Download A1.1.1.1.1 Compare and/or order any real numbers. Note: Rational

A1.1.1.1.1
Compare and/or order any real numbers.
Note: Rational and irrational may be mixed.
1. Which of the following inequalities is true for all
real values of x?
A.
B.
A.
, which expression has a value
B.
C.
D.
7. Which sequence of numerals is equivalent to:
C.
D.
2. Which of the following represents the greatest
value?
A. 6 3
6. When
less
than ?
A.
B.
C.
D.
C. (6 3 )2
B. 36
D.
66
63
A1.1.1.1.2
Simplify square roots
8. An expression is shown below.
3. If you were to order the real numbers below
from the largest to the smallest, which real
number would be the third in your list?
2 51x
Which value of x makes the expression
equivalent to 10 51 ?
A. 5
A. -5
C. -2p
B. -5.5
D. - 24
4. Compare the two absolute value expressions
and choose the statement below that is true.
Expression 1: -33 - 0
Expression 2: 0 - -33
a.
b.
c.
d.
Expression 1 is greater than Expression 2.
Expression 2 is greater than Expression 1.
The expressions are equal.
There is not enough information for a
comparison.
5. Four numbers are shown.
B. 25
C. 50
D. 100
9. An expression is shown below.
87x
For which value of x should the expression be
further simplified?
A. x = 10
B. x = 13
C. x = 21
D. x = 38
10. Which expression is equivalent to ( 2x 2 )4 ?
A. 2x 4
B. 4x 4
C. 4x 8
D. 8x 8
11. Which number equals 3 56 ?
A. 6 14
B. 12 7
C. 15 6
D. 8 28
12. On the number line, point R represents the
square root of a number.
Which shows these numbers ordered from
least to greatest?
A.
B.
C.
D.
Which value could be the square root of the
number represented by R?
A. 137
B. 149
C. 165
D. 173
A1.1.1.2.1
Find the Greatest Common Factor (GCF)
and/or the Least Common Multiple (LCM) for
sets of monomials.
13. Two monomials are shown below.
450x2y5
3,000x4y3
What is the least common multiple (LCM) of
these monomials?
A. 2xy
C. 150x 2 y 3
B. 30xy
D. 9,000x 4 y5
14. Which expression is the greatest common
factor of
125t 3m5 + 60t 4 m4 + 85t 5 m2 ?
A. 5t 3m 2
B. 5t 4 m 2
C. 5t 4 m 4
A1.1.1.4.1
Use estimation to solve problems.
19. A theme park charges $52 for a day pass and
$110 for a week pass. Last month, 4,432 day
passes were sold and 979 week passes were
sold. Which is the closest estimate of the
total amount of money paid for the day and
week passes for last month?
A. $300,000
B. $400,000
C. $500,000
D. $600,000
20. Joel has a 50-meter roll of copper wire that
weighs 7.5 kilograms. Approximately how
many meters of wire will be in a new shipment
that weighs 502.5 kilograms?
A. 75 m
B. 610 m
C. 3,350 m
D. 3,770 m
D. 5t 5 m 5
A. ns(s 2 +1)
C. ns(s 2 + s)
A1.1.1.5.1
Add, subtract, and/or multiply polynomial
expressions (express answers in simplest
form).
Note: Nothing larger than a binomial multiplied
by a trinomial.
B. ns(s 2 + n)
D. ns 2 (s + n)
21. A polynomial expression is shown below.
15. Which of the following is equivalent to
ns 3 + n2 s ?
A1.1.1.3.1
Simplify/evaluate expressions involving
properties/laws of exponents, roots, and/or
absolute values to solve problems.
Note: Exponents should be integers from -10
to 10.
1
8
B.
1
4
C. 16
D. 32
17. Which expression is the same as (a 2b -3 )-4 ?
A. a 2b 7
B.
1
2 7
ab
C.
b12
a8
D.
a8
b12
18. Which expression is the correct simplification
of
A. 0
?
B.
The expression is simplified to
8x 3 + 6x 2 +15x + 6 .
What is the value of m?
A. -8
16. Simplify 2(2 4 )-2
A.
(mx 3 + 3)(2x 2 + 5x + 2) - (8x 5 + 20x 4 )
C. 1
D.
B. -4
C. 4
D. 8
22. Simplify (a 3 - 5a + b - 2) - (3a 3 + 5a - b + 2)
A. -2a 3
B. -2a 3 + 2b
C. -2a 3 -10a + 2b
D. -2a 3 -10a + 2b - 4
23. What polynomial equals (x + 6)(2x – 3)?
A. 2x 2 + 9x -18
B. 2x 2 +12x + 3
C. x 2 + 8x - 9
D. x 2 -11x + 6
24. The sum of 4x 3 + 6x 2 + 2x - 3 and
3x 3 + 3x 2 - 5x - 5 is
A.
B.
C.
D.
30. What is the sum of
7x 3 + 3x 2 - 3x - 8
7x 3 + 3x 2 + 7x + 2
7x 3 + 9x 2 - 3x - 8
7x 6 + 9x 4 - 3x 2 - 8
A1.1.1.5.2
Factor algebraic expressions, including
difference of squares and trinomials.
Note: Trinomials are limited to the form
ax2+bx+c where a is equal to 1 after factoring
out all monomial factors.
25. When the expression x 2 - 3x -18 is factored
completely, which is one of its factors?
A. (x – 2)
B. (x – 3)
C. (x – 6)
D. (x – 9)
26. Which expression is a factor of 4x 2 +10x + 6 ?
A. 2(x+3)
B. 2x+3
C. 4(x+3)
D. 4x+3
27. Which expression represents y 4 - 36 in
simplest factored form?
A. (y 2 + 4)(y2 - 9)
B. (y + 4)(y + 3)(y - 3)
D. (y 4 - 36)(y +1)
28. Which of the following is a factor of
6x 2 -13x + 5 ?
B. 2x – 1
C. 3x + 1
A.
C.
B.
D.
31. When the following expression is simplified,
what is the numerator?
6x 2 + 21x + 9
4x 2 -1
A. 3(x+1)
B. 3(x + 3)
C. 3(2x + 3)
D. 3(x + 3)
A1.1.2.1.1
Write, solve, and/or apply a linear equation
(including problem situations).
32. Mr. and Mrs. Rodriguez are taking their
children to Colonial Williamsburg. A 1-day
admission pass is $33 for an adult and $16.50
for a child. If they pay a total of $115.50
admission for themselves and their children,
how many children do they have?
A. 2
B. 3
C. 4
D. 5
33. Luigi earns $8 per hour baby-sitting and $10
per hour working at a movie theater. If he
baby-sits 50 hours in a year, how many hours
would he need to work at the theater in order
to earn $3,000 for a computer? Which
equation represents this situation where x is
the number of hours he would need to work at
the theater?
C. (y 2 + 6)(y2 - 6)
A. x + 1
-x + 7
2x + 5
and
?
2x + 4
2x + 4
D. 6x - 1
A1.1.1.5.3
Simplify/reduce a rational algebraic
expression.
A. 400 + 10x = 3,000
B. 500 + 8x = 3,000
C. 8x + 10x = 3,000
D. 10x = 3,400
34. A taxi ride cost $29.40. The driver charged $3
plus $0.40 per 0.2 mile traveled. How far did
the taxi travel on this trip?
A. 9.8 mi
B.13.2 mi
C. 66 mi
D.73.5 mi
; x ¹ -4, -2, 0
29. Simplify
35. Which of the following equations has an
infinite number of solutions?
A.
C.
B.
D.
A. x 
1
2
B. 2x 1  x  3
C. 3x  5  2x 1  x
D.  x 1  1  x
36. Michael paid $6.00 for a ticket to a football
game. Soft drinks at the game cost $0.75.
Michael bought x drinks at the game. Which
equation represents the total amount(y)
he spent?
A. y = (6 + 0.75)x
B. y = 6x + 0.75
C. y = 6 – 0.75x
D. y = 6 + 0.75x
A1.1.2.1.2
Use and/or identify an algebraic property to
justify any step in an equation-solving
process.
Note: Linear equations only.
37. Stan’s solution to an equation is shown
below.
Given: n+8( n+20) =110
Step 1: n+8n+20 =110
Step 2:
9n+20 =110
Step 3:
9n=110 −20
Step 4:
9n=90
Step 5:
9n 90
=
9
9
Step 6:
n=10
Which statement about Stan’s solution is true?
A. Stan’s solution is correct
B. Stan made a mistake in step 1
C. Stan made a mistake in step 3
D. Stan made a mistake in step 5
38. One of the steps Jamie used to solve an
equation is shown below.
39. Solve 3(x+5) = 2x + 35
Step 1:
Step 2:
Step 3:
Step 4:
3x + 15 = 2x + 35
5x + 15 = 35
5x = 20
x=4
Which is the first incorrect step in the solution
shown above?
A. Step 1
B. Step 2
C. Step 3
D. Step 4
A1.1.2.1.3
Interpret solutions to problems in the context
of the problem situation.
Note: Linear equations only.
40. Francisco purchased x hot dogs and y
hamburgers at a baseball game. He spent a
total of $10. The equation below describes the
relationship between the number of hot dogs
and the number of hamburgers purchased.
3x + 4y = 10
The ordered pair (2, 1) is a solution of the
equation. What does the solution (2, 1)
represent?
A. Hamburgers cost 2 times as much as hot dogs.
B. Francisco purchased 2 hot dogs & 1 hamburger.
C. Hot dogs cost $2 each & hamburgers cost $1
each.
D. Francisco spent $2 on hot dogs & $1 on
hamburgers.
41. The data in the table show the cost of renting
a bicycle by the hour, including a deposit.
–5(3x + 7) = 10
–15x + –35 = 10
Which statements describe the procedure
Jamie used in this step and identify the
property that justifies the procedure?
A. Jamie added –5 and 3x to eliminate the parentheses.
This procedure is justified by the associative property.
B. Jamie added –5 and 3x to eliminate the parentheses.
This procedure is justified by the distributive property.
C. Jamie multiplied 3x and 7 by –5 to eliminate the
parentheses. This procedure is justified by the
associative property.
D. Jamie multiplied 3x and 7 by –5 to eliminate the
parentheses. This procedure is justified by the
The equation of the line that fits the data is
c = 5h + 5. An ordered pair that is a solution
to the equation is (3 , 20). What does that
solution represent?
A. The deposit for renting the bicycle for 3 hours is
$20.
B. The cost is $20 to rent a bicycle for 3 hours.
C. The deposit is $3 when the total cost is $20
D. The cost is $3 for renting a bicycle for 20 hours
distributive property.
42. Marcy and Troy disagreed about the answer to 46. Anna burned 15 calories per minute running
for x minutes and 10 calories per minute hiking
a problem. Marcy said that the equation they
for y minutes. She spent a total of 60 minutes
were working on had more than one solution.
If Marcy is correct, on which of these
running and hiking and burned 700 calories.
equations could they have been working?
The system of equations shown below can be
used to determine how much time Anna spent
A. 2x + 4 = 3x + 4
C. 2x + 4 = 2(x + 2)
on each exercise.
B. 2x + 4 = 3x + 5
D. 2x + 4 = 2(x + 3)
15x + 10y = 700
43. Which of the following is not a correct
description of the graph of the function
y = −2x − 7?
A The graph of the function contains the point (−2, −3),
and when the value of x increases by 1 unit, the
value of y decreases by 2 units.
B The graph of the function contains the points
(−1, −5), (2, −11), and (4, −15).
C The graph of the function is a line that passes
through the point (0, −7) with a slope of −2.
D The graph of the function contains the points (0, −7),
(1, −9), and (3, −1).
A1.1.2.2.1
Write and/or solve a system of linear
equations (including problem situations) using
graphing, substitution, and/or elimination.
Note: Limit systems to two linear equations.
44. Adult tickets to a museum cost $10 while
children’s tickets cost $6. Suppose that at the
end of one day the museum had sold 5,000
tickets and had received $42,000 in
admission fees.
Which system of equations could represent
this situation if x is the number of adult’s
tickets sold and y the number of children’s
tickets sold?
A.
C.
B.
D.
45. Rosilita paid $10.85 for 3 loaves of bread and
2 gallons of milk. A gallon of milk costs $0.91
more than twice the cost of a loaf of bread.
Which equation could Rosilita use to find the
cost x of one loaf of bread?
x + y = 60
What is the value of x, the minutes Anna spent
running?
A. 10
B. 20
C. 30
D. 40
47. If ( x, y) is the solution to the system of
equation, y= 2x – 4 and y = x + 1, what is
-x 2 - y ?
A. -21
B. -19
C. 19
D. -31
48. Edith is using substitution to solve the system
of equations below. What should the first step
be? Choose the correct first step from the
choices below.
y  3x
2 x  8 y  2
A. 2 x  8(3 x)  2
B. 3(2 x  8 y )  2
C. 2(3x)  8 y  2
D. 3(2 x  8 x)  2
49. A company is comparing two different postage
plans for next year. The company can
purchase a postage plan where the total cost,
c1, is $45,000 plus $3,000 per mailing, where
n is the number of mailings. The cost, c2, of
the other plan is $0.35 for each piece, p,
mailed. Which of the following is a set of
equations modeling the costs of the two
plans?
A. c1 = 45000n + 3000
c2 = 0.035p
B. c1 = 45000 + 3000n
c2 = 0.35 + p
C. c1 = 45000n + 3000
c2 = 0.35 + p
D. c1 = 45000 + 3000n
c2 = 0.35p
A.
B.
C.
D.
50. Southern Phone Company is promoting a new
cell phone service plan: a customer can make
up to 500 minutes of calls each month for
$39.99. If the number of minutes used in a
month exceeds 500, then the function
cІ = 0.40(m − 500) + 39.99
describes the monthly charge, c, in dollars in
terms of m, the total number of minutes used.
Which of the following statements best
describes this function?
A. A. If the total number of minutes used is more than 500,
then every minute beyond 500 costs 40 cents.
B. Every minute used costs 40 cents, regardless of the
total number of minutes used.
C. The first 500 minutes used costs 40 cents each, after
which there is an additional charge of $39.99.
D. If the total number of minutes used is more than 500,
then every minute used costs 40 cents.
51. The sum of the perimeters of two different squares
is 32 cm, and the difference between their
perimeters is 8 cm. If x represents the side length
of the larger square and y represents the side length
of the smaller square, which of the following
systems of equations could be used to find the
dimensions of the squares?
A.
A1.1.2.2.2
Interpret solutions to problems in the context
of the problem situation.
Note: Limit systems to two linear equations.
52. Which description best compares the graphs
given by the equations:
and
Time
First Trip
Second Trip
2 Days
1 Day
Distance
Traveled
275 Miles
95 Miles
Cost
$140.75
$59.75
According to this table, how much did the
rental company charge per day and per mile?
A.
B.
C.
D.
$17 per day and $0.45 per mile
$36 per day and $0.25 per mile
$8.45 per day and $0.54 per mile
$70.38 per day and $0.63 per mile
54. Samantha and Maria purchased flowers.
Samantha purchased 5 roses for x dollars
each and 4 daisies for y dollars each and
spent $32 on the flowers.
Maria purchased 1 rose for x dollars and 6
daisies for y dollars each and spent $22. The
system of equations shown below represents
this situation.
5x + 4y = 32
x + 6y = 22
A. A rose costs $1 more than a daisy.
B. Samantha spent $4 on each daisy.
C. Samantha spent more on daisies than she did on
roses.
D. Samantha spent over 4 times as much on daisies
as she did on roses.
D.
-6x + 15y = 5
Trip
Which statement is true?
C.
B.
53. A salesman rents a car for two trips from the
same rental company. The rental company
charges a daily fee plus a charge for each mile
driven.
30x + 12y = 4?
A. Parallel
B. Coincident
C. Perpendicular
D. Intersecting but not perpendicular
55. Consider the system of equations below.
x+y=6
y = -x + 2
Which statement correctly describes the
graphs of these equations?
A. The lines are parallel.
B. The lines coincide.
C. The lines intersect at (2, 4)
D. The lines intersect at (−2, 8).
A1.1.3.1.1
Write or solve compound inequalities and/or
graph their solution sets on a number line
(may include absolute value inequalities).
56. Choose the inequality below that matches the
solution represented on the number line
shown.
-4 -3 -2 -1 0 1 2 3 4 x
A.
x
3
1  x 1
B. x  1  3
C. x  1  3
D. x2  2 x  3  0
57. Solve:
A.
C.
B.
D.
A1.1.3.1.2
Identify or graph the solution set to a linear
inequality on a number line.
58. The solution set of an inequality is graphed on
the number line below.
The graph shows the solution set of which
inequality?
A. 2x + 5 < –1
B. 2x + 5 ≤ –1
C. 2x + 5 > –1
D. 2x + 5 ≥ –1
59. Which number line displays the solution set of
the inequality: 2x  7  15
A.
C.
B.
D.
60. How many solutions does an inequality like
have?
61. Consider the inequality 6x + y < p
What must be true about the value of p in
order for the origin to be part of the solution?
A. p £ 0
B. p < 0
C. p ³ 0
D. p > 0
A1.1.3.1.3
Interpret solutions to problems in the context
of the problem situation.
Note: Limit to linear inequalities.
62. A baseball team had $1,000 to spend on
supplies. The team spent $185 on a new bat.
New baseballs cost $4 each. The inequality
185 + 4b ≤ 1,000 can be used to determine
the number of new baseballs (b) that the team
can purchase. Which statement about the
number of new baseballs that can be
purchased is true?
A. The team can purchase 204 new baseballs.
B. The minimum number of new baseballs that can
be purchased is 185.
C. The maximum number of new baseballs that can
be purchased is 185.
D. The team can purchase 185 new baseballs, but
this number is neither the maximum nor the
minimum.
A1.1.3.2.1
Write and/or solve a system of linear
inequalities using graphing.
Note: Limit systems to two linear inequalities.
63. A system of inequalities is shown below.
Which graph shows the solution set of the
system of inequalities?
A.
C.
B.
D.
A. One
B. Two
C. Infinite
D. None
64. Which graph best represents the solution to
the system of linear inequalities?
A.
C.
B.
D.
A1.1.3.2.2
Interpret solutions to problems in the context
of the problem situation.
Note: Limit systems to two linear inequalities.
65. Tyreke always leaves a tip of between 8%
and 20% for the server when he pays for his
dinner. This can be represented by the
system of inequalities shown below, where y
is the amount of tip and x is the cost of dinner.
y > 0.08x
y < 0.2x
Which of the following is a true statement?
A. When the cost of dinner (x) is $10, the amount of
tip (y) must be between $2 and $8.
B. When the cost of dinner (x) is $15, the amount of
tip (y) must be between $1.20 and $3.00.
C. When the amount of tip (y) is $3, the cost of
dinner (x) must be between $11 and $23.
D. When the amount of tip (y) is $2.40, the cost of
dinner (x) must be between $3 and $6.