jefferson math project regents by chapter

JEFFERSON MATH PROJECTREGENTS BY CHAPTER

794 NY Math Regents Exam Questions Sorted by Amsco Chapter

INTEGRATED ALGEBRA(Answer Key)

www.jmap.org

Dear Sir

I have to acknolege the reciept of your favor of May 14. in which you mention that you have finished the 6.first books of Euclid, plane trigonometry, surveying & algebra and ask whether I think a further pursuit ofthat branch of science would be useful to you. there are some propositions in the latter books of Euclid, & someof Archimedes, which are useful, & I have no doubt you have been made acquainted with them. trigonometry,so far as this, is most valuable to every man, there is scarcely a day in which he will not resort to it for some ofthe purposes of common life. the science of calculation also is indispensible as far as the extraction of thesquare & cube roots; Algebra as far as the quadratic equation & the use of logarithms are often of value inordinary cases: but all beyond these is but a luxury; a delicious luxury indeed; but not to be indulged in byone who is to have a profession to follow for his subsistence. in this light I view the conic sections, curves of thehigher orders, perhaps even spherical trigonometry, Algebraical operations beyond the 2d dimension, andfluxions. Letter from Thomas Jefferson to William G. Munford, Monticello, June 18, 1799.

Math Regents Exam Questions - Amsco Integrated Algebra Chapter 1 Page 1www.jmap.org

[1] D

[2] D

[3] C

[4] B

[5] A

[6] C

[7] B

[8] A

[9]

[2] No, and a correct justification is given.[1] No, but an incomplete or partiallyincorrect explanation is given.[0] No, but no explanation is given.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[10] A

[11] D

[12]

[2] An irrational number is written, and anappropriate explanation is written, such as anirrational number cannot be written as afraction or as a repeating or terminatingdecimal.[1] An irrational number is written, such as πor the square root of a nonperfect square, butno explanation or an inappropriateexplanation is written.or [1] A correct definition of an irrationalnumber is written, but the example is missingor is inappropriate.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[13] A

[14] B

[15] A

[16] B

[17] B

[18] A

[19]

[2] 196, and an appropriate explanation isgiven.[1] An incorrect answer is chosen, but anappropriate explanation is given.or [1] 196, but no explanation or anincorrect explanation is given.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[20] A

[21]

[2] 2 45

8 3 1 2 3, , . , ,π and appropriate

work is shown, such as converting each valueto a decimal equivalent.[1] All values are correctly converted todecimal equivalents, but the order is notindicated or is indicated incorrectly.or [1] One or two computational errors aremade in finding decimal equivalents, butthe appropriate order is indicated.or [1] Appropriate work is shown, but oneconceptual error is made, such as indicatingthe order from greatest to least.

or [1] 2 45

8 3 1 2 3, , . , ,π , but no work is

shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[22] A

[23] A

[24] A

[25] A

[26] A


[27] D

[28] B

[29] B

[30] A

[31] D

[32] C

[33] B

[34] B


[1] B

[2] B

[3] D

[4] D

[5]

[3] All three examples are illustrated underdivision correctly, such as 2 0÷ , − ÷2 4,− ÷ −2 4, and correct explanations are given.[2] Only two of the three examples areillustrated and explained correctly.or [2] All three examples are illustratedcorrectly, but only one explanation is given oris correct.or [2] The division examples and explanationsare correct, but at most two incorrectexamples are also shown, such as examplesfor addition, subtraction, or multiplication.[1] The division examples and explanationsare correct, but more than two incorrectexamples are shown, such as examples foraddition, subtraction, or multiplication.or [1] All three examples are illustratedcorrectly, but no correct explanation is given.or [1] Only one correct example with acorrect explanation is given.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[6] C

[7] C

[8] C

[9] D

[10] D

[11] D

[12] D

[13] D

[14] C

[15] B

[16] A

[17] A

[18] A

[19] A

[20] C

[21] C

[22] D

[23] A

[24] B

[25] A

[26] B

[27] C

[28] B

[29] D

[30]

[2] 0, and an appropriate explanation is given,such as 0 is the number that when added toany number results in that number or does notchange it, or 1 + 0 = 1, 2 + 0 = 2, and 3 + 0 =3.[1] 0, but no explanation or an incorrectexplanation is given.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[31] B

[32] B

[33] C

[34] B


[35]

[2] 1, and an appropriate explanation is given,such as when 1 is added to 3, the result is theidentity element, 4; therefore 1 is the inverseof 3.[1] 1 + 3 = 4, but the identity element is notidentified.or [1] 4 is identified as the inverse becausethe identity element and inverse element areconfused.or [1] 1, but no explanation or an incorrectexplanation is given.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[36] C

[37] A


[1] D

[2] D

[3] A

[4] C

[5] A

[6] B

[7]

[2] No, and an appropriate explanation isgiven or the expression is evaluated correctly.[1] No, and the correct order of operations isused to evaluate 2 3 52( ) ,+ but onecomputational error is made.or [1] One conceptual error is made inevaluating the expression, but the question isanswered appropriately.or [1] Appropriate work is shown, but thequestion is not answered.[0] No, but no explanation or an inappropriateexplanation is given.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[8] B

[9] B

[10] B

[11] D

[12] B


[1] D

[2] D

[3] A

[4] B

[5]

[2] 6, and appropriate work is shown, such assolving the equation 2x + 3 = 15 or trial anderror with at least three trials and appropriatechecks.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] A correct equation is written, but nofurther correct work is shown.or [1] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but no solutionis found.or [1] 6, but no work or fewer than three trialsand appropriate checks are shown.[0] A zero response is completely incorrect,irrelevant or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[6] C

[7] C

[8] B

[9]

[4] $167.50, and appropriate work is shown,such as 350x + (150)(130) = 1.25(62,500) ortrial and error with at least three trials withappropriate checks.[3] Appropriate work is shown, but onecomputational error is made.[2] Appropriate work is shown, but more thanone computational error is made.or [2] $167.50, but only one trial with anappropriate check is shown.[1] $167.50, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[10]

[2] 21 and the student shows an appropriatesolution, such as the equation x + x + 1 + x +2 = 63 or trial and error.[1] Appropriate work is shown, but anincorrect answer is found.or [1] An incorrect equation is shown, but it issolved appropriately to find an answer, suchas x + x + 2 + x + 4 = 63.or [1] 21 but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[11] D

[12] B

[13]

[2] 4, and appropriate work is shown.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 4, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[14] B

[15] B

[16] B

[17] D


[18]

[2] 10, and appropriate work is shown, suchas solving the equation or trial and error withat least three trials and appropriate checks.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but no solutionis found.or [1] 10, but no work or fewer than threetrials and appropriate checks are shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[19] B

[20] C

[21] D

[22]

[2] 18 and correct substitution, F = 95

(-8) +

32, is shown.[1] A correct substitution method is shown,but one computational error is made.or [1] The answer is not rounded to thenearest integer, such as 17.6 or 17 .or [1] The student substitutes -8 for F, butthen solves appropriately for C.or [1] The student substitutes +8 for C, butthen solves appropriately for F.or [1] 18 but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[23]

[2] 50, and appropriate work is shown, such

as solving the equation 10 59

32= −( ).F

[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] Correct substitution is made into theequation, but no further correct work isshown.or [1] 50, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[24] D

[25]

[3] 3 hours and an appropriate method orequation is shown, such as 45(x + 1) = 60x.[2] An appropriate method is shown, but anincorrect answer is found, such as4 hours (the truck's time) or 180 milestraveled.[1] An appropriate equation or method isshown, but no answer is found, such asshowing an equation that reflects a one-hourdifference in time but it is not solved.or [1] 3 hours and no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[26] A


[27]

[2] Bob, and appropriate work is shown, suchas using the distance formula to calculate thetwo travel times or setting up a proportion.[1] Appropriate work is shown, but onecomputational or conceptual error is made,but an appropriate answer is found.or [1] Appropriate work is shown, but noanswer or an incorrect answer is found.[0] Bob, but no work or inappropriate work isshown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[28]

[2] 5, and appropriate work is shown, such assolving the linear equation 80x + 100x = 900,using a diagram or proportion or trial anderror.[1] Appropriate work is shown, but onecomputational error is made.or [1] 5, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[29]


as 15150

2=x

.

[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as expressing

the answer as 13

hour.

or [1] 20, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[30] D

[31] B

[32]

[3] 4 and an appropriate method is shown,such as calculating A at 6 mph and B at 2mph through arithmetic, formula, orextending the graph to 60 minutes.[2] The speeds of 6 and 2 are found but nottheir difference.or [2] Their difference is found but not inmiles per hour.[1] Only distances of 4.5 miles and 1.5 milesare found.or [1] The speeds found are incorrect but thenare subtracted appropriately.or [1] 3 times as fast and no appropriateexplanation is given.or [1] 4 and no appropriate explanation isgiven.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[33]

[3] 12, and appropriate work is shown, suchas finding the rates of both vehicles and thensubtracting 48 from 60.[2] Appropriate work is shown, but onecomputational error is made.or [2] The rates of both vehicles are foundcorrectly, and appropriate work is shown, butthey are not subtracted.or [2] The rates of both vehicles are foundcorrectly, and the correct difference is found,but no work is shown.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] The rates of both vehicles are foundcorrectly, but no work is shown, and thedifference is not found.or [1] 12, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[34]

[3] 50, 1.5, and 10, and appropriate work isshown.[2] Appropriate work is shown, but onecomputational error is made.[1] Appropriate work is shown, but oneconceptual error is made.or [1] Appropriate work is shown, but two ormore computational errors are made.or [1] 50, and appropriate work is shown, butno further correct work is shown.or [1] 1.5, and appropriate work is shown, butno further correct work is shown.or [1] 10, and appropriate work is shown, butno further correct work is shown.or [1] 50, 1.5, and 10, but no work is shown.[0] 50 or 1.5 or 10, but no work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[35] C

[36] B

[37] C

[38] B

[39] B

[40]

[2] 6 2x − or an equivalent expression, andappropriate work is shown, such as2 2 3 2 4 6 2( ) ( ) .x x x+ + − = −[1] The length is represented correctly as2 3x + and the width as x − 4, but therepresentation of the perimeter is determinedincorrectly.or [1] The length, the width, and the perimeterare represented appropriately, but by avariable other than x.or [1] One or both dimensions are representedincorrectly, but the perimeter is representedappropriately.[0] One or both dimensions are representedincorrectly, and the perimeter is notdetermined.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[41]

[3] 18, and appropriate work is shown.[2] Appropriate work is shown, but onecomputational error is made.or [2] Appropriate work is shown, and thevalue of x is found, but no further correctwork is shown.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] A correct expression is written for theperimeter of each figure, but no furthercorrect work is shown.or [1] 18, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[42] B

[43] C

[44] C

[45] D

[46] C


[47] A

[48] D

[49] D

[50] C

[51] A

[52] C

[53]

a [1] S + 243

or S3

8+

b [1] 11.5or [1] Correct substitution into an incorrectpart a is shown, and the answer is given to thenearest tenth of an inch.a and b[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[54] A

[55] B

[56] B

[57] D

[58] C

[59]

[3] -5, -3, -1, and appropriate work is shown,such as solving the inequality or trialand error with at least three trials andappropriate checks.[2] Appropriate work is shown, but onecomputational error is made.or [2] Appropriate work is shown, and the

inequality x ≥ −5 13

is written, but no further

correct work is shown.or [2] The trial-and-error method is used tofind the correct solutions, but only twotrials and appropriate checks are shown.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but thesolutions are not found.or [1] -5, -3, -1, but no work or only one trialwith an appropriate check is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[60] D

[61] C

[62] A

[63] D


[64]

[2] A correct graph is drawn on the numberline, with a closed circle at the left end and anopen circle at the right end.[1] Appropriate work is shown, but onegraphing error is made, such as writing anincorrect scale on the number line.or [1] Appropriate work is shown, but oneconceptual error is made, such as using aclosed circle instead of an open circle.or [1] A correct inequality is written, but thegraph is not drawn.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[65]

[2] 65, and appropriate work is shown, suchas solving the inequality 15 225 750x ≥ + ortrial and error with at least three trials andappropriate checks.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but no solutionis found.or [1] 65, but no work or fewer than threetrials and appropriate checks are shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[66]

[3] 7, and appropriate work is shown, such assolving the inequality 15 22 120x + ≥ , solvingan equation, or trial and error with at leastthree trials and appropriate checks.[2] Appropriate work is shown, but onecomputational or rounding error is made.or [2] The trial-and-error method is used tofind a correct solution, but only two trials andappropriate checks are shown.[1] Appropriate work is shown, but two ormore computational or rounding errors aremade.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] An incorrect equation of equaldifficulty is solved appropriately.or [1] A correct inequality or equation iswritten, but no further correct work is shown.or [1] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but no solutionis found.or [1] 7, but no work or only one trial with anappropriate check is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[67] D

[68] C

[69]

[2] 6, and appropriate work is shown, such as0.70x + 0.30 ≤ 5.00 or trial and error withthree trials and appropriate checks.[1] The inequality is solved correctly, but thenumber of doughnuts is not found.or [1] The trial-and-error method is used tofind a correct solution, but fewer than threetrials are shown.or [1] 6, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[70]

[3] 15 and an appropriate method orexplanation is shown, such as trial and erroror the inequality 6x + 15 ≥ 100.[2] An appropriate method is shown, but itstops at 14.[1] An appropriate method is shown, but noanswer is found.or [1] 15 and no explanation is given.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[71] B


[1] A

[2] A

[3] D

[4] A

[5] B

[6] B

[7] C

[8] D

[9] A

[10] D

[11] D

[12] A

[13] B

[14]

[2] 4 10 22x x+ + , and appropriate work isshown, such as ( ) ( ).9 3 4 5 7 62 2x x x x+ − − − −[1] The setup is correct, but the distribution ofthe negative sign is incorrect.or [1] 14 4 102x x− − , but appropriate work isshown.or [1] 4 10 22x x+ + , but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[15] C

[16] C

[17] C

[18] D

[19] B

[20] C

[21] D

[22] A

[23] A

[24] B

[25] A

[26] D

[27] D

[28] C

[29] D

[30] B

[31] C

[32] B

[33] B

[34] D

[35] A

[36] D

[37] A

[38] D

[39] A

[40] B

[41] A

[42] A

[43] C

[44] D

[45] D

[46] D

[47] B

[48] D

[49] A

[50] C


[51] A

[52] C

[53]

[3] 499 days and appropriate work is shown,

such as 17 000 000

1420 24

, , milesmileshour

hoursday

×.

[2] Appropriate work is shown, but onecomputational error is made or the studentincorrectly calculates 17 107. × by onedecimal place.or [2] Appropriate work is shown, but theanswer is rounded incorrectly or is notrounded.[1] 17 107. × = 17,000,000 is shown.

or [1] 17 101420

11 9718317. , .× = hours is shown.

or [1] 34,080 miles in 1 day is shown.or [1] 499 but no work is shown.[0] The student does not understand scientificnotation.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[54] B

[55] C

[56] D

[57] D

[58] A

[59] C

[60] D

[61] A

[62] A

[63] A

[64] D


[1] B

[2] B

[3] A

[4] C

[5]

[4] $52,950, $35,300, and $88,250 and anappropriate method is shown, such as 3x + 2x+ 5x = $176,500.[3] A correct equation is set up or multiplied

by correct fractional values 310

, 210

, and 510

,

but a computational mistake is made, andthree appropriate values are found.or [3] An appropriate method is shown, butnot all three values are found.[2] The equation is set up correctly, butnumerous computational mistakes are made,and three appropriate values are found.or [2] An incorrect equation is shown, butthree appropriate values are found.or [2] An appropriate equation is shown but issolved only for x (17,650).[1] The equation is set up correctly, but noappropriate values are found.or [1] Three correct answers are found, andno work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[6] D

[7] D

[8]

[4] $68,000, and appropriate work is shown.[3] $119,000 and $51,000, and appropriatework is shown, but the answers are notsubtracted to find the difference.or [3] Appropriate work is shown, but onecomputational error is made.[2] Appropriate work is shown, but more thanone computational error is made.[1] The value for one share ($17,000) isfound, but no further correct work is shown.or [1] $68,000, but no work is shown.[0] $17,000 or $119,000 or $51,000, and nowork is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[9] D

[10] B

[11] B

[12] D

[13]

[2] $178.50, and appropriate work is shown,such as solving a proportion, using a table, ortrial and error with at least three trials andappropriate checks.[1] Appropriate work is shown, but onecomputational error is made.or [1] An appropriate proportion is set up, butno solution or an incorrect solution is found.or [1] An incorrect proportion is set up, but anappropriate solution is found.or [1] $178.50, but no work is shown or fewerthan three trials with appropriate checks areshown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[14]

[2] 6 23

or 6 hr 40 min or 6 66. or an

equivalent answer, and appropriate work isshown.[1] 400 min, but the answer is not convertedinto hours.or [1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but theanswer is rounded to the nearest hour.

or [1] 6 23

or 6 hr 40 min or 6 66. or an

equivalent answer, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[15] B

[16] C

[17] B

[18]

[2] 319, and appropriate work is shown.[1] A correct proportion is shown, but nosolution or an incorrect solution is found.or [1] An incorrect proportion of equaldifficulty is solved appropriately.or [1] Appropriate work is shown, but onecomputational error is made.or [1] 319, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[19] B

[20]


as a diagram or 122 75. = x .

