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MATH 111 Winter 2004 Practice Final, Exams of Algebra

University of Oregon (UO)Algebra

A practice final exam for a university-level mathematics course, math 111, from winter 2004. The exam covers various topics including functions, logarithms, equations, polynomial functions, and calculus. Students are required to define concepts, find equations, graph functions, and solve problems.

Typology: Exams

Pre 2010

Uploaded on 07/22/2009

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Practice Final MATH 111 Winter 2004
NAME:
[11] Let f&g, be functions, and x&ybe real numbers.
TF(fg)(x) = (gf )(x)
TF(f
g)(x) = ( g
f)(x)
T F x2=ydefines xas a function of y
T F x−2 is a factor of 1
2x4−2x2+x−2
T F log(log(e)) = 0.
T F The diameter of a circle varies directly with the radius.
Right answers will not get credit without supporting work. Note ”unde-
fined” and ”no solution” are possible answers.
1. [2] Define the absolute value of a real number c.
2. [2] Define log x=y
3. [3] Find the equation for a line that perpendicular to the line with end points (51,60)
and (53,50).
4. [3] Given kx2+ 5x−2 = 0, what does khave to be to ensure 2 real solutions? Give
answer in interval notation?
1
pf3
pf4
pf5

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Practice Final MATH 111 Winter 2004

NAME:

[11] Let f & g, be functions, and x & y be real numbers. T F (f g)(x) = (gf )(x) T F (fg )(x) = ( (^) fg )(x) T F x^2 = y defines x as a function of y T F x − 2 is a factor of 12 x^4 − 2 x^2 + x − 2 T F log(log(e)) = 0. T F The diameter of a circle varies directly with the radius.

Right answers will not get credit without supporting work. Note ”unde-

fined” and ”no solution” are possible answers.

  1. [2] Define the absolute value of a real number c.
  2. [2] Define log x = y
  3. [3] Find the equation for a line that perpendicular to the line with end points (51, 60) and (53, 50).
  4. [3] Given kx^2 + 5x − 2 = 0, what does k have to be to ensure 2 real solutions? Give answer in interval notation?
  1. [5] What is the diameter of the circle described by: 3x^2 + 9x + 30 + 3y^2 = 24y?
  2. [11] Given f (x) = (^2) x^1 +3 :
    • [5] Compute the difference quotient. Recall the difference quotient is:

f (x) =

f (x + h) − f (x) h

  • [2] Graph f (x).
  • [2] Find the inverse graphically on the above graph.
  • [2] Algebraically find the inverse of f (x).
  1. [7] Given f (3) = 0, use the factor theorem to find the other roots of x^4 − 3 x^3 − 25 x^2 +75x
  2. [3] Simplify: 2 − log 5 (25z).
  3. [4] Solve for x: 4x^ − 3 ∗ 2 x^ = 10. hint: use a substitution
  4. [4] Draw the complete graph of f (x) = log 2 (^12 x + 3) + 1, using only graph transforma- tions. List the transformations in order.
  1. [4] Your given a 16 oz mocha that is a rather weak 3% espresso. You, knowing you’ll be up late studying mathematics, would rather like a 30% espresso drink. Realizing this you purchase an espresso machine. How much weak mocha do you discard and replace with straight espresso to have a 16 oz mocha with the desired concentration?
  2. [2] How long will a loan take to triple at 20% interest compounted quarterly?
  3. [2] After much research, Uncle Joe has found a function, P (x), describing his profit for the number, x, of wing-dig he produces. How many wing-digs should be make to maximize profit given that the function for profit is:

P (x) = −100(x − 75)^2 + 600