fcat mathematics sample items for grade 8 all questions are from the fcat mathematics item...

FCAT Mathematics FCAT Mathematics Sample Items for Grade Sample Items for Grade

88

FCAT Mathematics FCAT Mathematics Sample Items for Grade Sample Items for Grade

88

All questions are from the FCAT Mathematics Item Specification for Grades 6 - 8

Table of ContentTable of Content

Strand A Slides 3 – 16

Strand B Slides 17 – 36

Strand C Slides 37 – 56

Strand D Slides 57 – 74

Strand E Slides 75 - 89

understands the relative size ofintegers, fractions, and decimals; numbersexpressed as percents; numbers with exponents;numbers in scientific notation; radicals;absolute value; and ratios.

MC

A. -2º, -17º, -34º, -27ºB. -2º, -27º, -34º, -17ºC. -34º, -27º, -17º, -2ºD. -34º, -17º, -27º, -2º

1) The coldest temperatures on record for foursouthern states are -2ºF, -27ºF, -34ºF, and -17º F.Which of the following shows these temperatures in order from least to greatest?

understands that numbers can berepresented in a variety of equivalent forms,including integers, fractions, decimals,percents, scientific notation, exponents,radicals, and absolute value. (Also assessesA.1.3.1 and A.1.3.3)

MC, GR

2) Mr. Link has harvested 27 acres of his 36-acre

orange grove, or 27/36 of the grove. What is another way

to express this number?

Other Correct Responses: 9/12, 0.75

3 / 4


MC, GR

3) In 1992, the Orlando International Airport served approximately 21,000,000 passengers. Which of the following is NOT another way of expressing the number 21,000,000?

A. 2.1 × 107

B. 21 × 106

C. 21 millionD. 2.1 million


MC, GR

How many students are in Steve’s poetry club?

2 1

4) Steve’s friend wants to know how many students are in Steve’s poetry club. Steve used the expression below to represent the number of students in the club.

understands and uses exponential and scientific notation.

MC, GR

5) A space shuttle can travel at a speed of 3 × 107

meters per hour. At this speed, how far will it travel in24 hours? A. 3.0 × 107 meters B. B. 3.0 × 108 meters C. 7.2 × 107 meters D. 7.2 × 108 meters

understands and uses exponential and scientific notation.

MC, GR

6) What is the value of the following expression?

93 – 54

1 0 4

understands and explains theeffects of addition, subtraction, multiplication, and division on whole numbers, fractions,including mixed numbers, and decimals, including the inverse relationships of positive and negative numbers.

MC

7) When multiplying a whole number greater than 1 by a positive fraction less than 1, the product is which of the following?

A. greater than the whole number B. less than the whole number C. less than the fraction D. equal to 1

selects the appropriate operation to solve problems involving addition, subtraction,multiplication, and division of rationalnumbers, ratios, proportions, and percents, including the appropriate application of the algebraic order of operations.

MC, GR

8) In what order should the operations be performed in the expression below?

4 + 8 ÷ 2 × 3 – 1

A. ÷, +, –, × B. ÷, ×, +, – C. ×, +, ÷, – D. +, ÷, ×, –

selects the appropriate operation to solve problems involving addition, subtraction,multiplication, and division of rationalnumbers, ratios, proportions, and percents, including the appropriate application of the algebraic order of operations.

MC, GR

9) What is the value of the expression below? 3 −1

4 + 8 ÷ 2 × 3

1 / 8

Other Correct Responses: 2/16, 0.125

adds, subtracts, multiplies, anddivides whole numbers, decimals, and fractions,including mixed numbers, to solve real-world problems, using appropriate methods of computing, such as mental mathematics, paper and pencil, and calculator.

MC, GR

10) Todd bought a pair of sneakers, originally priced at $64.95 and marked down 15%. The sale price was then further reduced by 10%. How much did Todd pay for the sneakers, including 6% sales tax?

A. $48.71 B. $49.69 C. $51.64 D. $52.67


MC, GR

11) Kirk and his father are on a 200-mile bicycle trip across Florida. They plan to ride for five days. During the first four days, they traveled the following distances: 45.8 miles, 42 miles, 41.5 miles, and 38.4 miles. How many more miles do Kirk and his father have to travel to reach their 200-mile goal?

3 2 . 3


MC, GR

12) Ramón is purchasing 2 pairs of pants priced at $21 per pair, 3 shirts priced at $10 each, and 1 pair of shoes priced at $36. All of these prices are before tax. The price of every item Ramón is purchasing will be reduced by 20% when his total purchase is being calculated, before tax is added. What dollar amount will be subtracted from Ramón’s total purchase, before tax?

2 1 . 6

uses estimation strategies topredict results and to check the reasonablenessof results.

(Also assesses A.4.2.1, B.2.3.1,and B.3.3.1)

MC

13) Margo wants to cover the top of her table with a mosaic pattern made of different-colored tiles. The tiles come in boxes that each contain 125 tiles. Margo has determined that Section 1 of the table top, shown in the drawing below, will require approximately 57 tiles to complete the pattern.

uses estimation strategies topredict results and to check the reasonablenessof results.

(Also assesses A.4.2.1, B.2.3.1,and B.3.3.1)

MC

Which is closest to the whole number of boxes of tiles Margo should purchase to complete the mosaic design for the entire table top?

A. 6B. 10C. 200D. 600

uses concrete and graphic modelsto derive formulas for finding perimeter, area, surface area, circumference, and volume of two- andthree-dimensional shapes, includingrectangular solids and cylinders.

(Also assessesB.1.2.2 and B.2.3.1)

Grades 6–7 MC, GRGrade 8 GR, SR

14) Sachi is building a brick patio and needs to determine its total area. The dimensions of the patio are shown in the diagram below.

11 feet

13 feet

16 feet

9 feet




1 5 4

What is the total area, in square feet, of the patio?




15) A cylindrical column 12 centimeters in diameter is strengthened by wrapping one steel band around the base of the column, with no overlap. What should be the length of the steel band in centimeters (cm)?

2 6 4 / 7

Other Correct Responses: 37.68, 37.71




16) Calvin is preparing a training schedule and needs to determine the distance around the school track. The track coach gave him the drawing below and told him that the track is composed of two straight segments with the ends of the track in the shape of semicircles with a radius of 35 meters.

What is the distance around the track? In the Answer Book, show your work or explain in words how you determined the distance.

90 meters

35 meters 35 meters




In the Answer Book Show your work or explain in words how you determined the distance.

Distance __________________

A correct and complete response includes the distance and valid work or explanation as shown below. •A distance ≈ 400 meters or 399.8 meters or 70π+ 180 meters (using 3.14 for π) AND Valid work that leads to a correct response (using22/7 for π): 90 m + 90 m = 180 m,22/7 × 70 = 220 m,220 m + 180 m = 400 mOR an explanation similar to the following:The length of the two straight segments of the track is 90 m + 90 m = 180 m. The distance around one end of the track is half the distance around a circle. The distance around both ends of the track is the circumference of a circle.

uses concrete and graphic modelsto derive formulas for finding rates, distance,time, and angle measures.


Grade 6 (Assessed with C.1.3.1)

Grades 7–8 MC, GR

17) Under water, a sound wave travels 73,920 feet in 14 seconds. What is the speed of a sound wave in feet per second?

5 2 8 0




Grades 7–8 MC, GR

18) Dominic drove from Salt Lake City, Utah, to Bryce Canyon National Park in 6 hours and 45 minutes at an average speed of 48 miles per hour. What is his driving distance, in miles?

A. 208B. 302.4C. 309.6D. 324




Grades 7–8 MC, GR

19) The drawing below shows the distances, in miles, between some Florida cities.




Grades 7–8 MC, GR

Henry will drive from Ft. Myers to Naples and then will drive along the Tamiami Trail to Miami at an average rate of 60 miles per hour. How many hours should it take Henry to drive nonstop from Ft. Myers to Miami using this route?

2 . 4

understands and describes how thechange of a figure in such dimensions as length, width, height, or radius affects its other measurements such as perimeter, area, surfacearea, and volume.

(Also assesses C.2.3.1)

MC, GR

20) A park sculpture has a base in the shape of a rectangular prism. The sculpture’s base has a volume of 960 cubic inches. An artist is making a model of the sculpture with dimensions half the size of the actual sculpture. What is the volume of the base on the artist’s model?

