Pre-Algebra Semester Exam Review 2016

Transcription

1 Pre-Algebra Semester Exam Review 016 Multiple Choice Identif the choice that best completes the statement or answers the question. 1. What kind of number is? rational not a real number irrational natural number. What kind of number is 0? rational not a real number irrational negative number 3. Which of these expressions is true?. A square box lid has an area of 0 square inches. Which is the best estimate of the length of one side? 6.0 inches 6.5 inches 6.3 inches 7.0 inches 5. Estimate to the nearest whole number and then to the nearest tenth. 8, 8. 9, 9.3 8, 8.3 9, What is written in scientific notation? 7. What is written in scientific notation? 8. What is written in standard notation? 9. Which of these expressions is true?

2 10. e is an irrational number approximatel equal to.718. Between which pair of square roots does e fall? and and and and 11. The graph shows the relationship between the number of hours h Bree has been hiking and the total distance d she has traveled, in kilometers. d h Which statement is true? The slope of the line is 8. The slope of the line is 1. To find the slope of the line, ou could divide the total number of hours hiked b the total distance. To find the slope of the line, ou could multipl the total number of hours hiked b the total distance. 1. Carlita goes jogging, and her GPS collects the data for her distance over time. What would the rate of change for that data represent? Carlita s distance from home Carlita s starting point Carlita s distance over time, or speed Carlita s time since she left home 13. What equation could be written for this table? 1. Which is the rule for the function table?

3 15. Lamar starts his own painting business. He pas for some supplies to begin, and then charges a fixed amount per room. The graph shows a linear function that models Lamar s profit per room x What does the initial value represent? The number of rooms he paints The amount he charges per room The amount he spends in supplies The amount of profit he makes per room 16. Vincent s savings over several weeks are shown in the table. If a linear function models Vincent s savings over time, how much mone did he initiall have? Time (weeks) Savings (dollars) The graph shows the cost per hour of renting a power tool Cost x Hours Which of the following best describes the relationship between cost and the number of hours? linear and proportional relationship non-linear relationship linear, non-propotional relationship

4 18. Which graph is NOT that of a function? 19. Which of these functions is not a linear function? 1. Does the graph represent as a function of? Explain wh or wh not. 6 (, ) ( 1, 1) (1, 1) (, ) 6 6 x 6 Yes, because both and have the same -coordinate. Yes, because for each -coordinate, there is exactl one -coordinate. No, because both and have the same -coordinate. No, because for each -coordinate, there is exactl one -coordinate.

5 0. Carla is given the graph of a function x 3 5 She transforms the function several times. For one transformation, the image is not a function. Which is an image that is not a function? x x x x 3 5

6 . Use the graph to explain wh is or is not a function of. 6 (3, 3) (, ) 6 6 x 6 (, ) (3, 3) is a function of because both and have the same -coordinate. is a function of because for each -coordinate, there is exactl one -coordinate. is not a function of because both and have the same -coordinate. is not a function of because for each -coordinate, there is exactl one -coordinate. 3. What is a function? A function assigns to each input exactl one output. A function assigns to each input at least one output. A function assigns outputs to inputs. A function assigns to each input more than one output.. Which equation is graphed?

7 5. The graph shows the relationship between a candle s height h, in centimeters, and time t, in hours, as the candle burns. What function models this relationship? Height (cm) 0 h t Time (hours) 6. A bathtub filled with 0 gallons of water drains at an average rate of 3 gallons per minute. What is the rate of change and initial value of the linear function that models the amount of water in the bathtub after it starts draining? The rate of change is 0 gallons per minute, and the initial value is 3 gallons. The rate of change is 3 gallons per minute, and the initial value is 0 gallons. The rate of change is gallons per minute, and the initial value is 0 gallons. The rate of change is gallons per minute, and the initial value is 3 gallons. 7. Lnn is walking from her house to the grocer store. The table shows the distance she has left to walk. What is the rate of change for the linear function represented b the table? Time (minutes) Distance (blocks) blocks per minute block per minute block per minute blocks per minute 8. Speedeez Go Carts charges $10 plus $.50 per lap. Which best describes the relationship between total cost and the number of laps? linear and proportional relationship non-linear relationship linear, non-propotional relationship 9. Which points are on the graph of a linear function?,, and,, and

