Math 121, Spring 1997
Final Exam , Dr. Howard
Show all work. Circle your final answers.
 
1.
Solve for x if 5x2-2 = 3x.
2.
Solve by completing the square: 7x2-14x+6 = 0.
3.
Factor the expression 4x3+6x2-10x.
4.
Completely factor the expression (3x+2)-3-9x(3x+2)-4.
5.
Reduce the expression [(x2+3x-10)/( x2+2x-15)].
6.
Simplify the expression [(x+1)/( x2-1)] ¸[(x2+1)/( x-1)].
7.
Solve for x given that 3[2x-(7x-1)] = 5x+13.
8.
A telephone call costs $0.31 for the first minute, plus $0.24 for each additional minute. Write an algebraic expression for the cost of a call lasting x minutes.
9.
Given the function f(x) = x2-3x+4, evaluate and simplify the expression
 
f(x+2)-f(2).
 
 
10.
Find an equation of the line that passes through the point (3,10) and is parallel to the line x-3y = 1.
11.
Write an equation for the line that passes through the points (3,-1) and (-4,1).
12.
Solve the inequality 14-2x £ 5.
13.
Solve the inequality -2 < 3x+1 < 7.
14.
Solve for x if 1/x-[1/( x+1)] = 1.
15.
Solve for x if |x2-2x| = x.
16.
The length of a rectangular room is 2 feet longer than the width. Write an algebraic expression for the perimeter of the room with width of x feet.
17.
Determine which graph below represents y as a function of x by using the vertical line test.
18.
Over which interval(s) is the function with graph as below decreasing?
19.
Let A = {0,2,4} and B = {1,3,5}. Fill in the missing number below so that the set of ordered pairs represents a function from A to B.

 
(0, 3),    ( ___ , 5),    (2, 1).
 
 
 
 
 
20.
Use the change of base formula to determine which of the following is equal to log27:

 
(a). [log2/ log7] (b). [ln2/ ln7] (c). [ln7/ ln2]
 
 
(d). 2log7 (e). None of these
 
 
 
 
 
21.
Write the following expression as the logarithm of a single quantity:
 
1
4		 logb16-2logb5+logb7.
 
 
22.
Solve for x if 32x = 81.
23.
Solve for x if ln(7-x)+ln(3x+5) = ln(24x).
24.
Find the balance after 15 years if $1500 is invested in an account that pays 81/2% compounded quarterly.
25.
Solve the following system using the method of substitution:
x+y 
 
= 1
 
x2+3y2
 
= 21
 
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