Math 106 Preliminary Problems

The following problems cover material which you may recall from previous course work in algebra.
You may not recall all of these topics or how to do the problems precisely.
Use your texts or notes from previous courses to help solve these problems.
You might also look at this web resource.

  • Purple Math website
  • You can e-mail me any questions you have on these problems - or bring them to the first class any questions. 
    We'll use these as a foundation for our preliminary work.
    1.  The line L goes through the point (3,2) with a slope of -4. 
      A. Give an equation for L. 
      B. What is the X intercept of L ? 

    2. For this problem letbe defined by f (x) = 5x2 + 3. 
      A. Find the following. Simplify you answer when possible. 
        i) f (1)                       iii) f (1+h)           ii) f (h)                     iv) [f (1+h) - f (1)]/h 
      B. Find any number(s) z where f (z) = 23. 
      C. For which values of x is f (x) < 23? Express your answer as an interval. 

    3. When possible , find the slope of the line connecting each of the following pairs of points. [ Write "NO SLOPE" if appropriate.] 
      A. (2,-2)   (3,1)           B. (4,1)    (-3,-1)             C.  (-4,1)   (-3,-1) 

    4. The price of a stock on Wednesday morning was approximately linear in its relation to the time. At 8 A.M. it was $40 and at 10 A.M. it was $46. Estimate this stock's price on Wednesday morning at 8:40 A.M. 

    5. Old MacDonald has a farm, and on that farm she has some sheep and a pasture with a 200 meter long stone wall. She wants to enclose a rectangular section of the pasture for a small sheep pen using the wall for one side and 140 meters of fencing she was given by her uncle Milo for the other three sides. Let x denote the length of the fence that will be attached to the wall used as a side for the pen. 
      Which of the following equations express the area of the pen, A, as a function of x.
    i.. A = x ( 70 - x)                     ii.. A = 2 x ( 140 - x)
    ii.. A = x ( 140 - x)                  iv.. A = x ( 200 - (l/2)x)
    v. A = 2 x ( 70 - x)                  vi. A = 2 x ( 200 - x)