Algebra Practice EOC Spring 2016 Name:___________________________________

Algebra Practice EOC
Spring 2016
1.
(A.10A) Simplify
the polynomial expression below.
(−𝑥 2 + 5𝑥) − (6𝑥 2 + 𝑥 − 2)
2.
Name:___________________________________
5.
If possible, use the difference of two
squares to rewrite the binomial 25 − 49𝑦².
(A.10F)
A. −7𝑥 2 + 6𝑥 + 2
A. (5 + 7𝑦)(5 − 7𝑦)
B. 5𝑥 2 + 6𝑥 − 2
B. (5 + 7𝑦²)(5 − 7𝑦²)
C. 5𝑥 2 + 6𝑥
C. (5 + 7𝑦)(5 − 7𝑦)
D. −7𝑥 2 + 4𝑥 + 2
D. It is not possible to factor this binomial
using the difference of two squares.
(A.10D) Which
expression is equivalent to
3
5
2𝑚 (2 𝑚 + 1) + 3 (3 𝑚 − 2)?
6.
A. 3𝑚2 + 5𝑚 − 1
B.
3
4
𝑚2 +
23
9
𝑚−6
A rectangular prism has a width of 𝑥
inches, a length of 𝑥²𝑦 inches, and a height of
𝑦² inches. Which expression represents the
volume in cubic inches of this rectangular
prism?
(A11.B)
A. 4𝑥²𝑦²
C. 3𝑚2 + 7𝑚 − 6
D.
3
B. 4𝑥³𝑦³
5
𝑚2 + 9 𝑚 − 1
4
C. 𝑥²𝑦²
D. 𝑥³𝑦³
3.
(A10.E) Which
function is equivalent to
𝑓(𝑥) = 6𝑥 − 13𝑥 + 5?
2
7.
A. 𝑓(𝑥) = (3𝑥 − 1)(2𝑥 + 5)
B. 𝑓(𝑥) = (3𝑥 − 5)(2𝑥 − 1)
Which expression is equivalent
12𝑥 6 𝑦 −4 𝑧 2
to
?
3𝑥 2 𝑦 −6 𝑧 3
(A11.B)
C. 𝑓(𝑥) = (3𝑥 − 1)(2𝑥 − 5)
A.
D. 𝑓(𝑥) = (3𝑥 − 5)(2𝑥 + 1)
4.
B.
Which expression is equivalent to
−6𝑥² − 11𝑥 − 4?
(A10.E)
A. (3𝑥 + 7)(3𝑥 − 3)
B. (−3𝑥 + 4)(2𝑥 − 1)
8.
9𝑥 8 𝑧 5
𝑦 −10
4𝑥 8 𝑧 5
𝑦 −10
C.
D.
9𝑥 4 𝑦2
𝑧
4𝑥 4 𝑦 2
𝑧
If 𝑓(𝑥) = (𝑥 − 3)2 + 4 and 𝑔(𝑥) = 𝑥 3 + 2,
which statement is true?
(A.12B)
C. (3𝑥 − 7)(3𝑥 + 3)
A. 𝑓(−2) = 𝑔(−3)
D. (−3𝑥 − 4)(2𝑥 + 1)
B. 𝑓(0) = 𝑔(−1)
C. 𝑓(8) = 𝑔(3)
D. 𝑓(2) = 𝑔(1)
9. (A.12B) If 5 is an element in the domain of
𝑓(𝑥) =
7𝑥−22
4
, what is the corresponding
element in the range?
11. (A.12D) The first five terms in a pattern are shown
below.
−0.5, −0.25, 0, 0.25, 0.5, . . .
If the pattern continues, which expression can
be used to find the nth term?
A. 0.75𝑛 − 1.25
B. −0.25𝑛 − 0.25
Record your answer and fill
in the bubbles on your
answer document.
10.
Which representation does not show y as
a function of x?
