Download Advanced Algebra II Semester #1 Review Questions Handout

Advanced Algebra II
Semester #1
Review Questions Handout
If you want to be as successful as possible on the exam, there is no
substitute for hard work and preparation. The questions in this
handout are designed to help you identify topics that you feel very
confident about and topics that you may need to spend more time on
and get help with if necessary to master. If you struggled with a section
of questions, look the topics up in your notes/text, spend additional
time reviewing the concepts, work additional problems, and get help if
needed.
The best way to prepare for any exam is to form study groups and
attack the concepts/material together. Work cooperatively on the
problems and help each other out when someone doesn’t understand a
problem/concept. Explaining the material to someone else is a great
way to master concepts.
Finally, I have all of the lectures on my hard drive if you need to listen
to my explanations of certain topics one more time. Bring me a flash
drive and we can look up and transfer the lectures you need from my
computer to your flash drive.
Directions: Complete each of the following. Use your notes, work together, and ask for help
as needed.
1) Check all of the different number sets that the number “23” a part of?
_____ Complex Numbers
_____ Real Numbers
_____ Imaginary Numbers
_____ Rational Numbers
_____ Irrational Numbers
_____ Integers
_____ Whole Numbers
_____ Natural/Counting Numbers
2) Check all of the different number sets that the number “-7” a part of?
_____ Complex Numbers
_____ Real Numbers
_____ Imaginary Numbers
_____ Rational Numbers
_____ Irrational Numbers
_____ Integers
_____ Whole Numbers
_____ Natural/Counting Numbers
3
3) Check all of the different number sets that the number “ ” a part of?
5
_____ Complex Numbers
_____ Real Numbers
_____ Imaginary Numbers
_____ Rational Numbers
_____ Irrational Numbers
_____ Integers
_____ Whole Numbers
_____ Natural/Counting Numbers
4) Check all of the different number sets that the number “ 23 ” a part of?
_____ Complex Numbers
_____ Real Numbers
_____ Imaginary Numbers
_____ Rational Numbers
_____ Irrational Numbers
_____ Integers
_____ Whole Numbers
_____ Natural/Counting Numbers
5) Check all of the different number sets that the number “ 53i ” a part of?
_____ Complex Numbers
_____ Real Numbers
_____ Imaginary Numbers
_____ Rational Numbers
_____ Irrational Numbers
_____ Integers
_____ Whole Numbers
_____ Natural/Counting Numbers
6) Check all of the different number sets that the number “0” a part of?
_____ Complex Numbers
_____ Real Numbers
_____ Imaginary Numbers
_____ Rational Numbers
_____ Irrational Numbers
_____ Integers
_____ Whole Numbers
_____ Natural/Counting Numbers
7) Check all of the different number sets that the number “ 144 ” a part of?
_____ Complex Numbers
_____ Real Numbers
_____ Imaginary Numbers
_____ Rational Numbers
_____ Irrational Numbers
_____ Integers
_____ Whole Numbers
_____ Natural/Counting Numbers
8) Check all of the different number sets that the number “ 34  5i ” a part of?
_____ Complex Numbers
_____ Real Numbers
_____ Imaginary Numbers
_____ Rational Numbers
_____ Irrational Numbers
_____ Integers
_____ Whole Numbers
_____ Natural/Counting Numbers
9) Check all of the different number sets that the number “ .2396654... ” a part of?
_____ Complex Numbers
_____ Real Numbers
_____ Imaginary Numbers
_____ Rational Numbers
_____ Irrational Numbers
_____ Integers
_____ Whole Numbers
_____ Natural/Counting Numbers
10) What is the sum of 56 and 93?
11) What is the quotient of 244 and 4?
12) What is the quotient of
13) What is the sum of
3
6
and ?
5
7
3
6
and ?
5
7
14) What is the difference of
15) What is the product of
3
6
and ?
5
7
3
6
and ?
5
7
16) Simplify the following expressions:
a) 3  2 x  5 y  3  4 3x  5 y  8
c)
5
3  6i
e) 2  5  3i   4  6  7i 
b)  2 x  43x  5
d)  5  6i  4  7i 
f)
 x  3  5 3x  4  2  2x  6
17) Solve each of the following. Graph the solutions for the inequalities. Set up 2 cases when
absolute value is involved.
a) 3x  5  5  x  4  9
b) x 2  5 x  6
c) 2 x  7  x  4  7 x  4
d) 3  x  5  2 x  6
e) x 2  8 x  9  0
f) 3x  2  11 or 2x+5  21
g) 3x  2  x  7   6x  9
h) 3x 2  5 x  2  0
i) 2x  5  15 and 3x-4  23
j) 3 2 x  3  27
k) 3x 2  5 x  1  4
l) 2 x  5  4  12
m) 2 x  3  6  18
n) 2 x  5  5  14
18) Determine the equation of the line that passes through the point (4,3) and has slope
3
.
2
Write the equation in slope-intercept form.
19) Find the equation of the line that passes through the point (6,5) and runs parallel to the
line 5 x  2 y  4 . Write the equation in slope-intercept form.
20) Write the equation of the line that passes through the point (4,7) and runs parallel to the
x-axis.
21) Write the equation of the line that runs through the point (-5,6) and runs perpendicular to
the line 5 x  3 y  12 . Write the equation in slope-intercept form.
22) Given the function f  x  
2
x  4 , find f (6) .
3
3x  4 if x  -3