[1] Appropriate work is shown, but no answeror an incorrect answer is found.or [1] 45, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[21]

[2] 15, and any equivalent proportion,equation, or fraction conversion is shown,

such as 1216 20

= x .

[1] An appropriate proportion, equation, orfraction conversion is shown, but onecomputational or conceptual error is made.or [1] An incorrect proportion, equation, orfraction conversion is shown, but anappropriate answer is found for the incorrectproportion.or [1] 15, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[22]

[2] 78.6%, and appropriate work is shown.[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 78.6%, but no work is shown.[0] A zero response is completely incorrect,irrelevant, incoherent or is a correct responsethat was obtained by an obviously incorrectprocedure.

[23] D

[24]

[2] 20, and appropriate work is shown, suchas (180 ÷ 0.9) - 180.[1] A partial answer is found, such as 200students are enrolled, but 180 is notsubtracted from the answer.or [1] An appropriate equation is shown, butone computational error is made, but 180 issubtracted.or [1] An answer of 18 is found by subtracting180 x 0.9 from 180.or [1] 20, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[25] A


[26]

[3] No, it will not differ and the student showsthat both methods lead to $47.08, such as $55x .80 = $44, $44 x 1.07 = $47.08, $55 x 1.07= $58.85, and $58.85 x .80 = $47.08.[2] Both ways are computed, onecomputational mistake is made, and anappropriate answer is found.or [2] Both ways are computed correctly, butno comparison is found.[1] At least one way is computed correctly,but no comparison is found.or [1] Both ways are computed incorrectly,but an appropriate comparison is found.[0] Both ways are computed incorrectly, andno comparison is found.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[27]

[2] $40, and appropriate work is shown.[1] Appropriate work is shown, but onecomputational error is made.or [1] $40, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[28]

[3] $800, and appropriate work is shown,such as 0.15x + 50 = 170 or a table of valuesor trial and error with at least three trials andappropriate checks.[2] Appropriate work is shown, but onecomputational error is made.or [2] The trial-and-error method is used tofind the correct solution, but only two trialsand appropriate checks are shown.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] Appropriate work is shown, but the $50per day is not included in his pay, resulting inan answer of $1,133.33.or [1] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but no solutionis found.or [1] $800, but no work or only one trial withan appropriate check is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[29]

[2] 44, and appropriate work is shown, suchas 0.8(200 - 145).[1] Appropriate work is shown, but onecomputational or conceptual error is made.or [1] 44, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[30]

[2] 20.7, and appropriate work is shown, such

as 141288683748 100

= x .

[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 20.7, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[31] C

[32] C

[33]

[3] 1,095 and 1,209, and appropriate work isshown.[2] Appropriate work is shown, but onecomputational error is made.or [2] Appropriate work is shown, but awhole-number solution is not found.or [2] 5% of CD cases is rounded to 58, but58 is added to or subtracted from 1,152appropriately.or [2] Appropriate work is shown, but onlyone correct solution is found.[1] Appropriate work is shown, but more thanone computational error is made.or [1] 5% of CD cases is rounded to 58, but58 is added to or subtracted from 1,152, butone computational error is made.or [1] 5% of 1,152 is found, but no furtherwork is shown.or [1] 1,095 and 1,209, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[34]

[2] 42.85714286 or an equivalent answer, andappropriate work is shown.[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] An answer of 30 is found by dividing1.8 by 6.or [1] An answer of 70 is found by dividing4.2 by 6.or [1] 42.85714286 or an equivalent answer,but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[35] D

[36] A

[37] A

[38] C

[39]

[2] 70.92, and appropriate work is shown,such as a proportion.[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 70.92, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[1] D

[2] D

[3]

[2] 75, and appropriate work is shown.[1] Appropriate work is shown, but onecomputational error is made.or [1] An incorrect equation of equaldifficulty, such as x + 5x = 180, is solvedappropriately, and an appropriate anglemeasure is found.or [1] A correct equation is written and solvedfor x, but no further correct work is shown.or [1] 75, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[4] D

[5] C

[6] A

[7]

[3] 120, and appropriate work is shown, suchas 6t + 30 + 8t – 60 = 180.[2] The student finds correctly the unknown, t= 15, but does not find the measure of angle4.or [2] Appropriate work is shown, but onecomputational error is made.[1] The student forms an incorrect equation,such as setting the two angles equal, andarrives at t = 45 and an angle of 300.or [1] 120, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[8]

[3] 95, and appropriate work is shown, suchas 3 20 60 180x x− + + = .[2] Appropriate work is shown, but onecomputational error is made.or [2] A correct equation is written andsolved for x, but m∠ROY is not found.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but oneconceptual error is made, such as writingthe equation x x+ = −60 3 20, but anappropriate answer is found.or [1] A correct equation is written, but nofurther correct work is shown,or [1] 95, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[9] A

[10] A

[11]

[3] 80, and appropriate work is shown.[2] x = 30 is shown, but the student fails tosubstitute to find m AEC∠ .or [2] x = 30 is shown, but the student statesthat the answer is 100° , by finding thesupplement of ∠AEC .or [2] The student makes one computationalerror in the solution of the correct equation4x - 40 = x + 50 but appropriately substitutesthe incorrect value to solve for m AEC∠ .[1] The student makes one computationalerror in the solution of the correct equation 4x- 40 = x + 50 and fails to substitute to findm AEC∠ .or [1] The student makes more than onecomputational error in the solution of thecorrect equation 4x - 40 = x + 50, butappropriately substitutes the incorrect value tosolve for m AEC∠ .or [1] 80, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[12]

[4] 112.5, and appropriate work is shown,such as solving the equation 5 20 50x x− = + .[3] Appropriate work is shown, but onecomputational error is made.or [3] m BED∠ = 67 5. or m AEC∠ = 67 5. , butno further correct work is shown.[2] Appropriate work is shown, but two ormore computational errors are made.or [2] Appropriate work is shown, but oneconceptual error is made, but an appropriatemeasure for ∠CEB is found.or [2] A correct equation is written and solvedfor x, but no further correct work is shown.[1] Appropriate work is shown, but oneconceptual error and one computational errorare made.or [1] 112.5, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[13] B

[14] D

[15] A

[16]

[3] 65, and appropriate work is shown, suchas setting the given angles equal to each otherand determining the value of x to be 16, andcorrect substitution is shown.[2] The given angles are set equal to eachother, the correct value of x is determined, butno substitution is shown.or [2] The given angles are set equal to eachother, and substitution is shown, but onecomputational or substitution error is made.[1] The given angles are set equal to eachother, but no further work is shown.or [1] An incorrect equation is solvedappropriately, such as 5x – 15 + 2x + 33 =180.or [1] 65, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[17] B

[18] A

[19] A

[20] D

[21]

[2] 57°, and appropriate work is shown, suchas determining that m FYD m BXY∠ ≅ ∠ and∠AXY is supplementary to ∠BXY .or [2] 57°, and a correctly labeled diagramwith appropriate angles is shown.[1] ∠CYX or ∠BXY is determined, but onecomputational error is made in subtracting tofind m AXY∠ .or [1] An angle is determined incorrectly, butan appropriate solution is found.or [1] 57°, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[22]

[2] 31, and appropriate work is shown, suchas 5x + 25 = 180.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as setting thegiven angles equal to each other.or [1] A correct equation is written, but nofurther correct work is shown.or [1] 31, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[23]

[4] 146, and appropriate work is shown, suchas solving the equation 2x = 5x - 51.[3] Appropriate work is shown, but onecomputational error is made.or [3] The measure of ∠FHB or ∠DGH isfound to be 34, and appropriate work isshown, but no further correct work is shown.[2] Appropriate work is shown, but two ormore computational errors are made.or [2] Appropriate work is shown, but oneconceptual error is made, such as solving theequation 2x + 5x - 51 = 180.or [2] The correct equation is solved for x =17, but no further correct work is shown.[1] Appropriate work is shown, but oneconceptual error and one computational errorare made.or [1] The correct equation is written, but nofurther correct work is shown.or [1] 146, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[24] B

[25]

[4] m A m B and m C∠ = ∠ = ∠ =20 59 101, , ,and appropriate work is shown.[3] Appropriate work is shown, but onecomputational error is made.or [3] A correct equation is written andsolved, and the correct measures for theangles are found, but they are not labeled orare labeled incorrectly.[2] Appropriate work is shown, but two ormore computational errors are made.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] A correct equation is written and solvedfor x, but the measures of the angles are notfound.or [2] An incorrect equation of equaldifficulty is solved appropriately, and thethree angles are found.[1] Appropriate work is shown, but oneconceptual error and one computational errorare made.or [1] A correct equation is written, but nofurther correct work is shown.or [1]m A m B and m C∠ = ∠ = ∠ =20 59 101, , ., butno work is shown.[0] m A or m B or m C∠ = ∠ = ∠ =20 59 101,but no work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[26] B

[27] B

[28] C

[29] C

[30] C

[31] B

[32] C

[33] D


[34]

[2] 29, and appropriate work is shown, suchas 92 – 63 = 29.[1] The correct application of the exteriorangle theorem is shown, but one or morecomputational errors are made.or [1] The correct application ofsupplementary angles and the sum of theangles of a triangle are shown, but one ormore computational errors are made.or [1] m BCA∠ is calculated incorrectly, butthe sum of the angles in a triangle is usedappropriately.or [1] 29, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[35]

[2] 120, and appropriate work is shown, suchas m CDB∠ = − =180 130 150 andm CBA∠ = + =70 50 120 or correctly labeledangles in a diagram.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] m CBD∠ = 60 is found, but no furthercorrect work is shown.or [1] 120, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[36] D

[37]

[2] 32, and appropriate work is shown, suchas a diagram or “let” statements and anappropriate equation, such as 5x + 20 = 180.or [2] 32, and an appropriate trial-and-errormethod with at least two trials andappropriate checks are shown.[1] Appropriate work is shown, but onecomputational error is made.or [1] An incorrect equation set equal to 180°is shown, but it is solved appropriately, suchas 4x + 20 = 180; or an incorrect equation setequal to 360° is shown, such as 5x + 20 =360.or [1] 32, and an appropriate trial-and-errormethod with less than two trials andappropriate checks are shown.or [1] 32, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[38]

[2] An isosceles triangle that is not acute isdrawn, and its three angles are labeled, suchas 20, 20, 140 or 45, 45, 90.[1] An isosceles triangle is drawn that showsan angle that is not acute, but the base anglesare not labeled.or [1] The three angles are stated correctly,but no triangle is drawn.[0] The triangle that is drawn and labeled isnot isosceles or is acute.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.


[39]

[3] The student draws an obtuse triangle andall sides and all angles are correctlycalculated, such as by using 120°, 30°, and30° and sides 4, 4, and 10.[2] The student has the angles correctlyindicated and the two congruent sidesmarked, but the length of the longest side isincorrect or is missing.or [2] All sides are correctly marked, but theangles do not add to 180°, but an obtuse angleand two congruent angles are shown.[1] Only the angles are correctly shown.or [1] Only the sides are correctly shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[40]

[3] 135 and appropriate work is shown.[2] The two correct angles of 65° and 70° arefound, but their sum is not identified as theanswer to the question.or [2] 65° or 70° and an appropriate sum isfound.[1] Either the 65° or the 70° is correctlyidentified.or [1] Two incorrect angle measures arefound, but they are added correctly.or [1] 135 and no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[41]

[2] 30, and appropriate work is shown or anappropriate explanation is given.[1] Angles of the equilateral triangle areshown to be 60°, but x is not determined or isdetermined incorrectly.or [1] 30, but no work is shown or noexplanation is given.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[42] A

[43]

[2] 40, and appropriate work is shown, suchas x = − +180 70 70( ) or correctly labeling allthe angles in the diagram.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] A correct equation is written, but nofurther correct work is shown.or [1] The measures of ∠ACB and ∠ABCare both found to be 70°, but no furthercorrect work is shown.or [1] An incorrect equation of equaldifficulty is solved appropriately.or [1] 40, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[44] A

[45] D

[46]

[2] A correct construction is drawn to find themidpoint of BC , showing both sets of arcsand a line connecting A with the midpoint.[1] A correct construction is drawn to find themidpoint of BC , but the median is not drawn.or [1] The construction is appropriate, but acompass and a straightedge are not used.[0] No construction arcs are shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[47]

[2] A correct construction is drawn, showingthe arcs intersecting above and below AB,and the perpendicular line is drawn.[1] All of the construction arcs are drawn, butthe perpendicular line is not drawn.[0] A drawing that is not an appropriateconstruction is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.


[48]

[2] A correct construction is drawn, showingthe arcs intersecting above and below AB ,and line c is drawn.[1] A correct construction is drawn, but line cis not labeled.[0] A drawing that is not a construction isshown with arc marks sketched.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[49] A

[50] C

[51] C

[52] A

[53] C

[54] A

[55] D

[56] D

[57]

[2] The student draws a parallelogram, whichis not a rectangle, with four sides and fourangles labeled, such as angles of 60, 120, 60,and 120 and sides of 4, 6, 4, and 6.[1] A parallelogram or rhombus, not a square,is drawn, which does not have measures forall lengths or angles.[0] Angles and/or lengths are not appropriatefor a parallelogram.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[58] D

[59]

[3] 102, and appropriate work is shown, suchas using the equation 2x + 10 + 3x = 180 or anequivalent equation.[2] The equation 2x + 10 + 3x = 180 is solvedcorrectly for x, but m B∠ is not determined oris determined incorrectly.[1] Appropriate work is shown, but onecomputational error is made or x is notdetermined.or [1] The equation 2x + 10 + 3x = 360 issolved correctly, and an answer of 210 isfound.or [1] 102, but no work is shown.[0] The equation 2x + 10 = 3x where x = 10 isgiven.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[60]

[3] 120, and appropriate work is shown, suchas solving the equation 5 2 12 180x x+ + = .[2] Appropriate work is shown, but onecomputational error is made.or [2] The correct equation is solved for x, butno further correct work is shown.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] A correct equation is written, but nofurther correct work is shown.or [1] An incorrect equation of equaldifficulty is solved appropriately, and anappropriate measure is found for ∠D.or [1] 120, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[61]

[2] 96, and appropriate work is shown, suchas an algebraic solution or a correctly labeleddiagram.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 96, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[62] B

[63]

[4] 12 and an appropriate method is shown,such as ( ) .AB 2 2 29 8= +[3] An incorrect length is found for AE, butthen it is used to correctly complete theproblem.or [3] An appropriate method is shown, butone computational mistake is made.or [3] An appropriate method is shown, butthe answer is not given to the nearest foot,such as 145 .[2] AE = 8 and one computational mistake ismade using the Pythagorean theorem.or [2] An incorrect length is found for AE, butthen it is used to complete the problemcorrectly, but the answer is not rounded.[1] AE = 8 is found, but the Pythagoreantheorem is not used.or [1] 12 and no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[64] B

[65] B

[66]

[4] $148.54, and appropriate work is shown.[3] The correct pre-tax amount of $137.54 isfound, but no tax or an incorrect tax is shown.or [3] Appropriate work is shown, but onecomputational error is made.[2] The correct area of 46 ft2 is found, but nocost is shown.or [2] Appropriate work is shown, but morethan one computational error is made.or [2] An incorrect area is determined, such asby adding or multiplying all sides, but then afinal cost including tax is determinedappropriately.[1] An incorrect area is shown, and onecomputational error is made.or [1] $148.54, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[67]

[4] The side equals 2.3 and the area equals25.5, and appropriate work is shown.[3] Appropriate work is shown, but onecomputational or rounding error is made.[2] Appropriate work is shown, but oneincorrect formula is used, such as using anincorrect trigonometric function, butappropriate answers are found.or [2] Appropriate work is shown to find thecorrect side, but no further correct work isshown.[1] The radius equals 3 and the central angleequals 45°, but no further correct work isshown.or [1] The side equals 2.3 and the area equals25.5, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[68] D

[69] D

[70] A

[71] B


[72] C

[73] B

[74] C

[75] C

[76]

a [1] Either (x – 2)(x + 1)(2x) = V or the sameexpression without “= V” is shown.or [1] 2 2 43 2x x x− − or an equivalentexpression is shown.b [1] 864or [1] The student substitutes appropriatelyinto an incorrect part a equation.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[77]

[3] 3, 12, and 30 and an appropriatearithmetic method or equation is shown, suchas 40 10803x = .[2] An appropriate equation or method isshown, but not all three dimensions are found.or [2] An appropriate method is shown, andalthough one computational mistake is made,the student does find three dimensions basedon this mistake, such as dividing 1080 by 40incorrectly.[1] The student shows that multiplication isrequired to find volume but sets up anincorrect method and does not find threedimensions.or [1] 3, 12, and 30 and no work is shown.[0] The sum is used instead of the product,or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[78]

[2] 20, and appropriate work is shown, suchas 3 360 14 12, ( ).÷ ×[1] Appropriate work is shown, but onecomputational error is made.or [1] 20, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[79]

[3] 27 and an appropriate method orexplanation is shown, such as

( )( )( )16

13

23

127

= of a cubic foot, thus 27

bricks needed or, in inches, 172864

27= . A

labeled drawing is an acceptable explanation.[2] An appropriate method for finding volumeis shown, but one computational mistake ismade.[1] Correct conversion into feet is shown.or [1] The volume of 64 cubic inches isfound.or [1] 27 and no explanation is given.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[80]


as calculating ( )( )

36 1449 9××

or drawing a

labeled diagram.[2] Appropriate work is shown, but onecomputational error is made.[1] Appropriate work is shown, but more thanone computational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 64, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[81]

[3] 5-inch box and appropriate work is shown,including showing a diameter between 4 and5.[2] The correct diameter is shown, but thewrong box size is chosen.or [2] The correct radius is shown, but the 3-inch box is chosen.[1] The correct diameter or radius is shown,but no box is chosen.or [1] An appropriate radius between 2 and 3is shown, using the incorrect formulaA r= π 2 , and the 3-inch box is chosen.

or [1] An appropriate diameter, usingA r= π 2 , is shown, but the appropriate box is

chosen.or [1] An appropriate radius, using A r= π 2 ,is shown, but no box is chosen.or [1] The 5-inch box is chosen, but no workis shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[82]

[3] 47, and appropriate work is shown.[2] Appropriate work is shown, but onecomputational or rounding error is made.or [2] The correct numerical value of thevolume of the cup ( 20π or its equivalent) andthe volume of the tank (3,000) are shown, butthe solution is not completed.[1] The correct volume of only the cup oronly the tub is shown.or [1] 47, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[83]

[3] 2.6, and appropriate work is shown, suchas ( ) ( ) .5 5 5 7 7• • = • h[2] Appropriate work is shown, but onecomputational or rounding error is made.[1] Appropriate work is shown, but two ormore computational or rounding errors aremade.or [1] Appropriate work is shown, but oneconceptual error is made, such as using anincorrect formula.or [1] The volume of both of the cubes isfound correctly, but no further correct work isshown.or [1] 2.6, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[84]

[3] 12, and appropriate work is shown, suchas calculating volume = 5 760, in3 anddividing by 500 in3.[2] Appropriate work is shown, but onecomputational or rounding error is made.or [2] The volume is found incorrectly bymultiplying 24 16 18× × , but it is divided by500 and rounded appropriately, resulting in ananswer of 14.[1] Appropriate work is shown, but two ormore computational or rounding errors aremade.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] The volume of 5,760 is found correctly,but no further correct work is shown.or [1] 12, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[85]

[4] 11, and appropriate work is shown, suchas solving the quadratic equation3 5 150x x( )+ = or trial and error with at leastthree trials and appropriate checks.[3] Appropriate work is shown, but onecomputational error is made.or [3] Appropriate work is shown todetermine that 5 is the shorter side of the box,but the shorter side of the original sheet is notfound or is found incorrectly.or [3] An incorrect quadratic equation ofequal difficulty is solved appropriately, andan appropriate shorter side of the originalsheet is found.[2] Appropriate work is shown, but more thanone computational error is made.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] An incorrect quadratic equation ofequal difficulty is solved appropriately, butthe shorter side of the original sheet is notfound.or [2] A correct quadratic equation is setequal to zero, but no further correct work isshown.or [2] The trial-and-error method is used tofind a correct solution, but only two trials andappropriate checks are shown.[1] Appropriate work is shown, but oneconceptual error and one computational errorare made.or [1] One conceptual error is made in findingthe shorter side of the box, and thecorresponding shorter side of the originalsheet is not found or is found incorrectly.or [1] A correct quadratic equation is written,but it is not set equal to zero, and no furthercorrect work is shown.or [1] 11, but no work or only one trial withan appropriate check is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[86]

[4] 21 by 23, and appropriate work is shown,such as solving the equation765 3 4 6= − −( )( ).x x[3] Appropriate work is shown, but onecomputational error is made.or [3] Appropriate work is shown, but onlyone dimension is found.[2] Appropriate work is shown, but two ormore computational errors are made.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] An incorrect equation of equaldifficulty is solved appropriately, andappropriate dimensions are found.or [2] A correct quadratic equation is writtenin standard form, but no further correct workis shown.[1] Appropriate work is shown, but oneconceptual error and one computational errorare made.or [1] An incorrect equation of equaldifficulty is written, and one computationalerror is made, but appropriate dimensions arefound.or [1] An incorrect equation of equaldifficulty is solved appropriately, but onecomputational error is made when finding thelength.or [1] 21 by 23, but no work is shown.[0] 21 or 23, but no work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.


[87]

[2] 2.6, and appropriate work is shown, suchas solving the equation ( ) .10 20003+ =x[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] The equation ( )10 20003+ =x iswritten, but no further correct work is shown.or [1] An incorrect equation of equaldifficulty is solved appropriately.or [1] 2.6, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[1] A

[2] A

[3] C

[4] D

[5] C

[6] A

[7]

[3] 14 2 , and appropriate work is shown,such as using the Pythagorean theorem ordrawing a correctly labeled diagram thatshows the isosceles right triangle.[2] Appropriate work is shown, but onecomputational error is made.or [2] Appropriate work is shown, but theanswer is expressed as a decimal or theradical is not simplified.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but onecomputational error is made, and the answeris not expressed as a radical in simplest form.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 14, the side of the square is foundcorrectly, but no further correct work isshown.or [1] 14 2 , but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[8] C

[9]

[2] 8 and the use of trigonometry, thePythagorean theorem, or Pythagorean triple isshown.[1] The Pythagorean theorem or trigonometryis used, but a computational mistake is madeor substitution is incorrect, such as6 102 2 2= + x .[1] 8 and no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[10]

[2] 16, and appropriate work is shown, suchas the Pythagorean theorem, the Pythagoreantriple, or trigonometry.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as using anincorrect trigonometric function.or [1] 16, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[11]

[2] 15, and appropriate work is shown, suchas using the Pythagorean theorem,Pythagorean triples, or trigonometricfunctions.[1] The data are substituted incorrectly, but anappropriate answer is found and is roundedcorrectly.or [1] Appropriate work is shown, but one ormore computational errors are made.or [1] 15, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[12] C

[13] A


[14]

[2] 2.8, and appropriate work is shown, suchas 3 12 2 2= + ( ) .BC[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] The length of BD is found to be 3, butno further correct work is shown.or [1] 2.8, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[15]

[3] 3, and appropriate work is shown, such asusing a 3:4:5 right triangle, correctproportions, or the Pythagorean theorem witha proportion.[2] Appropriate work is shown, and the valueof the side is determined to be 5, but n = 3 isnot found.[1] A correct proportion is set up, but noanswer or an incorrect answer is found.or [1] 3, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[16] A

[17]

[2] An appropriate explanation is written,such as defining special isosceles righttriangles, or appropriate work is shown, suchas using legs of six and finding thehypotenuse.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[18]

[2] 171 or 13 or 13.1 or 13.08 or anequivalent answer, and appropriate work isshown, such as the use of the equation of acircle ( )x y r2 2 2+ = or the Pythagoreantheorem.[1] Appropriate work is shown, but onecomputational error is made.or [1] Incorrect analysis is shown, such as x =5 and y = 14, but the work is concludedappropriately.or [1] A correct answer is found, but no workis shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[19]

[4] 9.4, and appropriate work is shown, suchas the use of the Pythagorean theorem.[3] Appropriate work is shown, but onecomputational or rounding error is made.[2] Appropriate work is shown, but more thanone computational or rounding error is made.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] An incorrect diagonal of the base isfound, but an appropriate solution is found.or [2] Only the diagonal of the base is foundcorrectly, but appropriate work is shown, suchas 3 42 2 2+ = d or use of 3–4–5 righttriangles.[1] Appropriate work is shown, but oneconceptual error and one computational orrounding error are made.or [1] The Pythagorean theorem is used tofind the length of the straw, but theappropriate legs are not used.or [1] 9.4, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[20] D

[21] A

[22] D


[23] A

[24]

[3] 109 meters and appropriate work is shownby using an appropriate trigonometric ratio,

such as tan 32175

° = y .

[2] 109 meters but one rounding error ismade.or [2] The student uses an appropriatetrigonometric function with an inverted ratio,

such as tan32 175°=y

, but completes the

calculation appropriately, such as showing280 meters.[1] The student uses an incorrecttrigonometric ratio but completes thecalculation appropriately.or [1] The student uses an inverted tangentratio and makes one computational orrounding error.or [1] The student uses the correcttrigonometric ratio but solves it incorrectly ordoes not solve it at all.or [1] 109 meters but no work or explanationis shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[25]

[4] 116 and an appropriate method is shown.[3] An appropriate method is shown, but theanswer is left in an inappropriate form, suchas 116.2.or [3] An appropriate method is shown, but 3feet is not added, and the answer is left 113.or [3] Tangent function is used, butcomputational mistakes are made, but 3 feet isadded to the incorrect value and the answer isfound correctly.[2] An incorrect trigonometric function isused, 3 feet is added, and the answer isrounded correctly.or [2] Tangent function is used, butcomputational mistakes are made, and 3 feetis not added to an incorrect answer.[1] 116 and no work is shown.or [1] An incorrect trigonometric function isused, and 3 feet is added to the incorrectanswer, but the answer is rounded incorrectly.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[26] B

[27]

[4] 28.2, and an appropriate equation is

shown, such as tan 6215

= x .

[3] Appropriate work is shown, but theanswer is rounded incorrectly.or [3] The student uses the correct tangentfunction and rounds the answer, but makesone computational error.[2] The student uses the correct tangentfunction, but makes several errors.or [2] An incorrect trigonometric function isused, but appropriate work is shown.[1] The tangent function is indicated, but theratio is set up incorrectly.or [1] 28.2, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[28]

[2] 117.6, and appropriate work is shown,

such as tan .7825

° = x

[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as using anincorrect trigonometric function, but anappropriate solution is found.or [1] A correct trigonometric equation iswritten, but no further correct work is shown.or [1] 117.6, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[29]

[2] 10, and appropriate work is shown.[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as using anincorrect trigonometric function.or [1] Appropriate work is shown, but thelength of the ladder is found.or [1] 10, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[30]


as tan .6620

° = x

[2] A correct trigonometric ratio is used, andvalues are substituted correctly, but onecomputational or rounding error is made, orthe calculator is left in radian mode.[1] Appropriate work is shown, but two ormore computational or rounding errors aremade.or [1] Appropriate work is shown, but oneconceptual error is made, such as using anincorrect trigonometric ratio.or [1] An incorrect diagram is drawn, but anappropriate solution is found.or [1] A correctly labeled diagram is drawn,but no further correct work is shown.or [1] A correct trigonometric ratio is written,but no further correct work is shown.or [1] 45, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[31]

[4] 2,058, and appropriate work is shown,such as the accompanying diagram andequation.

[3] Appropriate work is shown, including acorrect diagram and the use of the tangentfunction, but one computational error is made.or [3] Appropriate work is shown, including acorrect diagram and the use of the tangentfunction, but the answer is not rounded or isrounded incorrectly.[2] A correct diagram is drawn, but anincorrect trigonometric function is selected,but it is solved and rounded appropriately.or [2] A correct diagram is drawn and thetangent function is selected, but no furtherwork is shown.or [2] An incorrect diagram is drawn, but theappropriate trigonometric function, based onthe drawing, is selected, solved, and roundedappropriately.[1] An incorrect diagram is drawn and anincorrect trigonometric function is selected,but it is solved and rounded appropriately.or [1] Only a correct diagram is drawn.or [1] 2,058, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[32]

[4] 114" (9 feet 6 inches) and 37" (3 feet 1inch) and appropriate work is shown, such as

sin cos7210

7210

° = ° =x and y or use of the

Pythagorean theorem.[3] An incorrect diagram is drawn, butappropriate work and an appropriate solutionfor that diagram are shown.or [3] Appropriate work is shown, but theanswers are rounded to the nearest foot andthen converted to inches, arriving at 120" and36".or [3] The setup is correct, but the answers arenot converted to the nearest inch.[2] One correct dimension is shown, such as114" (9 feet 6 inches) or 37" (3 feet 1 inch).or [2] Only one error involving interchangingsine and cosine is made.or [2] An incorrect diagram is drawn, and thesolution is appropriate for the diagram but isnot rounded to the nearest inch.[1] The student switches sine and cosine anddoes not round to the nearest inch.or [1] The student uses the correcttrigonometric function to compute one sidecorrectly but does not convert it to the nearestinch.or [1] 114" (9 feet 6 inches) and 37" (3 feet 1inch) but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[33]

[4] x = 19.62990915 and y = 9.814954576 orequivalent answers, and appropriate work is

shown, such as sin 60 17° =x

and

tan60 17°=y

or the Pythagorean theorem.

[3] Appropriate work is shown, but onecomputational or rounding error is made.or [3] Appropriate work is shown, and thecorrect answers are found, but not identified.[2] Appropriate work is shown, but oneconceptual error is made, such as

sin 6017

° = x .

or [2] Appropriate work is shown, but morethan one computational or rounding error ismade.[1] Appropriate work is shown, but twoconceptual errors are made, such as

sin 6017

° = x and tan 6017

° = y .

or [1] x = 19.62990915 and y = 9.814954576or equivalent answers, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[34]

[4] Length of ladder =11 and distance fromthe base of the ladder to the wall = 4, andappropriate work is shown, such as using sineand then tangent or the Pythagorean theorem.[3] Appropriate work is shown, but onecomputational or rounding error is made.or [3] Appropriate work is shown, but thecorrect answers are not labeled or are labeledincorrectly.[2] Appropriate work is shown, but two ormore computational or rounding errors aremade.or [2] Appropriate work is shown, but oneconceptual error is made, such as using oneincorrect trigonometric ratio.or [2] Appropriate work is shown, but onlythe length of the ladder or the distance fromthe base of the ladder to the wall is found.or [2] Two correct trigonometric equationsare written, but no further correct work isshown.[1] Appropriate work is shown, but oneconceptual error and one computational orrounding error are made.or [1] Only one correct trigonometricequation is written, and no further correctwork is shown.or [1] Length of ladder = 11 and distancefrom the base of the ladder to the wall = 4, butno work is shown.[0] Length of ladder = 11 or distance from thebase of the ladder to the wall = 4, but no workis shown.or [0] 11 and 4, but no work is shown, and thesolutions are not labeled.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.


[35]

[3] 12 and the equation tan x = 4202000

= .21 is

shown.or [3] 12 and the Pythagorean theorem and anappropriate trigonometric function arecorrectly used.[2] Tan function is correctly used, but theanswer is not rounded, such as 11.859.or [2] The setup is correct, but onecomputational mistake is made, and anappropriate angle is found.or [2] The answer is incorrectly expressed,such as tan x = 12.[1] The tan function is set up correctly, butthe angle is not computed.or [1] 12 and no work is shown.

or [1] 12 and sin x = 4202000

is used.

or [1] 78 and cos x = 4202000

is used.

[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[36]


as solving the equation sin .x = 37

[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as using anincorrect trigonometric function.or [1] A correct trigonometric equation iswritten, but no further correct work is shown.or [1] 25.4, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[37]

a [2] 59, and the equation tan x = 280170

is

shown, or the Pythagorean theorem is usedfirst to find the hypotenuse, and either sine orcosine is used correctly to find x.[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] 59, but no work is shown.b [2] 122, if the Pythagorean theorem is usedor if a trigonometric function of the angle isused before it was rounded to 59°.

or [2] 120, if cos59 170=hyp

is used.

or [2] 123, if sin59 170=hyp

is used.

[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] 122 or 120 or 123, but no work isshown.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.


[38]

a [2] 56, and appropriate work is shown, such

as tan A = 64

or finding the hypotenuse and

then using sine or cosine or usingproportional sides of similar triangles.[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] The length of the hypotenuse is foundcorrectly, but no further correct work isshown.or [1] 56, but no work is shown.b [2] 12, and appropriate work is shown, such

as sin5615

= h .

or [2] An appropriate answer is found basedon an incorrect angle found in part a.[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 12, but no work is shown.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[39]


as 12 162 2 2+ = r , 50 − =r s , and sin x = 1630

.