8 ,, and,, and 30. Carlos records a proof of the Pthagorean Theorem. What is the area of the dark gra figure in Step 3? 31. What is the value of? The distance between two points is. One of the points is. Which could be the other point? Explain our answer. because because because. because

9 33. What is the distance between points and shown on the coordinate plane? Round our answer to the nearest unit. 9 B x 3 A Miles is plaing catch with his frien He throws the baseball from point to point shown on the coordinate plane, where each unit represents 1 ar How far does Miles throw the baseball? Round our answer to the nearest ar 6 B 6 6 x A 6 ards 6 ards 7 ards 8 ards 35. Your middle school is having a carnival. Admission into the carnival is $8, and each game inside the carnival costs $0.50. Which of the following inequalities represents the possible number of games that can be plaed with $0? 36. Solve.

10 37. Compan A rents cop machines for $300 a month plus $0.05 per cop. Compan B charges $600 a month plus $0.01 per cop. For which number of copies do the two companies charge the same amount? 5000 copies 7000 copies 6000 copies 7500 copies 38. How man solutions does the equation Infinitel man solutions One solution No solutions The number of solutions cannot be determine have? 39. What is a possible result of simplifing the equation? 0. In the triangle, and. What is? Which set of angles does NOT form a triangle?,, and,, and,, and,, and. and are similar triangles. If and, what is? 3. Solve the sstem of equations.. Franco is solving a sstem of linear equations algebraicall. He find that there are an infinite number of solutions. Which is a possible step in his solution?

11 5. Giovani solves a sstem of equations algebraicall. He concludes that the lines are parallel. Which could be the final line of his solution? 6. Cara graphs a sstem of linear equations and identifies a point as the solution. Where is the point located? the origin the x-intercept the -intercept the intersection of the two lines 7. Chloe, Tarina, and Lizette solved the sstem of equations shown. Chloe claims the solution is (3, 8). Tarina claims the solution is ( 6, 10). Lizette claims the solution is (1, 6). Which statement is true? Chloe s solution is correct. Lizette s solution is correct. Tarina s solution is correct. None of the solutions are correct. 8. What is the solution of the linear sstem? 9. How can ou tell if an ordered pair is a solution of a sstem of linear equations b examining the graphs of the equations? Neither line passes through the point represented b the ordered pair. Just one of the lines passes through the point represented b the ordered pair. Both lines pass through the point represented b the ordered pair. You cannot tell whether an ordered pair is a solution of a sstem of linear equations b examining the graphs of the equations. 50. What solution(s) does the sstem of equations have?. There are infinitel man solutions. The onl solution is. The onl solution is. There are no solutions.

12 51. Trud and Xander are saving mone from their newspaper route earnings. Their savings, in dollars, is related to the time, in weeks, after the start working. Trud s savings are given b the equation, and Xander s savings are given b the equation. What is the meaning of the solution of the sstem of equations? Trud and Xander both have $50 saved after 10 weeks of working on their newspaper routes. Trud and Xander both have $10 saved after 50 weeks of working on their newspaper routes. Trud and Xander both have $170 saved after weeks of working on their newspaper routes. Trud and Xander both have $130 saved after weeks of working on their newspaper routes. 5. Sklar is buing watermelon and pineapple for a fruit sala Watermelon costs $0.59 per pound, and pineapple costs $.9 per poun Sklar bus 7 pounds of fruit and spends $9.3. How much does Sklar spend just on pineapple? $.36 $3.00 $.00 $6.87 Numeric Response 1. The figure illustrates one wa to model the Pthagorean Theorem: On graph paper, ou can draw a right triangle with legs of 3 units and units, and then draw squares with these side lengths that share a side with the triangle. Then ou can draw a third square whose area is equal to the sum of the areas of the first two squares, and then cut it out and place one of its sides against the hpotenuse of the triangle to see that the length of the hpotenuse is 5 units. Suppose ou wanted to model the Pthagorean Theorem in this wa for a right triangle with legs of 5 units and 1 units. What value would ou use for the side length of the square that is placed against the hpotenuse?

