Name Per Basic Skills Keystone Exams Practice Test 1.) A theme park charges $52 for a day pass and $110 for a week pass. Last month, 4,432 day passes and 979 week passes were sold. Which of the following is the closest estimate of the total amount of money paid for the day and week passes for last month? $300,000 $400,000 $500,000 $600,000 2.) Open Response: Evaluate the expression to the right. Make sure to show your steps on a separate piece of paper. You may use a calculator. Consider only positive roots. Place your final answer here: 3.) One of the steps Jamie used to solve an equation is shown to the right. Which of the descriptions below correctly describes both the procedure Jamie used in this step and the property that justifies this procedure? Jamie added and to eliminate the parentheses. This procedure is justified by the associative property. Jamie added and to eliminate the parentheses. This procedure is justified by the distributive property. Jamie multiplied and by to eliminate the parentheses. This procedure is justified by the associative property. Jamie multiplied and by to eliminate the parentheses. This procedure is justified by the distributive property. 4.) Finish solving the equation in the previous problem for Jamie. Show your steps on a separate piece of paper and make sure to check your work. Place your final answer here: 5.) Jenny has a job that pays her $8 per hour plus tips ( ). Jenny worked for 4 hours on Monday and made $65 in all. Which equation could be used to find, the amount Jenny made in tips? ( )
6.) Francisco purchased hot dogs and 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: The ordered pair ( ) is a solution of the equation. What does the solution ( ) represent? Hamburgers cost 2 times as much as hot dogs. Francisco purchased 2 hot dogs and 1 hamburger. Hot dogs cost $2 each and hamburgers cost $1 each. Francisco spent $2 on hot dogs and $1 on hamburgers. 7.) A pizza restaurant charges for pizzas and adds a delivery fee. The cost ( ), in dollars, to have any number of pizzas ( ) delivered to a home is described by the equation. Which of the statements below is true? The cost of 8 pizzas is $11. The cost of 3 pizzas is $14. Each pizza costs $8 and the delivery fee is $3. Each pizza costs $3 and the delivery fee is $8. 8.) The amount of gasoline remaining in a certain car can be described by the equation, where is the amount of gasoline remaining (in gallons) and distance driven since the tank was full. is the a.) Use the equation described above to fill in the missing values in the table to the right. b.) How many miles can this car travel on a single gallon of fuel? c.) How many miles can this car travel on a single tank of fuel? d.) Graph the relationship between and using the graph provided to the right: e.) On a separate piece of paper, explain why the slope drawn in this graph must be negative.
9.) Jeff s restaurant sells hamburgers. The amount charged for a hamburger ( ) is based on the cost for a plain hamburger plus an additional charge for each topping ( ), as shown in the equation below: What does the number 0.60 represent in this equation? the number of toppings the additional cost for each topping the cost of a plain hamburger the cost of a hamburger with one topping 10.) Ahava is traveling on a train. The train is going at a constant speed of 80 miles per hour. How many hours will it take for the train to travel 1,120 miles? 14 hrs. 90 hrs. 80 hrs. 17 hrs. 11.) Before deciding on the train, Ahava also considered taking an airplane. The airplane can travel the same 1,120 miles in 12 hours less time than the train. What is the speed of the airplane in miles per hour (mph)? 560 mph 93 mph 373 mph 107 mph Linear Equations 12.) Open Response: Nolan has $15.00, and he earns $6.00 an hour babysitting. An equation that can be used to determine how much money in dollars ( ) Nolan has after any number of hours of babysitting ( ) is a.) After how many hours of babysitting will Nolan have $51.00? b.) How much money will Nolan have after babysitting for ten hours? 13.) The diagram to the right shows 5 identical bowls stacked one inside the other. The height of 1 bowl is 2 inches. The height of a stack of 5 bowls is 5 inches. Which equation below would give you the height of a stack of bowls ( ), given any number of these bowls ( )? ( ) ( ) ( ) ( )
14.) Open Response: Use the equation you found in the previous problem to answer the following: a.) How tall would a stack of 10 of these bowls be? b.) How many bowls would a stack 20 inches tall contain? 15.) Tim s scores the first five times he played a video game are listed below: Tim s scores follow a pattern. Which equation can be used to determine his score this video game times? after he has played ( ) 16.) The table to the right shows values of has a function of. Which linear equation best describes the relationship between and? 17.) A juice machine dispenses the same amount of juice into a cup each time the machine is used. The equation below describes the relationship between the number of cups ( ) into which juice is dispensed and the gallons of juice ( ) remaining in the machine: Use this equation to answer the following questions: a.) How many gallons of juice are in the machine when it is full? b.) What is the maximum number of cups this machine can fill before being reloaded? 18.) Sally believes the more time she spends in the grocery store, the more money she spends. Her recent purchases are recorded in the table to the right. Which linear equation best fits this trend?
Inequalities 19.) 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 can be used to determine the number of new baseballs ( ) that the team can purchase. Which statement about the number of new baseballs that can be purchased is true? The team can purchase 204 new baseballs. The minimum number of new baseballs that can be purchased is 185. The maximum number of new baseballs that can be purchased is 185. The team can purchase 185 new baseballs, but this is neither the maximum nor the minimum. 20.) Graph the solution set to the inequality on the number line below. 21.) What is the solution to the compound inequality? 22.) Graph the solution you found in the previous problem on the number line provided below: 23.) The solution set to an inequality is graphed on the number line below. The graph shows the solution set of which inequality?
24.) David correctly graphed an inequality as shown below: The inequality David graphed was originally in the form the correct expression.. Fill in the blank with Rates of Change 25.) Open Response: Hector s family is on a car trip. When they are 84 miles from home, Hector begins recording their distance driven ( ), in miles, after hours in the table to the right: a.) Use this table to write an equation that describes the distance driven in terms of : b.) Assuming this pattern continues, how far will Hector s family have driven after five hours? 26.) Open Response: 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 to the right shows the relationship between the number of model airplanes sold and the running total of Ben s profit. a.) Write a linear equation, in slope-intercept form, to represent the amount of Ben s total profit ( ) based on the number of model airplanes ( ) he sold: Use the equation you found in part a to answer the following: b.) How much did Ben spend on his model-building materials? $ c.) What is the fewest number of planes Ben would have to sell in order to make a profit?
27.) A ball rolls down a ramp with a slope of. At one point the ball is 10 feet high, and at another point the ball is 4 feet high, as shown in the diagram to the right. What is the horizontal distance ( ), in feet, the ball traveled as it rolled down the ramp from 10 feet high to 4 feet high? 6 9 14 15 Graphing 28.) The graph of a linear equation is shown to the right. Which of the equations below describes this graph? 29.) Georgia is purchasing treats for her classmates. Georgia can spend exactly $10.00 to purchase 25 fruit bars, each equal in price. Georgia can also spend exactly $10.00 to purchase 40 granola bars, each equal in price. Use this information to complete the following exercises: a.) Write an equation in standard form which can be used to find all combinations of fruit bars ( ) and granola bars ( ) that will cost exactly $10.00 : b.) Put this equation in slope-intercept form: c.) Graph the equation from part b on the graph provided to the right. 30.) Open Response: Consider the graph you drew in the previous problem. Explain what the slope of the line means in the context of the word problem:.
31.) The graph below displays the carbon dioxide ( ), in metric tons, for each traveler on an airplane and each traveler on a train. Use the data from this graph to complete the following exercises: a.) Write an equation that describes the metric tons of CO2 produced ( in terms of miles traveled ( ): ) by a traveler on an airplane b.) A traveller traveled to her destination on a train and returned home on an airplane. Her total carbon footprint for the trip was 0.42 metric tons of CO2 produced. How far, to the nearest mile, is her destination from her home? Data & Probability 32.) The scatter plot to the right shows the cost ( ) of ground shipping packages from Harrisburg, PA, to Minneapolis, MN, based on the package weight ( ). Which equation best describes the line of best fit? 33.) Use the line of best fit from the previous problem to predict how much it might cost you to ship a 50 lb. package from Harrisburg to Minneapolis:
34.) The daily high temperatures, in degrees Fahrenheit ( F), of a town are recorded for one year. The median high temperature is 62 F. The interquartile range of high temperatures is 32. Which is most likely to be true? Approximately 25% of the days had a high temperature less than 30 F. Approximately 25% of the days had a high temperature greater than 62 F. Approximately 50% of the days had a high temperature greater than 62 F. Approximately 75% of the days had a high temperature less than 94 F. 35.) Vy asked 200 students to select their favorite sport and then recorded the results in the bar graph below: Vy will ask another 80 students to select their favorite sport. Based on the information in the bar graph, how many more students of the next 80 asked will select basketball rather than football as their favorite sport? 10 20 25 30 36.) The points scored by a football team are shown in the stem-and-leaf plot to the right. What was the median number of points scored by this team? 24 27 28 32
