Algebra 1 Keystone Exam Test Design the Exam Is Divided Into Two Modules

Name ______

Algebra 1 Keystone Exam Test Design – The exam is divided into two modules:

Module 1 / Module 2
Operations and Linear Equations and Inequalities / Linear Functions and
Data Organization

The exam has two types of questions:

Multiple Choice Questions / Multiple Choice Point Values / Constructed Response Questions / Constructed Response Point Values
Number of Operational Questions / 18 / 18 / 3 / 12
(4 points each)
Number of Field Test Questions / 5 / 0 / 1 / 0
Total PER MODULE / 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

A. Word Problems Using Systems of Equations

1. Owners of a coffee shop purchased 60 pounds of Guatemalan coffee beans and 90pounds of Nicaraguan coffee beans. The total purchase price was $180. The next weekthey 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 poundfor 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 willbe charged $1.00 to connect and $0.50 per minute. If he places a collect call with theoperator he will be charged $3.00 to connect and $0.25 per minute. In how many minuteswill the phone card and the collect call cost the same?

A. 5 min

B. 5 1/3 min

C. 8 min

D. 16 min

3. A boat takes 6.5 hours to make a 70-mile trip upstream and 5 hours on the 70-milereturn trip. Let v be the speed of the boat in still water, and c be the speed of thecurrent. 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 thedownstream part, relating boat speed, distance, and time.

B. Solve the equations in part A for the speed of the current. Round your answer to thenearest 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.

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 barand will be sold for $3.25. The students need to raise at least $200 to cover their tripcosts.

A. Write an inequality that relates the number of candles c and the number of bars ofsoap s to the needed income.

B. The wholesaler can supply no more than 80 bars of soap and no more than 140candles. Graph the inequality from part Aand these constraints, using number ofcandles for the vertical axis.

C. What does the shaded area of your graph represent?

The Marathon

Bethany and Calista are sisters who both run marathons. Today theyare racing against each other in the same marathon. Because thereare thousands of people racing, Bethany and Calista are assignedrandom starting positions. Bethany starts at the starting line, whileCalista starts a half-mile behind the starting line.Calista runs one mile in 12 minutes, while Bethany runs one mile in15 minutes. So, although Calista starts behind Bethany, she hopes topass her sister at some point during the race.Let x represent the amount of time in hours that Bethany or Calistarun and let y represent distance after the starting line in miles.

1. The rate or speed at which someone runs is frequently stated inmiles 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 equationsthat 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 sisterscatch up to each other. ______

D. who is in the lead after 2 hours if each sisterkeeps running at a steady pace. ______

5. A marathon is 26.2 miles. Which sister do youthink will cross the finish line first? Explain. ______

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 hoursof tutoring after which Jen and Robert will have the same amount of money.

2. The height of one cup is 5 inches. The height of 4 stacked cups is 12 inches.

A. Write an equation using x and y to find theheight of a stack based on any number ofcups.

B. Describe what the x and the y variablesrepresent.

C. What is the height in inches of a stack of 12 cups?

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 $125and 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. Newpocket protectors cost $5 each. The inequality can be used to determine the numberof new pocket protectors (p) that the club can purchase. Which statement about the number of pocketprotectors 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 orthe minimum.

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

D. Systems of Inequalities

1. Evan always drives between 45 and 60 miles per hour on his commute. The distance he travelscan be represented in the system of inequalities below, where x is the number of minutes and yis the number of miles.

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 on the number line.

3. Graph the solution set to on the number line below.

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?

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 is factored completely, which is one of its factors?

3. Simplify

4. Shawn creates a rectangular garden with a width that is 2 meters shorter than its length, as shown below.

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 . Determine the new distance. Show all work. Explain why you did each step.

5. Which expression has the same value as ?

6. Simplify:

7. Simplify:

F. Radical Practice

1. For what value of x should the expression be further simplified?

2. For what value of x should the expression be further simplified?

3. Find the least common multiple (LCM) for the two polynomials?

4. Find the least common multiple (LCM) for the two polynomials?

5. Which value of x makes equivalent to?

6. Which value of x makes equivalent to ?

7. Simplify

8. Simplify

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.

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?

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:

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?

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?

5. Which equation is equivalent to ?

6. What is the y-intercept of the graph ?

H. Miscellaneous Topics

1. Which graph is symmetric with respect to the y-axis?

2. In the accompanying graph, if point P has coordinates (a, b), which point has coordinates

(-b, a)?

Point A
Point B
Point C
Point D

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?

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?

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?

15 ft
36 ft
60 ft
100 ft

6. What is the image of (x, y) after a translation of 3 units right and 7 units down?

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?

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 / Total Profit
12 / $68
15 / $140
20 / $260
22 / $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

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?

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.

3. Which graph does not show y as a function of x?

A.B.

C.D.

4. The table shows the amount of water y in a tank after x minutes have elapsed.

x (minutes) / 2 / 4 / 6 / 8
y (gallons) / 80 / 60 / 40 / 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?

J. Probability and Statistics

1. Which of the following descriptions best categorizes the histogram?

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?

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

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?

5. Find the mode and median in the following dot-plot:

Median ______

Mode ______

K. Data Analysis

1. Which regression equation best fits the data shown?

2. The relationship shown is linear. Predict the number of calculators that were sold in 2012.

Year / Number of Calculators Sold
(in millions)
1995 / 432
1996 / 446
1997 / 460
1998 / 474

Use the Box and Whisker plot to answer questions 3 and 4.

3. What is the median of the data shown?

4. Using the box and whisker, what is the best estimate of the percentage of the data less than 42?

5. What is the range of data shown in the stem and leaf plot?