Name __________________________________
Algebra 1 Keystone Exam Test Design – The exam is divided into two modules:
Module 1
Operations and Linear
Equations and Inequalities
Module 2
Linear Functions and
Data Organization
The exam has two types of questions:
Number of
Operational
Questions
Number of Field
Test Questions
Total PER
MODULE
Multiple Choice
Questions
Multiple
Choice
Point
Values
Constructed
Response
Questions
Constructed
Response
Point Values
18
18
3
12
(4 points each)
5
0
1
0
23
18
4
12
NOTE: Each Module has a total of 30 points. Module 1 and Module 2 will have a
combined total of 60 points, with approximately 60% multiple choice points and 40%
constructed response points.
Algebra 1 Keystone Exam Review Topics
Module 1 & 2
A. Word Problems Using Systems of Equations
B. Inequalities and Systems
C. Scatter Plots
D. Systems of Inequalities
E. Polynomials
F. Radical Practice
G. Linear Equations
H. Miscellaneous Topics
Module 2
I. Linear Functions, Domain, and Range
J. Probability and Statistics
K. Data Analysis
1
A. Word Problems Using Systems of Equations
1. Owners of a coffee shop purchased 60 pounds of Guatemalan coffee beans and 90 pounds of
Nicaraguan coffee beans. The total purchase price was $180. The next week they purchased 80
pounds of Guatemalan coffee and 20 pounds of Nicaraguan coffee, and the cost was $100. Write
and solve a system of equations to find the cost per pound for both the Guatemalan and
Nicaraguan coffee beans.
2. Sam needs to make a long-distance call from a pay phone. With his prepaid phone card, he
will be charged $1.00 to connect and $0.50 per minute. If he places a collect call with the
operator he will be charged $3.00 to connect and $0.25 per minute. In how many minutes will
the phone card and the collect call cost the same?
A. 5 min
B. 5 1/3 min
C. 8 min
D. 16 min
2
3. A boat takes 6.5 hours to make a 70-mile trip upstream and 5 hours on the 70-mile return trip.
Let v be the speed of the boat in still water, and c be the speed of the current. The upstream speed
of the boat is v - c and the downstream boat speed is v + c.
A. Write two equations, one for the upstream part of the trip and one for the downstream part,
relating boat speed, distance, and time.
B. Solve the equations in part A for the speed of the current. Round your answer to the nearest
tenth of a mile per hour and show your work.
C. How long would it take the boat to travel the 70 miles if there were no current? Round your
answer to the nearest minute and show your work.
3
4. Students are raising money for a field trip by selling scented candles and specialty soap. The
candles cost $0.75 each and will be sold for $1.75, and the soap costs $1.25 per bar and will be
sold for $3.25. The students need to raise at least $200 to cover their trip costs.
A. Write an inequality that relates the number of candles c and the number of bars of soap s to
the needed income.
B. The wholesaler can supply no more than 80 bars of soap and no more than 140 candles. Graph
the inequality from part A and these constraints, using number of candles for the vertical axis.
C. What does the shaded area of your graph represent?
4
The Marathon
Bethany and Calista are sisters who both run marathons. Today they are racing against each other
in the same marathon. Because there are thousands of people racing, Bethany and Calista are
assigned random starting positions. Bethany starts at the starting line, while Calista starts a halfmile behind the starting line. Calista runs one mile in 12 minutes, while Bethany runs one mile in
15 minutes. So, although Calista starts behind Bethany, she hopes to pass her sister at some point
during the race. Let x represent the amount of time in hours that Bethany or Calista run and let y
represent distance after the starting line in miles.
1. The rate or speed at which someone runs is frequently stated in miles per hour.
A. What is Bethany’s speed in miles per hour? _______________
B. What is Calista’s speed in miles per hour? _______________
2. Write a linear equation in slope-intercept form that describes
A. Bethany’s distance as a function of time. ___________________________________
B. Calista’s distance as a function of time. ___________________________________
3. On the grid, graph the system of equations that you wrote for question 2.
4. Use your graph to estimate
A. who is in the lead after 15 minutes (0.25 hour). ________________
B. the time when Calista will catch up to Bethany. ________________
C. how far after the starting line the sisters catch up to each other.
__________________
D. who is in the lead after 2 hours if each sister keeps running at a
steady pace. ___________________________________
5. A marathon is 26.2 miles. Which sister do you think will cross the
finish line first? Explain.