C. 0.25𝑛 − 0.75
D. −0.5𝑛 + 0.25
(A.12A)
12. (A.3A) The slope of the line that passes through
1
the points (−6, 𝑤) and (−10, 4) is . What is
A.
8
the value of w?
A. 36
B.
9
2
C. 34
D.
1
2
B.
C.
D.
13. (A.3A) Which table shows the same rate of
5
change of y with respect to x as 𝑦 = 4 − 8 𝑥?
14. (A.3B) Tara creates a budget for her weekly
expenses. The graph shows how much money is
in the account at different times. Find the slope
of the line. Then tell what rate the slope
represents.
A. The slope is -50. The amount of money in
the account is decreasing at a rate of $50
every 2 week.
B. The slope is -0.02. The amount of money in
the account is decreasing at a rate of $0.02
every week.
C. The slope is -50. The amount of money in
the account is decreasing at a rate of $50
every week.
D. The slope is 50. The amount of money in
the account is increasing at a rate of $50
every week.
15. (A.3B) Find the slope from the table below.
A. -6
B. -3
C. 6
D. 3
16. (A.3C) The owner of a store buys large boxes of
candy bars from a warehouse and repackages
them in smaller boxes in his store. The store
owner packages 4 candy bars in each small box.
Each large box contains 24 candy bars. Which
graph represents the relationship between x
large boxes and y small boxes?
17. (A.3C) The graph below shows the relationship
between the number of gallons of fuel
remaining in a truck and the number of hours
the truck has been driven.
What does the x-intercept of the graph
represent?
A. The number of gallons of fuel in the
truck before any driving occurred.
B. The number of hours the truck was
driven before running out of fuel.
C. The number of gallons of fuel the truck
can hold.
D. The number of hours required to use
one gallon of fuel.
18. (A.3C) What is the zero of the linear function
graphed below?
Record your answer and fill in the bubbles on
your answer document.
19.
(A.3D) Which
graph represents the inequality
−2𝑥 + 7𝑦 ≤ 112?
20. (A.3D) Which coordinate pair is in the solution set
for 𝑦 < 1 − 6𝑥?
A.
B.
C.
D.
(1, 0)
(1, −1)
(0, 1)
(−1, 1)
23. (A.4C) The scatterplot below shows the
relationship between the number of baseballs
used in 14 games and the number of pitches
thrown in these games.
21. (A.3F) Which of the following graphs best
represents a system of equations that has no
solution?
Based on the scatterplot, what is the best
prediction of the number of baseballs that will
be used if 275 pitches are thrown?
A. 150
B. 60
C. 100
24. (A.2A) Function f is graphed below.
22.
(A.4C) The
population of Webb Count, Texas,
from the year 2000 through 2010 is shown in
the graph. If the trend shown in the graph
continues, what will be the population of Webb
County in 2015?
A.
B.
C.
D.
307,000
278,000
471,500
158,000
What is the range of f?
A. {𝑥|−2 ≤ 𝑥 < 4}
B. {𝑥|−2 < 𝑥 ≤ 4}
C. {𝑦|−3 < 𝑦 ≤ 3}
D. {𝑦|−3 ≤ 𝑦 < 3}
D. 160
25. (A.2A) A plane can carry a maximum cargo weight
of 160,000 pounds. A company uses one of
these planes to ship 2,000-pound containers.
The total cargo weight is a function of the
number of containers in the plane. What is the
greatest value in the domain for this situation?
Record your answer and fill in the bubbles on
your answer document.
28. ((A.2C) Airline passengers pay $439 to fly to
California. For this price, customers may check
2 pieces of luggage. There is a fee of $25 for
each additional piece of luggage a passenger
wants to check. Which function can be used to
find the amount in dollars a passenger has to
pay to fly p pieces of luggage, where 𝑝 ≥ 2?
A. 𝑐 = 25𝑝 + 439
B. 𝑐 = 25(𝑝 − 2) + 439
26. (A.2B) What is the equation in standard form of
the line that passes through the point (4, −8)
1
and has a slope of 4 ?