A. 120 cubic inches B. 240 cubic inches C. 480 cubic inches D. 960 cubic inches



MC, GR

21) A rectangular lot on wildlife preserve land has dimensions of 5 miles by 8 miles. If the dimensions of the lot are doubled, by how many times will the area increase?

4



MC, GR

22) Meri will increase the length of her rectangular patio and rectangular driveway by 5 feet, as shown in the diagram below.



MC, GR

By how many square feet will the total area of the patio and driveway increase when the length of each is increased as shown?

1 5 0

constructs, interprets, and uses scale drawings such as those based on number lines and maps to solve real-world problems.

(Also assesses B.2.3.1)

MC, GR

23) Hector is going to visit relatives in Bellville this summer. He wants to know how far Bellville is from his home in Aimsworth. He found the map below.

On the map, Hector measured a total of 3 inches from Aimsworth to Bellville. Based on the map scale above, how many miles is it from Aimsworth to Bellville?

A.15 milesB.30 milesC.50 milesD.60 miles



MC, GR

24) Carmello is making a model of our solar system. He wants his model to look like the one shown below.

The average distance between the orbital paths of Mercury and Venus is approximately 31.2 million miles. According to the scale above, how far apart, in centimeters, should the orbital paths be on the model?



MC, GR

The average distance between the orbital paths of Mercury and Venus is approximately 31.2 million miles. According to the scale above, how far apart, in centimeters, should the orbital paths be on the model?

5 . 2



MC, GR

25) Mr. Ogimachi will travel from Holt City to Valley View for a business trip. He plans to leave Holt City at 6:45 a.m. He used the map below to estimate the distance from Holt City to Valley View, and determined the distance on the map to be 9 centimeters (cm).



MC, GR

If Mr. Ogimachi drives at an average rate of 60 kilometers (km) per hour without stopping, which of the following is closest to the time he should arrive in Valley View?

A. 8:20 a.m.B. 8:25 a.m.C. 9:00 a.m.D. 10:45 a.m.

solves problems involving units ofmeasure and converts answers to a larger orsmaller unit within either the metric orcustomary system.

MC, GR

26) The round steel rod shown below is 5.75 feet long. If a steelworker cuts the steel rod into 10 equal pieces, approximately how many inches long will each piece be?

A. 0.479 inches B. 0.575 inches C. 5.75 inches D. 6.9 inches

solves problems involving units ofmeasure and converts answers to a larger orsmaller unit within either the metric orcustomary system.

MC, GR

27) The distance from Robert’s house to a boat dock is 425 meters. Robert walks to the dock and back to his house each day. After 3 days, how far, in kilometers, will Robert have walked?

2 . 5 5

understands the basic properties of,and relationships pertaining to, regular and irregular geometric shapes in two and threedimensions.


MC

28) Triangle ABC is an isosceles triangle.

What is the measure of Angle A?

A. 44°B. 68°C. 112°D. 136°

understands the basic properties of,and relationships pertaining to, regular and irregular geometric shapes in two and threedimensions.


MC

29) The figure below is composed of several triangles.

Which of the following pairs of line segments in the figure must be parallel?

understands the geometric conceptsof symmetry, reflections, congruency, similarity,perpendicularity, parallelism, andtransformations, including flips (reflections),slides (translations), turns (rotations), andenlargements. (Also assesses B.1.3.3, C.1.2.1, C.1.3.1, and C.3.3.1)Grades 6–7 MCGrade 8 MC, ER

30) Before she can enter a race, Jasmine needs to know the height of her sailboat. Jasmine is 5 feet tall and casts a shadow 6 feet long, as shown below.

If the lengths of the sailboat’s shadow and Jasmine’s shadow at the same time of day are known, which of the following properties could be used to find the height (h), in feet, of the sailboat?A. congruencyB. parallelismC. symmetryD. similarity


31) Look at the figures below showing a floor tile design. Figure 1 was transformed to make the new design in Figure 2 using only two steps.


Complete the following in the Answer Book:

Part AExplain in words how Figure 1 can be transformed to Figure 2 in only two steps. Use mathematical terms to describe the transformation.

Part BOn the grid, draw Figure 3 by making the followingtransformations to Figure 2: Rotate Figure 2 ninety degrees clockwise around point D and reflect the rotated figure over vertical line n. Be sure to label this new figure as Figure 3, and also label points A, B, C, and D.

Part CExplain in words whether Figures 1, 2, and 3 are congruent or not, and why.


A correct and complete response includes appropriateResponse explanations and an appropriate drawing.Part A• An explanation similar to the following:First I reflected Figure 1 over line n. Then I rotated itclockwise 90° about point C1.• ORI rotated Figure 1 90° counterclockwise about point C andreflected it over line n.• OR other valid explanationANDPart B• Correctly drawn and labeled figure, as shown on the grid.

ANDPart C• An explanation similar to the following:All three figures are congruent because their size and shapeare exactly the same; only their positions are different.• OR other valid explanation.


32) The diagram below shows a side view of a bridge. In the diagram, ABC is congruent to DEF.

Which statement about BAC and DEF must be true?

A. They must have equal measuresB. They must each measure at least 45 degreesC. Their measures must have a sum of 90 degreesD. Their measures must have a sum of 180 degrees


33) The Wilford Outdoor Advertising Agency sought a building whose side was tall enough to accommodate an 18-meter high rectangular billboard. The advertising artist found a building he thought might work. He is 2 meters tall and on the morning he examined the building, he cast a shadow 0.5 meter long, while the building cast a shadow 4 meters long.


Part A Write a proportion which could be used to find the height of the side of the building. Let x represent the height of the side of the building in meters.

Part B Use your proportion in Part A to find the height of the building. Show all work necessary to justify your answer.

Part C The advertising artist came back to the building at 4:00 in the afternoon to recheck the building. At that time, his shadow was 1.5 meters long. How long, in meters, should the building’s shadow have been at that time? Show all work necessary to justify your answer.

represents and applies geometric properties and relationships to solve real-worldand mathematical problems.

(Also assessesC.2.3.1, C.2.3.2, and C.3.2.2)

Grades 6 MCGrades 7 MC, GRGrade 8 MC, SR

34) Jack wants to make ΔLMN similar to ΔPQR. He has plotted points L and M on the grid below and needs to place point N. Which of the following coordinates of point N would make ΔLMN similar to ΔPQR?

A. ( 0, -1)B. (-3, -1)C. (-1, -1)D. (-6, -1)




35) You are designing a camping tent with an octagon-shaped base and have drawn a diagram of the base on the coordinate grid below.




Complete the following in the Answer Book:Part AHow many lines of symmetry does this diagram have?Part BDraw all the lines of symmetry on the diagram and determine the coordinates for the point at which the lines intersect.

A correct and complete response includes the correctResponse number of lines of symmetry, a correct drawing of the lines of symmetry on the grid, and the correct coordinates for the point of intersection as shown below.

Part A• Lines of symmetry = 4ANDPart B• Four lines of symmetry correctly drawn on the diagram• AND Coordinates = (4, 3)




36) In architecture, coordinate planes are used to help make design layouts for buildings. The grid below represents a building layout with several points plotted.




Part A On the coordinate plane above, plot and label points C (-5, -2) and F (6, 9).—– —– —– —– Then draw the following line segments: AC, BC, DF, and EF.

Part B The distance between points C and F is the widest part of the building. What is the width, in feet, of the widest part of the building? Show all work necessary to justify your answer.




Top-Score Response

identifies and plots ordered pairs inall four quadrants of a rectangular coordinatesystem (graph) and applies simple properties of lines.

MC

37) What are the coordinates of the y-intercept of line QR?

A. (2, 0)B. (0, 2)C. (-1, 0)D. (0, -1)

describes a wide variety of patterns, relationships, and functions throughmodels, such as manipulatives, tables, graphs, expressions, equations, and inequalities.

(Also assesses A.5.3.1)

MC, GR

38) A graphic artist has drawn the pattern shown below.

If the artist continues the pattern, what will Row 15 look like?



MC, GR

39) Use the function table to find the value of y when x = 5.

1 6



MC, GR

40) The diagram below shows some rows of Pascal’s triangle.

Which of the following should be in row 5 of Pascal’s triangle?



MC, GR

41) The femur, or thighbone, is the longest bone in the human body. Scientists can calculate a person’s approximate height by measuring the length of the person’s femur. The table below shows the linear relationship between femur length (f) and a person’s height (h).



MC, GR

1 6 9

A scientist measures a human femur bone that is 40 centimeters long. What is the value of h when f has a value of 40?

creates and interprets tables, graphs, equations, and verbal descriptions toexplain cause-and-effect relationships.


