Download Algebra 1 Final Exam REVIEW Name

Algebra 1 Final Exam REVIEW
Second Semester 2012
Name ________________
This will be a 25 point assignment. 15 points for completion and the last 10 points will be randomly selected
questions graded for accuracy.
ALL WORK THIS PACKET AND FINAL ANSWERS ON ANSWER SHEET.
YOU WILL TURN IN THIS PACKET + THE ANSWER SHEET.
Useful Formulas:
x
 b  b  4ac
x
2a
2
z=

Study each system of equations. If the system has only one solution, name
the solution. If the system has NO solutions, write NO SOLUTION. If the
system has INFINTELY many solutions, write INFINITE SOLUTIONS.
2 lines
1.
ONE (
)
2.
ONE (
)
NO SOLUTIONS
INFINITE SOLUTIONS
3.
ONE (
)
NO SOLUTIONS
INFINITE SOLUTIONS
NO SOLUTIONS
INFINITE SOLUTIONS
4.
Use the graphing method to determine the solution of the system of
linear equations.
2
y=− x+1
3
y=
2
x−3
3
5.
Use the elimination method to determine the solution of this system
of equations.
5x + 3y = 26
−2x + 3y = −2
6.
Describe the steps you have to take to solve the given system of
equations using elimination. Finish the problem and find the solution!
2x + 5y = 17
x − 3y = −8
7.
Describe the steps you have to take to solve the given system of
equations using elimination. Finish the problem and find the solution!
3x + 4y = −1
2x + 7y = −5
8. One number is 8 more than another number. The sum of the numbers is 6.
What are the numbers? (hint: set up a system of equations to help yourself solve)
9.
In the expression x-9, what is the exponent?
what is the leading coefficient?
10.
Simpify 54 • 515. Write the answer as a power to a power.
11.
Simplify (34)8. Write your answer as a power to a power.
12.
Simplify (−2x5y3)6
13.
Evaluate (a • a3)2 when a = 2.
14.
Simplify:
exponents.
x−12 • x5 • x−3
Your answer should not contain negative
15.
Rewrite (7x−2y)(-6xy−3) without negative exponents.
16.
Simplify:
x8
Your answer should not contain negative exponents.
x2
17.
Simplify (5x)2 • (2x)0
18.
Simplify (3xy)4(−2x)2
19.
 2x 
Simplify 

 3 
3
4
 3x y 6 xy
•
5 x 7
2 xy
6
20.
Simplify
21.
Rewrite 9.4 x 105 in decimal form.
22.
Rewrite 0.00000000257 in scientific notation.
2
23.
Evaluate the product (8.3 x 108) • (6.1 x 10-3) and express the answer
in scientific notation.
24.
Evaluate
1.5 x 10
6.5 x 10
4
9
hint: please let your calculator help you!!!!
25.
Find the sum: (7x2 + 3x - 5) + ( -4x + 5x2 + 8y3)
26.
Find the difference: (3x2 + 8x + 1) - (−x2 − 8x + 6)
27.
A rectangle has a length of 4x - 1 and a width of x + 7. Which
expression would represent the perimeter? (draw a picture to help yourself)
28.
Simplify: (4x2 + 7x − 6) − (3x2 + 9x − 8) + ( -7x2 + 5)
29.
Simplify: 6x(2x2 - 4)
30.
Simplify: (2x - 5)(x + 7)
31.
Simplify: (x + 10)(x − 10)
32.
Find the product of (x + 2)(3x2 − 5x + 6)
33. The length of a rectangle is (3x + 5). The width is (x − 2). Find the area.
Match each trinomial with its factor. You will not use all choices.
_____34.
x  8x  15
_____35.
x 2  8x  15
_____36.
x  2x  15
F.
(x  5)(x  3)
G.
(x  5)(x  3)
H.
(x  5)(x  3)
J.
(x  5)(x  3)
2
2
Match each trinomial with its factor. You will not use all choices.
_____37.
x  4x  4
_____38.
x 4
_____39.
x2  4
A.
Prime
B.
(x  2)(x  2)
C.
(x  2)(x  2)
D.
(x – 2)2
2
2
Match each trinomial with its factor. You will not use all choices.
2
_____40.
9x − 4
_____41.
9x2 + 12x + 4
_____42.
F.
Prime
G.
(3x – 2)2
H.
(3x  2)(3x  2)
J.
(3x  2)(3x  2)
2
9x + 4
43. Factor the following trinomials, which one is a perfect square trinomial?
A) x2 + 6x - 16
B) x2 + 8x + 16
44. Factor the following trinomials, which one is a perfect square trinomial?
A) 4x2 + 12x + 9
45.
Simplify: (4x - 3)2
B) 49x2 + 28x + 4
46.
Find the mean, median, and mode for this data set. Round to the
nearest hundredth if necessary.
12, 15, 12, 17, 18, 17, 20, 14, 12
mean ______
47.
median ______
8
What is
What is
What is
What is
What is
the
the
the
the
the
14
16
12
mode ______ std. deviation _____
23
27
median of the data represented above?_____
smallest value in the data set?_____
first quartile of the data set?_____
third quartile of the data set?_____
mean? ________
Simplify each expression.
48.
51.
49 ______
 100 ______
49.
52.
 16 ______
121
______
81
50.
 25 ______
53.
7
______
64
Solve each equation. Exact answers only, no decimal answers.
54.
x2 = 225
55.
57.
Simplify
24
58.
Simplify
7
25
59.
Simplify −7 20
60.
Simplify
61.
Simplify:
62.
Simplify:
5 •
7
2
512a b
3
6
48x y
8
-4x2 = 44
56. 2(x + 2)2 = 10
63.
Write the following equations in standard form:
A) 2x + 5 = x2
B) x2 + 5 = 2x
C) 7 + x2 = 5x
64.
Name the solutions of the equation (x - 5)(x + 6) = 0
65.
Name the solutions of the equation x2 - 6x + 9 = 0.
66.
Identify b in the following equation x2 − 3 = -5x
67.
Given a = 2; b = −3; c = −5, find b2 − 4ac
68.
Name the zeros of the function shown in the graph. _____
Give the factors of these zeros: _______________
69.
Find the solutions to: 2x2 – 7 = x (leave answers in exact form, no
decimals)
70. What is the discriminant for the following equation: -x2 – 5x - 10 = 0
71. For the same equation: -x2 – 5x - 10 = 0 How many solutions will you
get?
A) two real solutions
B) one real solution
C) no real solutions
72. What does it mean to have a z-score of -5?
73. Scientists conducted an aerial survey of a seal sanctuary and recorded
the number x of seals they observed during each survey. The numbers of
seals were normally distributed with a mean of 82 seals and a standard
deviation of 12.1 seals. Find the z-score for a sample of 95 seals.
74.
Completely factor:
75.
Completely factor:
2x2 + 10x + 12
3x2 − 75
76. Make a box and whiskers plot for this data set.
20, 12, 8, 24, 15, 17, 11, 8, 32
77. Solve this equation using the quadratic formula!!
x2 + 6x = 40
Provide both the exact answers and the decimal answers.
78. a) Your PSAT score was a 450 on the writing portion. The national
mean was 550 and the national standard deviation was 42. Show how you
would find the z-score for your PSAT score.
b) According to your z-score are you average? Above average? Below
average?
c) What PSAT score (to the nearest whole number) would be
associated with a z-score of 3 ?
79. Simplify:
 4 x 512 x y
3
10
13
80. Solve : (be sure to provide all solutions)
81. Solve: (be sure to provide all solutions)
82. Solve and graph your solutions for the following situation:
83. Solve and graph your solutions for the following situation: