Midterm Practice: The Number System

Transcription

1 Midterm Practice: The Number System. The locations of the values for p and r are shown on the number line. Determine the location on the number line that best represents the sum of p + r. Select a place on the number line to plot the point. (7.NS.b-). At 8 a.m. on Sunday morning, the temperature was Fahrenheit ( F ). A student recorded the change in temperature at 8 a.m. for the next three days. (NS.b-) The change in temperature from Sunday to Monday was F. The change in temperature from Monday to Tuesday was + F. The change in temperature from Tuesday to Wednesday was F. Circle the number line that shows a point representing the temperature, in degrees Fahrenheit, on Wednesday morning at 8 a.m.. Determine which expressions are equivalent to ( + 6 ). Select each correct answer. (NS.c-) a. ) + ( 6 b. + ) + ( 6 c. + ( ) 6 d. ) ) + ( + ( e. ) ) 6 ( + ( 6. Complete the equation to make a true statement. Drag and drop the appropriate number into each box. (7.NS.c-) = 7 +. Determine the value of the expression (7.NS.d)

2 6. Here is an expression: Which situation matches this expression? (NS.b-) a. An athlete runs kilometers in minutes. At that rate, how many kilometers does the athlete run in minute? b. A teacher fills an empty white pitcher with gallon of water and an empty blue pitcher with gallon of water. How many more gallons of water are now in the white pitcher than in the blue pitcher? c. Mr. Smith has pound of beans. He uses pound of beans each week. At that rate, for how many weeks will his beans last? d. A worker cuts pieces of string that are each yard in length. How many pieces of string can the worker cut from a piece of string that is yard in length? 7. Here is an expression: Which situation can be modeled using this expression? (7.NS.b-) a. Kim has cups of flour. She uses cup of flour for a recipe. How many cups of flour does Kim have remaining? b. Alex has pages to read for homework. So far, he has finished of his homework. How many pages has Alex read so far? c. Ben has a -foot-long sandwich. He cuts the sandwich into -foot-long pieces. How many pieces of sandwich does Ben have? d. Stacy has hours to get ready for a concern. She spends hour showering. How many hours does Stacy have remaining to get ready? 8. Which of the following expressions represent a number greater than? (NS.c) Select each correct answer. a. b. c. d. e. f. 9. A scientist removed a sample of 9. grams of a chemical from a container. The sample was grams less than of the total mass of the chemical in the container. (D.) 0 What was the total mass, in grams, of the chemical in the container before the scientist removed the sample of 9. grams? Show your work or explain how you know.

3 0. The bottom of the inside of a rectangular prism is complete covered with a layer of letter cubes, as shown. The edges of each letter cube are inches long. (D.) a. What are the length and width, in inches, of the bottom of the inside of the prism? b. The height inside the rectangular prism is foot. How many layers of letter cubes can fit inside the prism? Show or explain how your determined your answer. c. The weight of the prism when empty is pound. The weight of the prism when it is completely filled with letter cubes is pounds. What is the weight, in ounces, of one letter cube? Show or explain how you determined your answer.. Points Q, R, S, and T are plotted on the number line. (7.C.) a. Which two plotted points have a sum of zero? b. Explain how the number line can be used to show that the sum of the two points you identified is zero. c. Explain how the number line can be used to determine the sum of the point T and.

4 . A weather forecaster reported that the total amount of rainfall for the month was 0.7 inch. He also reported that this amount was 0. inch below the average amount of rainfall for the same month during that last ten years. The forecaster summarized his findings in this table. (NS.) What was the average amount of rainfall, in inches, for this month during the last ten years?. Jackie wrote the expression shown. (7.C.7-) ( ) + a. Circle the computation that can be performed first to determine the correct value of this expression b. Jackie made an error when trying to determine the value of the expression. Describe the error that Jackie made. c. Determine the correct value of the expression. Be sure to show all of the steps you used.

5 . Over a period of hours, the outside temperature changed an average of. Fahrenheit per hour. Select from the drop-down menus to correctly complete the sentence. (NS.) The temperature by degrees Fahrenheit from the beginning to the end of the -hour period.. A town s low temperature for January was -8 o Fahrenheit ( o F). The difference between the town s high temperature and low temperature for January was o F. What was the town s high temperature, in degrees Fahrenheit, for January? (7.NS.) 6. In Fairbanks, Alaska, the temperature one day was -8 o F. On that same day, the temperature was 8 degrees higher in Honolulu, Hawaii. What was the temperature in Honolulu, Hawaii, on that day? (7.NS.) 6 o F 7 o F 8 o F 0 o F Midterm Practice: Ratios and Proportional Relationships 7. A person operating a machine can mow 0.7 acres in hour. What is the rate, in acres per hour, that the person can mow? Write your answer as a decimal. (RP.) acres per hour 8. Katie completes of a craft project in of an hour. (RP.) Enter your answer in the boxes. At this rate, what fraction of the craft project does Katie complete in one hour? Give your answer in fraction form. 9. Which graphs represent a proportional relationship between x and y? (RP.a) Circle each correct answer.

6 0.The table shows the number of pages a student reads and how many minutes it takes the student to read those pages. (7.RP.a) Which statement best describes the relationship in the table? a. The number of minutes is proportional to the number of pages, with a unit rate of. minutes per page. b. The number of minutes is proportional to the number of pages, with a unit rate of. minutes per page. c. The number of minutes is proportional to the number of pages, with a unit rate of. minutes per page. d. The relationship in the table is not proportional.. The cost of pumpkin seeds is proportional to their weight. A -ounce bag of pumpkin seeds costs $6.00. Circle the unit rate for the pumpkin seeds. (RP.b) $0. per ounce. $0. per ounce. $0.0 per ounce. $0.60 per ounce.. This table represents a proportional relationship between x and y. (RP.b) Based on the values in the table, complete the sentence shown. Write your answer as an improper fraction. When x increases by, y increases by. Purple paint is made from mixing red paint and blue paint. The diagram shows the relationship between the amount of red paint and the amount of blue paint needed to make purple paint. What fraction of each gallon of purple paint is red paint? (7.RP.b)

7 . The graph shows the numbers of quarts of yellow paint that must be mixed with different numbers of quarts of red paint to make a certain shade of orange paint. (RP.c) Based on the graph, write an equation (in the form y = k x) that shows the relationship between the number of quarts of yellow paint, y, and the number of quarts of red paint, x, needed to make the shade of orange paint.. An empty tank is filled with water at a constant rate. The table shows w, the number of gallons of water in the tank after m minutes. (7.RP.c) Which equation represents the relationship shown in the table? a. w =.m b. w = 6.m c. w = m d. w = 66m 6. The graph shows the amount of protein contained in a certain brand of peanut butter. (RP.d) Describe the meaning of the point (6, 0) on the graph. Select from the drop-down menus to correctly complete the sentence. The number 0 represents the number of for every 6 6

8 7. The graph shows the relationship between the number of pounds of potatoes (x) and the total cost of potatoes (y). Select each correct statement about the points on the graph of the relationship. (7.RP.d) a. The point (, 0.60) means that pound of potatoes costs $0.60. b. The point (, 7.0) means that pounds of potatoes costs $7.0 per pound. c. The point ( 0, ) means that pounds of potatoes costs $0.00 per pound. d. The point (, ) means that pounds of potatoes costs $.00. e. The point ( 0, 8) means that 8 pounds of potatoes costs $0.00. f. The point ( 0, ) means that 0 pounds of potatoes costs $ Devon graphed a line that contains the points shown in this table. (C.6-) Devon concluded that the points in the table represent a proportional relationship for these reasons: Reason : The table contains the point (, ). Reason : The table contains only positive values. Reason : The line that contains these points is straight. Which of Devon s reasons is an actual condition for a proportional relationship? What is the other condition that must be met for a proportional relationship? x y The table shows the cost of renting a boat for different amounts of time. (7.D.) a. Determine the missing values in the table, and plot the five data points on the coordinate plane. b. Write an equation to represent the total cost of renting a boat, y, for x days. c. The boat rental company gave a rowing team a discount of $0 off for every days of rental. The team rented a boat for days. Their coach paid % of the total discounted rental cost. The remaining rental cost was divided equally among the team members. Determine the total cost for the team to rent a boat. Determine the cost per team member. 7

9 0.A factory has two types of machines. (RP.-) The factory has 6 cutting machines and stamping machines. Each cutting machine cuts 0 parts every minutes. Each stamping machine staples parts every 0 seconds. a. How many parts can all 6 cutting machines cut in minute? 0 parts 0 parts 0 parts parts b. The factory needs to stamp,0 parts. How many minutes will it take for all stamping machines to stamp,0 parts? 0 minutes minutes minutes 60 minutes c. One of the cutting machines is shut down for repairs. How many parts can the remaining machines cut in hours? 788 parts,6 parts 8,0 parts 7,0 parts d. All of the machines are kept cool by circulating cold water through them. The water makes complete cycle through a 0 foot long tube every seconds. Correctly complete the statement about the distance traveled by the water in minutes and number of complete cycles the water makes in minutes. The water travels feet and completes cycle in minutes Midterm Practice: Expressions and Equations. A rectangular sheet of paper has a length of x inches and a width of inches. Rico folds the paper in half once vertically and once horizontally, forming four smaller equal-sized rectangles, as shown in this diagram. (C.8) a. Write an expression that represents the perimeter, in inches, of one of the four smaller rectangles. x b. Rico concludes that the sum of the perimeters of all four smaller rectangles is equal to twice the perimeter of the larger rectangle. Show or explain all of the steps of your reasoning to verify whether or not Rico s conclusion is correct. 8

10 . An expression is given: ( x ).7(x + ) Which expression is equivalent to the given expression? (EE.) a. 0.x 6.0 b. 0.x +.00 c. 0.x +.0 d. 0.x.00. Julian will factor the expression 6xyz + xy 6x by dividing each term by a common factor. (EE.) Which possible common factor could Julian use? Circle each correct answer. 6 8 x x 8 x y 6 y xy. Which expression is equivalent to? (7.EE.) x + a. (x + ) b. (x + ) c. (x + ) d. (x + ). The price of a certain item is P dollars. The sales tax on the item is 7%. Which expressions represent the total cost of the item, in dollars, after the tax has been applied? Select each correct answer. (EE.) 0.07P.07P P P P ( )P 6. Howard has a garden in the shape of a rectangle. (EE.) The length is. meters. The width is. meters. Howard will increase both the length and the width by 0% each. a. What will be the perimeter, in meters, of the enlarged garden? b. By how many square meters will the area of the garden increase? 7. A box contains 8 snack-sized bags of popcorn. (7.EE.a-) The weight of the box when it is empty is ounces. The weight of the box with all the bags of popcorn is ounces. What is the weight, in ounces, of each bag of popcorn? Write your answer as a decimal. 9