Download Algebra 1 Final Exam REVIEW Name Second Semester 2011

Algebra 1 Final Exam REVIEW
Second Semester 2011
Name ________________
Due Date: ON THE DAY OF YOUR EXAM!
This will be a 25 point assignment: 15 points for completion and the last 10 points will be randomly selected
questions graded for accuracy. No late papers will be accepted, plan ahead if you are not going to be in
class on the date due.
Useful Formulas:
x
 b  b  4ac
x
2a
2
z=

Study each system of equations. How many solutions does each system
have?
2 lines
1.
A. ONE (
)
B. NO SOLUTIONS
C.
2.
INFINITE SOLUTIONS
A. ONE (
)
B. NO SOLUTIONS
C.
3.
INFINITE SOLUTIONS
A. ONE (
)
B. NO SOLUTIONS
C.
INFINITE SOLUTION
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.
Use the elimination method to determine the solution of this system
of equations.
2x + 5y = 17
x − 3y = −8
7.
Use the elimination method to determine the solution of this system
of equations.
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 and 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:
17.
Simplify (5x)2 • (2x)0
18.
Simplify (3xy)4(−2x)2
19.
 2x 
Simplify 

 3 
x8
Your answer should not contain negative exponents.
x2
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.
1.5 x 10
6.5 x 10
4
24.
Evaluate
25.
Classify the equation 7 + 5x + 2x3 by degree and number of terms. (this
9
should have two names)
26.
Find the sum: (7x2 + 3x - 5) + ( -4x + 5x2 + 8y3)
27.
Find the difference: (3x2 + 8x + 1) - (−x2 − 8x + 6)
28.
A rectangle has a length of 4x - 1 and a width of x + 7. Which
expression would represent the perimeter?
29.
Simplify: (4x2 + 7x − 6) − (3x2 + 9x − 8) + ( -7x2 + 5)
30.
Simplify: 6x(2x2 - 4)
31.
Simplify: (2x - 5)(x + 7)
32.
Simplify: (x + 10)(x − 10)
33.
Find the product of (x + 2)(3x2 − 5x + 6)
34. The length of a rectangle is (3x + 5). The width is (x − 2). Find the area.
Match each trinomial with its factors. You will not use all choices.
_____35.
x  8x  15
_____36.
x  8x  15
_____37.
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
2
Match each trinomial with its factor. You will not use all choices.
_____38.
x  4x  4
_____39.
x 4
_____40.
x 4
A.
Prime
B.
(x  2)(x  2)
C.
(x  2)(x  2)
D.
(x  2)(x  2)
2
2
2
Match each trinomial with its factor. You will not use all choices.
_____41.
2
9x − 4
F.
Prime
G.
(3x  2)(3x  2)
H.
(3x  2)(3x  2)
J.
(3x  2)(3x  2)
2
_____42.
9x + 12x + 4
_____43.
9x2 + 4
44. Factor the following trinomials, which one is a perfect square trinomial?
A) x2 + 6x - 16
B) x2 + 8x + 16
45. Factor the following trinomials, which one is a perfect square trinomial?
A) 4x2 + 12x + 9
B) 49x2 + 28x + 4
46.
Simplify: (4x - 3)2
47.
Find the mean, median, and mode for this data set.
12, 15, 12, 17, 18, 17, 20, 14, 12 mean_____ median_____ mode_____
48.
23
27
16
12represented by the box and whiskers
What is the median of the data
plot?_____
8
14
What is the smallest value in the data set?_____
What is the first quartile of the data set?_____
What is the IQR? _______
Simplify each expression.
49.
52.
49 ______
 100 ______
50.
 16 ______
121
______
81
53.
51.
 25 ______
54.
7
______
64
Solve each equation. Exact answers only, no decimal answers.
55.
x2 = 225
56.
58.
Simplify
24
59.
Simplify
7
25
60.
Simplify −7 20
-4x2 = -44
57. 2(x + 2)2 = 10
61.
Simplify
62.
Simplify:
63.
Simplify:
5 •
7
2
512a b
3
6
48x y
8
64.
Write the following equations in standard form (hint: set = 0):
A) 2x + 5 = x2
B) x2 + 5 = 2x
C) 7 + x2 = 5x
65.
Name the solutions of the equation (x - 5)(x + 6) = 0
66.
Name the solutions of the equation x2 - 6x + 9 = 0.
67.
Identify b in the following equation x2 − 3 = -5x
68.
Given a = 2; b = −3; c = −5, find b2 − 4ac
69.
Name the zeros of the function shown in the graph.
Give the factors of these zeros: _______________
70.
Find the solutions to: 2x2 – 7 = x (leave answers in exact form, no
decimals)
71. What is the discriminant for the following equation: -x2 – 5x - 10 = 0
72. For the same equation in #71: -x2 – 5x - 10 = 0 How many solutions will
you get?
A) two real solutions
B) one real solution
C) no real solutions
73. What does it mean to have a z-score of -5?
74. 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.
2x2 + 10x + 12
75.
Completely factor:
76.
Completely factor:
77.
Make a stem and leaf plot for this data.
15, 20, 9, 32, 27, 19, 16, 28, 31, 7, 11, 19, 34
3x2 − 75
78. Make a box and whiskers plot for this data set.
20, 12, 8, 24, 15, 17, 11, 8, 32
List any outliers (SHOW ALL WORK!!!)
79. Solve this equation using the quadratic formula!!
x2 + 6x = 40
Provide both the exact answers and the decimal answers.
80. 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.
According to your z-score are you average? Above average? Below average?
81. Simplify:
 4 x 512 x y
3
10
13