[3] Appropriate work is shown, but onecomputational error is made.or [3] Appropriate work is shown to find r =20 and s = 30 and the trigonometric equation

sin x = 1630

is written, but it is not solved or is

solved incorrectly.[2] Appropriate work is shown, but two ormore computational errors are made.or [2] Appropriate work is shown, but oneconceptual error is made, such as using anincorrect trigonometric function to find theangle.or [2] The lengths of rand s are foundcorrectly, but no further correct work isshown.or [2] Incorrect lengths are found for rand s,but the sine function is used correctly to findan appropriate angle.[1] Appropriate work is shown, but oneconceptual error and one computational errorare made.or [1] The length of r is found correctly, butno further correct work is shown.or [1] 32, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[40]


as sin50200

° = x .

[3] An appropriate analysis is shown, but onecomputational or rounding error is made.[2] An incorrect trigonometric function is

used, such as cos50200

° = x , but it is carried

to an appropriate final answer and is roundedcorrectly.[1] An incorrect trigonometric function isused and solved appropriately, but it isrounded incorrectly.or [1] Only an appropriate diagram is shown.or [1] 153, but no work is shown.[0] Use of the Pythagorean theorem, such as200 502 2 2= + x , is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[41]


as tan .5262

= x

[3] Appropriate work is shown, but onecomputational or rounding error is made.or [3] An incorrectly labeled diagram isdrawn, but the appropriate trigonometricfunction is used, and an appropriate answer isfound.[2] Appropriate work is shown, but two ormore computational or rounding errors aremade.or [2] Appropriate work is shown, but oneconceptual error is made, such as using anincorrect trigonometric function or ratio.[1] Appropriate work is shown, but oneconceptual error and one computational orrounding error are made.or [1] A correctly labeled diagram is drawn,but no further correct work is shown.or [1] A correct equation is written, but nofurther correct work is shown.or [1] An incorrectly labeled diagram isdrawn, but an appropriate equation is written,but no further correct work is shown.or [1] 79.4, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[42]

[4] 41.4, and appropriate work is shown, suchas 200 28 200 18tan tan .°− °[3] Appropriate work is shown, but onecomputational or rounding error is made.or [3] Appropriate work is shown to find thecorrect height of the cliff and the correctcombined height of the lighthouse and thecliff, but they are not subtracted.[2] Appropriate work is shown, but two ormore computational or rounding errors aremade.[2] Appropriate work is shown, but oneconceptual error is made, such as using anincorrect trigonometric function.or [2] Appropriate work is shown to find thecorrect height of the cliff or the correctcombined height of the lighthouse and thecliff, but no further correct work is shown.[1] Appropriate work is shown, but oneconceptual error and one computational orrounding error are made.or [1] A correct equation is written to find theheight of the lighthouse, but no further correctwork is shown.or [1] 41.4, but no work is shown.[0] The correct height of the cliff or thecorrect combined height of the lighthouse andcliff is found, but no work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[43] C


[1] D

[2] B

[3] D

[4] C

[5] B

[6] A

[7] A

[8] A

[9] A

[10] B

[11] C

[12] D

[13] B

[14] D

[15]

[2] 12 and an appropriate explanation isgiven.[1| The student uses an appropriate method,

such as showing k −−

=23 1

5 or graphing of a

line through (1,2) having a slope of 5, but thecorrect answer is not found.or [1] 12 and no explanation is given.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[16] C

[17] D

[18] A

[19] B

[20] C

[21] B

[22] C

[23] D

[24] B

[25]

[2] A correct equation is written, such as

y x= − +32

4 or ( ) ( ).y x− = − −4 32

0

[1] An appropriate equation is written, butone computational error is made or oneincorrect substitution is made.[1] An appropriate equation is written, butone conceptual error is made, such as writingan equation for a parallel line going through(0,4) or for a perpendicular line that does notgo through (0,4).

or [1] The slope is identified correctly as − 32

or the y-intercept as 4, but no equation or anincorrect equation is written.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[26]

[3] Three correct equations are shown, suchas y x= + 7, y x= − − 6, and 2 2 12y x= − .[2] Only two correct equations are shown.[1] Only one correct equation is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[27] C

[28] A

[29] A

[30] C

[31] A

[32] C

[33] D

[34] B


[35] C

[36] B

[37] A

[38] A

[39] B

[40] B

[41] B

[42] C

[43] A

[44] D

[45] A

[46] A

[47] A

[48] C

[49]

[2] $1.48, and appropriate work is shown,such as providing a correctly labeled table orsolving the equation ( . )( . ) .139 1005 12 = C[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as using 1.05or 1.5 or using an incorrect exponent.or [1] A correct equation is written, but nofurther correct work is shown.or [1] An incorrect equation of equaldifficulty is solved appropriately.or [1] $1.48, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[50]

[2] 5,279.61, and appropriate work is shown,

such as 3 500 1 0 082512

12 5, ( . ) .( )+ ×

[1] Appropriate work is shown, but onecomputational or substitution error is made.or [1] 5,279.61, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[51]

[2] 65, and appropriate work is shown, suchas P( ) ( . ) .10 80 0 98 10=[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 65, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[52] A

[53] B

[54]

[2] 7,800, and appropriate work is shown.[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] 7,800, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[55] A


[1] C

[2]

[3] The student says the point does not lie onthe line and an appropriate method is shown,such as slope of -2 does not work with thenew point ( , )−25 81 and either other point(0,4) or (2,0), or accurately shows a graphwhere ( , )−25 81 is not on line .[2] The student says the point does not lie onthe line but gives an inappropriateexplanation of slope.or [2] The student tries to use slope conceptbut makes one computational mistake andgives an appropriate answer based on thismistake.[1] Only the slope of -2 is found.or [1] The correct diagram is drawn with nointerpretation.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[3]

[2] $390 or 390 and appropriate work isshown, such as a numerical table or theequation y = 30x + 90 or the expression 90 +30N.[1] Appropriate work is shown, but onecomputational error is made.or [1] $300 or 300 or a slope of 30 butappropriate work is shown.or [1] $390 or 390 but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[4] B

[5] D

[6] D

[7] A

[8] A

[9] A

[10] B

[11]

[4] $1.50 for one slice of pizza and $0.75 forone cola, and appropriate work is shown, suchas 3x + 2y = $6 and 2x + 3y = $5.25.[3] Appropriate work is shown, but onecomputational error is made.or [3] Appropriate work is shown, but onlythe price of one slice of pizza or the price ofone cola is found correctly.[2] Appropriate work is shown, but more thanone computational error is made.or [2] An incorrect system of equations ofequal difficulty is solved appropriately tocalculate the cost of one slice of pizza andone cola.[1] $1.50 for one slice of pizza and $0.75 forone cola, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[12]

[4] Milk Chocolate bar = $0.75 and CreamyNougat bar = $0.50, and appropriate work isshown, such as equations, a trial-and-errormethod with at least two trials andappropriate checks, or an algebraic or graphicsolution.[3] Appropriate work is shown, but onecomputational error is made.[2] The cost of one candy bar is determinedcorrectly with appropriate work shown, butno attempt is made to find the cost of theother candy bar.or [2] Appropriate work is shown, but morethan one computational error is made.[1] Appropriate work is shown, but no answeris found.or [1] Milk Chocolate bar = $0.75 andCreamy Nougat bar = $0.50, but no work isshown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[13]

[4] One doughnut is $0.75 and one cookie is$0.60, and appropriate work is shown, such asa system of equations, trial and error with atleast three trials and appropriate checks, or atable.[3] Appropriate work is shown, but onecomputational error is made.or [3] Appropriate work is shown, but onlyone correct answer is found, or two correctanswers are found, but they are not identifiedclearly as doughnuts or cookies, or thedoughnuts and cookies are labeledincorrectly.[2] Appropriate work is shown, but more thanone computational error is made.or [2] Two equations are written, one correctand one incorrect, but two appropriateanswers are found.or [2] The trial-and-error method is used tofind a correct solution, but only two trials andappropriate checks are shown.[1] Two correct equations are written, but nofurther correct work is shown.or [1] One doughnut is $0.75 and one cookieis $0.60, but no work or only one trial with anappropriate check is shown.[0] One correct equation is shown, and noanswer or only one appropriate answer isfound.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[14]

[4] $5 for the sprayer and $10 for thegenerator, and appropriate work is shown,such as x = hourly cost of sprayer and y =hourly cost of generator, and an appropriatesystem of equations is solved or a trial-and-error method is used, showing at least twotrials with appropriate checks.[3] Both correct equations are shown or anappropriate chart or trial-and-error method isused, but one computational error is made.or [3] Both correct equations are shown, andthey are solved for one value, but no furtherwork is shown.[2] Only one of the two equations is correct,but they are solved appropriately for bothvalues.or [2] Both correct equations are shown, butmore than one computational error is made.or [2] $5 for the sprayer and $10 for thegenerator, but only one trial is shown withappropriate checks.[1] Both equations are incorrect, but they aresolved appropriately for both values.or [1] Both correct equations are shown, butthey are not solved.or [1] $5 for the sprayer and $10 for thegenerator, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[15] D

[16] D

[17] D


[18]

a [2] An appropriate equation or system isshown, such as x + y = 148 and 12x + 9y =1410 or one equation such as 12(148 - x) + 9x= 1410 with variables identified.[1] The student shows appropriateequation(s), but variables are not defined.or [1] One mistake in equation(s) is made, oronly one equation with two variables isshown, but variables are defined.b(1) [1] 26 and an appropriate method isshown, such as solving the equation ormaking a table.or [1] An appropriate answer is found basedon incorrect equation(s) obtained in part a.b(2) [1] 122 and an appropriate method isshown, such as 148 - 26.or [1] An appropriate answer is found basedon incorrect equation(s) obtained in part a.b (l) and b (2) [1] 26 and 122 and no work isshown.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[19]

[3] Seth had 101, Jason had 51, and Raoul had104, and appropriate work is shown,such as x + 25 = (2x - 1) - 25 or trial and errorwith at least three trials and appropriatechecks.[2] Appropriate work is shown, but onecomputational error is made.or [2] 101, 51, and 104, and appropriate workis shown, but the solutions are not labeled orare labeled incorrectly.or [2] A correct equation is solved, but thenumber of CDs for only one boy is found.or [2] The trial-and-error method is used tofind a correct solution, but only two trials andappropriate checks are shown.[1] Appropriate work is shown, but more thanone computational error is made.or [1] Appropriate work is shown, but oneconceptual error is made, but an appropriatenumber of CDs is found for each boy.or [1] A correct equation is written, but nofurther correct work is shown.or [1] Seth had 101, Jason had 51, and Raoulhad 104, but no work or only one trial with anappropriate check is shown.[0] Seth had 101 or Jason had 51 or Raoul had104, but no work is shown.or [0] 101, 51, and 104, but no work is shownand the solutions are not labeled or arelabeled incorrectly.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.


[20]

[3] 374 grasshoppers and 187 crickets, andappropriate work is shown.[2] An appropriate equation is solved orappropriate work is shown, but only onecorrect answer is found, or two correctanswers are found but they are not identifiedclearly as grasshoppers or crickets, or thegrasshoppers and crickets are labeledincorrectly.or [2] Appropriate work is shown, but onecomputational error is made.[1] Appropriate work is shown, but more thanone computational error is made.or [1] An incorrect equation of equaldifficulty is solved appropriately.or [1] 374 grasshoppers and 187 crickets, butno work is shown.[0] 374 and 187, but no work is shown, andthe answers are not identified clearly asgrasshoppers or crickets.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[21]

[2] 4.5 and an appropriate method is shown,such as the equation 3 2 20x x+ + = or sometrial and error or arithmetic process.[1] An appropriate method is shown, but thecorrect answer is not found.or [1] 4.5 and no work is shown.or [1] The student solves the equationx x+ − =3 2 20 and answers 5.5.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[22]

[2] 42 nickels and 21 dimes, and appropriatework is shown, such as 0.1x + (0.05)2x = 4.20or a guess and a check with a minimum oftwo trials and appropriate checks or anotherappropriate method.[1] 42 nickels or 21 dimes, but appropriatework is shown.or [1] Appropriate work is shown, but noanswer or an incorrect answer is found.or [1] 42 nickels and 21 dimes, but no work isshown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[23]

[3] Four 20-cent and eight 32-cent stamps,and appropriate work is shown, such as asystem of equations, or a linear equation suchas 2x(.32) + .20x = 3.36, or trial and errorwith at least three trials and appropriatechecks.[2] Appropriate work is shown, but onecomputational error is made, but appropriatequantities are found for each stamp.or [2] Appropriate work is shown, but thequantity for only one of the stamps is found.or [2] Appropriate work is shown, but thesolutions are not labeled or the labels arereversed.or [2] The trial-and-error method is used tofind correct solutions, but only two trials andappropriate checks are shown.[1] Appropriate work is shown, but two ormore computational errors are made, butappropriate quantities are found for eachstamp.or [1] The trial-and-error method isattempted, and at least six systematic trialsand appropriate checks are shown, but nosolution is found.or [1] An incorrect equation or system ofequations of equal difficulty is solvedappropriately for both solutions.or [1] A correct equation or system ofequations is written, but no further correctwork is shown.or [1] Four 20-cent and eight 32-cent stamps,but no work or only one trial with anappropriate check is shown.[0] Four and eight, but no work is shown, andthe solutions are not labeled.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[24]

[4] 65 adult tickets and 85 student tickets andan appropriate equation is shown, such as7.50x + 4.75(150 - x) = 891.25, or any otheracceptable method is used.[3] Either 65 or 85 and appropriate work isshown.or [3] Appropriate work is shown, but onecomputational error is made that leads to twoappropriate answers.[2] An incorrect equation is shown, but it issolved appropriately for two answers.or [2] The correct equation is shown, but twocomputational errors are made.[1] Appropriate work is shown, but no answeris found.or [1] 65 and 85 but no work is shown.[0] Either 65 or 85 and no work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[25]

a [2] The student writes an appropriate systemof equations, such as b = f + 100 and 4b + 12f= 3,056, and defines the variables.or [2] The student writes an appropriateequation, such as 4(100 + x) + 12x = 3,056,and defines the variable.[1] A correct equation or correct equations areshown, but the variables are not defined.or [1] One error is made in the setup, such asb + f = 100.[0] The student only defines the variables.b [2] 266, and appropriate work is shown,using an algebraic solution or a correct trial-and-error method.or [2] Appropriate work is shown for anincorrect part a equation or system ofequations.[1] Work is shown, but the answer isinappropriate, such as $1,064.or [1] 266, but no work is shown.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.


[26]

[4] 36 T-shirts and 12 caps, and appropriatework is shown, such as an appropriate systemof equations or a correct trial-and-errormethod with at least two trials andappropriate checks.[3] Appropriate work is shown, but only thecorrect number of T-shirts or the correctnumber of caps is determined.or [3] One error is made, resulting in anincorrect number of T-shirts or caps, but thecorresponding number of the other item isdetermined appropriately.[2] An appropriate method is shown, but noanswer is found.or [2] The variables are represented correctly,and a correct equation or system of equationsis written, but the process is not completed.or [2] 36 T-shirts and 12 caps, but only onetrial and appropriate checks are shown.or [2] The variables are represented correctly,but an incorrect equation is written, but thesolution is completed appropriately.[1] 36 T-shirts and 12 caps, but no work isshown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[27]

[4] 210, and appropriate work is shown, suchas a system of equations or the linear equation5x + 2(295 – x) = 1,220.[3] Appropriate work is shown, but onecomputational error is made.or [3] Appropriate work is shown, but thenumber of children’s tickets is found as theanswer.[2] Appropriate work is shown, but two ormore computational errors are made.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] An incorrect equation of equaldifficulty is solved appropriately.or [2] 210, but a method other than analgebraic solution is used.[1] Appropriate work is shown, but oneconceptual error and one computational errorare made.or [1] The correct system of equations orlinear equation is written, but no furthercorrect work is shown.or [1] 210, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[28]

[2] 14 and 42, and appropriate work is shown,such as x + 3x = 56, a table, or trial and errorwith at least three trials and appropriatechecks.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but onlyone of the two lengths is found.or [1] A correct equation is written andsolved, but the lengths are not stated.or [1] An incorrect equation of equaldifficulty is solved appropriately.or [1] 14 and 42, but no work or fewer thanthree trials with appropriate checks areshown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[29]

[4] 17 nickels and 15 dimes, and appropriatework is shown, such as the equation 0.05x +0.10(32 - x) = 2.35 or trial and error with atleast three trials and appropriate checks.[3] Appropriate work is shown, but onecomputational error is made.or [3] Appropriate work is shown, and thecorrect answers are found, but they are notlabeled or are labeled incorrectly.or [3] Appropriate work is shown, but onlythe correct number of nickels or the correctnumber of dimes is found and labeled.[2] Appropriate work is shown, but two ormore computational errors are made.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] The trial-and-error method is used tofind the correct solution, but only two trialsand appropriate checks are shown.or [2] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but no solutionis found.or [2] An incorrect system of equations ofequal difficulty is solved appropriately forboth the number of nickels and dimes.or [2] A correct equation is solved for x, butno further correct work is shown.[1] Appropriate work is shown, but oneconceptual error and one computational errorare made.or [1] A correct equation is written, but nofurther correct work is shown.or [1] 17 nickels and 15 dimes, but no work oronly one trial with an appropriate check isshown.[0] 17 nickels or 15 dimes, but no work oronly one trial with an appropriate check isshown.or [0] 17 and 15, but no work is shown, andthe answers are not labeled or are labeledincorrectly.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[30] C

