Download ALGEBRA I END-OF-COURSE EXAM: PRACTICE TEST

Page 1
Algebra I
ALGEBRA I END-OF-COURSE EXAM: PRACTICE TEST
1. Order the following numbers from least to greatest: 3,
a.
19
, 3, 8.7  10 0,
2
62, 8.7  10 0, 3,
b.


c. 8.7  10 0, 3,
d. 3,
62,
19
,
2
62, 8.7  100 ,
19
2
62

19
2
62
19
, 8.7  100
2

2. If y  x  3, then when is y a positive number?

 3.
a. Always
Simplify
b. when x > -3
c. when x > 3
d. never
b. 4 5
c. 2 5
d. 5 2
20
a. 10
4. 
Solve the equation for a.
1
d  vt  at 2 
2
a. a 


2d
vt 3
b. a 
x
d  vt
t2
y 
5. Simplify the expression:
 x 5 y 3
a.
y17
x
b.


c. a 
2d  vt
t2
d. a 
2 10 2
y15
x5
c.
6. Determine what values of x the expression



Express your answer with an inequality.
Write your answer on the line.


y 23
x9
d.
y 26
x7
5  x is defined for.


What are the defined values of x? _____________________
2d  vt
t2
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Algebra I
3x 1
 8
5
41
a.
5
7. Solve:
b. 
41
5
c. 13

1
8. Which equation is y  x  5 in standard form?

3


1
1
a.  x  y  5
b. x  y  5
3
3
d. 13

c. x  3y 15
d. x  3y  15





1
9. Which of these is the equation of a line with y-intercept (0, 2) and slope ?
3
1
1
1
1
a. y  x  2
b. y  2x 
c. y  2x
d. 2y  x
3
3
3
3





10. Fred, Thomas, and Zachary worked at the ice cream store in the mall. Last week, Fred earned more money
than Thomas, but less than Zachary. The graph shows the money earned by Zachary and Thomas.
Which area of the graph represents Fred’s possible weekly pay?
a. P
b. R
c. S
d. T
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Algebra I
11. Tara’s cell phone plan costs $39.00 a month, which includes 100 text messages. After she uses all of her
text messages, it will cost her $.15 per text message.


Write an equation or inequality that could be used to determine the total cost of her cell
phone bill after her first 100 text messages.
If Tara only wants to spend $43 on her cell phone bill, how many text messages can she
send?
12. The equation 13  2 x  3  5 has two real solutions.
Determine the negative solution of the equation.
 your answer on the line.
Write
What is the negative solution of the equation? ________________
13. Write an equation of the line that passes through the pair of points.
(-5, -2), (3, -1)
a.
c.


y
1
11
x
8
8
1
11
y x
8
8


b. y 
1
11
x
8
8
d. y 
1
8
x
8
11
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Algebra I
14. A 1,500-gallon tank contains 200 gallons of water. Water begins to run into the tank at the rate of 75
gallons per hour. When will the tank be full but not overflowing?
a.
7 hours, 8 min
b. 17 hours, 20 min
c. 20 hours
d. 22 hours, 40 min
15. According to the graph, which statement best describes the slope?
a. As the distance traveled increases by 20, the amount
of gas in the tank decreases by 3.
b. As the distance traveled decreases by 3, the amount
of gas in the tank increases by 20.
c. As the distance traveled increases by 30, the amount
of gas in the tank increases by 2.
d. As the distance traveled decreases by 20, the amount
of gas in the tank decreases by 3.
16. Solve for x in 4  3x  2 14 .
Display the set of solutions that makes the compound inequality true by graphing them on the number line

below.
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Algebra I
17. Which is the graph of the solution set of the system of inequalities?
x  2y  10
2x  y  0

18. Write an equation of the line that is perpendicular to y 
1
y  x3
2
a.
b. y 
1
x7
2
1
x  8 and goes through (-4, 5).
2
c. y  2x  8
d. y  2x  3



20. In 2000, 5500 peopleattended the State B basketball tournament. The enrollment has been increasing
2% annually. Select the equation that would determine the total number of people who attend t years
after 2000.
a.
y  5500(.02)x
b. y  5500(0.2)x
c. y  5500(1.02)x
d. y  5500(1.2)x
21. You are a full time employee at a marketing firm. In order to maintain fulltime status you must work
 a minimum of 25 hours

 work more than 45
 hours in a week. You make $20
a week, and you cannot
per hour.


