North Carolina End-of-Grade Tests—Grade 8 - Public Schools of ...

NameGrade 8Form RNorth CarolinaRELEASEDPublic Schools of North Carolinawww.ncpublicschools.orgState Board of EducationDepartment of Public InstructionOffice Division of of Accountability and Services/North Technology ServicesCarolina Testing ProgramDivision Raleigh, North of Accountability Carolina 27699-6314 Services/North Carolina Testing ProgramRaleigh, North Carolina 27699-6314RELEASED FORMEnd-of-Grade Tests—Grade 8Mathematics–Calculator ActiveR© 2004 2007 2009 All rights reserved. This document may not be reproduced by any means, in whole or in part, without priorwritten permission from the North Carolina Department of Public Instruction, Raleigh, North Carolina.

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 20091. Which is the largest value?A 6 2B 4 3C 3 5D 2 102. What is the approximate length ofthe diagonal of a square if theperimeter of the square is 12 ft?ABCD1.7 ft3.5 ft4.2 ft12.7 ft3. Which set of real numbers containsonly rational numbers?A { 121, 196, 24, 12}13 5B { 144, , , 102 3 }C { 169, 5 , 121,142 4 }RELEASEDD { 169, 58 , 13 , 313 2 }4. A 70-foot tree has a 35-foot shadow. Ifthe building next to the tree has an80-foot shadow, how tall is thebuilding?ABCD160 feet120 feet115 feet40 feet5. Ralph’s garden is in the shape of asquare. How does the area of thegarden change if he doubles the lengthof each side of the garden?ABCDThe area is halved.The area is doubled.The area is tripled.The area is quadrupled.6. Constance bought a box to hold herjelly beans. The dimensions of the boxare 6 inches by 2 inches by 1 inch.The jelly beans weigh a total of36 ounces. If each cubic inch insidethe box can hold two ounces, howmany ounces of jelly beans will have tobe left out of the box?A 24B 18C 12D 6Page 1Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 20097. In the figure shown below, A′ BC ′ ′ is the image produced by applying a dilation toABC.C C’What is the scale factor for this dilation?ABCD13251252+ 7+ 6+ 5+ 4+ 3+ 2+ 1y+ 8— 8 — 7 — 6 — 5 — 4 — 3 — 2 — 1 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8— 1— 2— B’3— 4— B5— 6— 7— 8AA’RELEASEDxPage 2Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 20098. Which scatterplot shows a positive correlation between the variables?AC00yyxxBDRELEASED00yyxxPage 3Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 20099. The direct route from Marta’sapartment to work is a road that is astraight line. The road is closed forrepairs. Marta had to drive 8 mileswest and then 6 miles south to get towork. She returned home by the sameroute. How many miles would shehave saved round-trip if she had takenthe direct route?A 2B 8C 10D 2410. Harold took a survey on America’sfavorite movies by asking 50 studentsat his school to complete the survey.Which is the best reason why hissurvey may be flawed?RELEASEDABCDThe students were not old enoughto take a survey.Some students are not Americancitizens.The students may include peoplewho do not go to the movies.Harold is not getting a diverserepresentation from the Americanpopulation.Page 4Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200911. The data displayed represent what type of correlation?y3025ABCD2015105005 10 15 20 25 30 35a positive correlation where the y values are exactly predicted by the line of best fita negative correlation where the y values are exactly predicted by the line of best fita positive correlation where the y values are approximately predicted by the line ofbest fita negative correlation where the y values are approximately predicted by the line ofbest fitRELEASEDxPage 5Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200912. The Smiths made a scatterplot comparing their daily electricity costs to the outsidetemperature.807060504030200ySmith Family Electricity Costs50° 60° 70° 80° 90° 100°Daily High Temperature (°F)If the high temperature on a day is 95 ° , about how much will their cost for electricity beon that day?A $0.95B $0.70C $0.67D $0.64RELEASEDxPage 6Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200913. Which data will most likely show anegative correlation when graphed ona scatterplot?ABCDthe outside temperature and thenumber of people wearing glovesthe distance a student lives fromschool and the amount of time ittakes to get to schoolthe number of visitors at anamusement park and the lengthof the lines for the ridesa student’s height and gradepoint average14. Hector’s math test grades for the finalquarter are 89, 93, 100, 98, and 95.He has one more test to take thisquarter. All tests count equally.What is the minimum grade Hectormust make on the last test in order toobtain an average of at least 93?A 78B 79C 83D 9515. Solve for b:16.A 9B 6.2C 3D 1.433b = 81Which statement best describes thesimilarities of the graphs 2y= 5x+6and 2y= 3 x + ?7RELEASEDABCDThe y-intercepts are the same.The slopes are the same.The x-intercepts are the same.The graphs are identical.67Page 7Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200917. What is the slope of the line graphed below?yAB— 2−12C 1D 2+ 6+ 5+ 4+ 3+ 2+ 1— 6 — 5 — 4 — 3 — 2 — 1 0 + 1 + 2 +3 + 4 + 5 + 6— 1— 2— 3— 4— 5— 6RELEASEDxPage 8Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200918. The equation for a balanced seesaw iswd = wd . As shown in the figure1 1 2 2below, w1and w2are weights, and d2and d1are distances from the balancepoint.d 1d 2w 1w 2If w1= 50 pounds , d1= 5 feet , andw 2=100 pounds, what value ofd would balance the seesaw?ABCD22.5 feet5.0 feet7.5 feet10.0 feet19.— 2A line has a slope of and a3—y-intercept of 10. Which is anequation of the line?RELEASEDAB—2x− 3y= 30—2x− 3y= 10C 2x+ 3y= 10D—2x+ 3y= 30Page 9Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200920. Which is the correct graph for 3y= 2x−3?AC— 6— 6— 5— 5— 4— 4— 3— 3— 2— 2+ 6+ 5+ 4+ 3+ 2+ 1— 1 0— 1— 2— 3— 4— 5— 6+ 6+ 5+ 4+ 3+ 2+ 1— 1 0— 1— 2— 3— 4— 5y+ 1 + 2 + 3 + 4 + 5 + 6xBRELEASED— 6y+ 1 + 2 + 3 + 4 + 5 + 6xD— 6— 6— 5— 5— 4— 4— 3— 3— 2— 2+ 6+ 5+ 4+ 3+ 2+ 1— 1 0— 1— 2— 3— 4— 5— 6+ 6+ 5+ 4+ 3+ 2+ 1— 1 0— 1— 2— 3— 4— 5— 6yy+ 1 + 2 + 3 + 4 + 5 + 6+ 1 + 2 + 3 + 4 + 5 + 6xxPage 10Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200921. Mary’s fish tank can hold11 2 gallons of water. Which is thegreatest number of gallons of water itcan hold without overflowing?A 22B 15C 9D 522. Which choice lists the lengths in orderfrom least to greatest?ABCD1ft, 0.25 ft, 2 ft, 8 ft310.25 ft, ft, 8 ft, 2 ft310.25 ft, ft, 2 ft, 8 ft312 ft, 0.25 ft, ft, 8 ft323. The two legs of a right triangle havelengths 5 and 7. Which term bestdescribes the length of thehypotenuse?A an irrational number less than 9RELEASEDBan irrational number greaterthan 9C a rational number less than 9D a rational number greater than 924. If three is added to both the lengthand width of the rectangle, what willhappen to the area?ABCD2 in.5 in.The area will be four times theoriginal area.The area will be three times theoriginal area.The area will be 12 sq in. morethan the original area.The area will be 4 sq in. morethan the original area.Page 11Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200925. Joe wanted to know the distance across a river. He made a drawing with two similartriangles, as shown below.2.0 cm6.4 cmWhat is the distance across the river, x?ABCD1.6 m9.4 m16.0 m25.6 m5.0 