[31] C

[32] D

[33]

[3] $16,400, and appropriate work is shown,such as200 tickets sold at the door $32 = $ 6,400400 tickets sold in advance $25 = $10,000 $16,400[2] The correct number of tickets is shown,but one computational error is made incomputing the total amount of moneycollected.or [2] $6,400 and $10,000 are calculatedcorrectly, but they are not added to obtain thetotal.[1] The numbers of tickets, 200 and 400, arecalculated correctly.or [1] An appropriate solution is found, but itis based on incorrect numbers of tickets.or [1] $16,400, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[34]

[4] $6.15, and appropriate work is shown,such as solving simultaneous equations orusing a trial-and-error method.[3] $2.95 (movie) and $3.20 (game) arefound, but they are not added.or [3] Appropriate work is shown, but onecomputational error is made.[2] The system of equations is set upcorrectly, but one conceptual error leads to anappropriate solution.or [2] $2.95 (movie) or $3.20 (game), andappropriate work is shown.[1] $6.15, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[35]

[2] $6.85, and appropriate work is shown.[1] The correct rate for the first 5 minutes andthe correct rate for each additional minute isshown, but the cost of a 30-minute call is notfound.or [1] Appropriate work is shown, but onecomputational error is made.or [1] $6.85, but no work is shown.[0] The student calculates either the rate forthe first 5 minutes or the rate for eachadditional minute, but no further work isshown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[36]

a [1] $50b (1) [1] 5(2) [1] $125c [1] $10a, b, and c [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[37]

a [1] c = 10m + 100 for Ron's Rental and c =20m + 20 for Josie's Rental.b [2] Two lines, rays, or segments are graphedand labeled correctly, using values arrived atby using a table or by using the slope and y-intercept.[1] Two lines, rays, or segments are graphedcorrectly, but they are not labeled.or [1] One line, ray, or segment is graphedand labeled correctly, using values arrived atby using a table or by using the slope and y-intercept.c [1] 8or [1] An appropriate number of months isfound, based on an incorrect graph in part b.a, b, and c [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[38]

[4] y = 2x - 40, a correctly drawn graph with aslope of 2 and a y-intercept of -40, and 20,and appropriate work is shown.[3] Appropriate work is shown, but onecomputational or graphing error is made.or [3] The equation and graph are correct, butthe breakeven point is missing or is incorrect.[2] Appropriate work is shown, but more thanone computational or graphing error is made.or [2] An incorrect equation is written, but anappropriate graph is drawn, and anappropriate breakeven point is identified.[1] An incorrect equation is written, but anappropriate graph is drawn, but the breakevenpoint is missing or is incorrect.or [1] A correct equation is written, but thegraph is incorrect, and the breakeven point isnot identified.or [1] y = 2x - 40 and 20, but no work isshown and no graph is drawn.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[39]

[3] 5, and appropriate work is shown, such asthe equation 60 + 5x = 135 - 10x, or trial anderror with at least three trials and appropriatechecks, or a graph.[2] Appropriate work is shown, but onecomputational or graphing error is made.or [2] The trial-and-error method is used tofind a correct solution, but only two trials andappropriate checks are shown.[1] Appropriate work is shown, but more thanone computational or graphing error is made.or [1] 5, but no work or only one trial with anappropriate check is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[40]

[3] 20, and appropriate work is shown, suchas an equation, trial and error, or a graph.[2] Appropriate work is shown, such as 12.95+ 0.25x = 14.95 + 0.15x, but onecomputational error is made.or [2] Appropriate work is shown, but ananswer of $17.95 is found.or [2] 20, and only a check is shown.[1] The student starts appropriate work to findwhen the prices are equal but does notcomplete it, such as starting to solve thecorrect equation, showing one incorrect trial,or drawing an incomplete graph.or [1] 20, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[41]

[3] 345, and appropriate work is shown, suchas solving the inequality 1450 500 000x > , ,solving an equation, or trial and error with atleast three trials and appropriate checks.[2] Appropriate work is shown, but onecomputational or rounding error is made.or [2] The trial-and-error method is used tofind a correct solution, but only two trials andappropriate checks are shown.[1] Appropriate work is shown, but two ormore computational or rounding errors aremade.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] A correct inequality or equation iswritten, but no further correct work is shown.or [1] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but no solutionis found.or [1] 345, but no work or only one trial withan appropriate check is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[42] B

[43]

a [2] 3 and an appropriate method is shown,such as trial and error or the equation32 8 26 10+ = +x x .[1] 3 and no work is shown.or [1] An appropriate method is shown, but anincorrect answer is found.b (1) [1] Best Cable Company and anappropriate explanation is given.b (2) [1] $24 and an appropriate explanationis given.b (l) and b (2) [1] Best Cable Company and$24 and no work is shown.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[44] A

[45]

[2] More than 6 hours, and appropriate workis shown, using a graphic or algebraicsolution.[1] Appropriate work is shown, but onecomputational error or an error in analyzingthe results is made.or [1] More than 6 hours, but no work isshown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[46] B

[47] B

[48] B


[49]

[4] Both inequalities are graphed correctlyand at least one is labeled, and the solution setis labeled S.[3] Appropriate work is shown, but onegraphing error is made, such as drawing asolid line for y x> − 4 or shading incorrectly,but the solution set is labeled S.or [3] Both inequalities are graphed correctlyand at least one is labeled, but the solution setis not labeled or is labeled incorrectly.or [3] Both inequalities are graphed correctly,the solution set is labeled, but neitherinequality is labeled.[2] Appropriate work is shown, but two ormore graphing errors are made, but anappropriate solution set is labeled.or [2] Appropriate work is shown, but oneconceptual error is made, such as graphing thelines y x= − + 2 and y x= − 4 and labelingthe point of intersection S.[1] One inequality is graphed and shadedcorrectly, but no further correct work isshown.or [1] The lines y x= − + 2 and y x= − 4 aregraphed correctly, but no solution isindicated.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[50]

[4] The inequalities x ≤ 10, y ≤ 12, and x + y≤ 16 are graphed and shaded correctly on thegiven set of axes.[3] All inequalities are graphed and shadedcorrectly, but one incorrect type of line(dashed or broken) is used.or [3] All three inequalities are graphedcorrectly, but one inequality is not shaded oris shaded incorrectly.or [3] The inequality x + y ≤ 16 is graphedcorrectly, but an error is made in graphingeither the horizontal or vertical line, but theyare shaded appropriately.or [3] Only two of the three inequalities aregraphed correctly, but all three are shadedappropriately.[2] All three inequalities are graphedcorrectly, but two are shaded incorrectly.or [2] Only two of the three inequalities aregraphed and shaded correctly.[1] Only one of the three inequalities isgraphed and shaded correctly.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[1] C

[2] A

[3] B

[4] B

[5] B

[6] B

[7] C

[8] C

[9] A

[10] C

[11] A

[12] D

[13]

[2] 3(x + 7)(x - 2), and appropriate work isshown.[1] Appropriate work is shown, but onecomputational error is made.or [1] A conceptual error is made, such asincomplete factoring.or [1] 3(x + 7)(x - 2), but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[14] C

[15] B

[16]

[2] 5(n + 4)(n - 4), and appropriate work isshown.[1] Appropriate work is shown, but onefactoring error is made or the expression isnot simplified completely.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[17]

[2] 3a(x – 3)(x + 3), and appropriate work isshown.[1] Appropriate work is shown, but onefactoring error is made, or the expression isnot factored completely.or [1] 3a(x – 3)(x + 3), but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[1] D

[2] C

[3] C

[4] A

[5] B

[6]

[2] 20 and an appropriate explanation isgiven, such as the number cannot be writtenas a repeating or terminating decimal or itcannot be written as a fraction or it is not aperfect square.[1] 20 and an inappropriate explanation orno explanation is given.or [1] 20 and a correct explanation is given,but one other number is also identified asirrational.[0] All three numbers are identified asirrational.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[7] B

[8] C

[9] B

[10]

[2] 30 2, and appropriate work is shown.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] Appropriate work is shown, but theanswer is not in simplest radical form.or [1] 30 2, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[11]

[2] 5 22rs , and appropriate work is shown.[1] A partially correct answer is found, suchas 5 2 4r s or 5 22 2s r , and appropriate workis shown.or [1] 7 07 2. rs , but appropriate work is shown.or [1] 5 22rs , but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[12] B

[13] C

[14] A

[15] C

[16] B

[17] B

[18] B

[19] D

[20] A

[21] C

[22] B

[23] C

[24] A

[25] D

[26] D


[1] D

[2] C

[3]

[2] 3, and appropriate work is shown, such asfactoring or trial and error with at least threetrials and appropriate checks.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as not rejectingthe negative root.or [1] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but no solutionis found.or [1] 3, but no work or fewer than three trialsand appropriate checks are shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[4] A

[5] B

[6] A

[7] D

[8] D

[9] C

[10] A

[11] D

[12]

[3] –8 and 5 and appropriate work is shown,such as factoring or trial and error.[2] The student shows correct factoring into(x + 8)(x – 5) or correct use of the quadraticformula but finds only one correct value for x.[1] Correct factoring is shown, but no valuesare found.or[1] Incorrect factoring is shown, but twoappropriate values are found.or[1] Either –8 or 5 is arrived at by trial anderror.or[1] –8 and 5 and no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[13]

[3] –7 and 4, and appropriate work is shown,such as factoring.[2] Correct factoring (x + 7)(x – 4) is shown,but only one correct value of x is found.or [2] Correct factoring is shown, but thenegative value of x is rejected.[1] Correct factoring is shown, but the valuesof x are not found.or [1] Incorrect factoring is shown, butappropriate values are found.or [1] Only one value is found by trial anderror.or [1] –7 and 4, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[14]

[3] -6 and 4, and appropriate work is shown,such as factoring or trial and error with atleast three trials and appropriate checks.[2] Appropriate work is shown, but onecomputational error is made.or [2] Appropriate work is shown, but onlyone correct value for x is found.or [2] The trial-and-error method is used tofind the correct solutions, but only two trialsand appropriate checks are shown.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] The equation is factored correctly, butno values are found.or [1] The equation is factored incorrectly, buttwo appropriate values are found.or [1] -6 and 4, but no work or only one trialwith an appropriate check is shown.[0] -6 or 4, but no work or only one trial withan appropriate check is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[15] A

[16] D

[17] C

[18] C

[19] D

[20] A

[21] C

[22] D

[23]

[3] 5, and appropriate work is shown, such asthe quadratic equation (x + 7)(x - 3) = 24 ortrial and error with at least three trials andappropriate checks.[2] A correct quadratic equation is written,but one computational error is made infinding Tamara's age.or [2] 12 and 2 are found as the sisters' ages,but Tamara's age is not found.or [2] The trial-and-error method is used tofind the correct solution, but only two trialsand appropriate checks are shown.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] A correct quadratic equation is written,but no further correct work is shown.or [1] An incorrect equation of equaldifficulty is solved appropriately for Tamara'sage.or [1] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but no solutionis found.or [1] 5, but no work or only one trial with anappropriate check is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[24]

[3] 4, 6, and 8, and appropriate work isshown, such as the correct quadratic equationor trial and error with at least three trials andappropriate checks.[2] The correct quadratic equation is solved,but one computational error is made, but threeappropriate ages are listed.or [2] The correct quadratic equation issolved, but the negative root is not rejected,but three appropriate ages are listed.or [2] The correct quadratic equation issolved, but only one age is found.or [2] The trial-and-error method is used tofind a correct solution, but only two trials andappropriate checks are shown.[1] An incorrect equation of lesser difficultyis solved appropriately, and the three ages arelisted.or [1] An incorrect quadratic equation ofequal difficulty is solved appropriately, andthe three ages are listed.or [1] The correct quadratic equation isshown, but more than one computational erroris made.or [1] The correct quadratic equation isshown, but no further correct work is shown.or [1] 4, 6, and 8, but no work or only onetrial with an appropriate check is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[25]

[4] 3, 5, and 7, and appropriate work isshown, such as an appropriate quadraticequation or trial-and-error method.[3] An appropriate equation is written andsolved, but one computational error is made.or [3] An appropriate equation is written andsolved, but the even solutions are also listed.[2] An incorrect quadratic equation is shown,but it is solved appropriately.or [2] Integers are misrepresented, but thesubsequent quadratic equation is solvedappropriately.or [2] An appropriate equation is written andsolved, but more than one computational erroris made.or [2] The correct solution is given, but onlyone trial is shown with appropriate checkswhen a trial-and-error method is used.[1] A linear equation is solved appropriately.or [1] 3, 5, and 7, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[26] A

[27] C


[28]

[4] 16 and appropriate work is shown, such asW W( ) .+ =2 15[3] Appropriate work is shown, but onecomputational error is made.or [3] L = 5, W = 3, and the perimeter = 16,but no work is shown.[2] Appropriate work is shown, but more thanone computational error is made.or [2] L = 5, W = 3, and appropriate work isshown, but the perimeter is not found.or [2] The length and width are incorrect, butthe perimeter is computed appropriately.[1] Length and width are appropriatelydefined in terms of a single variable.or [1] 16 but no work is shown.[0] L = 5 and W = 3 but no work is shown,and the perimeter is not found.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[29]

[4] Width = 20 and length = 25 and anappropriate algebraic equation is shown, suchas x x2 5 500 0+ − = .[3] A correct quadratic equation is shown, butone error is made.or [3] A correct quadratic equation is shown,but solved for only one dimension.[2] An appropriate solution is shown, but thestudent fails to reject the negative root andfinds two sets of dimensions.or [2] The quadratic equation ( )( )5 500x x = issolved appropriately for both dimensions,x = 10 and 5 50x = .[1] The student writes only the correctquadratic equation or only the equationx x( )+ =5 500 or fails to solve the equationcorrectly.or [1] The student writes a linear equationfrom x x( ) ,+ =5 500 such as 2 5 500x x+ = ,but solves that equation appropriately.or [1] A correct equation is shown for theperimeter and solved appropriately.or [1] ( )( )5 500x x = is solved correctly foronly one dimension.or [1] 20 and 25 but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[30]

[4] x x( )+ =10 144 or an equivalent equationand 8 = width and 18 = length, andappropriate work is shown.[3] Appropriate work is shown, but onecomputational error is made.or [3] A correct equation is used and a correctsolution is found, but only one dimension isidentified.[2] An appropriate solution is found to anincorrect equation of equal difficulty.or [2] A correct equation set equal to zero isshown, with no further work or incorrectwork.[1] A conceptual error is made, such aswriting the equation 2 2 10 144x x+ + =( ) , butthe dimensions are found appropriately.or [1] x x( )+ =10 144 and 8 = width and 18 =length, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[31]

[4] w w( ) ,+ =3 40 width = 5, and length = 8,and appropriate work is shown.[3] w w( )+ =3 40 and appropriate work isshown, but one computational error is madein finding the length and width.or [3] w w( )+ =3 40 and appropriate work isshown, but only the width is found.[2] w w( )+ =3 40 and appropriate work isshown, but the length and width are notidentified.or [2] w w( )+ =3 40 and appropriate work isshown, but more than one computational erroris made in finding the length and width.or [2] An incorrect equation of equaldifficulty is solved appropriately for thelength and width.[1] w w( ) ,+ =3 40 but no further correct workis shown.or [1] Appropriate work is shown, but oneconceptual error is made, such as solving theequation 2 2 6 40w w+ + = .or [1] w w( ) ,+ =3 40 width = 5, and length =8, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[32] C

[33] A

[34] C

[35] C


[36]

a [3] A parabola is correctly graphed through(0,0), (1,5), (2,8), (3,9), (4,8), (5,5), and (6,0).[2] The correct table of values is shown but isnot graphed through the entire domain.or [2] The correct points are graphed but as abroken line graph not a curve.or [2] At least three values are correctlycalculated and graphed.[1] At least two of the values are correctlycalculated, and the student tried to graph allpoints.b [1] 3or [1] The correct time, x, for an incorrectgraph in part a is found.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[37]