Define the domain and range in the context of the problem.
Write your answer on the line.
Domain: ____________________ Range: ____________________
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Algebra I
22. Only chocolate and vanilla ice cream cones are sold at an ice cream store. In one day, the number of
chocolate cones sold was 1 more than 4 times the number of vanilla cones sold. A total of 121 cones
were sold that day.
Let c = the number of chocolate cones sold.
Let v = the number of vanilla cones sold.
 Write equations to determine the number of chocolate cones sold that day.
 Use the equations to determine the number of chocolate cones sold that day.
Show your work using words, numbers, and/or diagrams.
23. The chart shows the amount of total salary (commission plus base salary) paid to employees of a store
that specializes in big screen televisions.
Which equation best represents the total
salary (T) that an employee makes for
selling any number of television sets (n)?
a. T = 50n + 100
b. b. T = 100(n + 50)
c. c. T = 100n + 50
d. d. T = 50(n + 100)
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Algebra I
24. Mr. Shindler begins traveling east on Interstate 90 from Spokane with a full tank of gasoline. His car
has a 15-gallon gas tank and gets 30 miles per gallon during highway travel.
Let m = the number of miles Mr. Shindler has driven
Let g = the number of gallons of gas remaining in his tank
 Select and justify in the answer box which equation describes the relationship between the
number of miles Mr. Shindler has traveled and the number of gallons remaining in his gas
tank.
a. g  15  30m
b. m  30g 15
30
m
d. d. m 
 15
g
30


Show your work using words, numbers, and/or diagrams.
c. g  15 


25. Which function best represents the values in the table below?
x
-3
-1
0
2
5
a.

f(x)
-27
-1
0
8
125
b. f (x)  x
f (x)  x 3

c. f (x) 

1
x
d. f (x)  x

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Algebra I
26. Look at the function:
f (x)  2x 2  4x  5



Evaluate f (x) at f (3) .
Write your answer on the line.

What is

f (3) = ___________________________________
27. 
Which best describes the difference(s) between the graphs of f (x)  5x 
3
3
and g(x)  10x  ?
4
4
a. The graph of f(x) is twice as steep as the graph of g(x).
b. The graph of f(x) is half as steep as the graph of g(x).


c. The graph of f(x) has a y-intercept of 5 while g(x) has a y-intercept of 10.
d. Both A and C are true.
28. Graph A is the graph of y  2(3)x and graph B is the graph of y  3(2)x .
Which statement about the two graphs is true?
a. Both graphs
A and B rise at the same rate. 

b. Graph B rises at a faster rate than graph A.
c. Graph A rises at a faster rate than graph B.
d. The y-intercept of graph A is above the y-intercept of graph B.
29. Solve the equation 3x  729 .
a. x = 5
b. x = 6
c. x = 243
d. x = 726

30. Brad and Tom are comparing their classes' scores on a math test. Both of their classes had mean
scores of 80 on the test, but Brad's class had a range of 6 while Tom's class had a range of 30. If the
highest possible score was 100, which class had the LOWEST score in it?
a. Brad's class had the lowest score in it.
b. Tom's class had the lowest score in it.
c. The lowest score occurred in both classes.
d. It cannot be determined from the information.
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Algebra I
31. Which table represents the recursive formula:
an = an-1 - 6
32. Marcy recorded and graphed the daily height of a growing plant. Marcy's graph was linear. Which
table could be Marcy's data?
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Algebra I
33. This graph shows the relationship between the age of a planet in millions of years and the number of
moons the planet has.
Which of these statements is true about the graph?
a. The dependent variable is the number of moons.
b. The independent variable is the number of moons.
c. Since the number of moons is staying the same, there is no dependent variable.
d. Since the number of moons is staying the same, there is no independent variable.
34. A college professor at the University of Washington surveyed 150 students at the university. The
students were asked if they prefer in class or take home tests. The professor drew the conclusion:
“One out of four college students prefer take home tests.” Explain why this conclusion is misleading.
a.
The professor surveyed a small sample of the population at one university but made the
conclusion about the entire population of college students.
b. The survey question was biased toward in class tests.
c. The students were not selected randomly.
d. The sample size was too small.
35. At a particular company, every employee receives a 4% cost-of-living increase to their salary.
What impact does this cost-of-living increase have on the mean and on the range of employee salaries at
the company?
a. The mean increases but the range does not change.
b. The mean does not change but the range increases.
c. The mean and range both increase.
d. The mean and range do not change.
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Algebra I
36. The graph shows the stock value for a technology company from 2002 to 2005. From this graph,
draw a line that fits the data and determine what is the most likely value of the stock for the year
2000?
a. $0
b. $10
c. $20
d. $30
37. Vance graphed the relation between fund-raising profits for the chess club and the number of
members.
Which equation represents a line that fits the
1
data?

a.
y  29n 180
b.
y  60n 180
c.
2
y  n 180
3
d.
y



200
n 180
3
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Algebra I
38. Which term best describes the scatterplot?
a. Positive correlation
b. Negative
correlative
c. Zero correlation
d. Perfect correlation
English Sentences and Mathematical Sentences
39.
Match each mathematical sentence on the left with its translation on the right.
Then, for each mathematical sentence, declare what the variable “x” represents.
___a.
2x  8  22
x means_____________________
___b.
x  2(x  2)  (x  2)  22
1. Rob’s number is equal to twice Bob’s number. Cob’s number is
eight times larger than two less than Bob’s number. The sum of
Rob’s number and Cob’s number is 22.
2. Jenna earned $22 by working 2 hours and receiving an $8 bonus.
x means_____________________
___c.
2x  8(x  2)  22
3. Toby’s cup can hold 8 times as many ounces of water as Terry’s.
Together, the cups hold 22 ounces of water.
x means_____________________
___d.
x  8x  22
x means_____________________
4. A 22-ounce metal bracelet is created by mixing gold, silver, and
zinc. There are two ounces less zinc than gold, and there is twice as
much silver as zinc.
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Algebra I
40. Pearl’s work for solving this system of equations is shown here. All her work is correct.
Which method is she using?
System:
y = –5 – x
Pearl’s Solution:
2x + (–5 – x) = 20
2x + y = 20
x – 5 = 20
+5 +5
x = 25
A. Equal Values method
y = -5 –(25)
B. Substitution
y = -30
C. Elimination
D. Multiplication and then Elimination
41. Edith is using substitution to solve the system of equations below. What should the first step be?
y  3x
2x  8y  2
A. 2x  8(3x)  2
B. 3(2x  8y)  2
C. 2(3x)  8y  2
D. 3(2x  8x)  2
42. Mrs. Goolsby wants to use Elimination to solve the system of equations below.
Choose the best first step.
3x  y  5
2x  3y  10
A.
B.
C.
D.
Multiply the first equation by 2.
Multiply the second equation by 3.
Multiply the first equation by 3.
Multiply the second equation by 2.
43. Mr. Glass solved a system of equations using substitution and got the following result: 12 = -4
a. What should he write as his final answer?
b. What does this tell you about the graph of the sytem?
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Algebra I
Decide whether the relation defines a function.
44. (6,7), (6,9), (1,4), (4,4), (8,1)
A) Not a function
B) Function
Find the domain and range.
45. (4,4), (1,1), (2,8), (2,3)}
a. domain = {-4,8,1,3}; range = {-4,-2,-1}
C) domain = {-4,-2,-1}; range = {4,8,1,3}
Given the function, find the indicated value.
46. Find f(-2) when f(x) = 2x2+4x+4.
a. 20
B) 0
B) domain = {-4,-2,-1,2}; range = {-4,8,1,3}
D) domain = {-4,-2,-1,-12}; range = {-4,8,1,3}
C) -4
D) 4
Solve the system by graphing.
47. y – 4x = 2
5y = 20x + 10
6
y
4
2
x
-6
-4
-2
2
4
6
-2
-4
-6
The x-value of the solution is:
A) -1.5
B) 1
Solve the system.
48. 2x + 3y = -5
3x – 5y = 21
The y-value of the solution is:
A) 2
B) 7
C) Infinite # of solutions
D) No solution
C) -3
D) No solution
C) 16 p12
D) 16 p 7
Simplify the expression.


49. 4 p 3  4 p 4
a.
p7
16

B) 16 p12
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Algebra I
Simplify the expression. Write the answer with positive exponents.
4 x11 y12 z 7
50.
2 x 3 y 9 z10
a.
x8 y 3
2z3
B) 2 x 8 y 3
C) x 8 y 3 z 3
D)
2 x 8 y 3
z3
Simplify. Use positive exponents to write the answer.
x 
x 
x
51.
7
5 4
 2 8
a.
x4
B)
1
x 11
C)
1
x 43
D) x 43
Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none
of these.
52. 10x 4  3w3  7w  5y 5  4
a. degree 5; trinomial
B) degree 5; none
Perform the indicated operations.