cmmRELEASEDxPage 12Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200926. A square tile has an area of110 square centimeters. Which is thebest estimate of the length of oneside?ABCD10.0 centimeters10.5 centimeters11.0 centimeters11.5 centimeters27. The vertices of a rectangle are( 0, 0 ), ( 0, 4 ), ( 2, 4 ), ( 2, 0 ). Whichof the following points is a vertexfor the image produced by adilation with a scale factor of 1 2 ?A ( 0, 3)B ( 0, 2)C ( 0, 1)D ( 2, 1)RELEASEDPage 13Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200928. Kendra has a rectangular poster board with dimensions of 10 ft by 4 ft. She would like tocut this poster board into 6 pieces, so she can construct a box.4 ft10 ftIf she uses the indicated cutting guides, what will be the dimensions of her box?A 2 ft × 2 ft × 4 ftB 4 ft × 4 ft × 2 ftC 5 ft × 2 ft × 1 ftD 10 ft × 4 ft × 1 ftRELEASEDPage 14Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200929. Which scatterplot displays a negative correlation?AC3231.53130.53029.52928.52827.51985 1990 1995 2000 20052002200019981996199419921990198827 28 29 30 31 32BD3231.53130.53029.52928.52827.51985 1990 1995 2000 20050.201985 1990 1995 2000 2005RELEASED1.41.21.00.80.60.4Page 15Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200930. Which suggestion would result in anunbiased sample that would bestrepresent the favorite books of thewhole eighth-grade class?ABCDAsk five randomly chosenstudents from each class in theeighth grade.Ask eighth-grade girls.Ask randomly choseneighth-grade students who playsports.Ask students in the library afterschool.31. This scatterplot could show therelationship between which twovariables?RELEASEDABCDyspeed of an airplane (x) vs.distance traveled in one hour (y)outside air temperature (x) vs. airconditioning costs (y)age of an adult (x) vs. height of anadult (y)distance traveled (x) vs. gasremaining in the tank (y)xPage 16Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200932. According to the pattern established in the scatterplot, what y-value would correspond toan x-value of 11?A 32B 25C 15D 8y20181614121086420x5 10 15 20 25 30 35 40RELEASEDPage 17Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200933. Bill collected and plotted data concerning gestation and longevity for a science project.353025201510500Animal Gestation vs. Longevity100 200 300 400Gestation (in Days)Based on the line of best fit shown, about how long would an animal be expected to live ifits gestation period is 300 days?ABCD10 years12 years20 years22 years34. A rental company charges a flat fee of $50 to rent a jet ski. In addition, renters must pay$17.50 per hour of ski use. Which equation correctly represents the total cost, c, to rent ajet ski for h hours?A c = 50.00h+17.50RELEASEDB c = 17.50h+50.00C c = 32.5hD c = 67.5hPage 18Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200935. Heather recorded the 7 a.m. temperature at her house the first five days of four differentmonths. Which data are nonlinear?ACJanuary BDay °F12345—1491419March DDay °F123454151465153FebruaryRELEASEDDay12345Day12345April°F3129272523°F5357616569Page 19Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200936. 