𝑝
C. 𝑐 = 25 + 439
D. 𝑐 =
𝑝−2
25
+ 439
A. 𝑥 − 4𝑦 = 36
B. 𝑥 − 4𝑦 = 28
29. (A.2D) The value of y varies directly with x. Which
function represents the relationship between x
20
and y if 𝑦 = 3 when 𝑥 = 30?
C. 𝑥 − 4𝑦 = −36
D. 𝑥 − 4𝑦 = −28
A. 𝑦 = 200𝑥
27.(A.2C) A graph is shown below.
2
B. 𝑦 = 9 𝑥
C. 𝑦 =
110
3
𝑥
9
D. 𝑦 = 2 𝑥
30. (A.2H) A tennis player broke the old record for the
most matches won in a tournament by at least
2 matches. Which inequality can be used to find
all possible values of t, the number of matches
the player won, in terms of r, the old record?
Which of the following equations are
represented by the graph?
3
I.
𝑦 = −2𝑥 − 2
II.
2𝑥 − 3𝑦 = 6
III.
𝑦 = (𝑥 − 2)(𝑥 − 3)
IV.
2
𝑦 − 2 = 3 (𝑥 − 6)
A. II and IV
B. I and III
C. II and III
D. I and IV
𝑟
A. 𝑡 ≤ 𝑟 − 2
C. 𝑡 ≤ 2
B. 𝑡 ≥ 2𝑟
D. 𝑡 ≥ 𝑟 + 2
31. (A.2I) A spiral notebook contains 30 more
sheets of paper than a memo book. The total
number of sheets of paper in 3 spiral notebooks
and 5 memo books is 810. Which system of
equations can be used to find s, the number of
sheets of paper in one spiral notebook, and m,
the number of sheets of paper in one memo
book?
A. 𝑠 − 𝑚 = 30
3𝑠 + 5𝑚 = 810
C. 𝑠 − 𝑚 = 30
5𝑠 + 3𝑚 = 810
B. 𝑠 + 𝑚 = 30
3𝑠 + 5𝑚 = 810
D. 𝑠 + 𝑚 = 30
5𝑠 + 3𝑚 = 810
32. (A.2I) A college student needs 11 classes that
are worth a total of 40 credits in order to
complete her degree. The college offers both 4credit classes and 3-credit classes. Which
system of equations can be used to determine
f, the number of 4-credit classes the student
can take to complete her degree, and h, the
number of 3-credit classes?
A. 𝑓 + ℎ = 40
4ℎ + 3𝑓 + 11
C. 𝑓 + ℎ = 40
4𝑓 + 3ℎ = 11
B. 𝑓 + ℎ = 11
4ℎ + 3𝑓 = 40
D. 𝑓 + ℎ = 11
4𝑓 + 3ℎ = 40
36. (A.5C) What is the value of x in the solution to the
system of equations?
3𝑥 = 2𝑦 + 14
𝑦 = −6𝑥 + 18
A.
10
3
B. −2
C. 2
D. −
10
3
37. (A.6A) The function below can be used to model
the area of a rectangle in square inches, A, if
the rectangle has a perimeter of 72 inches and
a width of w inches.
𝐴 = 36𝑤 − 𝑤²
33. (A.5A) What is the value of x in the following
equation? 6(𝑥 + 8) = 5(𝑥 − 4)
A. 28
B. −12
C. −68
D. −69
34. (A.5A) What is the solution of the equation
4𝑦 + 𝑦 + 1 = 7(𝑦 − 1)
A. −4
B. 4
C. 3
D. −3
35. (A.5C) One wall inside a shoe store is used to
display walking shoes and running shoes. There
are 135 pairs of shoes in this display. There are
1.5 times as many pairs of walking shoes as
there are running shoes on display. How many
pairs of walking shoes and running shoes are on
display?
