Grade 12 Mathematics Answers - Fldoe

Grade 12 MathematicsAnswer KeyThis booklet contains the answers to the sample items from the National Assessment of Educational Progress (NAEP)included in the NAEP Grade 12 Mathematics Sample Questions Booklet. It also references the corresponding CommonCore State Standards. Additional NAEP items can be accessed at www.nces.ed.gov/nationsreportcard/itmrls.SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics (NCES),National Assessment of Educational Progress (NAEP).This answer booklet and the corresponding Grade 12 Mathematics Sample Questions Booklet are posted athttp://www.fldoe.org/asp/naep/naep-pt.asp.

NAEP GRADE 12 MATHEMATICS ANSWER KEYCONTENTSNAEP GRADE 12 NUMBER PROPERTIES AND OPERATIONS . 3Question 1 - Multiply a 3-digit number by a decimal number . 4Question 2 - Estimate amount of time for problem in context . 4Question 3 - Find the cost of mailing a letter, based on its weight . 5Question 4 - Calculate an expected value, given a percentage . 5Question 5 - Given the scale, determine the length of a side . 6Question 6 - Identify effect of changing certain digits on a number’s value . 6Question 7 - Estimate property value, given tax rate and amount . 7Question 8 - Determine the remainder in an algebraic setting . 7Question 9 - Determine a weight of a letter given mailing cost . 8Question 10 - Solve a problem involving fractions. 9Question 11 - Determine proportional enlargement of photograph. 10NAEP GRADE 12 ALGEBRA . 11Question 1 - Determine a nonequivalent expression . 11Question 2 - Solve problem involving numerical sequence . 11Question 3 - Subtract rational expressions . 12Question 4 - Solve a system of linear equations . 12Question 5 - Find annual rate of population growth . 13Question 6 - Interpret characteristics of graph in a context . 15NAEP GRADE 12 MEASUREMENT . 19Question 1 - Compare units of volume . 19Question 2 - Solve problem involving area in context . 19Question 3 - Calculate the measure of an angle in a triangle . 20Question 4 - Find actual dimensions of room drawn to scale. 20Question 5 - Identify a 90-degree angle in a figure . 21Question 6 - Find the length of the sides of a square . 21Question 7 - Solve a problem using trigonometry . 22Question 8 - Find range for area given precision of linear measurements. 22Question 9 - Use trigonometry to find height of object. 23Question 10 - Solve a multi-step problem with a rectangle and sphere . 23NAEP Grade 12 Mathematics Answers to Sample QuestionsFlorida Department of EducationDivision of Accountability, Research, and Measurement; Office of AssessmentJuly 20132

NAEP GRADE 12 GEOMETRY . 25Question 1 - Find the missing dimension of a room . 25Question 2 - Find the measure of angle between streets . 25Question 3 - Find length of side in a 30-60-90 triangle . 26Question 4 - Analyze properties of quadrilateral inscribed in circle . 26Question 5 - Determine which triangle is not a 30-60-90 right traingle . 27Question 6 - Identify the 3-D figure resulting from folding paper . 27Question 7 - Prove that given figure is a parallelogram . 28Question 8 - Perform multiple transformations of segment in xy-plane . 31NAEP GRADE 12 DATA ANALYSIS . 33Question 1 - Solve problem using data in a table . 33Question 2 - Analyze correlations of two data sets in a scatterplot . 33Question 3 - Identify linear equation that best fits data in a scatterplot . 34Question 4 - Identify appropriate method for selecting random sample . 34Question 5 - Make a prediction based on data in scatterplot . 35Question 6 - Calculate probability of indepenent events . 36Question 7 - Determine the type of graph to best represent a situation . 37Question 8 - Determine conditional probablity from two-way table . 37Question 9 - Solve a data-related problem and justify the answer . 39Question 10 - Use survey results to make an inference. 39Question 11 - Solve a problem involving color patterns . 40Mathematics Common Core (MACC) State Standards (CCSS) DomainsEE Expressions and EquationsF FunctionsG GeometryMD Measurement and DataNBT Number and Operations in Base TenNF Number and Operations FractionsNS Number SystemsOA Operations and Algebraic ThinkingRP Ratios and Proportional RelationshipsSP Statistics and ProbabilityF-BF Building FunctionsA-SSE Seeing Structure in ExpressionA-APR Arithmetic with Polynomials andRational ExpressionsA-REI Reasoning with Equations and InequalitiesG-SRT Similarity, Right Triangles, and TrigonometryG-CO CongruenceS-ID Interpreting Categorical and Quantitative DataNAEP Grade 12 Mathematics Answers to Sample QuestionsFlorida Department of EducationDivision of Accountability, Research, and Measurement; Office of AssessmentJuly 20133

NAEP GRADE 12 MATHEMATICSAlignment to Mathematics Common Core (MACC) State Standards (CCSS) andAnswers to NAEP Sample QuestionsNAEP GRADE 12 NUMBER PROPERTIES AND OPERATIONSQuestion 1, MACC.6.NS.2.3Description: Multiply a 3-digit number by a decimal numberDifficulty: EasyComplexity: LowCorrect answer is BAnswersPercent chosen by Florida’s participating students*B63%A12%C12%D5%E7%Omitted1%Question 2, MACC.6.RP.1.3c and MACC.7.RP.1.3Description: Estimate amount of time for problem in contextDifficulty: MediumComplexity: LowCorrect answer is DAnswersPercent chosen by Florida’s participating students*D52%A14%B12%C15%E7%NAEP Grade 12 Mathematics Answers to Sample QuestionsFlorida Department of EducationDivision of Accountability, Research, and Measurement; Office of AssessmentJuly 20134

Question 3, MACC.6.EE.2.6Description: Find the cost of mailing a letter, based on its weightDifficulty: EasyComplexity: LowThe correct answer is CNational Data1Question 4, MACC.6.RP.1.3cDescription: Calculate an expected value, given a percentageDifficulty: EasyComplexity: LowCorrect answer is CNational Data1Grade 12 mathematics state-level results for Florida are only available for 2009. Only national-level results are available forthe other assessment years.5NAEP Grade 12 Mathematics Answers to Sample QuestionsFlorida Department of EducationDivision of Accountability, Research, and Measurement; Office of AssessmentJuly 2013

Question 5, MACC.7.G.1.1 and MACC.7.RP.1.3Description: Given the scale, determine the length of a sideDifficulty: MediumComplexity: LowCorrect answer is BNational DataQuestion 6, MACC.3.NBT.1.2 and MACC.4.NBT.2.4Description: Identify effect of changing certain digits on a number’s valueDifficulty: MediumComplexity: LowCorrect answer is ANational DataNAEP Grade 12 Mathematics Answers to Sample QuestionsFlorida Department of EducationDivision of Accountability, Research, and Measurement; Office of AssessmentJuly 20136

Question 7, MACC.3.NBT.1.1, MACC.4.NBT.1.3, MACC.5.NBT.2.5, and MACC.6.NS.2.2Description: Estimate property value, given tax rate and amountDifficulty: MediumComplexity: ModerateCorrect answer is CNational DataQuestion 8, MACC.4.OA.2.3 and MACC.4.NBT.2.6Description: Determine the remainder in an algebraic settingDifficulty: HardComplexity: ModerateThe correct answer is ENational DataNAEP Grade 12 Mathematics Answers to Sample QuestionsFlorida Department of EducationDivision of Accountability, Research, and Measurement; Office of AssessmentJuly 20137

Question 9, MACC.6.EE.2.6 and MACC.6.EE.2.7Description: Determine a weight of a letter given mailing costDifficulty: MediumComplexity: ModerateSolution:Any number of ounces greater than 4 but less than or equal to 5.4 oz 5Score & DescriptionCorrectCorrect response with correct work and correct label - must say ounces.PartialCorrect response (or correct process) with computational error; includes an answer of 4 with everythingelse correct.ORCorrect response without work or labels.IncorrectIncorrect response including all papers where 43 cents is used as cost of additional ounce.National DataNAEP Grade 12 Mathematics Answers to Sample QuestionsFlorida Department of EducationDivision of Accountability, Research, and Measurement; Office of AssessmentJuly 20138