13 . Find the unknown length. Round to the nearest tenth if necessar. 3. In the figure, if l and k are parallel lines, what is the value of in degrees? (The figure ma not be to scale.). In the figure, and. (The figure ma not be drawn to scale.) What is the measure of 5. The angle of a vehicle's turn is measured as shown. Use this information to draw a diagram that helps ou answer the question that follows. (Figure ma not be drawn to scale.) Kendell Road and Linden Road are parallel roads. Vida is traveling south on Kendell Road when she makes a 35 left turn, leaving Kendell Road and heading in a southeasterl direction towards Linden Roa When she reaches Linden Road she makes a right turn and travels south. What was the measure, in degrees, of the right turn?

14 6. What is the value of x? (The figure ma not be drawn to scale.) Short Answer 1. Identif the number as rational or irrational. Explain our reasoning.. is between two integers. Find the two integers. 3. is between two integers. Find the two integers.. A square kitchen floor has an area of 500 square feet. Estimate the length of one wall to the nearest tenth of a foot. 5. Approximate to the nearest whole number, to one decimal place, and to two decimal places. Show all work. 6. A bookstore orders a shipment of books. The books weigh 3. lb each. How much will the shipment of 100 books weigh? Write our answer in scientific notation. 7. A dog eats 8 cups of dog food in das and alwas eats at this rate. What is the unit rate in this situation? Graph the line that represents the relationship between dog food consumed, in cups, and time, in das. Dog food consumed (cups) 50 c t Time (das)

15 8. The equation represents the number p of points scored in relation to the number g of field goals made in tackle football. Graph the equation on the coordinate plane below and state the unit rate. Points p g Field goals 9. Find the slope of the line that passes through the points (5, ) and (3, 1). 10. Find the slope of the line that passes through the points and. 11. Find the point-slope form equation for the line that passes through the point and has a slope of. 1. The table shows a hot air balloon s height h, in feet, during a descent at various times t, in seconds. Use the table s first two ordered pairs to find the hot air balloon s rate of change. Is the rate of change constant? Explain. What was the hot air balloon s height at the time the descent began? Write h as a linear function of t. Time Height (feet) (seconds) Jillian and Sean are hiking on a mountain. Jillian s hike is modeled b the linear function, and Sean s hike is modeled b the linear function, where is the distance, in miles, from the base of the mountain and is the time, in hours, since the start of the hike. What is Jillian s rate of change? What does this rate tell ou about her direction of movement? What is Sean s rate of change? What does this rate tell ou about his direction of movement? Without actuall graphing the functions, compare the graphs of Jillian s hike and Sean s hike.

16 1. Alfonso is paing off his student loans. The graph shows the balance, in thousands of dollars, he has left to pa at time, in ears. What is the initial value of the linear function represented b the graph? What does this number mean? Balance (thousands of dollars) 50 B t Time (ears) 15. Short Response The following measurements were taken of a tree. Age 5 months 8 months 13 months 15 months Height 1. feet. feet 3.6 feet. feet Do the age and height show direct variation? If so, write the equation of variation. If not, explain wh not. 16. Determine if the relationship represents a function.

17 17. Determine whether each of the following graphs represents as a function of. If the graph does not represent as a function of, explain wh x x Tell whether the equation is a direct variation. Explain. If the equation is a direct variation, identif the constant of variation. 19. Determine whether the equation is linear:. 0. Determine whether the equation is linear:. 1. Tell whether the equation is a linear equation.. Tell whether the equation is a linear equation. 3. Find the -intercept of the line represented b.

18 . Use the image shown to explain the Pthagorean Theorem. 5. Could the following set of numbers be the measures of the sides of a right triangle: 5, 1, 13? 6. Find the length of the unknown side to the nearest tenth. 7. Could the following set of numbers be the measures of the sides of a right triangle: 7,, 5? 8. A right triangle has legs of lengths. Find the unknown length of the hpotenuse. Round to the nearest tenth if necessar. 9. The cit commission wants to construct a new street that connects Main Street and North Boulevard as shown in the diagram. The construction cost has been estimated at $110 per linear foot. Find the estimated cost for constructing the street. 30. A telephone worker needs to run a guide wire from the top of a 0-foot telephone pole to the groun He measures the distance from the base of the pole to the point of the ground where the wire would end to be 30 feet. Use the Pthagorean Theorem to find the length of wire that the worker will nee

