232 Algebra 2A
Review for Semester 2 Exam—June, 2015
Review Sheets
See attached sheets.
Multiple Choice Practice Problems in the Text (answers are given)
Chapter 7
page 460
#1C, 2A, 3D, 4C, 5B, 6C, 8E, 9B
Chapter 8
page 527
#2D, 3A, 4D, 5D, 6B, 7A, 8C
Chapter 9
page 580
#1A, 4A, 5E, 7D, 8B
Chapter 10
page 646
#1A, 2A, 3D, 4D, 5E, 6B
Old quizzes and tests
Take your old quizzes and tests to the MRC to get help making corrections, if needed.
Use old quizzes and tests as additional study guides.
Topics on the exam
Chapter 7
simplify expressions with rational exponents, including laws of exponents
simplifying nth roots: numbers and variables
solve equations: using nth roots; radical equations; equations with rational exponents
composition of functions
inverses of linear functions
Chapter 8
exponential growth and decay equations; word problems
the number e
definition of logarithms
change of base formula for logs
finding inverses of log functions
domain and range of log functions
expanding and condensing log expressions
solving exponential and log equations
Chapter 9
simplify, add, subtract, multiply, divide rational expressions (review factoring)
simplify complex fractions
solve rational equations: a) proportions b) LCD method
Chapter 10
Complex fractions
equation of perpendicular bisectors
equations and graphs of:
circles (center at origin)
inverse variation y=k/x
Domain and Range
of random graphs
of functions
Name ________________________
1) Simplify:
a)
1
83
2) Simplify: a) 8
b)
2
3
1
2
 1
 22
4) Simplify: a)  1
 3
7





b) 64
6
Semester 2 Review
1
16 4
b) 32

3) Simplify: a) 49
232 Algebra 2A
c) 81
4
5

 1
 32
b)  1
 5
7
c) 27
1
4





1
4
2
3

c) 32
10
1
5
 1
 52
c)  1
 4
6





8
5) Simplify, using rational exponents; assume x and y have positive values:
a)
3
24 x 9 y 16
6) Solve:
a) ( x + 2)3 = 216
7) Solve:
a)
8) Solve:
3
x +6=0
a) -2x
3
2
= -54
b)
20 x 7 y 12
b) (x – 5)5 = -32
b)
x 1  4  0
2
3
b) 4 x  64
c)
3
56 x 6 y 8
c) ( x +3)4 = 16
c)
4
x 3 7
5
3
c) 3x = -96
9) The graphs of functions that are inverses are symmetrical with respect to the line:
10) If h(x) is given, find the inverse function h-1(x).
a) h(x) = 4x – 1
b) h(x) =
x2
3
_____________ .
c) h(x) = 2x + 5
11) If f(x) = x2 - 3 and g(x) = 2x + 3 and j(x) = 3x2 + 1, then
a) f(g(x)) =
b) g(f(x)) =
c) j(g(x)) =
13) The annual fundraising at a certain college in 1990 was $104,000. During the next twenty years, the
money raised increased by 4% per year. What was the approximate money raised in 1999?
14) The number of bacteria in a dish was given to be 20,000 at 12:00 p.m. The amount of bacteria present
per hour decreased by 8 percent per hour. How many bacteria could be found at 8:00 p.m. that same night?
1
15) Given the function: f ( x)  200    , is f(x) an example of exponential growth or exponential decay?
4
2/3
16) Evaluate using a calculator: 2e
x
17) Evaluate: log 8 128
18) Rewrite this equation in exponential form: log 6 (8 x)  2
19) Find the inverse of this function: y  ln ( x  4) .
20) Find the domain and range of the function: f(x) = log x  4
21) Expand completely: log 5 (20 x )
22) Condense:
23) Solve:
1
ln 27  4 ln x
3
4 x  16  54
24) Factor: a) x 2  12 x  36
25) Simplify:
2a b c 
 4ab c 
26) Simplify:
x 2  4x  5
x 2  25
27) Simplify:
x 3  2x 2
x2 1

x 2  3x  2 x 2  x
28) Simplify:
x 2  3x  2
x 1
 2
x2
x 4
29) Simplify:
2x y 3
2
 5  2
2
y
4x
x y
30) Simplify:
x  1 2x  1
 2
3x
x
31) Simplify:
3
2
 2
x2 x 4
2
2 3
3
4
2
b) 2 x 2  10 x  100
c) x 3  25 x
d) 8 x 3  125
x
1
32) Simplify: 2
2
1
3
 15 x  16
33) Solve: a)

x
4
34) Solve: a)
5 3x 7 x


4 2
6
b)
x( x  1)  2 x  1

4
10
b)
2x
x5
 2
1
x 1 x 1
35) Find the distance between the points (4, -3) and (6, 2).
36) Find the midpoint of the line segment joining the points (-4, 7) and (0, -1).
37) Find the equation of the perpendicular bisector of the line segment joining the two points
( 1, 7) and (-3, 2).
38) State the radius of each circle.
a) x 2  y 2  49
b) x 2  y 2  7
c) x 2  y 2  32
39) State the radius of each circle:
a) 2 x 2  2 y 2  32
b) 5 x 2  5 y 2  200
c) 3x 2  3 y 2  33
40) Make a table of values with at least 3 points and graph:
y  x 3
41) Solve for x. (no decimals)
42) Simplify:
 7  log 2 (5x)  3
x
6

x3 x5
43) Graph the following: x2  y 2  4
44) review the test you had on domain and range (the first page front and back)