Question 10, MACC.5.NF.2.6 and MACC.5.NF.2.7Description: Solve a problem involving fractionsDifficulty: HardComplexity: ModerateSolution:or equivalentScore & DescriptionCorrectCorrect response.IncorrectIncorrect response.National DataNAEP Grade 12 Mathematics Answers to Sample QuestionsFlorida Department of EducationDivision of Accountability, Research, and Measurement; Office of AssessmentJuly 20139

Question 11, MACC.7.RP.1.2b and MACC.7.RP.1.2cDescription: Determine proportional enlargement of photographDifficulty: HardComplexity: ModerateSolution:where x the length of the enlarged pictureTo be a proportional enlargement, the picture should be 5 inches bythe same ratio of width to length as the 4-inch by 6-inch picture.inches because that maintainsScore & DescriptionCorrectCorrect response with justification.IncorrectIncorrect response.National DataNAEP Grade 12 Mathematics Answers to Sample QuestionsFlorida Department of EducationDivision of Accountability, Research, and Measurement; Office of AssessmentJuly 201310

NAEP GRADE 12 ALGEBRAQuestion 1, MACC.6.EE.1.3 and MACC.6.EE.1.4Description: Determine a nonequivalent expressionDifficulty: EasyComplexity: LowCorrect answer is DAnswersPercent chosen by Florida’s participating students*D57%A14%B10%C5%E14%Question 2, MACC.912.F-BF.1.2Description: Solve problem involving numerical sequenceDifficulty: MediumComplexity: LowCorrect answer is CAnswersPercent chosen by Florida’s participating students*C61%A7%B14%D13%E5%NAEP Grade 12 Mathematics Answers to Sample QuestionsFlorida Department of EducationDivision of Accountability, Research, and Measurement; Office of AssessmentJuly 201311

Question 3, MACC.912.A-SSE.1.2 and MACC.912.A-APR.4.6Description: Subtract rational expressionsDifficulty: HardComplexity: LowCorrect answer is DAnswersPercent chosen by Florida’s participating students*D21%A34%B10%C29%E5%Question 4, MACC.8.EE.3.8b and MACC.912.A-REI.3.6Description: Solve a system of linear equationsDifficulty: MediumComplexity: LowSolution:Answer:,Solution (not required in response):NAEP Grade 12 Mathematics Answers to Sample QuestionsFlorida Department of EducationDivision of Accountability, Research, and Measurement; Office of AssessmentJuly 201312

Question 4, continuedScore & DescriptionCorrectBoth values correctPartialOne correct value onlyIncorrectIncorrect responseFlorida Data36%Correct7%Partial53%Incorrect4%Off Task0%20%40%60%80%100%Question 5, MACC.912.A-SSE.1.1 and MACC.912.A-SSE.2.3cDescription: Find annual rate of population growthDifficulty: HardComplexity: ModerateSolution:(a) Answer: 50,000Solution (not required in response):In 1990,(b) Answer: 6.5% (or 0.065) (Accept responses from 6% to 7%, inclusive)NAEP Grade 12 Mathematics Answers to Sample QuestionsFlorida Department of EducationDivision of Accountability, Research, and Measurement; Office of AssessmentJuly 201313

Question 5, continuedSolution (not required in response):In 2001,Score & DescriptionCorrectBoth parts correctPartial 1Part (a) correct onlyPartial 2Part (b) correct onlyIncorrectIncorrect responseFlorida Data6%Correct43%Partial 140%Incorrect2%Off Task7%Omitted0%20%40%60%NAEP Grade 12 Mathematics Answers to Sample QuestionsFlorida Department of EducationDivision of Accountability, Research, and Measurement; Office of AssessmentJuly 201380%100%14

Question 6, MACC.8.EE.3.8c, MACC.912.A-REI.3.6, and MACC.912.A-REI.4.10Description: Interpret characteristics of graph in a contextDifficulty: HardComplexity: HighSolution:There are three components in this response.Note: Sample responses for partial credit.NAEP Grade 12 Mathematics Answers to Sample QuestionsFlorida Department of EducationDivision of Accountability, Research, and Measurement; Office of AssessmentJuly 201315