[4] 100 and a correct parabolic arch is drawn,and appropriate work is shown, such as atable of values for the parabola or correctlylabeled points.[3] 100 and a correct parabolic arch is drawn,but no table of values or labeled points areshown.or [3] 100 and a correct parabolic arch isdrawn, and appropriate work is shown, but noscale or an incorrect scale is shown.or [3] A correct parabolic arch is drawn, butthe maximum height is missing or isincorrect.[2] An incorrect parabolic arch is drawn, butan appropriate maximum height is found.or [2] A correct height is determinedalgebraically, but a parabolic arch is notdrawn.or [2] 100 and an appropriate parabolic arch isdrawn, but it is not drawn between0 20≤ ≤x .[1] A correct parabolic arch is drawn, but nowork is shown, such as a table of values orcorrectly labeled points, and the maximumheight is missing or is incorrect.or [1] 100, but no work is shown and noparabolic arch is drawn.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[38]

a [3] A parabola with points graphed at (0,0),(1,32), (2,48), (3,48), (4,32), and (5,0) isshown. [Points do not have to be labeled onthe graph for full credit.][2] Appropriate work is shown, such as atable of values, but one graphing error ismade.or [2] The correct points are graphed, but theparabola is drawn incorrectly, such asconnecting (2,48) and (3,48) as a line segmentor not connecting the points at all.or [2] At least four correct values are found,and the parabola is graphed appropriately.or [2] A correct table of values is shown forall values from 0 to 5, but no graph is drawn.[1] Two or three correct values are found, andthe parabola is graphed appropriately.or [1] A correct table of values is shown foran incorrectly transcribed equation, such ash t t= +8 402 , but no graph is drawn.b [1] 2.5 is found algebraically or identifiedfrom a table or from the graph of theparabola.or [1] An appropriate value of t is found,based on an incorrect graph.or [1] 2 < t < 3 is given as the range of valuesbased on the line segment drawn in part a.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[39]

a [3] A parabola is correctly graphed through(0,0), (1,10), (2,16), (3,18), (4,16), (5,10), and(6,0).[2] A correct table of values is shown, but notall the points are graphed correctly.or [2] The correct points are graphed but as abroken-line graph, not a curve.or [2] At least four values are calculatedcorrectly and graphed.[1] The student has at least two of the valuescalculated correctly and has tried to graph allthe points.[0] Fewer than two values are calculatedcorrectly.b [1] A maximum height of 18 is found.or [1] Correct y is found for an incorrectgraph in part a.a and b [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[40]

[4] A correct graph is drawn, and 3.[3] 3, and appropriate work is shown, but onegraphing error is made.or [3] A correct graph is drawn and the points0.5 and 3.5 are identified, but the difference isnot calculated.[2] Appropriate work is shown, but two ormore graphing errors are made.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] 3, but a method other than a graphicsolution is used.[1] Appropriate work is shown, but oneconceptual error and one graphing error aremade.or [1] A correct graph is sketched with t = 0to t = 4, but no further correct work is shown.or [1] 3, but no work is shown and no graph isdrawn.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[41] B


[42]

[3] y x x= + −2 3 18 , and appropriate workleading from the roots to the equation isshown.[2] Appropriate work is shown, but onecomputational error is made.or [2] x x2 3 18 0+ − = , but appropriate workis shown.or [2] Only the correct factors (x + 6) and (x –3) are shown.[1] Appropriate work is shown, but more thanone computational error is made.or [1] Only the roots –6 and 3 are shown,such as x = –6, x = 3.or [1] y x x= + −2 3 18 , but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[43] D

[44] C

[45]

[4] 3, and an appropriate algebraic or graphicsolution is shown.[3] The equation is graphed correctly, but thetime to reach the ground is not identified.or [3] Appropriate work is shown for analgebraic solution, but either no solution isfound or the negative root is not rejected.or [3] An appropriate algebraic solution isshown, but one computational error is made.[2] The equation is graphed incorrectly, butan appropriate time to reach the ground isidentified.or [2] The equation is factored incorrectly, butan appropriate solution is found.[1] 3, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[46]

[4] A correct graph is sketched and 1.25, andappropriate work is shown.[3] A correct graph is sketched, but onecomputational or rounding error is made indetermining the time.or [3] Appropriate work is shown, but oneerror is made in sketching the graph, such asthe axes are not labeled or are labeledincorrectly, but the time is determinedcorrectly.or [3] A correct graph is sketched andappropriate work is shown to calculate thetime, but the negative root is not rejected.[2] Appropriate work is shown, but two ormore computational, rounding, or graphingerrors are made.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] A correct graph is sketched, but nofurther correct work is shown.or [2] Appropriate work is shown to calculatethe time, but no graph or an incorrect graph issketched.[1] Appropriate work is shown to calculatethe time, but one computational or roundingerror is made, and no graph or an incorrectgraph is sketched.or [1] Appropriate work is shown to calculatethe time, but the negative root is not rejected,and no graph or an incorrect graph issketched.or [1] 1.25, but no graph or an incorrect graphis sketched, and no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[47] D


[48]

[4] Correct graphs are drawn, and (0,5) and(4,–3) are stated.[3] Both equations are graphed, but onegraphing error is made, but appropriatesolutions are stated.or [3] Both graphs are drawn correctly, butonly one solution is stated.[2] Both graphs are drawn correctly, but nosolutions are stated.or [2] Both equations are graphed, but two ormore graphing errors are made, butappropriate solutions are stated.or [2] Appropriate work is shown to find (0,5)and (4,–3), but a method other than graphingis used.or [2] Both equations are graphed, but oneconceptual error is made.[1] Both equations are graphed, but oneconceptual error and one graphing error aremade.or [1] (0,5) and (4,–3) are stated, but no workis shown.[0] (0,5) or (4,–3) is stated, but no work isshown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[49]

[4] (10,0) and (1,9), and both graphs aredrawn correctly.[3] Both graphs are drawn correctly, but onlyone solution is stated correctly.or [3] One graph of equal difficulty is drawnincorrectly, but the solutions are appropriate,based on the graphs.[2] (10,0) and (1,9), but the problem is solvedalgebraically instead of graphically.or [2] One graph of equal difficulty is drawnincorrectly, and only one solution isappropriate, based on the graphs.[1] Both the parabola and the line are graphedincorrectly, but the solutions are appropriate,based on the graphs.or [1] Incorrect solutions result from analgebraic method.or [1] (10,0) and (1,9), but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[50]

[4] 9 and 26, and appropriate work is shown,such as graphing and labeling the equationsand identifying the points of intersection.[3] Both functions are graphed correctly, andthe points of intersection are indicated, butthe prices are not stated.or [3] The parabola is graphed correctly, butthe line is graphed incorrectly, but appropriateprices are stated.[2] The line and the parabola are graphed andlabeled, but a conceptual error is made, suchas only one price is found because the graphof the parabola is incomplete.or [2] The line is graphed correctly, but theparabola is graphed incorrectly, butappropriate prices are stated.or [2] 9 and 26, but only an algebraic solutionis shown.[1] Both the line and the parabola are graphedincorrectly, but appropriate prices are stated.or [1] 9 and 26, but no work is shown.[0] 9 or 26, but no work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[51] D

[52]

[4] (–3,–5) and (1,3), and appropriatealgebraic work is shown.[3] Appropriate algebraic work is shown, butx = –3 and x = 1 are given as the solution.or [3] Appropriate algebraic work is shown,but only one correct solution is given, such as(1,3).[2] (–3,–5) and (1,3), but a graphic solution isshown.or [2] Correct substitution and an algebraicequation set equal to zero are shown, but theresult is not factored, such as x x2 2 3 0+ − = .[1] Any correct substitution is shown, such as2 1 3 22x x x+ = + − .or [1] (–3,–5) and (1,3), but no algebraic workis shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[53]

[4] (-1,-2) and (2,13), and appropriate work isshown, such as an algebraic or graphicsolution or trial and error with at least threetrials and appropriate checks.[3] Appropriate work is shown, but onecomputational or graphing error is made.or [3] Appropriate work is shown, but onlyone solution is found or only the x- or the y-values are found.[2] Appropriate work is shown, but two ormore computational or graphing errors aremade.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] The trial-and-error method is used tofind the correct solutions, but only two trialsand appropriate checks are shown.or [2] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but no solutionis found.or [2] Both equations are graphed correctly,but neither ordered pair is identified.or [2] Only one equation is graphed correctly,but an appropriate solution is found.or [2] An incorrect quadratic equation ofequal difficulty is solved appropriately, andappropriate solutions are found.[1] Appropriate work is shown, but oneconceptual error and one computational orgraphing error are made.or [1] One equation is graphed correctly, butno further correct work is shown.or [1] An incorrect equation of a lesser degreeof difficulty, such as a linear equation, issolved appropriately.or [1] A correct substitution is made and thesystem of equations is simplified to a singlequadratic equation set equal to zero, but nofurther correct work is shown.or [1] (-l,-2) and (2,13), but no work or onlyone trial with an appropriate check is shown.[0] (-1,-2) or (2,13), but no work or only onetrial with an appropriate check is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[54]

[4] (3,14) and (–2,–1) and either an algebraicor a graphic solution is shown.[3] An appropriate method is shown, but onlyone correct ordered pair is identified.or [3] An appropriate method is shown, butone computational mistake is made.or [3] An appropriate method is shown, butvalues are given only for x.[2] The substitution is correct, but thequadratic produced is not factored correctly.or [2] Both equations are graphed correctly,but neither ordered pair is identified.[1] Only one equation is graphed correctly.or [1] The substitution is incorrect, but itproduces a linear equation that is solvedcorrectly.or [1] Only the substitution is correct.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[55]

[4] Yes, and appropriate work is shown, andan appropriate justification is given.[3] Appropriate work is shown, and anappropriate justification is given, but onecomputational error is made, or the negativevalue of t is not rejected.[2] An appropriate graph or equation isshown, such as 16 8 15 02t t− − = .[1] An incorrect graph or equation of equaldifficulty is used, but an appropriate solutionis found.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[1] B

[2] C

[3] C

[4] B

[5] A

[6] C

[7] C

[8] D

[9] A

[10] B

[11]

[2] 33 5

xx y+

[1] One correct factoring is shown, either3x(3x – 5y) or (3x – 5y)(3x + 5y).[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[12]

[2] xx

+−

15

, and appropriate work is shown.

[1] Only one expression is factored correctly,such as (x + 5)(x + 1) or (x + 5)(x - 5), but anappropriate simplification is done.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[13] C

[14] A

[15]

[2] − −+

xx

310 2

or an equivalent answer in

simplest form, and appropriate work isshown.[1] Either the numerator or the denominator isfactored completely.or [1] Appropriate work is shown, but3

31−

−= −x

x is not recognized.

or [1] − −+

xx

310 2

or an equivalent answer in

simplest form, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[16] B

[17] D

[18] D

[19] C

[20] B

[21]

[2] 4(x – 2) or 4x – 8, and appropriate work isshown.[1] The problem is factored correctly but notreduced to simplest form.or [1] Only two of the expressions arefactored correctly, but an appropriate answeris found.or [1] 4(x – 2) or 4x – 8, but no work isshown.[0] Only the formula for volume is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.


[22]

[2] x − 33

and multiplication by the reciprocal,

correct factoring, and canceling are shown.[1] The difference of two squares,x x x2 9 3 3− = + −( )( ), is factored correctly.or [1] Appropriate work is shown, but thefinal answer is incorrect.

or [1] x − 33

but no work is shown.


[23]

[4] x + 32


[3] Appropriate work is shown, but onecomputational, factoring, or simplificationerror is made.[2] Appropriate work is shown, but two ormore computational, factoring, orsimplification errors are made.or [2] Appropriate work is shown, but oneconceptual error is made, such as failing tomultiply by the reciprocal of g(x) or trying tosolve for x.[1] Appropriate work is shown, but oneconceptual error and one computational,factoring, or simplification error are made.

or [1] x + 32

, but no work is shown.


[24]

[6] − 83


[5] Appropriate work is shown, but onecomputational error is made.[4] Appropriate work is shown, but two ormore computational errors are made.[3] Appropriate work is shown, but oneconceptual error is made, such as notfactoring out -1 when canceling out 2 - x.[2] Appropriate work is shown, but oneconceptual error and one computational errorare made.

[1] − 83



[25]

[6] − −( ),x 3 − +x 3, or 3− x, andappropriate work is shown.[5] Appropriate work is shown, but onecomputational, factoring, or simplificationerror is made.[4] Appropriate work is shown, but twocomputational, factoring, or simplificationerrors are made.or [4] x − 3, and appropriate work is shown.[3] Appropriate work is shown, but three ormore computational, factoring, orsimplification errors are made.or [3] Appropriate work is shown, but oneconceptual error is made, such as notmultiplying by the multiplicative inverse.[2] Appropriate work is shown, but oneconceptual error and one computational,factoring, or simplification error are made.[1] − −( ),x 3 − +x 3, or 3− x, but no work isshown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[26] C

[27] A


[28] A

[29] C

[30] A

[31] B

[32] D

[33]

[2] 2 33

xx x

++( )

or 2 332

xx x

++

, and appropriate

work is shown.[1] Appropriate work is shown, but onecomputational error is made or the answer isnot simplified completely.or [1] Appropriate work is shown, but oneconceptual error is made.

or [1] 2 33

xx x

++( )

or 2 332

xx x

++

, but no work is

shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[34] D

[35] D

[36]

[6] x − 42


[5] Appropriate work is shown, but onecomputational error is made.[4] Appropriate work is shown, but two ormore computational errors are made.or [4] Appropriate work is shown, but −1 isnot factored out.[3] Appropriate work is shown, but oneconceptual error is made, such as notfollowing the correct order of operations.[2] Appropriate work is shown, but oneconceptual error and one computational errorare made.[1] Appropriate work is shown, but oneconceptual error and two or morecomputational errors are made.or [1] Appropriate work is shown, but twoconceptual errors are made.

or [1] x − 42



[37]

[3] 4, and appropriate work is shown.[2] Appropriate work is shown, but onecomputational error is made.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 4, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[38] C

[39] D

[40] A

[41] A

[42] A


[43] D

[44] B

[45]

[2] 2, and appropriate work is shown.[1] Appropriate work is shown, but onecomputational error or one conceptual error ismade.or [1] 2, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[46]

[2] 2.4 and appropriate work is shown.[1] The student shows correct use of thedistributive property to obtain 2x – 6 or otherappropriate algebraic technique.or [1] 2.4 and no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[47]

[2] 2.1, and appropriate work is shown.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 2.1, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[48]

[2] 38 and an appropriate method is shown,

such as 36.64 - (21 + 6.14) = 9.50 and 9 5025.

. =

38 or an equation such as 21 + .25c + 6.14 =36.64.[1] 38 and no work is shown.or [1] An appropriate method or equation isshown, but one computational mistake ismade.or [1] The answer of $9.50 for local calls isfound but is not divided by .25.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[49] B

[50] D

[51]

[2] 5 and appropriate work is shown, such assubstituting $18.11 for p and solving theequation correctly, or trial and error with atleast three trials and appropriate checks.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 5, but no work or fewer than three trialswith appropriate checks are shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[52] A

[53] C

[54] B


[55]

[2] 1 and -2, and appropriate work is shown.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] Appropriate work is shown, but onlyone value is found.or [1] 1 and -2, but no work is shown.[0] 1 or -2, but no work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[56]

[4] 3 and –5, and appropriate work is shown,such as x(x + 7) = 5(x + 3) or trial and errorwith at least three trials and appropriatechecks for each solution.[3] Appropriate work is shown, but onecomputational or factoring error is made.or [3] Appropriate work is shown, but onlyone correct solution is found.or [3] The trial-and-error method is used tofind both correct solutions, but only two trialsand appropriate checks are shown for eachsolution.[2] Appropriate work is shown, but two ormore computational or factoring errors aremade.or [2] A correct quadratic equation is writtenand factored, but no further correct work isshown.or [2] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but neithersolution is found.[1] A correct quadratic equation is written,but no further correct work is shown.or [1] 3 and –5, but no work or only one trialwith an appropriate check is shown.[0] 3 or –5, but no work or only one trial withan appropriate check is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[57]

[4] 2 and –3, and a correct quadratic equationis shown, such as x(x + 1) = 6, and solvedalgebraically.[3] The student shows a correct quadraticequation but makes one algebraic error andcarries it to solution or no solution for theequation generated.or [3] Correct work is shown, but only oneroot is found as the answer.[2] A correct quadratic equation is used, buttwo or more errors are made.or [2] An incorrect quadratic equation ofequal difficulty is shown and solvedappropriately.[1] The student cross multiplies but producesonly a linear equation that is solvedappropriately.or [1] 2 and –3, but no algebraic work isshown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[58]

[4] 6 and –2, and appropriate work is shown,such as an algebraic solution or trial and errorwith at least three trials and appropriatechecks.[3] Appropriate work is shown, but onecomputational or factoring error is made.or [3] Appropriate work is shown, but onlyone solution is found.[2] The correct quadratic equation is writtenin standard form.or [2] Appropriate work is shown, but two ormore computational or factoring errors aremade.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] The trial-and-error method is used tofind at least one solution, but only two trialsand appropriate checks are shown.or [2] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but no solutionis found.or [2] An incorrect quadratic equation ofequal difficulty is solved appropriately.[1] x x x2 11 12 7− − = − , but no further correctwork is shown.or [1] 6 and -2, but no work or only one trialwith an appropriate check is shown.or [1] An incorrect equation of a lesser degreeof difficulty is solved appropriately.or [1] Appropriate work is shown, but oneconceptual error and one computational orfactoring error are made.[0] 6 or -2, but no work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[59] B

[60]

[2] 1 and 2, 1 < h < 2, or 1 < 1.854 < 2, andappropriate work is shown.

[1] 33h

hh

=−

is shown, but one

computational error is made.or [1] The positive root, 1.854, is obtainedfrom the quadratic, but the two correctconsecutive integers are not stated.or [1] 1 and 2, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[61] B

[62]

[4] − ±3 377

or an equivalent answer, and

appropriate work is shown.[3] A correct quadratic equation is written andappropriate work is shown, but onecomputational or simplification error is made.or [3] An incorrect quadratic equation ofequal difficulty is solved appropriately.[2] A correct quadratic equation is written andappropriate work is shown, but twoor more computational or simplificationerrors are made.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] A correct quadratic equation is writtenin standard form, but no further correctwork is shown.[1] An incorrect equation of a lesser degree ofdifficulty is solved appropriately.

or [1] − ±3 377

or an equivalent answer, but

no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[63]

[4] 3 and 12


[3] Appropriate work is shown, but onecomputational error is made.or [3] Appropriate work is shown, but onlyone of the values is found.[2] Appropriate work is shown, but two ormore computational errors are made.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] The correct quadratic equation iswritten in standard form, but no furthercorrect work is shown.or [2] An incorrect quadratic equation ofequal difficulty is solved appropriately.[1] Appropriate work is shown, but oneconceptual error and one computational errorare made.or [1] An incorrect equation of a lesser degreeof difficulty is solved appropriately.

or [1] 3 and 12


[0] 3 or 12


or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[64]

[2] 8 or an equivalent answer, and appropriatework is shown.[1] The denominators are cleared correctly,such as 6 16 6 16( ) ( ),t t t t+ + = + but thefactoring is incorrect, or one error is madeusing the quadratic formula.or [1] The denominators are not clearedcorrectly, but an equation of equal difficultyis solved.or [1] 8 or an equivalent answer, but no workis shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[65]

[6] 3.5, and appropriate work is shown.[5] Appropriate work is shown, but onecomputational or rounding error is made.[4] A substitution error is made, resulting inan incorrect quadratic equation of equaldifficulty, but the incorrect equation is solvedappropriately.[3] A correct substitution is made, resulting inthe correct quadratic equation in standardform, but the equation is not solved.[2] A substitution error is made, resulting inan incorrect equation of equal difficulty, andone computational or rounding error is made.[1] 3.5, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[66] B


[1] C

[2] C

[3] B

[4] A

[5]

[2] 12

or an equivalent answer, and an

appropriate explanation is written.[1] A correct explanation is written, but theprobability is not stated.

or [1] 12

or an equivalent answer, but no

explanation is written.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[6] A

[7] C

[8] A

[9] D

[10] A

[11] D

[12] C

[13] D

[14] C

[15] A

[16]

[2] 6, and a correct tree diagram is drawn orsample space is listed.[1] A correct tree diagram is drawn or samplespace is listed, but no answer or an incorrectanswer is found.or [1] An appropriate answer is found, basedon an incorrect tree diagram or sample space.or [1] 6, but no tree diagram is drawn orsample space is listed.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[17]

[2] 12, and a correct tree diagram or a correctsample space is shown.[1] An incomplete tree diagram or samplespace is shown with at least 8 possiblecombinations shown, and an appropriatenumber of outfits is found.or [1] A correct tree diagram or sample spaceis shown, but the number of possible outfits ismissing or is incorrect.or [1] 12, but 3 4× is used to find the numberof outfits.[0] 12, but no work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[18]

a [1] A correct tree diagram or listing of all 8possibilities is shown.

b [1] 18

or [1] An appropriate answer is given for anincorrect part a tree diagram or listing.a and b[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[19]

[3] 49

, and a correct tree diagram or sample

space is shown.[2] A correct tree diagram or sample space isshown, but no probability or an incorrectprobability is given.or [2] An incorrect tree diagram or samplespace is shown, but an appropriate probabilityis found.[1] Appropriate work is shown, but oneconceptual error is made.

or [1] 49



[20] D

[21] B

[22] C

[23] D

[24] D

[25] D

[26]

[2] 72 and an appropriate method, such as3 6 4× × , is shown.[1] 72 and no explanation is given.or [1] An appropriate method is shown, butthe student has one computational mistake oran incomplete listing, such as 2 of the 3clothing categories.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[27] A

[28] C

[29] C

[30] C

[31] B

[32] B

[33]

[3] 1,344, and appropriate work is shown,such as 8 • 7 • 6 • 4.[2] Appropriate work is shown, but onecomputational error is made.[1] Appropriate work is shown, but two ormore computational errors are made.or [1] Appropriate work is shown, but oneconceptual error is made, such as basing theanswer on ordering an appetizer and a soup,using 5 • 3 • 7 • 6 • 4.or [1] 1,344, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[34] A

[35] D

[36] C

[37] A

[38] D


[39]

[3] 224

or an equivalent answer, and an

appropriate explanation is given orappropriate work is shown, such as a treediagram, sample space, or permutations.[2] Appropriate work is shown, but onecomputational error is made.or [2] Appropriate work is shown, but only anumerator or a denominator is determinedcorrectly.

or [2] 224

or an equivalent answer, but only

work for either the numerator or thedenominator is shown.[1] The probability of the tallest or theprobability of the shortest student being in theproper position is correct, such as .or [1] Only a tree diagram, sample space, orpermutations are shown.

or [1] 224


work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[40]

[3] 720


appropriate work is shown, such as 1525

1424

•

or 15 2

25 2

CC

.

[2] 1525

1424

• or 15 2

25 2

CC

is shown, but one

computational error is made or no furtherwork is shown.or [2] 15 2C and 25 2C are computed correctly,but no further work is shown.or [2] Appropriate work is shown, but onecomputational error is made.[1] The correct probabilities are found, butthey are added instead of multiplied.or [1] Only one of the two parts of theprobability is correct.or [1] Appropriate work is shown, but morethan one error is made.

or [1] 720


work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[41] A

[42] B

[43] D

[44] A

[45] A

[46] C

[47] D


[48]

[2] 120, and appropriate work is shown, suchas 1 • 5 • 4 • 3 • 2 • 1.[1] Appropriate work is shown, but onecomputational error is made.or [1] 720 and 6 6P or 6! is shown.or [1] 120, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[49] B

[50]

[2] 210, and appropriate work is shown, suchas 7 • 6 • 5 or 7 3P .[1] Appropriate work is shown, but no answeror an incorrect answer is found.or [1] 210, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[51] D

[52] A

[53]

[2] 8,100 and appropriate work is shown,such as 9 10 10 9× × × .[1] 10,000 but appropriate work is shown.or [1] Appropriate work is shown, but thestudent multiplies incorrectly.or [1] An appropriate pattern is shown, suchas 9 10 10 9× × × .or [1] 8,100 but no work is shown.[0] 38 is shown.or [0] The student attempts to use thecounting principle, but adds.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[54]

[4] 7 98 106. × or 7,980,000 and appropriatework is shown, such as 8 10 2 106 4× − × .[3] Appropriate work is shown, but onecomputational error is made.or [3] The student uses 1–9 instead of 0–9 asthe number of digits in 8 9 2 96 4× − × .[2] The student correctly produces only onepart, 8 106× or 2 104× , but carries theprocess to an appropriate result.or [2] Appropriate work is shown, but morethan one error is made.[1] The student produces only one part, 8 96×or 2 94× .or [1] 7,980,000 but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[55]

[2] 37,440 and appropriate work is shown,such as 2 x 26 x 10 x 9 x 8 or 2 1 26 1 10 3P P P× × .[1] Appropriate work is shown, but onecomputational or conceptual error is made.or [1] Appropriate work is shown for at leastone restriction, such as 2 x 26 or 10 x 9 x 8.or [1] 37,440 but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[56]

[3] Option 2 will yield 82,576,000 morepossibilities, and appropriate work is shown,such as 26 103 4• and 26 4 10 3P P• .[2] Appropriate work is shown, but onecomputational error is made, but theappropriate option is identified.or [2] The correct numbers of arrangementsare found for both Option 1 and Option 2, butthe question of which option will yield morearrangements is not answered or is answeredincorrectly.[1] Appropriate work is shown, but more thanone computational error is made, but theappropriate option is identified.or [1] Appropriate work is shown, but oneconceptual error is made, but the appropriateoption is identified.or [1] Either Option 1 or Option 2 is foundcorrectly, but no further correct work isshown.or [1] Option 2 will yield 82,576,000 morepossibilities, but no work is shown.[0] Option 2, but no work or inappropriatework is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[57] B

[58] B

[59] D

[60] A

[61] A

[62] A

[63] C

[64] C

[65] B

[66] B

[67] B

[68]

[2] 6 and appropriate work is shown, such asusing the combination 4 2C , listing all sixpossible outcomes, or drawing a correct treediagram.[1] A correct setup of combinations is shown,but an incorrect solution, such as leaving 4 2C ,or no integral solution is found.or [1] An appropriate list or tree diagram isshown, but an incorrect solution is found,such as 5, by omitting one of the possiblecombinations.or [1] 12 but a complete list or tree diagram isshown.or [1] 6 but no work is shown.[0] The answer is completely incorrect, suchas 4 2P or 4 3× .or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[69]

[2] 20,349, and appropriate work is shown,such as 21 5 20 349C = , .[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as determiningthe value of 21 5P .or [1] 20,349, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[70]

[3] 490, and appropriate work is shown, suchas 7•7•10.[2] Appropriate work is shown, but onecomputational error is made.or [2] Appropriate work is shown, but anincorrect answer is found, based on anincorrectnumber of possible dessert combinations oran incorrect number of soup or appetizerchoices.or [2] Appropriate work is shown, but anincorrect answer is found, based on one errorinthe tree diagram.

or [2] 1490

, but appropriate work is shown.

[1] 7, 7, and 10 are added instead ofmultiplied.or [1] The counting principle is usedcorrectly, but incorrect substitutions aremade, butan appropriate answer is shown.or [1] 490, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[71]

[3] 150, and appropriate work is shown, suchas 5 2 6 2C C• .[2] Appropriate work is shown, but onecomputational error is made.or [2] All the possible combinations of twomystery books and all the possiblecombinations of two biographies arecalculated, but the answers are not multiplied.[1] Appropriate work is shown, but more thanone computational error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as thecomputation 11 4 330C = .or [1] 150, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[72] C

[73]

[2] 10, and appropriate work is shown, suchas 5 2C or a diagram or a list.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 10, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[74] B

[75] D

[76]

a [2] 10 and an appropriate tree diagram, list,sample space, or 5 3 10C = is shown.[1] 10 and no work is shown.or [1] An appropriate method is shown, butnot all 10 possible combinations are listed

b [1] 110

or [1] An appropriate answer is found for anincorrect response in part a.

c [1] 410

25

0 4or or .

or [1] An appropriate answer is found for anincorrect response in part a.a and b and c [0] A zero response iscompletely incorrect, irrelevant, or incoherentor is a correct response that was obtained byan obviously incorrect procedure.


[77]

[4] 410

and appropriate work is shown, such

as the following illustration or any othercorrect method:

[3] Appropriate work is shown, but onecomputational error is made.

or [3] Appropriate work and complement 610

are shown.or [3] Appropriate work is shown, but theanswer is incomplete.[2] 5 2C and the work is appropriate butincomplete.or [2] 10 but appropriate work is shown.or [2] A correct sample space or tree diagramis shown.[1] Incorrect work leading to 0 1≤ ≤fractionor 0 100≤ ≤percent is shown.

or [1] 410



[78]

[3] 820


appropriate work is shown, such as using atree diagram or writing the equation6

20220

820

+ = .

[2] One computational error is made in

finding 620

or 220

, but an appropriate sum is

found.

or [2] 220

and 620

are found, but no sum is

shown.

[1] 620

or 220

, and appropriate work is

shown.or [1] An appropriate answer is found, usingreplacement with a tree diagram or an

equation such as 35

35

25

25

1325

• + • = .

or [1] 820




[79]

[4] No, and an appropriate explanation is

given, such as P P( ) ( ) .15 656

2 1256

= < =

[3] One of the two probabilities is foundcorrectly, but one computational error is madein finding the other, but an appropriateconclusion is drawn, based on the valuesfound.or [3] Replacement is used to conclude

P P( ) ( ) .15 664

2 1264

= < =

or [3] The two probabilities are foundcorrectly, but no conclusion or the incorrectconclusion is drawn.[2] One of the probabilities is found correctly,but one computational error is made infinding the other, and no conclusion or theincorrect conclusion is drawn.[1] An appropriate method is used, such as atree diagram or sample space, but theprobabilities are not determined or aredetermined incorrectly.

or [1] P P( ) ( ) ,15 656

2 1256

= < = but no work

is shown.[0] No, but no work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrectresponse that was obtained by an obviouslyincorrect procedure.

[80]

a [2] 3072

or an equivalent value is found and

an appropriate explanation is given.[1] An acceptable method is used correctly,such as a tree diagram, sample space, orcombinations, but the correct answer is notgiven.or [1] Replacement is used, and an answer of3681

or an equivalent is found.

or [1] 3072

and no work is shown.

b [2] 3672

or an equivalent value is found and

an appropriate explanation is given.or [2] An appropriate probability for anincorrect denominator for part a is found.[1] An appropriate method is shown, but onecomputational mistake is made.or [1] Replacement is shown, and the answer3681

or an equivalent is found.

or [1] The student does not take into account

both orders and answers 1872

or an equivalent.

or [1] 3672

and no work is shown.

or a and b[1] An error in method is made but theerroneous answer is interpreted correctly ineither part a or b or both.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[1] D

[2] D

[3]

[4] The student draws a histogram, a stem-and-leaf plot, or any other acceptablestatistical graph, with proper labels and a title.[3] The student makes one or two minorerrors, such as a lack of label, title, orconnected dots.[2] The student makes several minor errors orone major error, such as not accounting for all20 scores.[1] The student draws just the beginning of agraph.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[4]

[2] A correct stem-and-leaf plot is drawn,including a key.[1] The data are arranged correctly, butincorrect labels are written on the stem-and-leaf columns. [Columns do not need to belabeled for a full-credit response, but fullcredit may not be awarded if the columns arelabeled incorrectly.]or [1] The data are listed in the stem-and-leafplot, but not in ascending order.or [1] One or two of the scores are left out ofthe stem-and-leaf plot.or [1] Duplicate values are left out of thestem-and-leaf plot.[0] Incorrect labels are written on the stem-and-leaf columns, and scores are left out ofthe plot.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[5]

[3] The frequency table is completedcorrectly, showing frequencies of 6, 2, 4, 5,and 3, and a frequency histogram is drawnand labeled correctly.[2] The frequency table is completedcorrectly, but one graphing error is made,such as not labeling the axes, having nonequalintervals, or starting the x-axis at 50.or [2] The frequency table is completedincorrectly, but an appropriate frequencyhistogram is drawn.or [2] The frequency histogram is drawn andlabeled correctly, but the frequency table isnot completed.[1] The frequency table is completedcorrectly, but two or more graphing errors aremade.or [1] The frequency table is completedcorrectly, but no frequency histogram isdrawn or a bar graph is drawn.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[6]

[4] A correct table and histogram withappropriate labels and scales are shown, suchasthe table below.SCORE TALLY FREQUENCY40-49 / 150-59 / 160-69 /// 370-79 /// 380-89 /// 3[3] An incorrect table is shown, but thehistogram is appropriate, based on this table.or [3] A correct table is shown, but one erroris made on the histogram, such as usingincorrect labels or no labels.or [3] An incomplete table is shown, but thehistogram is correct.[2] An incomplete table is shown, and thehistogram is partially correct.or [2] A correct table is shown, and a correctbar graph is made.[1] A correct table is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[7]

a [2] An appropriate histogram is drawn withboth axes labeled with a correct numericalscale.[1] A correct bar graph is drawn.or [1] The parts of the histogram are notlabeled.or [1] Equal interval scales are not shown.or [1] One error on frequency calculation ismade.[0] Two or more mistakes on frequencycalculation are made.b [2] 60% and an appropriate explanation isgiven.[1] An appropriate method to find percent isshown, but a mistake is made in reading the

chart, such as 615

40% 915

= or is shown but

not given as a percent answer.or [1] 60% and no explanation is given.a and b[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[8]

a [3] The frequency table is completedcorrectly, and a histogram is drawn with acorrect scale and is labeled correctly.[2] One or two errors are made in thefrequency table, but an appropriate histogramis drawn.or [2] The frequency table is completedcorrectly, but one error is made in drawingthe histogram.[1] A correct histogram is drawn, but thefrequency table is not completed.b [1] The interval 91-100 is identified ascontaining the 75th percentile.or [1] The appropriate interval is identified,based on an incorrect frequency table in parta.a and b[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[9] C


[10] B

[11]

[2] 1,225, and appropriate work is shown,such as solving an equation or writing anexplanation.[1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] Appropriate work is shown, but theconversion from years to months is incorrect,but an appropriate solution is found.or [1] 1,225, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[12] A

[13]

[2] 77, and appropriate work is shown, suchas (76 + 78) ÷ 2.[1] 76 and 78 are identified.or [1] 77, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[14] A

[15]

[2] An appropriate explanation is given, suchas:One very high or very low score in eitherclass would have a great effect on the rangefor that class, but might not affect the medianat all. The range is the difference between thetwo most extreme values, the lowest and thehighest. The median, being the middle value,is not very sensitive to outliers or to extremevalues.or [2] Specific examples are shown toillustrate the situation.[1] An understanding of median and range isdemonstrated, but the specific situation is notexplained.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[16] A

[17]

[3] Mean = 79, median = 79, and mode = 78,and appropriate work is shown.[2] Appropriate work is shown, but only twoof the three measures of central tendency aredetermined and identified correctly.or [2] Appropriate work is shown and allthree measures of central tendency aredetermined correctly, but the measures are notidentified or are identified incorrectly.[1] Appropriate work is shown, but only oneof the three measures of central tendency isdetermined and identified correctly.or [1] Mean = 79, median = 79, and mode =78, but no work is shown.[0] 79, 79, and 78, but no work is shown, andthe answers are not identified or are identifiedincorrectly.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[18] C

[19] D

[20] B


[21] D

[22] B

[23]

[3] 34 and an appropriate explanation is

given, such as 38 46 23

= + x .

