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 $0.51 for the first minute, plus $0.11 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) with
slope m = 1/3.
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.
On your graphing calculator, sketch the graph of y = f(x), where f(x) =
2x3-3x2-12x+1 using the window
xmin=-4.7 ymin=-25
xmax=4.7 ymax=15
xscale=1 yscale=2
Determine from this graph all intervals on which f is increasing and
all intervals on which f is decreasing.
18.
The graph of y = f(x) is given below. On the same pair of axes, sketch
the graphs of y = f(x-1) and y = f(x)-1. Be sure to indicate which graph
is which.
19.
Iodine-125 is a radioactive isotope used in brain implants for the treatment
of cancer. The amount of the isotope present after t days is
Q(t) = Q0e-0.011589t millCuries,
where Q0 is the amount used initially. Find the half-life
of Iodine-125.
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 monthly.
25.
Solve the following system using the method of substitution: