GLCE/HSCE: Algebra I Assessments
Unit 1—Number Systems and Number Sense
L1.1.1 Know the different properties that hold in different number systems and recognize
that the applicable properties change in the transition from the positive integers to all
integers, to the rational numbers, and to the real numbers.
1. Which property of real numbers is utilized by rewriting 11x + 5xy as x(11 + 5y)?
A.
B.
C.
D.
Associative property of addition
Commutative property of addition
Closure property of multiplication
Distributive property of multiplication over addition
Answer: D
2. The diagram shows how some of the subsets of the set of real numbers are related. The letters
represent members of the sets.
v
Rational
u
Integers
Whole
Whole
Numbers
Numbers
Irrational
x
z
n pp q
s
r
t
w
y
Terrie wants to replace the letters with actual numbers. Which letter could be replaced with
 16 ?
A.
B.
C.
D.
n
r_
u
x
Answer: B
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3. Which of the following statements is NOT correct?
A.
B.
C.
D.
If a 0 and ab = ac, then b = c.
If a > 0, then 1/a < 0
If a > 0, then 1/a > 0
If ab = 0, then a = 0 or b = 0
Answer: B
L1.1.2 Explain why the multiplicative inverse of a number has the same sign as the
number, while the additive inverse of a number has the opposite sign.
1. Why is the additive inverse of a positive integer a negative integer?
A. The additive inverses of all integers are negative.
B. The inverse of a number is always the opposite sign of the number.
C. The product of a number and its additive inverse equals -1, so the number and its
inverse must have opposite signs.
D. The sum of a number and its additive inverse equals 0, so the number and its inverse
must have opposite signs.
Answer: D
2. Which equation is an illustration of the additive identity property?
A. x • 1 = x
B. x + 0 = x
C. x – x = 0
1
D. x • = 1
x
Answer: B
3. Which of the following is an example of the multiplicative identity?
A. m ∙ 0 = 0
B.
1
6 1
6
C.
n k
 1
k n
D.  12  12  1
Answer: C
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L1.1.3 Explain how the properties of associativity, commutativity, and distributivity, as
well as identity and inverse elements, are used in arithmetic and algebraic calculations.
1. Which of the following are true for all real numbers x, y and z?
I. x(y + z) = xy + xz
II. x + y + z = z + y + x
III. x - y - z = z - y – z
A.
B.
C.
D.
I only
II only
I and II only
I, II and III
Answer: C
2
m  8 , which property can be used to find what m equals?
3
Multiplicative Identity
Multiplicative Inverse
Additive Identity
Additive Inverse
2. In the equation,
A.
B.
C.
D.
Answer: B
3. Which statement cannot be justified by one of the properties of real numbers?
A. (4.25 + 5.75) + 9 = 4.25 + (5.75 + 9)
B. 15 - (8 ÷ 4) = (15 - 8) ÷ 4
C. (0 ∙ -5)7 = 0(-5 ∙ 7)
7
3
7
3
D. ( +
)+0=0+(
+
)
10 10
10 10
Answer: B
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L2.1.2 Calculate fluently with numerical expressions involving exponents. Use the rules of
exponents, and evaluate numerical expressions involving rational and negative exponents,
and transition easily between roots and exponents.
2
 5
1. Which of the following correctly simplifies the expression?  
 4
25
A.
16
25
B.
4
16
C.
5
16
D.
25
Answer: D
2. If the relationship shown below is true, then t could be
A. -
1
4
B. 0
1
C.
4
D. 4
Answer: C
3
 1
3. Which of the following correctly simplifies  4 5  ?
 
5
A.
12
B. 2
C.
5
64
D.
5
32
Answer: C
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Unit 2—Expressions, Equations, and Inequalities
L1.1.5 Justify numerical relationships.
1. If a < b and b = c, which statement must be true?
A.
B.
C.
D.
The values of a, b, and c are positive.
The values or a, b, and c are negative.
The value of a is less then the value of c.
The value of a is greater than the value of c.
Answer: C
2. Which is always a correct conclusion about the quantities in the function y = x + 4?
A.
B.
C.
D.
The variable x is always 4 more than y.
When the value of x is negative, the value of y is also negative.
The variable y is always greater than x.
The value of x increases, the value of y decreases.
Answer: C
3. Which inequality best describes the graph shown below?
A. y > – x + 5
B. y < – x + 5
C. y < – x + 5
D. y > – x + 5
Answer: D
L1.2.2 Interpret representations that reflect absolute value relationships in such contexts as
error tolerance.
1. What is the solution to |x – 5|  7
A.
B.
C.
D.
-35  x  35
-12  x  12
-12  x  2
-2  x  12
Answer: D
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L1.2.4 Organize and summarize a data set in a table, plot, chart, or spreadsheet; find
patterns in a display of data; understand and critique data displays in the media.
1. Tommy and Jeremy are pitchers for the baseball team and are being evaluated by the coach.
The speeds in miles per hour of each of their practice pitches are shown below.
Practice Pitch Speeds
Tommy
Jeremy
60
63
69
70
85
79
68
67
80
65
73
72
65
68
Which of the following statements is true regarding their performances?
A.
B.
C.
D.
Tommy has a lower mean speed.
Tommy has a greater range of speeds.
Tommy has a lower median speed.
Jeremy’s median speed is higher than Tommy’s mean speed.
Answer: B
2. The table below shows the relation between the number of members in a club selling cookies
and the predicted number of boxes sold.
Using the data shown above, which equation could be used to predict the number of boxes of
cookies that the club will sell?
A.
B.
C.
D.
b = 60g
b = 70g
b = 60g + 50
b = 50g + 50
Answer: C
Club Cookie Sales
Number of Number of
Members, g Boxes Sold, b
5
350
10
650
15
950
20
1250
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3. The Numbers in the table follow a linear pattern.
What is the missing y value?
A.
B.
C.
D.
182
180
176
172
x
2
4
6
8
28
30
y
14
26
38
50
170
?
Answer: A
L2.1.1 Explain the meaning and uses of weighted averages.
1. Mark’s test grades for the semester are listed in the table below. Which measure of data
would give him the highest grade?
A.
B.
C.
D.
Mean
Median
Mode
Range
Answer: C
2. Eduardo’s bowling scores for his first 3 games were 145, 136, and 156. If he wants to have
an average score of x after 4 games, which equation describes s, the score he needs for his
fourth game?
145  136  156
s
145  136  156
s
B. x =
3
145  136  156  s
C. x =
4
145  136  156  s
D. x =
3
A. x =
Answer: C
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3. Jimmy completed 7 of the 10 mathematics tests. His scores are 79, 86, 91, 87, 89, 100, and
85. The teacher has a policy of dropping the lowest score. Jimmy needs a final average of at
least 90% to receive an A. With which three scores below would he earn an A?
A.
B.
C.
D.
90, 86, 91
94, 78, 94
87, 90, 90
79, 96, 98
Answer: D
4. A student scored 85, 49, 67, and 83 on four tests. What score would the student need to make
on the next test to have a mean score of 75?
A.
B.
C.
D.
75
79
86
91
Answer: D
5. For the data set shown, which measure is the greatest?
A.
B.
C.
D.
{5, 6, 6, 8, 9, 10}
Mean
Median
Mode
Range
Answer: A
A1.1.1 Give a verbal description of an expression that is presented in a symbolic form,
write an algebraic expression from a verbal description, and evaluate expressions given
values of the variables.
1. A repairman estimated the cost of replacing a part in Mrs. James’ computer would be at most
$225. The estimate included $35 for the part, a $40 service charge, and $30 per hour for
labor. What is the maximum number of hours the repairman estimated for the job?
A.
B.
C.
D.
4½
5
5½
6
Answer: B
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2. Which problem is best represented by the number sentence 19 + 3(12 – x) = 40?
A. Ricardo spent $19, and Lydia spent 3 times $12 less than Ricardo. Together they
spent $40. How much did Lydia spend?
B. Juan earned $19 baby-sitting and sold 3 boxes of apples for $12 each. Now he has
$40. How much did he earn?
C. Gail earned $19 baby-sitting and mowed 3 lawns in less than 12 hours. She earned a
total of $40. How much did she earn per lawn?
D. Denise paid $19 for 1 regularly priced item and bought 3 items on sale that were
regularly priced at $12. She spent $40 in all. What was the price reduction on the 3
sale items?
Answer: D
3. Joe, who is the youngest member of the wrestling team at Northwood High School, is 5 years
less than one-half the age of the coach. If the coach is n years old, which expression
describes Joe’s age?
A.
B.
C.
D.
½n - 5
5 - ½n
2n + 5
2n - 5
Answer: A
A1.2.1 Write equations and inequalities with one or two variables to represent
mathematical or applied situations, and solve.
1. A manufacturing company has determined that its profit, p, should be at least $100,000 more
than $10.00 times the number of items manufactured, t. Which inequality represents the
company’s desired profit?
A.
B.
C.
D.
p > 100,010 + t
p  10t + 100,000
p  10t + 100,000
p < 100,000t + 10
Answer: C
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2. Paige has started saving for a new television. She saved $75 last month. She plans to add $50
each month until she has saved at least $400. Which inequality can be used to find m, the
number of months it will take Paige to save for her television?
A.
B.
C.
D.
50m - 75 > 400
75 + 50m > 400
50m - 75 < 400
75m + 50 > 400
Answer: B
3. Solve the equation 6n + 4 = 8n -2 + n
A.
B.
C.
D.
{2}
{1}
{-13}
{-16}
Answer: A
A1.2.3 Solve linear and quadratic equations and inequalities, including systems of up to
three linear equations with three unknowns. Justify steps in the solution, and apply the
quadratic formula appropriately.
1. A science test contains 40 questions. Some of the questions are worth 4 points each, and
some are worth 2 points each. The total test is worth 100 points. Which system of equations
can be used to find x, the number of questions worth 4 points, and y, the number of questions
worth 2 points?
A. 4x + 2y = 40
x + y = 100
B. 4x + 2y = 100
x + y = 40
C. 4x − 2y = 100
x + y = 40
D. 4x − 2y = 100
x − y = 100
Answer: B
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2. Mark has $4.95 in quarters and dimes. He has 3 times as many dimes as quarters. Which
system of equations can be used to find q, the number of quarters, and d, the number of
dimes, that Mark has?
A. d = 3q
0.10q + 0.25d
B. d = q + 3
0.25q + 0.10d
C. q = 3d
0.25q + 0.10d
D. q = 3d
0.10q + 0.25d
= 4.95
= 4.95
= 4.95
= 4.95
Answer: C
3. The quadratic function f(x) is evaluated for different values of x, as shown on the table.
x
f(x)
-4
-8
-2
-6
0
0
2
10
The graph of f(x) has a line of symmetry at x = -4.
For which other value of x is f(x) equal to 0?
A.
B.
C.
D.
-6
-7
-8
-9
Answer: C
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4. Which inequality best describes the graph shown below?
A. y > – x + 5
B. y < – x + 5
C. y < – x + 5
D. y > – x + 5
Answer: D
5. If Sally places a rocket that is 3 feet 6 inches tall atop a launch pad that is 1 foot 8 inches tall,
how tall will the entire unit, rocket and launch pad, be when she is done?
A.
B.
C.
D.
5 feet 4 inches
5 feet 2 inches
1 foot 8 inches
4 feet 2 inches
Answer: B
6. Glenn needs 1,500 boards to build a small rocket. Each board must be 3 feet long. If boards
are sold in 12 foot lengths, how many boards must Glenn buy and cut into 3 foot pieces to get
the 1,500 he needs?
**NOTE : Please ignore the kerf (the width of the cut a saw makes, often about an eighth of
an inch)
A.
B.
C.
D.
42
125
375
500
Answer: C
7. Ron paid $75.00 for 5 compact disks and a case. If the price of each compact disk was
$12.60, what was the price of the case?
A
B
C
D
$12.00
$12.50
$15.00
$63.00
Answer: A
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A1.2.4 Solve absolute value equations and inequalities, and justify steps in the solution.
1. Solve: │x + 2│ = 7
A.
B.
C.
D.
{5}
{-9}
{5, -9}
No Set
Answer: C
2. Solve:
A.
B.
C.
D.
[ -1/3 , -1/9]
[1/3, -1/9]
[1/3, 1/9]
[-1/3, 1/9]
Answer: A
3.
Solve: | 5y – 8| = 1
A.
B.
C.
D.
y = 7/5 and y = -9/5
y = - 7/5 and y = -9/5
y = 7/5 and y = 9/5
y = -7/5 and y = 9/5
Answer: C
4. What is the solution to |x – 5|  7
A.
B.
C.
D.
-35  x  35
-12  x  12
-12  x  2
-2  x  12
Answer: D
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A1.2.8 Solve an equation involving several variables (with numerical or letter coefficients)
for a designated variable. Justify steps in the solution.
1. Albert Einstein’s famous equation is E = mc2.
Which equation below is equivalent to E = mc2?
A. c = E – m
E
B. c =
m
C. c = E  m
D. c =
E
m
Answer: D
2. Solve the equation 5g + h = g, for g.
A. 5g = h + g
B. g = -h/4
C. g = h/4
D. h/4 = -g
Answer: B
3. Solve the equation v = r + at, for a
A. a = (v – r)/t
B. a = (v + r)/t
C. a = v – r/t
D. a = v + r/t
Answer: A
4. Solve the equation y = mx + b, for m.
A. m = y – b/x
B. m = (y - b)/x
C. m = (b – y)/x
D. m = (b + y)/x
Answer: B
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S2.2.1 For bivariate data that appear to form a linear pattern, find the least squares
regression line by estimating visually and by calculating the equation of the regression line.
Interpret the slope of the equation for a regression line.
1. A biology class measures the daily rainfall and the daily growth of a specific planet. The data
are shown in the chart below.
The line of best fit for these data is given by the equation y
= 0.5x + 0.15. What is the significance of the slope of this
line of best fit?
A. For rainfall of 0.1 inch, we expect the plant to grow
0.2 inch.
B. For every additional inch of rainfall, we expect the
plant to grow 0.15 inch.
C. For rainfall of 0.7 inch, we expect the plant to grow 1.1 inches.
D. For every additional inch of rainfall, we expect the plant to grow 0.5 inch.
Answer: D
2. A delivery service company maintains several vehicles. The table summarizes the cost for
auto insurance related to the number of vehicles insured.
Using the equation of a line of best fit for the data, which is
the closest estimate of the title cost of insuring eight
vehicles?
A.
B.
C.
D.
$5,050
$5,200
$5,500
$5,950
Answer: B
3. Which equation most closely defines the line of
best fit for the data?
A.
B.
C.
D.
y = 4.1x + 414
y = -4.1x + 414
y = 3.1x + 383
y = -3.1x + 383
Answer: D
Algebra I Assessments – August 2008 Revision
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Number of
Vehicles
1
2
3
4
5
6
Cost ($)
1,700
2,200
2,700
3,200
3,700
4,200
4. Which equation defines the linear line of best fit for the data in the table?
x
y
A. y = 19.5x – 0.35
70
4
B. y = -0.35x + 19.5
75
7
C. y = -19.5x + 0.35
80
8.5
D. y = 0.35x – 19.5
85
12
90
11
Answer: D
95 13.5
100
15
S2.2.2 Use the equation of the least squares regression line to make appropriate
predictions.
1. The scatterplot below compares x, the number of household members, and y, the weekly
amount spent on groceries, for eight families. A line of best fit has been drawn based on this
idea.
Based on the line of best fit, which
estimate is closest to the amount a
household with five members spends on
groceries per week.
A.
B.
C.
D.
$92.24
$112.10
$120.00
$139.90
Answer: B
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Unit 3—Functions
A2.1.1 Determine whether a relationship (given in contextual, symbolic, tabular, or
graphical form) is a function; and identify its domain and range.
1. What is the apparent range of the function of x shown?
A.
B.
C.
D.
The set of all real numbers greater than or equal to 4
The set of all real numbers greater than or equal to 1
The set of all real numbers less than or equal to 1
The set of all real numbers
Answer B
2. Which of the following does not represent a function of x?
A.
B.
C.
D.
Answer A.
3. Which set of ordered pairs is not a function?
A.
B.
C.
D.
{(-2, 3), (4, 1), (2, 1), (1, 5)}
{(1, 4), (2, 3), (3, 2), (4, 3)}
{(2, 3), (3, 2), (4, 4), (5, 2)}
{(-2, 3), (1, 4), (2, 3), (1, 5)}
Answer: D
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A2.1.2 Read, interpret, and use function notation and evaluate a function at a value in its
domain.
1. If f (x) =x2+2x+3, what is the value of f (x) when x=6?
A.
B.
C.
D.
27
42
51 _
60
Answer: C
2. What is the range of the function f (x) =
A.
B.
C.
D.
1
2
x  2 when the domain is {2, 4, 6}?
{8, 12, 16}
{0, 1, 2}
{-1, 0, 1}
{-1, 0, 21 }
Answer: C
3  x2
3. If f (x) =
, what is f (2)?
3 x
A.
B.
C.
D.
-2
-1
1
2
Answer: B
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A2.1.3 Represent functions in symbols, graphs, tables, diagrams, or words and translate
among representations.
1. Which of these data sets represents a function?
A.
C.
B.
D.
Answer: D
2. Which is the function described by the table of ordered pairs?
A.
B.
C.
D.
y=x+1
y = 3x
y = 2x + 3 _
y = x + 13
Answer: C
3. Which type of function is shown?
A.
B.
C.
D.
Absolute value
Exponential
Linear
Quadratic _
Answer: D
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A2.1.4 Recognize that functions may be defined by different expressions over different
intervals of their domains; such functions are piecewise defined.
1. If f is the piecewise function of
f(x) =

-3, if x < 0
2x-3, if x  0
evaluate f(2).
A.
B.
C.
D.
3
0
9
1
Answer: D
A2.1.5 Recognize that functions may be defined recursively. Compute values of and graph
simple recursively defined functions.
A2.1.6 Identify the zeros of a function and the intervals where the values of a function are
positive or negative, and describe the behavior of a function as x approaches positive or
negative infinity, given the symbolic and graphical representations.
1. Which is a zero of ƒ(x) = x2-15x+54?
A.
B.
C.
D.
3
5
9
15
Answer: C
2. Which of the following sets contains all the
apparent zeros for the function shown?
A.
B.
C.
D.
{1}
{-2, 0, 2}
{-2, 1, 2}
{-3, -1, 1, 3}
Answer: D
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A2.1.7 Identify and interpret the key features of a function from its graph or its formula(s).
1. What is the slope of the line through (3, 2) and (-1, -4)?
A. 3
3
B.
2
2
C.
3
D. 
3
2
Answer: B
3
2. Which is an equation for the line that passes through the origin and has a slope of ?
5
3
A. y =
5
3
B. x =
5
C. y = x
3
D. y = x
5
Answer: D
3. Which equation is the slope-intercept form of -x + 6y = 12?
1
A. y = x  2
6
1
B. y =  x  2
6
C. x = 6y +12
D. 6y = 12 + x
Answer: A
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4. Find the slope of the line through the pair of points. (20,4), (11, -1)
9
5
5
B.
9
A.
5
9
9
D. 5
C. -
Answer: B
A2.2.1 Combine functions by addition, subtraction, multiplication, and division.
1. Given: f (x) = x3 - 3x and g(x) = x2- 8. What is f (10) - g (10)?
A.
B.
C.
D.
608
783
862
878 _
Answer: D
A2.2.2 Apply given transformations to parent functions and represent symbolically.
1
1. This graph represents y = x
2
If the line in the graph is shifted down 3 units,
which is the equation for the new line?
1
A. y =  x
2
3
B. y = x
2
1
C. y = x  3
2
1
D. y = x  3
2
Answer: C
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2. Which of the following is most likely the equation
graphed below?
A.
B.
C.
D.
y = (x + 2)2 + 1
y = 5(x - 1)2 - 2
y = (x - 2)2 + 2
y = (x - 1)2 – 2
Answer: D
3. The graph below represents the equation y = 3x.
Which graph best represents y = 3x- 1?
A.
B.
C.
D.
Answer: B
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A2.2.3 Determine whether a function (given in tabular or graphical form) has an inverse
and recognize simple inverse pairs.
A2.3.1 Identify a function as a member of a family of functions based on its symbolic or
graphical representation; recognize that different families of functions have different
asymptotic behavior.
1. What type of equation is pictured below?
A.
B.
C.
D.
Quadratic equation
Linear equation in standard Ax + By = C
Absolute Value Equation
Linear equation in function notation
Answer: C
2. 3x + 6y = 32
A.
B.
C.
D.
Quadratic equation
Linear equation in standard Ax + By = C form
Absolute Value Equation
Linear equation in function notation
Answer: B
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A2.3.2 Describe the tabular pattern associated with functions having a constant rate of
change (linear); or variable rates of change.
1. The numbers in the table follow a linear pattern.
What is the missing y value?
A.
B.
C.
D.
182
180
176
172
Answer: A
2. Which kind of function best models the data in the table? Write an equation to model the data
A.
B.
C.
D.
cubic; y = x3 + 4x2 + 4x + 4
exponential; y = 1.8x
quadratic; y = x2 + 4x + 4
linear; y = x + 4
x
0
1
2
3
4
Answer: C
y
4
9
16
25
36
A2.3.3 Write the general symbolic forms that characterize each family of functions.
1. The function 5x – 3y = -15 is in:
A.
B.
C.
D.
slope-intercept form
y = mx + b form
standard form
parallel form
Answer: C
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Unit 4—Linear Functions
A3.1.1 Write the symbolic forms of linear functions (standard, point-slope, and slopeintercept) given appropriate information and convert between forms.
1. Larry made a scatterplot showing the apparent
height of a football at one-second intervals
during the time period the ball was in the air.
Which type of function would best fit the
data in this scatterplot?
A.
B.
C.
D.
Linear
Exponential
Logarithmic
Quadratic
Answer: D
2. The chart shows how the wholesale price of an item, p, depends on the cost of the materials needed to
produce the item, m. Which family of functions would best represent this data?
A.
B.
C.
D.
Linear
Exponential
Logarithmic
Quadratic
Answer: A
3. In which family of functions can the simple interest formula, A = P(1 + r)n, be found?
A.
B.
C.
D.
Linear
Exponential
Logarithmic
Quadratic
Answer: B
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A3.1.2 Graph lines (including those of the form x = h and y = k) given appropriate
information.
1. In the table, y varies directly with x.
Which equation best describes the data?
x
y
10
6
15
9
20
12
25
15
5
3
3
B. xy =
5
5
C. y = x
3
3
D. y = x
5
A. xy =
Answer: D
A3.1.3 Relate the coefficients in a linear function to the slope and x- and y- intercepts of its
graph.
A3.1.4 Find an equation of the line parallel or perpendicular to given line, through a given
point; understand and use the facts that non-vertical parallel lines have equal slopes, and
that non-vertical perpendicular lines have slopes that multiply to give -1.
1
1. Which is an equation for the line with a slope of
that passes through the origin?
2
1
A. y = x
2
B. y = 2x
1
C. y =
2
D. x = 0
Answer: A
Algebra I Assessments – August 2008 Revision
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2. What is the slope of the line 3y = 4x + 5?
A. 4
B. 2
5
C.
3
4
D.
3
Answer: D
3. Which is an equation for the line which contains (3, 4) and the origin?
3
x
4
4
B. y = x
3
C. y = 4x + 3
D. y = 3x + 4
A. y =
Answer: B
4. Which is equivalent to p6p2?
A.
B.
C.
D.
p8
2p8
p10
p12
Answer: A
5. The ordered pairs in the sets shown below are of the form (x, y). In which set is y a function
of x?
A.
B.
C.
D.
{(1, 3), (2, 6), (3, 1), (6, 3)
{(1, 3), (3, 1), (3, 4), (4, 3)}
{(1, _2), (1, 0), (1, 5), (1, 7)}
{(0, 3), (1, 4), (2, 4), (2, 8)}
Answer: A
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6. The total number, n, of employees at a company depends on the company’s yearly gross
profits according to the equation n =10p +20, where p is the yearly gross profit in millions of
dollars. If the yearly gross profit declined from 20 million dollars to 15 million dollars, what
was the decrease in the number of employees?
A.
B.
C.
D.
50
70
120
220
Answer: A
7. Which of these pairs of the form (x, y) could not lie on the graph of a function of x?
A.
B.
C.
D.
(1, 1) and (3, 1)
(1, 1) and (2, 1)
(1, 1) and (1, 2)
(1, 1) and (2, 2)
Answer: C
Algebra I Assessments – August 2008 Revision
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Unit 5—Models of Real World Functions
A2.4.1 Identify the family of function best suited for modeling a given real-world situation.
1. A loaded moving van weighs 5 tons. How many pounds would 10 loaded moving vans
weigh?
A.
B.
C.
D.
50 pounds
10,000 pounds
50,000 pounds
100,000 pounds
Answer: D
2. Erv ran the 110 meter high hurdles in 13.27 seconds. His teammate Willie ran the same race
in 12.91 seconds. Rounded to the nearest tenth of a second, how much faster was Willie's
time?
A.
B.
C.
D.
0.3 seconds
0.36 seconds
0.4 seconds
1.0 seconds
Answer: C
3. Roberta left for her dancing class at 3:45 p.m. Her dancing school is a 15 minute walk from
her house, and her class lasted one and one half hours. What time did she get home if she
went straight home?
A.
B.
C.
D.
5:15 p.m.
5:30 p.m.
5:45 p.m.
6:15 p.m.
Answer: C
Algebra I Assessments – August 2008 Revision
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A2.4.2 Adapt the general symbolic form of a function to one that fits the specifications of a
given situation by using the information to replace arbitrary constants with numbers.
1. A student scored 85, 49, 67, and 83 on four tests. What score would the student need to make
on the next test to have a mean score of 75?
A.
B.
C.
D.
75
79
86
91
Answer: D
2. Which is an equation for the line with a slope of ½ that passes through the origin?
A.
B.
C.
D.
y=½x
y = 2x
y = 1/2
x=0
Answer: A
3. Which is an equation for the line which contains (3, 4) and the origin?
A. y = ¾ x
B. y = 4/3 x
C. y = 4x + 3
D. y =3x +4
Answer: B
A2.4.3 Using the adapted general symbolic form, draw reasonable conclusions about the
situation being modeled.
1. Mrs. Crews bought 4 pencils and 3 pens for $ 5.60. Miss Houston bought 2 pencils and 3
pens of the same kind for $4.60. What was the price of each pencil and each pen?
A.
B.
C.
D.
$1.70 per pencil, $0.20 per pen
$0.50 per pencil, $1.20 per pen
$0.17 per pencil, $1.64 per pen
$0.80 per pencil, $0.80 per pen
Answer: B
Algebra I Assessments – August 2008 Revision
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2. The perimeter of a rectangular playing field is 244 feet. If its length is 2 feet longer than
twice its width, what are the dimensions of the field?
A.
B.
C.
D.
20 ft, 41 ft
21 ft, 40 ft
40 ft, 82 ft
42 ft, 80 ft
Answer: C
3. (3xy) (5x2+2xy+3y2) is equivalent to:
A.
B.
C.
D.
15x3y + 6x2y2 + 9xy3 _
15x3y + 2xy + 3y2
15x2y + 6x2y2 +9xy2
15x2 + 5xy + 3y2
Answer: A
_
Algebra I Assessments – August 2008 Revision
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Unit 6—Scatterplots and Correlations
S2.1.1 Construct a scatterplot for a bivariate data set with appropriate labels and scales.
1. Which scatterplot most likely has a line of best fit represented by y = 3x +1?
A.
B.
C.
D.
Answer: A
2. An engine is tested for torque output at different revolutions per minute.
Which equation most clearly defines the line of best
fit for the data?
A.
B.
C.
D.
y = 4.1x + 414
y = -4.1x + 414
y = 3.1x + 383
y = -3.1x + 383
Answer: D
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3. For the data set shown, which measure is the greatest? {5, 6, 6, 8, 9, 10}
A. Mean _
B. Median
C. Mode
D. Range
Answer: A
S2.1.2 Given a scatterplot, identify patterns, clusters, and outliers. Recognize no
correlation, weak correlation, and strong correlation.
1. The stem-and-leaf plots show the number of miles per gallon a family’s car and truck
averaged over the past few months.
What is the difference in the median number of miles per
gallon for the two vehicles?
A.
B.
C.
D.
7
9
10
11
Answer: D
2. If m varies directly as p, and m = 5 when p = 7, what is the constant of variation?
A. 35
B. 12
7
C.
5
5
D.
7
Answer: A
3. Which is a zero of (f) = x2 – 15x + 54?
A.
B.
C.
D.
3
5
9
15
Answer: C
Algebra I Assessments – August 2008 Revision
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S2.1.3 Estimate and interpret Pearson’s correlation coefficient for a scatterplot of a
bivariate data set. Recognize that correlation measures the strength of linear association.
1. Which of the following r values indicates a strong negative correlation for a regression line?
A.
B.
C.
D.
–1
0
–2
1
Answer: A
S2.1.4 Differentiate between correlation and causation. Know that a strong correlation does
not imply a cause-and-effect relationship. Recognize the role of lurking variables in
correlation.
1. In the scatter plot shown at the right, which statement best describes the correlation between
the days of the week and the number of bicycles sold?
A. There is a high negative correlation between the
days of the week and the number of bicycles
sold.
B. There is a low negative correlation between the
days of the week and the number of bicycles
sold.
C. There is a high positive correlation between the
days of the week and the number of bicycles
sold.
D. There is a low positive correlation between the
days of the week and the number of bicycles
sold.
Answer: C
S2.2.1 For bivariate data that appear to form a linear pattern, find the least squares
regression line by estimating visually and by calculating the equation of the regression line.
Interpret the slope of the equation for a regression line.
S2.2.2 Use the equation of the least squares regression line to make appropriate
predictions.
Algebra I Assessments – August 2008 Revision
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Unit 7—Quadratic Equations
A1.2.3 Solve linear and quadratic equations and inequalities including systems of up to
three linear equations with three unknowns. Justify steps in the solution, and apply the
quadratic formula appropriately.
1. Tickets for the Junior Varsity football game costs $3.50 for arrival before 4:00 p.m. and
$4.75 for arrival after 4:00 p.m. The total amount of ticket sales was $209.50. If 52 tickets
were sold in all, exactly how many tickets were sold to fans that arrived before 4:00 p.m.?
A.
B.
C.
D.
22
26
30
52
Answer: C
2. Solve system by elimination
A.
B.
C.
D.
2x – y = -6
-2x + 2y = 2
(-5, -4)
(-5, -6)
(-6, 5)
(5, -6)
Answer: A
3. Solve using substitution
A.
B.
C.
D.
y = -7x – 9
-4x + 6y = -8
(-1, -2)
(-1, 6)
(-1, -6)
(2, 6)
Answer: A
L2.1.4 Know that the imaginary number i is one of two solutions to x2 = -1.
1. What is one solution to the equation x2 = -1?
A.
B.
C.
D.
i
1
-1
i2
Answer: A
Algebra I Assessments – August 2008 Revision
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2. Which expression is equivalent to (4i – 7) – (6i + 3)?
A.
B.
C.
D.
-2i – 10
-2i – 4
2i – 4
10i – 10
Answer: A
A1.1.3 Factor algebraic expressions using, for example, greatest common factor, grouping,
and the special product identities.
1. The area of a rectangular field is (3x2 – x – 2) square units. If the width is (x – 1) units, which
expression represents the unit length of the field?
A.
B.
C.
D.
3x + 2
3x – 2
x+1
x–3
Answer: A
2. Factor completely: 7x2 – 4x -20
A.
B.
C.
D.
3(3x -7)(x+6)
(7x -10)(x + 2)
(3x + 7)( x – 10)
(7x + 10)(x – 2)
Answer: D
3. Factor completely:
A.
B.
C.
D.
25 + 40x + 16x2
(-5 + 4x)(5 + 4x)
(3 – 5x) 2
(5 + 4x) 2
(8 + 5x)(8 – 5x)
Answer: C
Algebra I Assessments – August 2008 Revision
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A1.2.2 Associate a given equation with a function whose zeros are the solutions of the
equation.
1. The graph pf the equation y = x2 – 3x – 4 is shown below.
For what value or values of x is y = 0?
A.
B.
C.
D.
x = -1 only
x = -4 only
x = -1 and x = 4
x = 1 and x = -4
Answer: C
2. Which equation best represents the function?
A.
B.
C.
D.
y = -x2 + x – 8
y = x2 + 2x – 8
y = -2x2 + x – 8
y = 2x2 – 2x + 8
Answer: B
Algebra I Assessments – August 2008 Revision
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A2.2.2 Apply given transformations to parent functions and represent symbolically.
1. The graph of f(x) is shown on the left. The graph on the right, g(x), was obtained by applying
transformations to this function.
Which best represents the equation of the transformed graph?
A.
B.
C.
D.
g(x) = -f(x + 2)
g(x) = f(x – 2) – 8
g(x) = -f(x – 2)
g(x) = f(x) – 2
Answer: C
A3.3.1 Write the symbolic form and sketch the graph of a quadratic function given
appropriate information.
1. Which of these parabolas has a vertex at (1, -4) and intercepts the x-axis at (-1, 0) and (3, 0)?
A.
B.
C.
D.
y = x2 – 2x
y = x2 + 2x
y = x2 – 2x – 3
y = x2 – 2x + 3
Answer: C
Algebra I Assessments – August 2008 Revision
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A3.3.2 Identify the elements of a parabola (vertex, axis of symmetry, direction of opening)
given its symbolic form or its graph, and relate these elements to the coefficient(s) of the
symbolic form of the function.
1. What is the vertex of the graph of the function y = 2(x – 3)2 + 5?
A.
B.
C.
D.
(-3, 5)
(3, 5)
(5, 3)
(5, -3)
Answer: B
2. In the graph of the function y = x2 + 5, which describes the shift in the vertex of the parabola
if, in the function, 5 is changed to –2?
A.
B.
C.
D.
3 units up
7 units up
3 units down
7 units down
Answer: D
A3.3.3 Convert quadratic functions from standard to vertex form by completing the
square.
1. The quadratic equation y = 2x2 – 4x -6 is written in standard form. When it is converted to
vertex form by completing the square, how will it be written?
A.
B.
C.
D.
y = (x – 1)2 – 4
y = (x – 1)2 – 8
y = 2(x – 1)2 – 6
y = 2(x – 1)2 – 8
Answer: D
2. Leanne correctly solved the equation x2 + 4x = 6 by completing the square. Which equation is
part of her solution?
A.
B.
C.
D.
(x + 2)2 = 8
(x + 2)2 = 10
(x + 4)2 = 10
(x + 4)2 = 22
Answer: B
Algebra I Assessments – August 2008 Revision
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A3.3.4 Relate the number of real solutions of a quadratic equation to the graph of the
associated quadratic function.
1
1. What is the total number of real solutions shown in the graph of y = (x – 2)2 – 4?
3
A. 0
B. 1
C. 2
D. 3
Answer: C
A3.3.5 Express quadratic functions in vertex form to identify their maxima or minima and
in factored form to identify their zeros.
1. For which form of the quadratic function are the zeros of the function more readily apparent?
A.
B.
C.
D.
y   x  0.5 - 6.25
2
y  x2 + x – 6
y = x(x +1) – 6
y = (x – 2)(x + 3)
Answer: D
Algebra I Assessments – August 2008 Revision
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Unit 8—Power Functions
L1.1.4 Describe the reasons for the different effects of multiplication by, or exponentiation
of, a positive number less than 0, a number between 0 and 1, and a number greater than 1.
1
n
1. If n is a positive integer, what is the value of 3 ?
A. the nth root of 3
B. the nth power of 3
3
1
C. the sum of 3 and  
n
D. the quotient of 3 and n
Answer: A
L2.1.2 Calculate fluently with numerical expressions involving exponents. Use the rules of
exponents, and evaluate numerical expressions involving rational and negative exponents,
and transition easily between roots and exponents.
3
1. Using the laws of exponents, which expression is equivalent to (x-2y6)(xy 2 )?
A. x-2y9
15
y2
B.
x
y9
C. 3
x
D. x3y9
Answer: B
2. When simplified, (2x2y3)4 equals
A.
B.
C.
D.
8x6y7
8x8y12
16x6y7
16x8y12
Answer: D
Algebra I Assessments – August 2008 Revision
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3. (3xy)(5x2 + 2xy + 3y2) is equivalent to
A.
B.
C.
D.
15x3y + 6x2y2 + 9xy3
15x3y + 2xy + 3y2
15x2y + 6x2y2 + 9xy2
15x2 + 5xy + 3y2
Answer: A
A1.1.2 Know the properties of exponents and roots and apply them in algebraic expressions
1. Which is equivalent to 4 256 ?
A.
B.
C.
D.
4
16
64
1,024
Answer: A
A1.2.6 Solve power equations and equations including radical expressions; justify steps in
the solution, and explain how extraneous solutions may arise.
1. What is the solution set for the equation
A.
B.
C.
D.
x  90 = x?
{-10}
{10}
{-9, 10}
{-10, 9}
Answer: B
2. A statistician calculates a measure of variability, V, of a group’s responses to a survey with
the following formula:
If S = 64 and n = 5, what is the value of V ?
A.
B.
C.
D.
2
4
8
16
Answer: B
Algebra I Assessments – August 2008 Revision
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A2.2.3 Determine whether a function (given in tabular or graphic form) has an inverse and
recognize simple inverse pairs.
1. Which pair of relationships represents inverse functions?
A.
B.
C.
D.
Answer: D
A3.2.1 Write the symbolic form and sketch the graph of an exponential function given
appropriate information.
1. Which is the symbolic form of an exponential function with an initial value of 2 and a rate of
growth of 2.5?
A.
B.
C.
D.
f(x) = 2.5(2)x
f(x) = 2(2.5)x
f(x) = 2x2.5
f(x) = 2.5x2
Answer: B
Algebra I Assessments – August 2008 Revision
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2. A scientist finds that the colony of bacteria he is studying doubles in size every 30 minutes. If
the colony contained 9 bacteria when the observations began, which equation models the size
of this colony of bacteria as a function of the number of hours, t, that the colony has been
allowed to reproduce?
A. f(t) = 9(230t)
B. f(t) = 2(9
t
30
)
1
t
2
C. f(t) = 9(2 )
D. f(t) = 9(22t)
Answer: D
3. When a ball is dropped from height h, it bounces to ⅔ of its initial height. When the ball
bounces a second time, it reaches ⅔ the height after the first bounce, and so on.
Which expression shows the height of the ball after its nth bounce?
n
2
A.   h
3
2 
B. n h 
3 
2 
C.  h 
3 
2
D. h n
3
n
Answer: A
4. The number of bacteria in a colony was growing exponentially. At 1 pm yesterday the
number of bacteria was 1000 and at 3 pm yesterday it was 4000. How many bacteria were
there in the colony at 6 pm yesterday?
A.
B.
C.
D.
16,000
8,000
32,000
64,000
Answer: C
A3.2.4 Understand and use the fact that the base of an exponential function determines
whether the function increases or decreases and how base affects the rate of growth or
decay.
Algebra I Assessments – August 2008 Revision
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A3.2.5 Relate exponential functions to real phenomena, including half-life and doubling
time.
1. Under optimal environmental conditions, the bacterium streptococcus lactis in a medium of
milk will double in population every 26 minutes. If the initial population of this bacteria is
100, which is closest to the amount of time, in hours, that is required for the population to
first exceed 12,000?
A.
B.
C.
D.
2
3_
7
10
Answer: B
A3.4.1 Write the symbolic form and sketch the graph of power functions.
1. Which graph best represents y = x7?
A.
B.
C.
D.
Answer: D
Algebra I Assessments – August 2008 Revision
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A3.4.2 Express directly and inversely proportional relationships as functions and recognize
their characteristics.
1. A company packs vegetables in cans in the shape of a right circular cylinder with a radius of
6 centimeters. The company plans to change to a smaller can with the same height but with a
radius of 3 centimeters. The volume of the new, smaller can is what percent of the volume of
the larger can?
A.
B.
C.
D.
3%
25% _
50%
75%
Answer: B
A3.4.3 Analyze the graphs of power functions, noting reflectional or rotational symmetry.
Algebra I Assessments – August 2008 Revision
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Unit 9—Exponential and Logarithmic Functions
A3.2.1 Write the symbolic form and sketch the graph of an exponential function given
appropriate information.
A3.2.4 Understand and use the fact that the base of an exponential function determines
whether the function increases or decreases and how the base affects the rate of growth or
decay.
A3.2.5 Relate exponential functions to real phenomena, including half-life and doubling
time.
1. Under optimal environmental conditions, the bacterium streptococcus lactis in a medium of
milk will double in population every 26 minutes. If the initial population of this bacteria is
100, which is closest to the amount of time, in hours, that is required for the population to
first exceed 12,000?
A.
B.
C.
D.
2
3
7
10
Answer: B
Algebra I Assessments – August 2008 Revision
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Unit 10—Polynomial Functions
A2.1.6 Identify the zeros of a function, the intervals where the values of a function are
positive or negative, and describe the behavior of a function as x approaches positive or
negative infinity, given the symbolic and graphical representations.
1. The graph of a function y = f(x) is shown on the coordinate plane below.
Which of the following does NOT appear to be a zero
of this function?
A.
B.
C.
D.
3
0
-2
-4
Answer: D
2. How many times does the graph of y = 2x2 – 2x +3 intersect the x-axis?
A.
B.
C.
D.
none
one
two
three
Answer: A
A2.1.7 Identify and interpret the key features of a function from its graph or its formula(s).
1. What will happen to the graph of y = 2x + 5 if the 2 is changed to a 3?
A.
B.
C.
D.
The slope of the new graph will be steeper.
The slope of the new graph will be less steep.
The new graph will be shifted up on the y-axis.
The new graph will be shifted down on the y-axis.
Answer: A
Algebra I Assessments – August 2008 Revision
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2. The graph of y = 4x + 1 is shown.
How would the graph change if the 4 in the equation were
replaced with a 2?
A. The line would be parallel with a shift up of 2
units.
B. The line would be parallel with a shift down of 2
units.
C. The line would have a greater slope, but it would
pass through the y-axis at the same point.
D. The line would have a lesser slope, but it would
pass through the y-axis at the same point.
Answer: D
3. When graphed, which function would appear to be shifted 2 units up from the graph of
f(x) = x2 + 1?
A.
B.
C.
D.
g(x) = x 2 – 1
g(x) = x 2 + 3
g(x) = x 2 – 2
g(x) = x 2 + 2
Answer: C
A2.2.2 Apply given transformations to parent functions and represent symbolically.
1. The graph of f(x) is shown on the left. The graph on the right, g(x), was obtained by applying
transformation to this function.
A.
B.
C.
D.
g(x) = -f(x + 2)
g(x) = f(x – 2) – 8
g(x) = -f(x – 2)
g(x) = f(x) – 2
Answer: C
Algebra I Assessments – August 2008 Revision
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A2.3.1 Identify a function as a member of a family of functions based on its symbolic or
graphical representation; recognize that different families of functions have different
asymptotic behavior.
1. Apples are sold for $0.89 per pound. If the cost of these apples is expressed as a function of
weight, what type of function is it?
A.
B.
C.
D.
linear
quadratic
exponential
circular
Answer: A
2. The graph below represents the relationship of
transported particle size to water velocity. The
graph best models which type of function?
A.
B.
C.
D.
linear
quadratic
logarithmic
trigonometric
Answer: C
A3.5.1 Write the symbolic form and sketch the graph of simple polynomial functions.
1. The graph of y = x3 is shown below.
Where would the graph of y = (x – 2)3 be
located, in relation to the given graph?
A.
B.
C.
D.
shifted two units up
shifted two units down
shifted two units to the right
shifted two units to the left
Answer: C
Algebra I Assessments – August 2008 Revision
51
A3.5.2 Understand the effects of degree, leading coefficient, and number of real zeros on
the graphs of polynomial functions of degree greater than 2.
1. What can be inferred from the exponent 3 in the function y = x3 – 4x2 + x + 6?
A.
B.
C.
D.
The function has a root at x = -3.
The function has a maximum at x = 3.
The function has an asymptote at x = 3.
The function has the possibility of the three real zeros.
Answer: D
A3.5.3 Determine the maximum possible number of zeroes of a polynomial function and
understand the relationship between the x-intercepts of the graph and the factored form of
the function.
1. The polynomial function y = 3x3 – 20x2 + 43x – 30 may be written in factored form as
y = (x – 2)(x – 3)(3x – 5). Based on the factored form, what are the zeros of the function?
A. x = 2, x = 3, and x =
5
3
B. x = -2, x = -3, and x =
5
3
C. x = 2, x = 3, and x = 5
D. x = -2, x = -3, and x = -5
Answer: A
A2.4.1 Identify the family of function best suited for modeling a given real-world situation.
1. Write the standard form of the equation of the line
A.
B.
C.
D.
5x +y =0
5x = 1
3x + y = 0
5x - y = 0
Answer: C
Algebra I Assessments – August 2008 Revision
52
y = -3x