MATH 154 FINAL

General Information:

The final exam will be on Monday, March 24, 2008

Room A-213 from 10:00 to 12:00 Noon

Office Hours during finals week:  10:30 -11:00 Monday

You may use a scientific calculator for the final

You must know the Quadratic Formula, the Pythagorean Theorem, and the two formulas that apply to arithmetic sequences.

Review of some of the "more difficult" concepts covered in Math 154. 

1.   State the quadratic formula:  If ax² +bx+c = 0 and a = 0, then:

2.  Solve for x:  x² -3x > 4  Make a sign-chart and show your work.

 3.  Does the graph of y = 2x² + x -1 open upward or downward?

4.  Solve (x+15)² -3(x+15)  -18 = 0  Show your work.  

5.  Solve the system 12y² -4x² = 9  and x= y²    Test all solution points.  List each point that satisfies both equations.

6.  Solve for x:   a)  8^2x-1  = 1/4                                            b)  7^3x-1 = 15

7.  Solve, using the quadratic formula:  6x² -7x = 3

8.  To determine the cost of an in-home repair, a plumber uses the linear function         C(n) = 40n + 30, where n is the time in hours and C(n) is the cost in dollars. 

a)  Find C(3)   and C(5)   

9.  Graph y = -  x.  Plot and label at least 5 points.  Clearly label both axes & origin on your graph.

a)  Is this a function?

b)  What is the domain?  ___________________     What is the range? ______________

10.  Are f(x) = 3x and g(x) = x/3 inverses? Yes or No _______________________

11.  Given f(x) = 2x -1, find f^-1(x).  Show your work.

12.  What is this strategy called?

13.  Show that f(x) and f^-1(x) are inverses.

14.  f(x) and f^-1(x) reflect across which line?

15.  The population of a certain country appears to be growing according to the formula P= 20e ^0.1t where P is the population in millions, and t is the number of years since 1990.  What was the population in 1990?  What will the population be in the year 2020?

16.  log₂ (4) =           log _1/3 (1) =                log ₁₆ (4) =         ln(1/e) =               log_a (a)^M =

17.  List the product and quotient rules for logarithms.

18.  Solve for x:  2 log(x) = log (20-x)

19.  Complete the square to find the center and radius: x² +y² = 8y +10x -32

20.  Sketch the graph of:   y² /9 -   x²   /4 = 1

21.  Write the first five terms for the sequence a_n =   1 

                                                                                   n+2

22.  Write the series 2+4+6+8+10+12+14 in summation notation.

23.  Find the sum of the positive integers from 1 to 100 inclusive.

a)  Write the formula            b)  Now use it to find the sum.

24. What kind of sequence is this?

25.  Find the sum:  1 + 2 + 3 + …..+ 48 

26.  Find the sum of the geometric series 1/3 + 1/9 + 1/27 + …. + 1/729