19 31. Maurice is cleaning out the rain gutters on his house. To get to the gutters, he places a ft ladder against the house so that the top of the ladder reaches the bottom of the gutters. He places the bottom of the ladder so that it is 7 ft from the house. Draw a right triangle to illustrate this situation. Approximatel how high off the ground are the gutters? Show our work. Round our answer to the nearest foot. 3. A public beach in Florida charges nonresidents $8 per da for a fishing license and $.50 per da for live bait. Florida residents pa an annual fee of $11 plus $1 per da for live bait. How man das must both a resident and a nonresident use the beach in one ear so that both pa the same amount? Show all work. 33. Solve. Tell whether the equation has infinitel man solutions or no solution. 3. Do the equations and have the same solution? Explain our reasoning b discussing the similarities and differences in the equations. 35. Which of the angles in the figure are supplementar to? 36. If line and line are parallel and measures, what is the measure of?

20 37. Are and similar? Explain. Show our work. (3 x + 3) B ( x ) A 10 C (5 ) E D F (1 + 6) 38. In the triangles below, and. B A F C D E What can ou conclude about and? Explain. Can ou conclude that and are similar? Explain our reasoning without using the angle-angle similarit criterion. Can ou conclude that and are congruent? Explain our reasoning.

21 39. The graph of a sstem of linear equations is shown. Write the solution of the sstem. 0. The graph of a sstem of linear equations is shown. Write the solution of the sstem. 1. You have $18 to spend for lunch during a 5 da work week. It costs ou about $1.50 to make a lunch at home and about $5 to bu a lunch. How man times each work week should ou make a lunch at home if ou want to bu lunch as often as possible?. You are buing beads and string to make a necklace. The string costs $1.50, a package of 10 decorative beads costs $.50, and a package of 5 plain beads costs $.75. You can spend onl $7.00 and ou need 150 beads. How man packages of each tpe of bead should ou bu? 3. The graph of the sstem of linear equations and is shown. What is the solution of the sstem? Verif the solution b substituting it into each equation x 8 1. Jesse owns a sporting goods store that sells skis and snowboards. The store earns a profit of $5 for each pair of skis sold and a profit of $6 for each snowboard sol If Jesse s store sells 83 pairs of skis and snowboards and earns a profit of $89 in November, how man pairs of skis and how man snowboards did the store sell that month?

22 Essa 1. For each of the situations, write an equation to describe the situation as a function. A. The temperature was 5 F at the start of the week. For the rest of the week, the temperature is expected to drop 10 F a da. B. T-shirts cost $.95 plus $5.00 shipping and handling. C. At a time when Bill had no mone and $100 in debts, he got a part-time job earning $30 a week.. Katarina puts 16 ounces of water in her dog s dish. After hours, there are 1 ounces of water. Assume that the amount of water continues to decrease at the same rate, and write a linear function to model the amount of water in the dog s dish over time. Identif the slope and the -intercept in terms of the situation. 3. For each of the situations, write an equation to describe the situation as a function. A. The temperature was 5 F at the start of the week. For the rest of the week, the temperature is expected to drop 10 F a da. B. T-shirts cost $.95 plus $5.00 shipping and handling. C. At a time when Bill had no mone and $100 in debts, he got a part-time job earning $30 a week.. Katarina puts 16 ounces of water in her dog s dish. After hours, there are 1 ounces of water. Assume that the amount of water continues to decrease at the same rate, and write a linear function to model the amount of water in the dog s dish over time. Identif the slope and the -intercept in terms of the situation. 5. Su, who is 5 feet tall, is standing at point D in the drawing. The top of her head is at point E. A tree in the ard is at point B with the top of the tree at point C. Su stands so her shadow meets the end of the tree's shadow at point A. Part A: Which triangles are similar? How do ou know? Part B: What is the ratio of the triangles? Part C: Find the height of the tree. (The distance from B to C.)

23 Semester Exam Essa Question: Explain how ou decide which part of a problem will be represented b the variable x and which part will be represented b the variable in a graph of the situation. Give an example. Qualit Expectation (to get FULL points): Begin b restating the question in our response. No less than 3 sentences. Response needs to be in complete sentences with correct punctuation. Use math vocabular in our explanation. (for example: independent, dependent, variable, etc.)