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ALGEBRA 2/TRIGONOMETRY MIDTERM REVIEW
1) What is the solution set for the equation
?
2) What is the solution set for the equation
?
3) What is the solution of the inequality
4) State the solution set of the inequality
5) Factor:
6) Factor:
?
7) Simplify:
x 3  3x 2  2 x  6 6 x  12 x 2  7 x  10
 4

x 2  5x
x  3x 3
25  x 2
8) Simplify:
9) Solve for x:
3
1

2x  1 3x  5
11) Solve for x:
x 1 1
 
12 4 3
13) Solve for x: x 2  5x  24 =0
10) Solve for x:
x x4

5 x  13
12) Solve for x:
1 1 1


6 12 x
2
14) Solve for x: x  9 x  10
15) Find the solution of the inequality x 2  x  30 algebraically.
16) Find the solution of the inequality
18) Simplify: 150  6
17) Find the sum: 3 6 + 5 24
19) Express
4
2 3
.
with a rational denominator, in simplest radical form.
20) Rationalize the denominator:
4
5 3
21) If x varies inversely as y, and x = 9 when y = 5, find x when y = 15.
22) If x varies inversely as y, and x = 20 when y =
1
5
, find y when x = .
2
2
23) Which of the following functions graphs are functions? Explain. Which of the following graphs are oneto-one? Explain
1)
3)
2)
4)
24) The domain for f ( x)  2 x  1 is  2  x  3 . Determine the range.
What is the smallest value and the largest value?
25) A function is defined by the equation
the range of the function.
. If the domain is
, find the minimum value in
26) A meteorologist drew the accompanying graph to show the changes in relative humidity during a 24hour period in New York City. What is the domain and range of this set of data?
27) Solve for x:
28) Solve for x:
29) Which graph is not a function?
1)
3)
2)
4)
30) Solve for x: 9 2 x 3  81
31) Solve for x: 43x  8 x1
32) Solve for x: log 5 x  2
33) Solve for x: log 2 ( x  3)  4
34) What is the solution set of the equation x² = 81?
35) What is the solution set of the equation x² – 100 = 0?
36) Factor Completely: x 3  4 x 2  4 x  16
37) Factor Completely: x 3  2 x 2  36 x  72
38) What is the solution set of the equation
?
39) What is the solution of the equation
?
40) Which graph represents the inverse of the equation
1)
2)
3)
4)
41) In the diagram below, figure b is the reflection of
What is the equation of figure b?
x 3 y 5
42) Simplify using positive exponents only: 7 2 .
x y
43) Simplify using positive exponents only:
?
6a 1b 4
.
a 5 b  2
in the line
.
44) Condense:
1
log 5 a  2 log 5 b
3
45) Condense: 5 log 2 x  (3 log 2 y 
1
log 2 z )
2
46) The air temperature in Dallas, Texas, over a 5-hour period is shown in the accompanying graph.
What is the domain and range?
1
3
5 2
8 3
3
8
x
7
47) Multiply: ( x  )( x  )
49) If Px  x 2  6x  5 , find:
a) P(2) =
b) P(-5)=

50) If f ( x) 
51) If
x
, find f(–5).
x  10
2
and
1
2
x
7
1
2
48) Find the product of (  )and (  )
, find
.
52) If f and g are two functions defined by
53) Simplify: log 4 (
and
1
).
64
, find
54) Simplify: log 2 8 .
55) Multiply: (1  5 )(3  5 )
56) Multiply: ( 6  7)( 6  7)
57) Is the graph below a function? Is it one-to-one? Explain.
58) Given f(x) = x² and g(x) = x + 1, find:
a) f(g(6))
.
b) g(f(-5))
59) Given f(x) = –3x and g(x) = x² – 1, find ( f  g )(7).
c) g(f(1))
60) Matt places $1,200 in an investment account earning an annual rate of 6.5%, compounded
continuously. Using the formula
, where V is the value of the account in t years, P is the principal
initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of
money, to the nearest cent, that Matt will have in the account after 10 years.
61) The formula for continuously compounded interest is
, where A is the amount of money in the
account, P is the initial investment, r is the interest rate, and t is the time in years. Using the formula,
determine, to the nearest dollar, the amount in the account after 6 years if $1000 is invested at an annual
rate of 4%.
62) If f ( x)  2 x  1 , find f
64) Simplify:
1
( x).
32 x 3 y 4 .
63)If f ( x)  2 x , find the inverse of the function.
65) Simplify: 108 x 2 y 5 z 8 .
66) Evaluate e x ln y when x = 4 and y = 2.
67) Evaluate e x ln y when x = 6 and y = 3.
68) Factor Completely: 18x 6  200 x 2 .
69) Factor Completely: 16 x 7  100 x .
70) On the axes below, for  1  x  2 graph the equation y  3 x and state the equation of the asymptote.
71) Simplify:
9  x2
2
72) Simplify: x  9 x  20
2x  6
x4
73) If log 2 x  3 and log y 25  
2
x
, find the numerical value of in simplest form.
3
y
74) If log a 16  2 and log 3 b  3 , find the numerical value of
a
to the nearest hundredth.
b