Answers to sample midterms

These are the answers to the sample midterms for Math 124. These are just the answers (not carefully worked-out solutions), which we've posted to help your studying. On the exam, you will have to show your work. I hope these are all correct, but I wouldn't be surprised if I'd made a few mistakes. If you find anything wrong, please let me know.

Notation: "sqrt" means the square root function. "pi" means the number pi, 3.1416...

Collingwood, Spring 2001

Click here for the sample midterm (PDF format).
  1. (a) -2     (b) 5     (c) does not exist
  2. (a) 2     (b) 2     (c) 4     (b) 0
  3. (a) 11 (You were allowed to use a calculator on this exam)
    (b) The answer is 10 (but the method is the focus of the problem)
    (c) t=(-2+sqrt(4+8y))/4    ("sqrt" means the square root function)
  4. (a) 6 (but again, the method is as important as the answer)
    (b) y=6x   
  5. (a) I(t) = 25 e0.175 t. (Or without a calculator: I(t) = 25 e(1/5) ln (60/25) t.)
    (b) 6.27 years.
  6. (a) -1/2. (The problem presumably meant the limit as x approaches 1, not as t approaches 1.)
    (b) The units are cells/hour. It tells you the growth rate of the cells.
    (c) 15     (d) x=1/sqrt(2), x=-1/sqrt(2)     (e) x=1, x=-1

Zhang, Spring 2001

Click here for the sample midterm (PDF format).
  1. (a) -1/2     (b) 0     (c) 0. (The problem presumably meant the limit as x goes to 0+, not as t goes to 0+.)
  2. (a) x=1 and x=-2     (b) y=1
  3. (a) all x except 0, pi, -pi, 2pi, -2pi, 3pi, -3pi, etc.
    (b) pi/6     (c) infinity. (Again, it should be a limit involving x, not t.)     (d) yes
  4. (a) y=ax+4     (b) y= -loga(x)     (c) g(x) = (loga(x))2
  5. (a) even. (We haven't talked about even and odd functions this quarter.)
    (b) all x     (c) It has no points of discontinuity.
    (d) The answer is 1/2 (but the method is the focus of the problem).

Perkins, Winter 2001

Click here for the sample midterm (PDF format).
  1. (a) does not exist     (b) -1/8     (c) 3/sqrt(2)
  2. Discontinuous when x=1
  3. pi/6, 5pi/6, 7pi/6, 11pi/6
  4. The answer is y=-10t+45 (but the method is the focus of the problem).
  5. a=1/2, b=1
  6. Phi-1(x) = ln ((2-y)/(1+3y)).

Leveque, Winter 2001

Click here for the sample midterm (PDF format).
  1. (a) all x except x=0     (b) y=ln(y/(y-2))
    (c) all x less than 0, and all x bigger than 2.
  2. (a) 1/5     (b) infinity
  3. (a) sqrt(x3+8)     (b) x=-2     (c) [0,infinity)
  4. (a) You should know that f(-1) = 0, f(-2) = 1, f(-4)=2, and f(-8)=3. You should also know that f(1) = 2.
    (b) does not exist (it's minus infinity)     (c) 1+e
    (d) is not defined     (e) 2     (f) 2     (g) 1
    (h) does not exist (it's infinity)
    (i) x=0 is the only vertical asymptote. y=1 is the only horizontal asymptote
  5. (a) discontinuous     (b) continuous     (c) continuous
  6. (a) 13 meters per second
    (b) The answer is -3 (but the method is the focus of the problem).
    (c) The answer is 13 (but the method is the focus of the problem).
Questions or comments? E-mail me at palmieri@math.washington.edu.

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