ) The power increases by a factor of (^94)
    2. None of the above