Grades 6–7 MC, GRGrade 8 MC, GR, SR

42) A holiday shop buys a box of ornaments for $51.00 and resells them for $7.00 per ornament. If x represents the number of ornaments in a box, which of the following expressions could be used to find the difference between the selling price and the cost of one box of ornaments?

A. 7x + 51 B. 7x − 51 C. 51x + 7 D. 51x − 7




43) What is the value of the expression -3x + 7, when x = -6?

2 5




44) Lyndsey is designing a border using a row of hexagonal tiles with each side measuring 1 foot. She made the following table to determine the perimeter of the border as the number of tiles used increases.

Part A Write a rule or expression that could be used to determine the perimeter of the border using any number of tiles (n).

Part B Based on the rule or expression you wrote in Part A, what will be the perimeter if Lyndsey uses 25 tiles in her border?




A correct and complete response includes a correct rule or expression and the correct answer for 25 tiles.

Valid expression equivalent to the following: 4n + 2

OR

Valid rule similar to the following: Multiply the number of tiles by four and then add two.

OR

other valid rule or expression written in words or symbols

AND

Valid answer equivalent to the following: 4(25) + 2 100 + 2

Perimeter = 102 feet

Top-Score Response




A. $120 B. $200 C. $6100 D. $36,000

45) The equation below is used to find C, the total charge in dollars, not including tax, for a purchase of company jackets ( j) that have a specific design and color.

)100

20(j

jC +=

What is the total charge, not including tax, for a purchase of 300 jackets?

represents and solves real-world problems graphically, with algebraic expressions, equations, and inequalities.


Grades 6–7 MCGrade 8 MC, SR

46) In professional ice hockey, a team earns 2 points for a win, 1 point for a tie, and 0 points for a loss. During the first half of the 1996-1997 season, one team had 8 losses and 10 ties, and had earned 62 points. Which of the following equations could be used to determine the number of wins (w) this team had?

A. 62 = w + 8 B. 62 = w + 10 C. 62 = 2w + 10 D. 62 = 2w + 8




47) The average yearly rainfall for a town in California is 14 inches. For the past 10 years, the yearly rainfall has been not more than 6 inches above or below that average. Which number line below shows the range of the yearly rainfall for the past 10 years?




A. 7x + 51 B. 7x - 51 C. 51x + 7 D. 51x - 7

48) A shop owner buys a box of identical photo albums for $51.00 and sells them for $7.00 per photo album. If x represents the number of photo albums in a box, which of the following expressions could be used to find the difference between the total selling price and the cost of 1 box of photo albums?




Part A Write an equation that could be used to determine the number of alligators (a) in the pond. (Assume that each alligator has 4 legs).

Part B Solve your equation from Part A to determine the number of alligators in the pond.

49) Samuel went with his family to Alligator Park. While they were waiting for the alligator show to start, a park employee told their group that if there were 3 more alligators in the pond, there would be a total of 140 legs on the alligators in the water.




A correct and complete response includes the correct equation and the correct answer as shown below.

•An equation equivalent to the following: 4n + 12 = 140

• OR other valid equation

AND

• The number of alligators = 32

Top-Score Response

uses algebraic problem-solvingstrategies to solve real-world problemsinvolving linear equations and inequalities.

MC, GR

A. 40,000 feet B. 30,000 feet C. 29,750 feet D. 27,750 feet

50) Miko is flying her plane within its safety limit at an altitude of 35,000 feet. To avoid a storm, she ascends 5,500 feet without going past the plane's safety limit. Based on the inequality of a + 5,500 ≤ 35,000, where a represents the original altitude in feet, which of the following could be the original altitude of the plane?


MC, GR

51) The Chatham County Water Department charges a monthly administrative fee of $9.40 and $0.0049 for each gallon of water used up to 5,000 gallons. The equation to figure the total cost, C, for use of up to 5,000 gallons is

C = 9.4 + (g × 0.0049),

where g is the number of gallons up to 5,000. What will be the monthly charge for a customer who used 4,100 gallons of water in one month?