[2] An appropriate method or equation isshown, but one computational mistake ismade.or [2] The student does not take intoconsideration two dogs of equal weight andgives an answer of 68.[1] The student understands weighted averagein that three dogs averaging 38 pounds musthave a total weight of 114 pounds but doesnot subtract the known weight.or [1] 34 and no explanation is given.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[24] B

[25] C

[26] D

[27]

[2] $350, and appropriate work is shown,

such as 14505

360+ =x or trial and error with

at least three trials and appropriate checks.[1] Appropriate work is shown, but onecomputational error is made.or [1] The total of the five salaries is shown tobe 5 x 360 = 1800, but no further correctwork is shown.or [1] $350, but no work is shown or fewerthan three trials with appropriate checks areshown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[28]

[3] 59 or 59º, and appropriate work is shown,

such as 63 2565

= + x or

56 + 72 + 67 + 61 = 256, 63 x 5 = 315, and315 – 256 = 59.[2] Appropriate work is shown, but onecomputational error is made.or [2] A value is chosen for Friday’stemperature that rounds to 63, such as 57 or61,but whose mean is not exactly 63, andappropriate work is shown.[1] A limited understanding of the concept ofthe mean is shown, such as the sum ofthe temperatures must be 315, but the giventemperatures are not subtracted.or [1] The correct mean of the four giventemperatures is calculated.or [1] 59 or 59º, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[29] D

[30]

[3] 95 and an appropriate method is shownthat obtains an answer, such as 344 - 249 or asimilar equation or method.or [3] Four scores are tried that round off toan average of 86, such as 93 or 94. Round offto 86 must be shown.[2] An appropriate method is shown, but onecomputational mistake is made.[1] The student understands weighted averageand shows that the average of 83 for 3 tests isa total of 249 points.or [1] 95 and no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[31] A


[32]

[3] 63, and appropriate work is shown, suchas 400 - (81 + 88 + 88) and determining thehighest and lowest possible scores remainingthat total 143.[2] Appropriate work is shown, but onecomputational error is made.[1] A total of 400 is shown, but oneconceptual error is made, such as 257 issubtracted, and then 143 is split into 72 and71, resulting in an answer of 71.or [1] Appropriate work is shown, but morethan one computational error is made.or [1] No answer or an incorrect answer isfound, but a list such as ___, ___, 81, 88, 88is shown.or [1] 63, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[33]

[4] Angelo is 66, Brandon is 26, and Carl is31, and appropriate work is shown, such assolving an equation or trial and error with atleast three trials and appropriate checks.[3] Appropriate work is shown, but onecomputational error is made.or [3] 66, 26, and 31, and appropriate work isshown, but the solutions are not labeled or arelabeled incorrectly.[2] Appropriate work is shown, but two ormore computational errors are made.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] The trial-and-error method is used tofind a correct solution, but only two trials andappropriate checks are shown.or [2] The trial-and-error method is attemptedand at least six systematic trials andappropriate checks are shown, but no solutionis found.or [2] Carl is 31, and appropriate work isshown, but the ages of the other men are notfound.or [2] An incorrect equation of equaldifficulty is solved appropriately.[1] Appropriate work is shown, but oneconceptual error and one computational errorare made.or [1] A correct equation is written, but nofurther correct work is shown.or [1] Angelo is 66, Brandon is 26, and Carl is31, but no work or only one trial with anappropriate check is shown.[0] Angelo is 66 or Brandon is 26 or Carl is31, but no work is shown.or [0] 66, 26, and 31, but no work is shown,and the answers are not labeled or are labeledincorrectly.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.


[34]

[4] Median = 91.5, mode = 92, and seventhtest score = 96, and appropriate work isshown.[3] Appropriate work is shown, but onecomputational error is made.or [3] Seventh test score = 96, but only themedian or the mode is found correctly, butappropriate work is shown.or [3] 91.5, 92, and 96, and appropriate workis shown, but the median and mode are notlabeled or are labeled incorrectly.[2] Appropriate work is shown, but two ormore computational errors are made.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] Both the median and the mode arefound and labeled correctly, and appropriatework is shown, but the seventh test score isnot found or is found incorrectly.or [2] Seventh test score = 96, and appropriatework is shown, but the median and the modeare not found or are found incorrectly.[1] Either the median or the mode is foundand labeled correctly, and appropriate work isshown, but no further correct work is shown.or [1] Median = 91.5, mode = 92, and seventhtest score = 96, but no work is shown.[0] Median = 91.5 or mode = 92 or seventhtest score = 96, but no work is shown.or [0] 91.5, 92, and 96, but no work is shownand the answers are not labeled.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[35] C

[36]

[4] Mean = 225,000, median = 175,000, andthe median is stated to be the best measure ofcentral tendency, an appropriate justificationis given, and appropriate work is shown.[3] Appropriate work is shown, but onecomputational error is made, but anappropriate measure of central tendency isstated, and an appropriate justification isgiven.or [3] Mean = 225,000, median = 175,000,and the median is stated to be the bestmeasure of central tendency, but nojustification is given.[2] Appropriate work is shown, but two ormore computational errors are made, but anappropriate measure of central tendency isstated, and an appropriate justification isgiven.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] Appropriate work is shown to findmean = 225,000 and median = 175,000, butno further correct work is shown.[1] Appropriate work is shown, but onecomputational error and one conceptual errorare made.or [1] Mean = 225,000 and median = 175,000,but no further work is shown.[0] Mean = 225,000 or median = 175,000, butno further work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.

[37] D

[38] B

[39] A

[40] D

[41] B

[42] B


[43]

[4] Correct cumulative frequencies of 7, 14,24, and 30 and a fully labeled correcthistogram are shown.[3] Incorrect cumulative frequencies areshown, but the histogram is appropriate forthe data.or [3] Correct cumulative frequencies areshown, but a partially incorrect histogram isshown, such as the axes not being labeled,having nonequal intervals, or the x-axisstarting at 50.[2] Only a frequency histogram is completedcorrectly.or [2] Only a correct cumulative frequencytable and a correct bar graph are shown.[1] An appropriate bar graph is shown, but itis based on frequencies, not the cumulativefrequency.or [1] Only a correct cumulative frequencytable is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[44]

[4] The table is completed correctly, and anappropriate cumulative frequency histogramis drawn and labeled.[3] The table is completed correctly, but oneerror is made in drawing the cumulativefrequency histogram or one or more labelingerrors are made.or [3] The table is not completed correctly,but an appropriate cumulative frequencyhistogram is drawn, based on the table.[2] One error is made in completing the table,and one graphing error is made in drawing thecumulative frequency histogram.or [2] The table is completed correctly, butone conceptual error is made, such as drawinga frequency histogram or a cumulativefrequency bar graph.[1] The table is completed correctly, but nohistogram is drawn.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[45] B

[46] A

[47] B

[48]

[2] y x= −108 2125. or an equivalent equationis written.[1] One conceptual error is made, such aswriting a regression equation that is notlinear.or [1] The expression 108 2125. x − is written,but no equation is written.or [1] The correct values are identified for aand b, but no equation is written.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[49]

[6] W = 44.6 and L = 43.2, the line of best-fitequation (y = –1.007559x + 88.137149) isshown, and an appropriate justification ofpoint (W , L ) fitting or not fitting, dependingon the rounding of the equation, is given.[5] W or L is incorrect, but the rest of thework is appropriate.or [5] All conditions of the problem are met,except it is not stated whether (W , L ) lies ordoes not lie on the line of best fit.or [5] W and L and the equation of the lineof best fit are correct, but one error results inan incorrect conclusion, such as thecalculation or interchanging of W and L .[4] Both W and L are incorrect, but the restof the work is appropriate.or [4] W and L are correct, but the equationof the line of best fit is incorrect, but thejustification is appropriate, based on theincorrect equation.or [4] W and L are correct, a correct scatterplot is drawn, a correct line of best fit isdrawn, (W , L ) is plotted correctly, and astatement indicating that the point does ordoes not fit the line is given, with anappropriate explanation, but no equation isused.or [4] All conditions of the problem are met,except for the justification of whether (W , L )lies on the line.[3] W and L are correct, but the equation ofthe line of best fit is stated incorrectly, and nofurther work is shown.[2] Only W and L are found correctly.[1] Only one mean is found correctly.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[50]

[4] y = –34739.71292x + 313309.0909 and209,090, and appropriate work is shown.[3] Appropriate work is shown, but onecomputational or rounding error is made.or [3] An incorrect linear equation with anegative slope is written, but an appropriateprice is found for three blocks from the beach.[2] Appropriate work is shown, but two ormore computational or rounding errors aremade.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] A correct linear function is written, butno further correct work is shown.or [2] An incorrect linear equation with apositive slope is written, but an appropriateprice is found for three blocks from the beach.[1] Appropriate work is shown, but oneconceptual error and one computational orrounding error are made.or [1] 209,090, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[51]

[4] y x= − +058 118509. . and 19.9, andappropriate work is shown.[3] Appropriate work is shown, but onecomputational or rounding error is made.[2] Appropriate work is shown, but two ormore computational or rounding errors aremade.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] A correct linear equation is written, butno further correct work is shown.or [2] An incorrect linear equation is written,but an appropriate percentage is found.[1] Appropriate work is shown, but oneconceptual error and one computational orrounding error are made.or [1] 19.9, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[52]

[6] y = –6.2x + 12,451.2; 20.2 thousand; and2008; and appropriate work is shown.[5] The correct equation is shown, but onlythe number of gallons or the year is correct.[4] The slope and y-intercept are incorrect,but the slope is negative and the number ofgallons and the year are appropriate, based onthe incorrect equation.[3] The slope and y-intercept are incorrect,but the slope is negative, but only the numberof gallons or the year is appropriate, based onthe incorrect equation.[2] The correct equation is shown, but thenumber of gallons and the year are notdetermined or are determined incorrectly.or [2] The incorrect equation y = 6.2x +12,451.2 is shown, but appropriate work isshown for the number of gallons and the year.[1] An incorrect equation is shown with anegative slope, and the number of gallons andthe year are not determined.or [1] 20.2 thousand and 2008, but no work isshown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[53]

[4] a y = 0.8344648562x + 14.64960064 or anequivalent answer expressed to threesignificant digitsand b 80, and appropriate work is shown.[3] One computational error is made or onerounding error is made with one of thenumbers in the equation, such as truncating ornot giving at least three significant digits.[2] Only the correct answer for either part a orpart b is found.or [2] Appropriate work is shown, but morethan one computational or rounding error ismade.[1] 78 is substituted into an incorrect linearequation, but it is evaluated appropriately.or [1] y = 0.8344648562x + 14.64960064 and80, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[54]

[4] x = 80, y = 20.8, and y = 0.25x + 0.8, andappropriate work is shown to prove that ( x ,y ) is a point on the line of regression.[3] Appropriate work is shown, but onecomputational error is made.[2] Appropriate work is shown, but two ormore computational errors are made.or [2] Appropriate work is shown, but oneconceptual error is made.[1] x = 80, y = 20.8, and y = 0.25x + 0.8, butno work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.


[55]

[6] A correct scatter plot, y = 0.62x + 29.18, r= 0.92, and 83; and appropriate work isshown.[5] Appropriate work is shown, but onecomputational or rounding error is made.or [5] A correct scatter plot, equation, andscore are shown, but no r-value is found.[4] A correct scatter plot and equation areshown, but the r-value and score are missingor incorrect.or [4] An incorrect equation is shown, but allfurther work is appropriate.or [4] The scatter plot is missing or incorrect,but all further work is appropriate.[3] The scatter plot is incorrect, but a correctequation and either a correct r-value or scoreare found.or [3] The scatter plot is correct, but anincorrect equation and either an appropriate r-value or score based on the incorrect equationare found.[2] Only a correct scatter plot is shown, andall further work is missing or incorrect.or [2] Only a correct equation is shown, andall further work is missing or incorrect.[1] An incorrect equation is shown, but anappropriate score is found.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[56]

[6] y = 0.01021x - 1.66787, 4.56, and 913,and appropriate work is shown.[5] Appropriate work is shown, but onecomputational or rounding error is made.or [5] The expression 0.01021x - 1.66787 iswritten and 4.56 and 913 are found, andappropriate work is shown.[4] Appropriate work is shown, but two ormore computational or rounding errors aremade.or [4] A correct equation is written, but eitherthe gross earnings or the number of theaters isnot found, but appropriate work is shown.or [4] An incorrect equation of equaldifficulty is written, but appropriate answersare found, and appropriate work is shown.[3] Appropriate work is shown, but oneconceptual error is made.or [3] y = 0.01021x - 1.66787, 4.56, and 913,but no work is shown.or [3] The expression 0.01021x - 1.66787 iswritten and either 4.56 or 913 is found, andappropriate work is shown.[2] Appropriate work is shown, but oneconceptual error and one computational orrounding error are made.or [2] A correct equation is written, but nofurther correct work is shown.[1] 4.56 and 913, but no work is shown.or [1] The expression 0.01021x - 1.66787 iswritten, but no further correct work is shown.[0] Either 4.56 or 913, but no work is shown.or [0] A zero response is completelyincorrect, irrelevant, or incoherent or is acorrect response that was obtained by anobviously incorrect procedure.


[57]

[6] p = 8.1875t + 72.7860, 1993, and 220.2,and appropriate work is shown.[5] Appropriate work is shown, but onecomputational or rounding error is made.or [5] The expression 8.1875t + 72.7860 iswritten and 1993 and 220.2 are found, andappropriate work is shown.[4] Appropriate work is shown, but two ormore computational or rounding errorsare made.or [4] A correct equation is written, but eitherthe year or the predicted value for 2008is not found, but appropriate work is shown.or [4] An incorrect equation is solvedappropriately.[3] Appropriate work is shown, but oneconceptual error is made.or [3] p = 8.1875t + 72.7860, 1993, and220.2, but no work is shown.or [3] The expression 8.1875t + 72.7860 iswritten and either 1993 or 220.2 is found,and appropriate work is shown.[2] Appropriate work is shown, but oneconceptual error and one computational orrounding error are made.or [2] A correct equation is written, but nofurther correct work is shown.or [2] 1993 and 220.2, but no work is shown.[1] The expression 8.1875t + 72.7860 iswritten, but no further correct work isshown.or [1] 1993 or 220.2, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

[58]

[4] f(x) = 98.8571x + 737.3333 or y =98.8571x + 737.3333 and day 14, andappropriate substitution is made, such as 2050= 98.8571x + 737.3333.[3] Appropriate work is shown, but onecomputational or rounding error is made.or [3] A correct linear regression equation iswritten and day 14, but no substitution ismade.or [3] The expression 98.8571x + 737.3333 iswritten and day 14, and appropriatesubstitution is made, but no equation iswritten.[2] Appropriate work is shown, but two ormore computational or rounding errors aremade.or [2] Appropriate work is shown, but oneconceptual error is made.or [2] A correct linear regression equation iswritten, but no further correct work is shown.or [2] An incorrect equation of equaldifficulty is solved appropriately.[1] Appropriate work is shown, but oneconceptual error and one computational orrounding error are made.or [1] The expression 98.8571x + 737.3333 iswritten, but no further correct work is shown.or [1] Day 14, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.

jefferson math project regents by chapter

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