 
53. 9 x 2  9 x 4  4  6 x 3  5  2 x 3 5x 4 3x 2
a.
C) degree 13; trinomial D) degree 14; binomial

4 x 4  8x 3  12 x 2  9
B) 14 x 4  8x 3  12 x 2  9
C) 4 x 4  4 x 3  6x 2  1
D) 14 x 4  8x 3  12 x 2  1
Multiply.
54. (-5x + 3y) (2x – 12y + 1)
a.
10x 2  60xy  5x  36 y 2
B) 10x 2  66xy  66 y 2
C) 10x 2  66xy  5x  36 y 2  3y
D) 10x 2  6xy  5x  36 y 2  3y
55. (-6 + x) (4x – 8)
a.
x 2  32 x  32
B) 4 x 2  48x  32
C) 4 x 2  33x  48
D) 4 x 2  32 x  48
B) 4 x 2  24 xy  9 y 2
C) 16x 2  24 xy  9 y 2
D) 4 x 2  9 y 2
56. (4 x  3 y) 2
a.


16x 2  9 y 2
4 
6 
4
6
57.  x   x  
a.
4
4
x2  x 
3
9
2
B) x 
4
9
2
C) x 
4
4
x
3
9
D) x 2 
4
9
Page 16
Algebra I
Factor the trinomial.
58. 12 x 2 y 2  11xy 2  15y 2
a.
3x  5 y 4x  3 y 
B) y
2
x  512 x  3
C)
4x  5 y 3x  3 y 
D) y 3x  54 x  3
2
Factor the polynomial.
59. 3x 6 y 2  81y 2
a.
2


3 y x 2 3 x 4 3x 2 9

2
 
x 3x

9
B) 3 y x 2 3 x 4 3x  9
D) 3 y
C) prime polynomial
2
2
4
3x 2
60. 49 x 2  16
a.
7 x  42
B)
7 x  47 x  4
C) prime polynomial
B)
2x  y 2x  5
C)
 3
 5
C)  , 
D)
7 x  42
61. 4 x 2  2 xy  10x  5y
a.
2x  y 2x  5
2x  5 y 2x 1
D) prime polynomial
3 3 
5 2 
D)  , 
Solve the equation by factoring.
62. 9b2  21b  1  9
a.
5 2 
 , 
3 3 
2
3
B)  , 
 5
 3
Find the cube root. Round to the nearest thousandth, if necessary.
63.
3
x12
64 y 6
a.
4 y2
x4
x4
B)
4 y2
x3
C)
4 y3
x4
D)
16 y 2
Use radical notation to write the expression. Simplify if possible.
64. 7 x
2
5
a.
7 x5
B)
5
49 x 2
5
C) 7 x 2
D)
5
7x2
Write with positive exponents. Simplify if possible.
 32
65. 25
a. -125
B) 125
C)
1
125
D) 
1
125
2
3
Page 17
Algebra I
66. 32
4 5
1
16
a.
B) 16
C) 
1
16
D) not a real number
Use the properties of exponents to simplify the expression. Write with positive exponents.
67.
x
4 5
x
x
6
5
3
7
1
a.
x
B) x
1
105
1
105
1
C)
x
181
105
D) x
181
105
Use the product rule to multiply. Assume all variables represent positive real numbers.
13x 2  13x5
68.
a.
169 x 8
B)
13x 4
C) x 4 26
D) 13x 3 x
Simplify the expression. Assume all variables represent positive real numbers.
3
69.
54 x 7
3
2x
a.
B) x 2 3 3
3x 2
C) x 2 3 2
D) 3x 2 3 x
Add or subtract. Assume all variables represent positive real numbers.
3x 3  3x 27 x 2  7 27 x 4
70.
a.
B)  x 3x  12 x 2 3
13x 2 3
C) x 3x  12 x 2 3
D) x 3x  12 x 2 3
Multiply, and then simplify if possible. Assume all variables represent positive real numbers.


71. 4 5  7 5 5  4
a.

