Algebra 2
Spring Final Exam Review #1 (FER1)
Concept Skills 1-10:
Name:
As you complete each of the following problems, keep your notes out
and your NOTECARD handy. For the notecard, label the skill, then write
NOTES (not example problems) to remind you of the steps necessary to
complete the work.
Skill #2 Simplifying Expressions with Exponents
Simplify the following expressions. Your answer should have positive
exponents only.
2
3
2
a)  
b) (
x 3 y 6 2
)
x2 y 4
Skill #1 Scientific Notation and Standard Notation
Convert between Standard and Scientific Notation
a) 3.46  108
b) 3.46 108
c) 0.000027
d) 2700000
c) (3a3b)(4ab2 )
d)
12 x 4 y 3
18 x 6 y
Multiply or divide the following and express your answer in scientific notation.
a) (2.5 103 )(4 107 )
b) (5 102 )(4 104 )
e)
c) (5 107 )  (2.5 103 )
d) (4 104 )  (2 102 )
35 x 7 y 2 z
42 x3 y 5 z 2
f) (5 x 3 y 2 )3
Skill #3 Write polynomials in standard form
Fill out the following charts:
Number of
Degree of Name of
polynomial polynomial
1
2
3
4+
a) 7  10x 2
i) and ii)
iii)
iii)
c) 8 x  2 x3  x5
i) and ii)
d) 3  8 x  7 x 2
i) and ii)
iii)
iii)
e) 20
i) and ii)
iii)
Name of
For
terms of the polynomial
each polynomial
poly
1
nomi
2
al
3
belo
w:
4+
i) Put
the polynomial in standard form
ii) Circle the lead coefficient
iii) Name the polynomial
b) 3 x  2 x 2  9  4 x 3
i) and ii)
Skill #4 Polynomial Addition and Subtraction
Add or subtract the following polynomials as indicated.
Leave your answer in standard form.
a) (6 x3  2 x 2  6 x  3)  (4 x  5 x3  6  x 2 )
b) ( x 2  2 x  3)  (2 x 2  4 x  9)
c) (4 x 2  7 x  5)  (3x  5 x3  8)
d) ( x 2  9 x  7)  (3x  2 x 2  9)
Skill #5 Polynomial Multiplication
Multiply the following polynomials.
a) 3a3b(4ab 2  a  4b)
b) (2 x  3)(4 x  9)
c) (2  x)(2  x)
e) ( x  6)(2 x 2  4 x  1)
d) (4 x  y)2
Skill #6 Factoring – GCF
Factor the following by factoring out the GREATEST COMMON FACTOR (GCF)
a) 12 x 2  3
b) 16 x5  40 x3
c) 63x 2 y  27 x 4 y  9 x3 y 2
Skill #9 Factoring - Difference of Two Squares
Factor the following Difference of Squares.
a) x 2  81
b) 9  49x 2
Skill #7 Factoring – Grouping
a) 2 x3  14 x 2  3x  21
c) 25 x 2  36 y 2
b) 6 x3  9 x 2  2 x  3
Skill #10 Factoring – Multi-step Factoring
a) 3x3  21x 2  30 x
b) 5 x3  20 x
c) 24 x  32 x  3x  4
3
d) 4 x 2  1
2
Skill #8 Factoring – Trinomials
a) x 2  8 x  15
b) 2 x 2  7 x  4
c) 3x 2 y  12 xy  63 y
c) 6 x 2  17 x  5
d) x 2  15 x  54
d) 6 x 2 y 2  22 xy 2  8 y 2