In this situation, which of the following best
describes the domain of the function?
A. 0 < 𝑤 < 6
B. 0 < 𝑤 < 72
C. 0 < 𝑤 < 18
D. 0 < 𝑤 < 36
38. (A.6A) What is the range of 𝑓(𝑥) = 𝑥 2 + 1?
A.
B.
C.
D.
All real numbers
All real number greater than or equal to 0
All real numbers greater than or equal to 1
All real numbers less than or equal to 1
39. (A.7A) The graph of the quadratic function r is
shown on the grid.
A. 90 pairs of walking shoes and 45 pairs of
running shoes.
B. 54 pairs of walking shoes and 81 pairs of
running shoes.
C. 45 pairs of walking shoes and 90 pairs of
running shoes.
D. 81 pairs of walking shoes and 54 pairs of
running shoes.
What is a solution to 𝑟(𝑥) = 0?
A. −50
B. 4
C. 13
D. −60
40. (A.7A) The graph models A, the area in square
feet of a rectangular porch with a length that is
0.56𝑤 less than 28 ft given a width of w feet.
44. (A.8A) What are the solutions to the equation
𝑥 2 − 4𝑥 = −1?
A. 𝑥 =
B. 𝑥 =
45.
Based on the graph, what is the width in feet of
the porch with the greatest area?
A. 175 ft
B. 50 ft
C. 25 ft
D. 350 ft
41. (A.7A) What are the x-intercepts of the graph of
the quadratic function 𝑓(𝑥) = 5𝑥 2 + 4𝑥 − 1?
A.
1
5
and − 1
1
C. 0 and − 1
2
B. − 5 and 1
2
D. − 5 and 1 5
42. (A.8A) The function 𝐿 = 0.8𝑇² models the
relationship between L, the length in feet of a
pendulum, and T, the period in seconds of the
pendulum. Which value is closest to the period
in seconds for a pendulum that is 30 ft long?
A. 5.4 s
B. 4.9 s
C. 6.8 s
−4±√20
2
4±√12
2
C.
𝑥=
D.
𝑥=
−4±√12
2
4±√20
2
(A.9B) A table of values for the exponential
function f is shown below.
Which situation could describe this function?
A. The value of a house increased by
3
approximately 24 % per year.
B. The value of a house increases by $3,850
per year.
C. The value of a house decreases by
3
approximately 24 % per year.
D. The value of a house decreases by $3,850
per year.
46. (A.9C) The table shows the population, p, of mice
in a field at the end of m months.
D. 6.1 s
43. (A.8A) What are the solutions to the equation
3𝑥 2 + 15𝑥 = 18?
A.
B.
C.
D.
𝑥
𝑥
𝑥
𝑥
= −3 and 𝑥 = −2
= −6 and 𝑥 = 1
= 6 and 𝑥 = 13
= 0 and 𝑥 = 1
Based on the data in the table, what will be the
population of mice in the field at the end of 8
months?
A. 192
B. 3,072
C. 1,536
D. 256
47. (A.9C) There were 417 cell phones sold at an
electronics store in January. Since then, cell
phone sales at this store have increased at a
rate of 3.75% per month. At this rate of growth,
which function can be used to determine the
monthly cell phone sales m months after
January?
A. 𝑝(𝑚) = 417(0.0375)𝑚
B. 𝑝(𝑚) = 417(1.0375)𝑚
C. 𝑝(𝑚) = 417(0.9625)(𝑚+1)
D. 𝑝(𝑚) = 417(0.0375)(𝑚+1)
48. (A.9D) The graph below shows the change in the
value of a car over several years.
Based on the information in the graph, which
conclusion appear to be true?
A. The car lost about one-half of its value every
3 years.
B. The car lost about one-quarter of its value
every year.
C. The car lost less of its value between years 9
and 10 than between year 1 and 2.
D. The car lost more of its value between years
9 and 10 then between years 1 and 2.