28  20 52  16 5 B) 48 5  16
C) 65 5
D) 128  51 5
Rationalize the denominator. Assume all variables represent positive real numbers.
72.
2
4
a3
a.
24 a
a
B)
24 a 3
a
C)
24 a 2
a
D) 24 a
Page 18
Algebra I
Use the square root property to solve the equation. Round to the nearest tenth, if necessary.
73.
 p  22  6
a. √2 − √6
b. 2 ± √6
c. −2 + √6
d. −2 ± √6
What is a quadratic equation?
75.
a.
b.
c.
d.
76.
An
An
An
An
equation
equation
equation
equation
that
that
that
that
has
has
has
has
two terms
four terms
degree 4
degree 2
Use the discriminant to determine how many real solutions exist for the
quadratic equation 3x2 + 4x + 2 = 0.
a.
77.
0 solutions
1 solution
2 solutions
3 solutions
Solve x2 + 4x – 32 = 0.
a.
{-8, -4}
b.
{8, 4}
c.
{-8, 4}
d.
{8, -4}
Page 19
Algebra I
78.
Which is a graph of a quadratic equation?
(a)
(b)
(c)
(d)
Which is one of the solutions to the equation 2x2 – x – 4 = 0?
79.
A
80.

1
 33
4

B
1
 33
4
C
1  33
4
D
Toni is solving this equation by completing the square.



ax2 + bx + c = 0 (where a > 0)
ax2 + bx = -c
b
c
x2  x  
a
a
?
Step 1:
Step 2:
Step 3:
Which should be Step 3 in the solution?

c b
x2    x
A
B
b a


C
b
b
c b
x  x
 
D
a
2a
a 2a 
2

x
b
c

a
ax
2
2
b
c  b 
 b 
x  x
 
2a
a
a 2a
2
1 33
4
Page 20
Algebra I
81.
Four steps to derive the quadratic formula are shown below.
I
II


III
IV
bx c

a
a
2
b  b 2  4ac

x

 2a
4a 2
x2 
b 2  4ac b
x

4a 2
2a
2
2
bx  b  c  b 
2
x 



a 2a
a 2a

What is the correct order for these steps?
82.
A
 I, IV, II, III
B
I, III, IV, II
C
II, IV,I, III
D
II, III, I, IV
Which statement best explains why there is no real solution to the quadratic equation
2x2 + x + 7 = 0?
A
The value of 12 – 4•2•7 is positive.
B
The value of 12 – 4•2•7 is equal to 0.
C
The value of 12 – 4•2•7 is negative.
D
The value of 12 – 4•2•7 is not a perfect square.
What is the solution set of the quadratic equation 8x2 + 2x + 1 = 0?
83.


A
 1 1 
 , 
 2 4 
C
1  7 1 7 
,


8 
 8

B
1 
D
no real solution
2,1 2

Page 21
Algebra I
The graph of the equation y = x2 – 3x – 4 is shown below.
84.
fx = x2 -3x-4
10
8
6
4
2
-15
-10
-5
5
10
15
-2
-4
-6
-8
-10
-12
For what value or values of x is y = 0?
A
x = -1 only
B
x = -4 only
C
x = -1 and x = 4
D
x = 1 and x = -4
How many times does the graph of y = 2x2 – 2x + 3 intersect the x-axis?
85.
A
86.
none
B
one
C
two
D
three
An object that is projected straight downward with an initial velocity, v, feet per second travels a
distance s = vt + 16t2, where t = time in seconds. If Ramon is standing on a balcony 84 feet above
the ground and throws a penny straight down with an initial velocity of 10 feet per second, in
approximately how many seconds will it reach the ground?
A
87.
2 seconds
B
3 seconds
C
6 seconds
D
8 seconds
The height of a triangle is 4 times greater than twice its base. The area of the triangle is 168 square
inches. Which number is closest to the base length?
A
7 in.
B
8 in.
C
9 in.
D
10 in.
What are the solutions to the equation 2x2 + 4x = 7?
88.
A

x
2  3 2
4
B

x
4  6 2
C
2

x
2  6 2
2
D

x
2  3 2
2
Page 22
89.
Algebra I
The graph of a parabolic curve is shown below. Which of the following equations is represented by
the graph?
10
8
6
4
2
-10
-5
5
10
-2
-4
-6
-8
-10
A
90.
B
x 2  2x  2
C
x 2  2x  2
D
5.6 s
B
3.5 s
C
4.2 s
D
0.1 s
What are the real roots of the quadratic function in the graph below?
6
A
-3 and 0
B
4.5 and 0
C
No real roots
D
-1.5
4
2
-5
5
10
-2
-4
-6
-8
92.
x 2  2x  2
A construction worker drops a tool from the top of a building that is 200 ft high. The height of the
tool above ground can be modeled by h = -16t2 + 200, where h is the height in feet and t is the time




in seconds. How long will it take for the tool to hit the ground?
A
91.
x 2  2x  2
The graph of the equation y = x2 + 2x + 3 intersects the x-axis at how many points?
A
0
B
1
C
2
D
3