_______________________________________________________
5
B. Inequalities and Systems
1. Jen has $10 and earns $8 per hour tutoring.
A. Write an equation to model Jen’s money earned (m).
B. After how many tutoring hours will Jen have $106?
Robert has $9 and makes $14 per hour tutoring.
C. Write an equation to model Robert’s money earned (m).
D. Using the equations written in A and C use the system of linear systems to find the number of
hours of tutoring after which Jen and Robert will have the same amount of money.
6
2. The height of one cup is 5 inches. The height of 4 stacked cups is 12 inches.
12 inches
5 inches
A. Write an equation using x and y to find the height of a stack based on any number of cups.
B. Describe what the x and the y variables represent.
C. What is the height in inches of a stack of 12 cups?
7
3. Write the compound inequality that models the given situation. Bob works at a gym and earns
$7.50 per hour. His paycheck from week to week is no less than $125 and no more than $215.
4. Write the compound inequality shown by the graph below.
5. The math club has $600 to spend on supplies. The club spends $115 on a TI-84 silver edition.
New pocket protectors cost $5 each. The inequality 115  5 p  600 can be used to determine the
number of new pocket protectors (p) that the club can purchase. Which statement about the
number of pocket protectors that can be purchased is true?
A. The team can purchase 97 pocket protectors
B. The minimum number of pocket protectors that can be purchased is 115.
C. The maximum number of new pocket protectors that can be purchased is 115.
D. The math club can purchase 115 new pocket protectors, but this number is neither the
maximum or the minimum.
8
C. Scatter Plots
1. If y tends to increase as x increases on a scatter plot, what is the correlation of the paired data?
A. positive
B. negative
C. relatively no
D. undefined
2. What is the correlation represented by the scatter plot shown?
A. positive
B. negative
C. relatively no
D. undefined
3. What is the correlation represented by the scatter plot shown?
A. positive
B. negative
C. relatively no
D. undefined
9
D. Systems of Inequalities
1. Evan always drives between 45 and 60 miles per hour on his commute. The distance he travels can be
represented in the system of inequalities below, where x is the number of minutes and y is the number of
miles.
y  0.75 x
yx
Which of the following is a true statement?
A. When the number of minutes he’s driven (x) is 60, the miles he has driven (y) is between 15 and 60.
B. When the number of minutes he’s driven (x) is 40, the miles he has driven (y) is between 30 and 40.
C. When the number of miles he’s driven (y) is 24, the time he has driven (x) is between 24 and 32.
D. When the number of miles he’s driven (y) is 36, the time he has driven (x) is between 27 and 36.
2. Graph the solution set to 2x  7  4x  13 on the number line.
3. Graph the solution set to 0  2x  6  10 on the number line below.
10
4. Giuseppe correctly graphed an inequality on the number line as shown below.
The inequality Giuseppe graphed was in the form -10 < _____?____ < 6.
What is an expression that can be put in place of the question mark so that the inequality would have the
same solution set as shown on the graph?
11
E. Polynomials
1. A Halloween attraction charges $52 for each day pass and $95 for each night pass. Last
October, 86 day passes were sold and 1,245 night passes were sold. What is the closest estimate
of the total amount of money paid for the passes last October?
A. $120,000
B. $130,000
C. $140,000
D. $150,000
2. When the expression x 4  x 2  12 is factored completely, which is one of its factors?
A.
B.
C.
D.
x2  4
x2  6
x2  2
x2
3. Simplify
2 x3  4 x 2  16 x
, x  0, 4, 5
2 x3  18 x 2  40 x
2 2 2
x  x
9
5
2
2
B. x 3  x 2  x
9
5
 x  4  x  2 
C.
 x  5  x  4 
A.
D.
x2
x5
12
4. Shawn creates a rectangular garden with a width that is 2 meters shorter than its length, as
shown below.
x-2
x
A. Write a polynomial expression, in simplified form, that represents the area of the garden.
B. Shawn adds a fence 3 feet from the edges of the garden. Write a polynomial expression, in
simplified form, that represents the total area enclosed by the fence.
C. Shawn is unhappy with his fence, so he decides to put a fence with a different distance from
the garden around the garden. The total area of the new fence and garden is x 2  6 x  8 .