2 9 . 4 9


MC, GR

52) The Chatham County Water Department charges a monthly administrative fee of $9.40 and $0.0049 for each gallon of water used up to 5,000 gallons. The equation to figure the total cost, C, for use of up to 5,000 gallons is

C = 9.4 + (g × 0.0049),

where g is the number of gallons up to 5,000. If a customer’s total cost was $29.49 for one month, what was the total number of gallons of water used that month?

4 1 0 0

collects, organizes, and displays data in a variety of forms, including tables, line graphs, charts, bar graphs, to determine how different ways of presenting data can lead to different interpretations.

(Also assesses E.1.3.3)

Grades 6–7 MC, GRGrade 8 MC, GR, ER

53) Each water molecule is made up of one oxygen atom that weighs approximately 16 atomic mass units (amu) and two hydrogen atoms that each weigh approximately 1 amu. Which of the displays below best shows the weight of an oxygen atom in proportion to the weight of the whole water molecule?




54) The plot below shows the heart rate for Micah’s students halfway through a kickboxing exercise class.




1 4

Micah said the optimum heart rate should be between 110 and 140 beats per minute. How many of the students’ heart rates shown on the plot are between 110 and 140 beats per minute?




55) Some students were asked in which room of the home they prefer to do homework. The table below shows the number of students who prefer to study in one of four different rooms.

Part A On the grid, construct a bar graph to show the number of students who study in each room.

Part B Complete the circle graph using the percent of students who prefer to study in each room.

Part C Determine which graph most clearly shows that more than half of the students prefer to study in the bedroom or the kitchen.




A correct bar graph similar to the following:

· OR other valid bar graph

AND

Top-Score Response




• A correct circle graph similar to the following:

• OR other valid circle graph AND • An explanation similar to the following: The circle graph is better because it clearly shows that more than half of the students prefer to study in the bedroom or the kitchen. OR The bar graph is better because it shows that more than 500 students prefer to study in the bedroom or the kitchen. • OR other valid explanation.

understands and applies the concepts of range and central tendency (mean, median, and mode).


MC, GR

56) The land areas of the seven continents are listed in the table below.

What is the approximate mean land area of the seven continents?

A. 17.3 million square milesB. 14.0 million square milesC. 8.3 million square milesD. 6.9 million square miles



MC, GR

57) Julio is doing a report about the quality of life in various countries. He found the following information about life expectancy.

What is the median life expectancy of people living in the countries listed above?



MC, GR

6 6

compares experimental results with mathematical expectations of probabilities.

MC

58) Pat is taking a vacation to a health spa. She has decided to participate in 1 sporting activity and 2 cooking activities while at the spa. Her choices in each category are shown below.

How many combinations of 1 sporting activity and 2 cooking activities could Pat choose from while at the spa?

A. 32B. 24C. 18D. 12


MC

59) A national ice cream company conducted a survey with a random sample of 100 people to find out which flavors of ice cream people like best. The results are shown below.


MC

A. 7 studentsB. 11 studentsC. 28 studentsD. 43 students

Beth and Stuart conducted the same survey during lunch with a sample of 25 students and got the results shown below.

If the results of Beth and Stuart’s survey had been like the national results, how many more students would have picked vanilla as their favorite ice cream?

determines odds for and odds against a given situation.


MC

A. 3 to 2B. 2 to 3C. 2 to 1D. 1 to 2

60) While playing for a local baseball team, Jamal hit the ball 20 out of 30 times at bat. Based on this record, what would be the odds in favor of Jamal hitting the ball the next time he comes up to bat?

determines odds for and odds against a given situation.


MC

61) In a group of 30 people, 27 are right-handed and the others are left-handed. If one person is selected at random from this group, what is the probability that the person selected will be left-handed?

formulates hypotheses, designsexperiments, collects and interprets data, and evaluates hypotheses by making inferences anddrawing conclusions based on statistics (range, mean, median, and mode) and tables, graphs, and charts.


MC

62) As a tree ages, the trunk of the tree gets bigger.Scientists can estimate the age of a tree by measuringthe distance around, or the circumference of, the treetrunk. A team of scientists believe that the trees in Floridaare older than the trees in Georgia, Alabama, andMississippi. In which of the following geographic areasshould the scientists measure the circumference of 200trees to best test their hypothesis?

A. one area of each state B. one area of Florida C. various areas of each state D. various areas of Florida

fcat mathematics sample items for grade 8 all questions are from the fcat mathematics item...

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