The test 2 will be held on Nov 6 (Monday 6 PM).  The location  of the test will be given by your instructor.       The test will cover  sections 2.2 through  4.2 in the syllabus.   NOTE:  This is just a review sheet.   The problems in the test will differ from these.  To do well in the test, first do the homework problems and then these.

MTH 111 - FALL 2000 - REVIEW  SHEET 2 - PRINT YOUR NAME_____________________

1.  Identify the vertex, axis of symmetry, x- and y-intercepts and sketch  y = - 2x2 + 4x  + 3.

2.  Find the remainder and the quotient when   x-1  divides 2x4 - 3x.

3.  Find the remainder when  x + 1  divides  5x 101 - 3x77 + 11x + 1.

4. Sketch the following functions:  (a)  f (x) = (2x + 3) / (x-4)    (b)  g (x) = 3x 2 / (x 2  - 4).

Your graphs must show symmetry, x- and y- intercepts, all asymptotes etc with all your work.

Do not just copy the graph from your calculator.

5.   Solve:  (a)   x2 + x - 2  > 0       (b) x3 + 4x2 - x - 4  < 0.   Graph the set on the x-axis.

6.  Solve for x:  (a)  4 2x - 1  =  1/2   (b)  10 3x+2 = 0.001   (c) log (1/8) x = - 4/3

(d) log (x) + log (2x) = 2  (e) ln (x) + ln (x+3) = 2 ln (2). (g)  e 5x - 2  = 1/ e

7.  Find the inverses of:  (a) f (x) =  log 3 (2x+5)  (b) g(x) = e   (c)  h(x) = x / (2x - 1)

8.  (a) Let f(x) = 3 -(x+1) .   Find f -1.   Sketch the graphs of  f  and  f -1   on the same coordinate axes.

(b) Let  g (x) = - 2 ln (x +3).  Sketch the graphs of  g  and  g -1   on the same coordinate axes.

9.  Let  ln 2 = A,  ln 3 = B,  ln 5 = C. Express  ln (32/75) in terms of  A, B and C.

10.  Use calculator to solve for x: (a) (1.62)x  = 1.25 (b) (1 + x)7 = 100  (c) 5x32x = 10

to  four significant places.

11. An observer stands on a level ground 200 meters from the from the base of a  TV tower.  The

angle  of elevation from the observer to the top of the tower is 26.5° .  Find the height of the

tower above the observer’s eye level?

12.  (a) A kite flies at a height of 60 ft when 130 ft of string is out.  Assuming that the string is in

straight  line what is the angle that it makes with the ground?

(b) Find the height of  a tree if  the   angle of elevation of its top changes from  20° to 40° as

the observer walks 75 towards  its base.