23) Given the function f ( x)  2x+5 if -3<x  4 find each of the following:
-3x+1 if x>4

a) f ( 1)
b) f (6)
c) f (8)
24) Graph each of the following:
a) 2 x  5 y  15
b) 3 x  4 y  8
25) Graph the following piecewise function:
26) Graph the following system of inequalities:
 4
 3 x  7 if x  -3
f ( x)  
1 x  2
if x>-3
 3
x  2 y  10
3x  2 y  2
x5
27) Graph the following step function:
3
-1

g ( x)  2
4

5
if x<-4
if -4  x<-1
if -1  x<2
if 2  x<5
if x  5
28) Find the common solution for the following system of equations:
29) Find the common solution for the following system:
5 x  2 y  10
3 x  6 y  18
3x  y  4
5x  3 y  9
30) Find the common solution for the following system:
x  6 y  2 z  8
 x  5 y  3z  2
3 x  2 y  4 z  18
31) Factor each of the following polynomials:
a) 2 x 3  20 x 2  50 x
b) x 2  9 x  22
c) 15 x 2  7 x  2
d) x3  8
e) x 3  16 x
f) x 4  27 x
32) Solve each of the following quadratic equations:
a) 4  x  5  32
b) x 2  6 x  18  0
c) x 2  13 x  36  0
d) 6 x 2  48  0
e) 6 x 2  31x  35
f) x 2  4 x  12
2
33) Determine how many solutions each of the following equations will have:
a) 3x  5  8
will have _____ solutions.
b) x5  9 x3  0
will have _____ solutions.
c) 3x3  2 x 2  5 x  6  0
will have _____ solutions.
d) x 2  4  0
will have _____ solutions.
34) Graph the following parabola:
y  x2  4x  1 .
35) Graph the following parabola by completing the square:
y  2 x 2  12 x  14
36) Graph the following parabola by completing the square:
y
1 2
x  2x 1
3
37) Graph the following absolute value equation:
y  2 x 3 4
38) Graph the following absolute value equation:
y
2
x4 5
3
39) Simplify each of the following:
2 1
3 2
a) 3
2
4 5
5 4
3 2 5
1 3 4
b) 5 4 1  2 5 0 6
3 0 2
4 2 0
2 5 5 1
c)
4 3 6 3
2
d) 2 3 6 5
.5
40) Solve and graph each of the following inequalities:
a) x 2  6 x  27  0
b)
 x  3  x 2  25  0
c) x 2  6 x  15  0
d) 2 x 2  6 x  3  0
41) Simplify each of the following radical expressions:
a) 3 27
c)
3
2 2
e) 3i 8
g)
2 5
3 6
b) 2 8  3 18  48
d)
2 5
4 3
f) 2 27  4i 12
h)
5
4  3i
42) Given the parabolic equation y 
3
2
 x  4   3 , what are the coordinates of the vertex?
5
43) What would the equation for the parabola, in vertex form, be if the vertex is  4,5 and
the vertical stretch value is -3?
44) Which way will the curve you found in question #41 open?
Good “Skill” On The Exam
There is no substitute for hard work, discipline,
dedication, and preparation. Luck is not
involved with you being successful on the
Semester Exam.