1( )ACWhich line has a slope of and passes through the point 2, 3 ?2+ 6+ 5+ 4+ 3+ 2+ 1y B— 6 — 5 — 4 — 3 — 2 — 1 0 + 1 +2 +3 + 4 +5 + x6— 1— 2— 3— 4— 5— 6+ 6+ 5+ 4+ 3+ 2+ 1y D— 6 — 5 — 4 — 3 — 2 — 1 0 + 1 + 2 + 3 + 4 + 5 +x6— 1— 2— 3— 4— 5— 6RELEASED+ 6+ 5+ 4+ 3+ 2+ 1y— 6 — 5 — 4 — 3 — 2 — 1 0 + 1 +2 + 3 + 4 + 5 + x6— 1— 2— 3— 4— 5— 6+ 6+ 5+ 4+ 3+ 2+ 1— 6 — 5 — 4 — 3 — 2 — 1 0 + 1 +2 + 3 + 4 + 5 +x6— 1— 6— 2— 3— 4— 5yPage 20Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200937.What is the equation of the line—1 —( 2 )that contains the point , 3and has a slope of 3?ABCDyyyy— 33x2= −— 173x2= −— 33x2= +— 173x2= +38. A cube has a volume of 24 cubic units.What is the approximate length ofeach side of the cube?RELEASEDABCD8 units4.9 units2.9 units2 unitsPage 21Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 2009939. The equation y = x + 32 can be used to find Fahrenheit temperature (y) when given5Celsius temperature (x). If this equation were graphed in a coordinate plane, what wouldbe the x- and y-intercepts?−A160x-intercept = ( 32, 0 ); y-intercept = ( 0,9 )−B x-intercept = ( 0, 32 ); y-intercept = ( 160 , 0)−C x-intercept = ( 0, 160 ); y-intercept = ( 32, 0)−9D x-intercept = ( 160 , 0 ); y-intercept = ( 0, 32)940. A truck rental company charges $20 plus 9 cents per mile. Joe’s friend offers to rent Joehis truck for $35 and won’t charge him mileage. What is the minimum number of milesJoe has to drive to save money using his friend’s truck?A 17B 55C 121D 1679RELEASEDPage 22Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200941. What is the order of the numbers fromleast to greatest?ABCD3 152, 16, , 1.673 151.6, 2, 16,715732, 1.6, , 1615731.6, 2, , 162, 16, , 1.63 15742. The formula s = 20 273 + T gives anestimate for the speed (s) of sound inmeters per second when the airtemperature is T° C. About how fastis the speed of sound when thetemperature is — 5C ° ?ABCD268 m/s278 m/s327 m/s333 m/s43. The solution to an inequality is x ≥ 5.Which number is included in thatsolution?A 10B 30C 2 5D 3 244. What is the perimeter of a trianglewhose dimensions are three times thesize of PQR ?RELEASEDABCDP23 ft27.1 ft69 ft81.3 ft7 ftR10 ft4.1 ft6 ftQPage 23Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200945. A tree has a shadow 12 feet long. Atthe same time, John, who is five feettall, has a shadow 4 feet long. IfSherry wants to find the height of thetree, which proportion should she use?ABCDx 5 =4 12x 8 =5 4x 5 =8 4x =512 446. Triangle ABC has vertices at A (2, 2),B (2, 7), and C (6, 3). This triangle isdilated by a scale factor of 3. What isthe location of point C′ ?A (2, 1)B (6, 6)C (6, 21)D (18, 9)47. The diagonal of a square televisionscreen measures 27 inches. What isthe approximate length of thescreen?RELEASEDABCD13 in.15 in.19 in.21 in.48. The coffee can below is 3 4 full.8 in.3 in.CoffeeHow much coffee is in the can?ABCDabout57 in.about 130 in.about 170 in.3about 226 in.333Page 24Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200949. Each point on the graph represents the relationship between the number of pencils in apackage and how much the package costs.8 16 24 32 40 48Number of Pencils per PackageWhich package has the highest cost for each pencil?ABCDWXYZ43210WXZRELEASEDYPage 25Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200950. Charles researched the price of video games over the last decade.Video Game Prices302520151051995 1997 1999 2001 2003Year2005Based on the data shown, what would be the projected price of a video game in 2005?A $9.50B $15.50C $18.00D $19.5051. Mr. Larson’s first math test resulted in the following grades:21, 23, 35, 43, 46, 50, 53, 59,62, 66, 66, 66, 67, 75, 89, 95A passing grade is anything above a 60. Mr. Larson says the central tendency for the classwas to fail the test. Which statistical measure supports his claim?ABCRELEASEDmodemedianupper quartileDmeanPage 26Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200952. Kevin made a scatterplot of noon temperatures for a two-week period.Noon Temperatures78°76°74°72°70°68°66°64°62°60°2 4 6 8 10 12 14 16 18DayWhich statement about the data is most accurate?ABCDThe temperature