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Algebra 1
Name: _______________________________________
Hour:
June 2014
Semester 2 Final Exam Review
Directions:
Show all your work to receive full credit.
The question numbers that are circled should be completed without a calculator.
Chapter 8:
1.)
Simplify. The final answer must have positive exponents. Leave all answers in exponential form.
a.) 81  86
e.)
i.)
b.) r 4  r5  r6
(2qr5 )3 (qr)6
5 4  55
5
j.)
6
  3t 5r 8 


f.)
(3x 4 y 2 ) 3
1
9x
c.)
(3c 4 )(2c 3d6 )
d.)
g.)
(4  3)2
x
h.)  
k.)
2  4
y
(2) 0 (3x 2 y 2 ) 1
4
2.)
Simplify:
3.)
 j5 
Simplify the expression using positive exponents.  
k9

8

4.) Rewrite 20  29 using positive exponents.
5.)
Rewrite the expression using positive exponents.  30  2x 1 y 1 


2
( x 2 )5
 3
8
y 
l.)
74
76
2
Algebra 1 Review
6.)
a.) 100
page 2
1 / 2
3/ 2
d.) 2162 / 3
7.)
3 / 2
b.) 121
c.) 81
e.) 27 1 / 3
f.) 3432 / 3
Write an exponential function to model the situation and tell what each variable represents.
A price of $130 increases 5% each year.
8.) Find the value of $1500 deposited for 8 years in an account paying 6% annual interest compounded yearly.
9.) Write an exponential function to model the situation.
A population of 290 animals decreases at an annual rate of 9%.
10.) Graph the function y
 3x .
1
x
11.) Graph the function y  4    .
2
Does this graph represent exponential
growth or exponential decay?
1
 
Does this graph represent exponential
growth or exponential decay?
1
1
12.) Multiple Choice: Which equation below represents exponential decay.
A. y  2.16t
B. y  0.89t
1
Algebra 1 Review
page 3
Chapter 9:
1.) True or False. 2x 2  x 1 is a polynomial.
2.) Use the polynomial 6x 3  6x  4 x5  2 to answer the questions below.
a.) Rewrite the polynomial in standard form.
b.) What is the degree?
c.) What is the leading coefficient?
d.) How many terms does the polynomial have?
e.) Classify the polynomial by the number of terms.
3.) Use the polynomial 4 x 2  3  2x to answer the questions below.
a.) Rewrite the polynomial in standard form.
b.) What is the degree?
c.) What is the leading coefficient?
d.) How many terms does the polynomial have?
e.) Classify the polynomial by the number of terms.
4.) Find the sum or difference.
a.)
(2a7  3a3  6)  (2a3  4  6a7 )
b.)
(3e 4  4)  (8e 3  2)
c.)
(6b3  3b2  8)  (2b3  8b2  6b  5)
d.)
(4z 4  4z3  6)  (6z 4  7z3  3)
e.)
(5x 4  5x 6  5)  (9x 6  7  3x 4 )
f.)
(5x 2  7 x)  (3x  2x 2 )
Algebra 1 Review
page 4
5.) Find the product. Write all final answers in standard form.
a.)
6(3x  4)
b.)
( x  3)( 4 x  5)
c.)
(2 x  3)(5 x  4)
d.)
( x  6)( x  6)
e.)
(9 x  4)(3x 2  6 x  1)
f.)
( 4 c  2) 2
g.)
( x 2  2x  3)( x  5)
h.)
i.)
( x 2  x )(3x  2)
( x  7)( x  4)
6.) Find the missing term(s) of the quadratic equation.
a.) (2x  9)2  4 x 2  __________  81
b.) (5x  2)2  25x 2  __________  _________
c.) (7x  6)2  __________  __________  __________
7.) Solve.
a.)
( x  4)(2x  2)  0
b.)
x(3x  4)( x  2)  0
c.)
(3x  1)( x  4)(2x  5)  0
8.) Factor completely then find all solutions.
a.)
x2  x  6 = 0
b.)
x 2  16x  63 = 0
c.)
x27x  12
=0
Algebra 1 Review
9.)
page 5
Factor completely then find all solutions.
d.) 4x 2  7x  2 = 0
e.) 49x 2  21x  2 = 0
g.) 3x 2  19x  6 = 0
h.)
36x 2  16 = 0
f.)
x 2  3x  10 = 0
i.)
x 2  6x  9 = 0
9.) Factor each polynomial completely.
a.)
2x 2  50y 2
b.)
p2  169q2
c.) 4x 2  12x  9
10.) Factor by grouping.
a.) x 3  3x 2  4 x  12
b.) x 3  4x 2  25x  100