Determine the new distance. Show all work. Explain why you did each step.
13
5. Which expression has the same value as  2g22  ?
5
A. 210
B. 2 5
C. 23
D. 2 4
6. Simplify:
A.
1
y
B.
1
y
C.
1
y  2y
D.
1
y  2y
2
1

y  2y y  2
2
2
2
7. Simplify:
A.
1
7m
B.
m7
m2
C.
m7
m2
D.
m7
m7
m2  49
m2  5m  14
14
F. Radical Practice
1. For what value of x should the expression be further simplified?
5x
A.
B.
C.
D.
x2
x  10
x  11
x  13
2. For what value of x should the expression be further simplified?
34x
A.
B.
C.
D.
x5
x7
x  13
x  17
3. Find the least common multiple (LCM) for the two polynomials?
300ab 2 c
500a 2bc 3
A.
B.
C.
D.
E.
100abc
100a 2b 2 c
100a 3b3c 4
1500abc
1500a 2b 2 c3
4. Find the least common multiple (LCM) for the two polynomials?
108xy 2
27xyz
A.
B.
C.
D.
E.
27xy
108xyz
108xy 2 z
2916xyz
2916x 2 y 3 z
15
5. Which value of x makes 5 7x equivalent to 15 21 ?
A. x  3
B. x  9
C. x  27
D. x  225
6. Which value of x makes 3 38x equivalent to 6 19 ?
1
A. x 
2
B. x  2
C. x  3
D. x  6

7. Simplify 3 3 27

1
A. 243 3
B. 54 3
C.
3
3
D.
3
9

8. Simplify 4 2 8
A.
B.
C.
1

8
8
8
2 2
4 2
2
D. 2 2
16
G. Linear Equations
You are driving home from the football stadium. You keep track of the remaining gasoline in
your car’s tank. The equation shown below can be used to find the gallons of gasoline remaining
(g) gas based on your distance (d) from home in miles.
g  15 
1
d
15
A. Complete the data chart using the equation.
Distance (d)
Gallons of
Gasoline
Remaining (g)
24
27
30
B. Why is the slope of the equation (in part B) negative?
17
2. The amount charged for each large pizza (p) is based on the cost of a plain pizza plus an
additional charge for each topping (t). The following equation models this relationship:
p  7  0.75t
What does the number 0.75 represent in the equation?
A. Number of toppings
B. Cost of a plain pizza (no toppings)
C. Additional cost for each topping
D. Cost of a pizza with one topping
3. A linear equation is graphed below.
Which equation describes the graph?
3
A. y   x  1
5
B. y 
3
x 1
5
3
C. y   x  1.5
5
5
D. y   x  1
3
18
4. Sally and her friends started a lemonade stand. Sally’s mom provides the start-up funding.
The kids earned the rest of the money from selling lemonade.
Cups of
Lemonade Sold
(x)
Total Money
Collected
(y)
10
$22.00
15
$24.50
20
$27.00
25
$29.50
A. Write a linear equation, in slope-intercept form, to represent the total amount of money from
selling lemonade (y) based on the number of cups (x).
B. How much did each cup of lemonade cost? What part of the equations tells us this
information?
C. How much money did Sally’s mom provide for start-up costs? What part of the equation tells
us this information?
19
5. Which equation is equivalent to 5  2  2 x  1  17 ?
A. 6x  1  17
B. 6x  3  17
C. 4x  6  17
D. 4x  3  17
6. What is the y-intercept of the graph 6 x  3 y  24 ?
A. 8
B. 3
C. 2
D. 24
20
H. Miscellaneous Topics
1. Which graph is symmetric with respect to the y-axis?
A.
B.
C.
D.
2. In the accompanying graph, if point P has coordinates (a, b), which point has coordinates
(-b, a)?
A. Point A
B. Point B
C. Point C
D. Point D
21
3. In the coordinate plane, the points (2, 2) and (2, 12) are the endpoints of a diameter of a circle.
What is the length of the radius of the circle?
A. 5
B. 6
C. 7
D. 10
4. A wheel has a radius of five feet. What is the minimum number of complete revolutions that
the wheel must make to roll at least 1,000 feet?
A. 31
B. 32
C. 33
D. 79
5. Delroy’s sailboat has two sails that are similar triangles. The larger sail has sides of 10 feet,
24 feet, and 26 feet. If the shortest side of the smaller sail measures 6 feet, what is the perimeter
of the smaller sail?