had a slight increase each day.The temperature had a slight decrease each day.There was a trend for the temperature to increase during the second week.There was a trend for the temperature to increase during the first week.RELEASEDPage 27Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200953. A scatterplot is shown to have anegative relationship between the twovariables. Which line of best fit couldrepresent that scatterplot?ABy = — 2x+ 4y =— 1C y = x − 5D y = 3x+ 454. Which would be an appropriate firststep to solve y = 5x + 3 for x?ABCDsubtract 3 from both sidesadd 3 to both sidessubtract 5 from both sidesadd 5 to both sides55. Brittany programs the treadmill sothat she will burn 3.2 calories perminute as she works out. What is theequation relating walking time (x) inminutes to total calories burned (y)?A y = 3.2xRELEASEDB y = 3.2 + xCDy =y =3.2xx3.256. The cost of attending the state fair is a$5.00 admission charge and $1.50 perride. Elizabeth’s mother gave herd dollars to spend at the state fair.Which equation could be used todetermine the maximum number ofrides, r, Elizabeth can go on?A r = 1.50d+ 5.00B r ( d )= + 5.00 ÷ 1.50C r ( d )= − 5.00 ÷ 1.50D r = 1.50d− 5.0057. The equation d = 65hdescribes thedistance (d) a vehicle travels inh hours. Based on this formula, howlong will it take a car to travel90 miles?ABCD98 minutes83 minutes43 minutes25 minutes58. Which equation is nonlinear?A 2x− y = 9By2= x +3C y = 2x−3D x = yPage 28Go to next page

E O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +NCDPI North Carolina Test of Mathematics. Grade 8 Form R RELEASED Fall 200959.What is the slope of the line that( )—( )passes through the points 1, 3 andABCD4,2 ?5335— 35— 5360.What is the equation of the line with2a slope of and a y-intercept of 4 ?3A 2x+ 3y= 12B 2x+ 3y= 4RELEASEDCD—3x− 2y= 4—2x− 3y= 12STOPEnd of Mathematics–Calculator ActivePage 29Go to next page

North Carolina Test of MathematicsGrade 8 Form R RELEASED Fall 2009Answer KeyCALCULATOR ACTIVEItem Number Correct Answer Goal1 A 1 – Number and Operations2 C 1 – Number and Operations3 C 1 – Number and Operations4 A 2 – Measurement5 D 2 – Measurement6 C 3 – Geometry7 C 3 – Geometry8 A 4 – Data Analysis and Probability9 B 3 – Geometry10 D 4 – Data Analysis and Probability11 C 4 – Data Analysis and Probability12 C 4 – Data Analysis and Probability13 A 4 – Data Analysis and Probability14 C 5 – Algebra15 C 5 – Algebra16 A 5 – Algebra17 D 5 – Algebra18 A 5 – Algebra19 D 5 – Algebra20 B 5 – Algebra21 B 1 – Number and Operations22 C 1 – Number and Operations23 A 1 – Number and Operations24 A 2 – Measurement25 C 2 – Measurement26 B 3 – Geometry27 B 3 – Geometry28 A 3 – Geometry29 B 4 – Data Analysis and Probability30 A 4 – Data Analysis and Probability31 D 4 – Data Analysis and Probability32 D 4 – Data Analysis and Probability33 C 4 – Data Analysis and Probability34 B 5 – Algebra35 C 5 – Algebra36 B 5 – Algebra37 A 5 – Algebra38 C 5 – Algebra39 D 5 – AlgebraRELEASEDE O G7 8 9 /4 5 6 *1 2 3 _0 +/_ . +31 July 2009 Page 1

North Carolina Test of MathematicsGrade 8 Form R RELEASED Fall 2009Raw to Scale Score ConversionRaw Score Scale Score0 3321 3332 3333 3344 3345 3356 3357 3368 3379 33710 33811 33912 34013 34114 34215 34316 34417 34518 34619 34720 34821 34922 35023 35124 35225 35326 35427 35528 35629 35730 35731 35832 35933 36034 36035 36136 36137 36238 36339 36340 36441 364RELEASED10 August 2009 Page 1

North Carolina Test of MathematicsGrade 8 Form R RELEASED Fall 2009Raw to Scale Score Conversion42 36543 36644 36645 36746 36747 36848 36949 36950 37051 37152 37253 37254 37355 37456 37557 37758 37859 38160 383RELEASED10 August 2009 Page 2