37.) John recorded the weight of his dog at different ages as shown in the chart to the right. Based on the line of best fit, what is Spot s weight most likely to be at 18 months? 27 lbs. 32 lbs. 36 lbs. 50 lbs. 38.) A number cube with sides labeled 1 through 6 is rolled two times, and the sum of the numbers that end face up is calculated. What is the probability that the sum of the numbers is 3? 39.) The box-and-whisker plot shown below represents the grades on Mr. Ali s history test: a.) What is the range of scores for this history test? b.) What is the best estimate for the percent of students scoring greater than 92 on the test? % c.) Mr. Ali wanted more than half of the students to score 75 or greater on the test. Explain how you know that more than half of the students did not score greater than 75:. 40.) Open response: The table to the right shows the winning times at the Steubenville Fun-Run Charity Race in the past five years. Unfortunately, the winning time for 2008 has been lost! However, before it was lost, it was recorded that the mean winning time over this period was 53.4 min. What was the winning time in 2008? min. Year Winning Time 2007 58.1 min 2008 2009 52.6 min 2010 57.3 min 2011 50.4 min
41.) The weight, in pounds, of each wrestler on the high school wrestling team at the beginning of the season is listed below. a.) What is the mean weight of the wrestlers? b.) What is the median weight of the wrestlers? c.) Two more wrestlers join the team during the season. The addition of these wrestlers has no effect on the mean weight of the wrestlers, but the median weight of the wrestlers increases 3 pounds. Determine the weights of the two new wrestlers: lbs. and lbs. 42.) Michael s test scores are shown in the chart to the right. Use the data in the chart to complete the following exercises: a.) Which of the following would be a good estimate for his mean test score? 72 83 92 66 b.) Assuming the tests were numbered in the order in which they were given, what kind of correlation is shown in the graph? positive negative none observed Functions 43.) The graph to the right displays the amount of money Alex and Pat will each have saved after their hours of babysitting. For what domain of will Alex have more money saved than Pat? 44.) The ordered pairs in the sets shown below are of the form ( ). In which set of ordered pairs is a function of? *( ) ( ) ( )+ *( ) ( ) ( )+ *( ) ( ) ( ) + *( ) ( ) ( )+
45.) Which graph below shows as a function of? 46.) The graph of a piecewise function is shown to the right. Which of the following is not in the range of the function? 0 3 4 5 Properties of Powers 47.) No calculators: The results of an experiment were listed in several numerical forms as shown to the right. Below, order the numbers listed from least to greatest:,,,,
48.) Which of the following inequalities is true for all real values of? ( ) ( ) 49.) For what values of is a true statement? For all real It is never true 50.) What is the least common multiple (LCM) of the monomials and? 51.) No calculators: Simplify the expression ( ). Consider only positive roots. 52.) The polynomial expression ( )( ) ( ) is simplified. The result was: What is the value of? 53.) Simplify the polynomial expression shown to the right. Assume that :
54.) In the previous problem, why did you have to assume that? Because at these values the denominator evaluates to. Because at these values the numerator evaluates to. Because is not defined for non-positive values of. Because is not defined for non-positive values of. 55.) When the expression is factored completely, which is one of its factors? ( ) ( ) ( ) ( ) Applications of Powers 56.) Consider the expression shown to the right. Which value of makes this expression equivalent to? 5 25 50 100 57.) An expression is shown to the right. For which value of should the expression be further simplified? 58.) One of the steps shown to the right is incorrect. Below, indicate the incorrect step and re-write it so that it is correct. step : 59.) Using the corrected step, evaluate:. Show all your work on a separate piece of paper and express your answer in simplified root form. 60.) If, what is the quotient when the operations shown to the right is performed:
61.) Open Response: Keng creates a paining on a rectangular canvas with a width that is four inches longer than the height, as shown in the diagram to the right: a.) Write a polynomial expression, in simplified form, that represents the area of the canvas: b.) Now assume that Keng adds a 3-inch-wide frame around all sides of his canvas. Write a polynomial expression, in simplified form, that represents the total area of the canvas and the frame : c.) Keng is unhappy with his 3-inch-wide frame, so he decides to put a frame with a different width around his canvas. The total area of the canvas and the new frame is given by the polynomial, where represents the height of the canvas. On a separate piece of paper, determine the width of the new frame. Show all your work and explain why you did each step. Place your final answer here: Systems 62.) Anna burned 15 calories per minute running for minutes and 10 calories per minute hiking for minutes. She spent a total of 60 minutes running and hiking and burned 700 calories. The system of equations shown below can be used to determine how much time Anna spent on each exercise. What is the value of, the minutes Anna spent running? 10 20 30 40
63.) Open Response: Nolan has $15.00, and he earns $6.00 an hour babysitting. Claire has $9.00. She makes $8.00 an hour babysitting. Use the system of linear equations below to find the number of hours of babysitting after which Nolan and Claire will have the same amount of money: hours: 64.) Samantha and Maria purchased flowers. Samantha purchased 5 roses for dollars each and 4 daisies for dollars each and spent $32 on the flowers. Maria purchased 1 rose for dollars and 6 daisies for dollars each and spent $22. The system of equations shown below represents this situation. Which of these statement is true? A rose costs $1 more than a daisy. Samantha spent $4 on each daisy. Samantha spent more on daisies than she did on roses. Samantha spent over 4 times as much on daisies as she did on roses. 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 to the right, where is the amount of tip and is the cost of dinner. Which of the following is a true statement? When the cost of the dinner ( ) is $10, the amount of the tip ( ) must be between $2 and $8. When the cost of the dinner ( ) is $15, the amount of the tip ( ) must be between $1.20 and $3.00 When the amount of the tip ( ) is $3, the cost of dinner ( ) must be between $11 and $23. When the amount of the tip ( ) is $2.40, the cost of dinner ( ) must be between $3 and $6.
66.) An apple farm owner is deciding how to use each day s harvest. She can use the harvest to produce apple juice or apple butter. The information she uses to make the decision is listed below. A bushel of apples will make 16 quarts of apple juice. A bushel of apples will make 20 pints of apple butter. The apple farm can produce no more than 180 pints of apple butter each day. The apple farm harvests no more than 15 bushels of apples each day. The information given can be modeled with a system of inequalities. When is the number of quarts of apple juice and is number of pints of apple butter, two of the inequalities that model the situation are and a.) Write 2 more inequalities to complete the system of inequalities modeling the information. inequalities:, b.) Graph the solution set of the inequalities from part A on the graph to the right. Shade the area that represents the solution set. c.) The apple farm makes a profit of $2.25 on each pint of apple butter and $2.50 on each quart of apple juice. On a separate piece of paper, explain how you can be certain the maximum profit will be realized when the apple farm produces 96 quarts of apple juice and 180 pints of apple butter. 67.) Open Response: The solution set to a system of inequalities is shown to the right. Write a system of 2 linear inequalities in slope-intercept form which would have the solution set shown in the graph:
68.) Consider the system shown to the right. Which of the graphs below describes the solution set to this system?
Keystone Exams Practice Test Answer Key 1.) A 2.) 17 3.) D 4.) 5.) D 6.) B 7.) C 8a.) 12a.) 6 hours 12b.) $75.00 13.) C 14a.) 8.75 in. 14b.) 25 bowls 15.) A 16.) B 17a.) 15 gallons 17b.) 180 cups 18.) B 19.) D 8b.) 20 miles 8c.) 320 miles 8d.) 20.) 21.) B 22.) 23.) C 24.) ( ) or 25a.) 25b.) 394 miles 26a.) 8e.) Because as the distance in miles driven increases, the amount of gasoline remaining must decrease. 9.) C 10.) A 11.) A 26b.) $220.00 26c.) 10 model planes 27.) B 28.) D 29a.) 29b.)
29c.) 42b.) A 43.) B 44.) C 45.) B 46.) B 47.) 30.) For every five additional fruit bars George buys, she must give up eight granola bars. [Other answers possible.] 48.) C 49.) C 31a.) 31b.) 1,167 miles 32.) D 33.) $40.61 34.) C 35.) D 36.) A 37.) C 38.) A 39a.) 40 39b.) 25% or 50.) D 51.) A 52.) C 53.) D 54.) A 55.) C 56.) B 57.) C 58.) Step 1: ( ) 59.) 60.) B 39c.) The median is 68, so half of all scores are less than or equal to 68. Therefore, more than half cannot be greater than 75. 40.) 48.6 min 41a.) 153 lbs. 41b.) 146 lbs. 41c.) 148 and 158 lbs. 42a.) B 61a.) 61b.) 61c.) 1 in. 62.) B 63.) 3 hours 64.) A 65.) B
66a.) 66b.) 66c.) The vertices of the feasible region are ( ), ( ) and ( ). The profits at these vertices are, respectively,, and. Therefore the maximum profit is at ( ). * = The can be found by solving the equation. 67.) 68.) A