A. 15 ft
B. 36 ft
C. 60 ft
D. 100 ft
6. What is the image of (x, y) after a translation of 3 units right and 7 units down?
A.
 x  3, y  7 
B.
 x  3, y  7 
C.
 x  3, y  7 
D.
 x  3, y  7 
22
7. Don placed a ladder against the side of his house as shown in the diagram below
Which equation could be used to find the distance, x, from the foot of the ladder to the base of
the house?
A. x  20 19.5
B. x  202  19.52
C. x  202  19.52
D. x  202  19.52
23
Last summer Ben purchased materials to build model airplanes and then sold the finished
models. He sold each model for the same amount of money. The table below shows the
relationship between the number of model airplanes sold and the running total of Ben’s profit.
Ben’s Model Airplane Sales
Model
Airplanes
Sold
12
15
20
22
Total Profit
$68
$140
$260
$308
A. Write a linear equation, in slope-intercept form, to represent the amount of Ben’s total profit
(y) based on the number of model airplanes (x) he sold.
y = ______________________________
B. How much did Ben spend on his model-building materials?
$ ______________________________
Continued on next page
24
Continued. Please refer to the previous page for task explanation.
C. What is the fewest number of model airplanes Ben needed to sell in order to make a
profit?
fewest number: ______________________________
D. What is a reasonable value in the range that would be a negative number?
25
I. Linear Functions, Domain, and Range
1. The graph of a function is shown below:
Which value is not in the range?
A. -3
B. -1
C. 2
D. 5
2. A cleaning service charges an hourly fee plus a fixed starting price. The cost (C) in dollars to
clean your house for a number of hours (h) is described by the function: C = 10h + 50. Which
statement is true?
A. The cost to clean your house for 2 hours is $60.
B. The cost to clean your house for 6 hours is $100.
C. Each hour costs $10 and the fixed starting price is $50.
D. Each hour costs $50 and the fixed starting price is $10.
26
3. Which graph does not show y as a function of x?
A.
B.
C.
D.
27
4. The table shows the amount of water y in a tank after x minutes have elapsed.
x (minutes)
y (gallons)
2
80
4
60
6
40
8
20
A. Write an equation in slope intercept form to find the amount of water (y) in gallons after a given
number of minutes (x).
B. Is water entering or leaving the tank?
C. How much water is in the tank after 3 minutes?
D. Find the slope and describe its meaning.
E. Find the x-intercept and y-intercept. What do these quantities describe in relation to the water
in the tank?
28
J. Probability and Statistics
1. Which of the following descriptions best categorizes the histogram?
y
4
2
2
4
x
A. skewed
B. uniform
C. symmetric
2. The two box-and-whisker plots below show the scores on a math exam for two classes. What do the
interquartile ranges tell you about the two classes?
60
70
80
90
Class A
60
70
80
90
Class B
A. Class A has more consistent scores
B. Class B has more consistent scores
C. Overall class A performed better than class B
D. Overall class B performed better than class A
29
3. Estimate each value using the box-and-whiskers plot.
Minimum:
_______
Q1:
_______
Median:
_______
Q3:
_______
Maximum:
_______
Interquartile Range: _______
4. What is the probability of rolling at least one 6 on a pair of dice?
11
36
1
B.
3
1
C.
6
1
D.
15
1
E.
16
A.
5. Find the mode and median in the following dot-plot:
Median _________
Mode ___________
30
K. Data Analysis
1. Which regression equation best fits the data shown?
A. y 
1
x5
2
B. y 
1
x  10
2
C. y 
5
x  10
2
D. y 
5
x  15
2
2. The relationship shown is linear. Predict the number of calculators that were sold in 2012.
Year
1995
1996
1997
1998
A.
B.
C.
D.
Number of Calculators Sold
(in millions)
432
446
460
474
642
656
670
684
31
Use the Box and Whisker plot to answer questions 3 and 4.
3. What is the median of the data shown?
A.
B.
C.
D.
20
48
51
58
4. Using the box and whisker, what is the best estimate of the percentage of the data less than
42?
A.
B.
C.
D.
10%
25%
33%
50%
5. What is the range of data shown in the stem and leaf plot?
A.
B.
C.
D.
20
36
45
58
32