Grade 12 Mathematics Answers

Grade 12 Mathematics Answer Key

This 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 Common Core State Standards. Additional NAEP items can be accessed at nces.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 at .

NAEP GRADE 12 MATHEMATICS ANSWER KEY CONTENTS

NAEP GRADE 12 NUMBER PROPERTIES AND OPERATIONS................................................. 3 Question 1 - Multiply a 3-digit number by a decimal number ........................................... 4 Question 2 - Estimate amount of time for problem in context ......................................... 4 Question 3 - Find the cost of mailing a letter, based on its weight ................................... 5 Question 4 - Calculate an expected value, given a percentage ......................................... 5 Question 5 - Given the scale, determine the length of a side............................................ 6 Question 6 - Identify effect of changing certain digits on a number's value ..................... 6 Question 7 - Estimate property value, given tax rate and amount.................................... 7 Question 8 - Determine the remainder in an algebraic setting ......................................... 7 Question 9 - Determine a weight of a letter given mailing cost ........................................ 8 Question 10 - Solve a problem involving fractions............................................................. 9 Question 11 - Determine proportional enlargement of photograph............................... 10

NAEP GRADE 12 ALGEBRA................................................................................................... 11 Question 1 - Determine a nonequivalent expression ...................................................... 11 Question 2 - Solve problem involving numerical sequence ............................................. 11 Question 3 - Subtract rational expressions ...................................................................... 12 Question 4 - Solve a system of linear equations .............................................................. 12 Question 5 - Find annual rate of population growth ....................................................... 13 Question 6 - Interpret characteristics of graph in a context ............................................ 15

NAEP GRADE 12 MEASUREMENT........................................................................................ 19 Question 1 - Compare units of volume ............................................................................ 19 Question 2 - Solve problem involving area in context ..................................................... 19 Question 3 - Calculate the measure of an angle in a triangle .......................................... 20 Question 4 - Find actual dimensions of room drawn to scale.......................................... 20 Question 5 - Identify a 90-degree angle in a figure.......................................................... 21 Question 6 - Find the length of the sides of a square ...................................................... 21 Question 7 - Solve a problem using trigonometry ........................................................... 22 Question 8 - Find range for area given precision of linear measurements...................... 22 Question 9 - Use trigonometry to find height of object................................................... 23 Question 10 - Solve a multi-step problem with a rectangle and sphere ......................... 23

2 NAEP Grade 12 Mathematics Answers to Sample Questions Florida Department of Education Division of Accountability, Research, and Measurement; Office of Assessment July 2013

NAEP GRADE 12 GEOMETRY ............................................................................................... 25 Question 1 - Find the missing dimension of a room ........................................................ 25 Question 2 - Find the measure of angle between streets................................................ 25 Question 3 - Find length of side in a 30-60-90 triangle .................................................... 26 Question 4 - Analyze properties of quadrilateral inscribed in circle................................ 26 Question 5 - Determine which triangle is not a 30-60-90 right traingle .......................... 27 Question 6 - Identify the 3-D figure resulting from folding paper ................................... 27 Question 7 - Prove that given figure is a parallelogram................................................... 28 Question 8 - Perform multiple transformations of segment in xy-plane......................... 31

NAEP GRADE 12 DATA ANALYSIS ........................................................................................ 33 Question 1 - Solve problem using data in a table ............................................................ 33 Question 2 - Analyze correlations of two data sets in a scatterplot ................................ 33 Question 3 - Identify linear equation that best fits data in a scatterplot ........................ 34 Question 4 - Identify appropriate method for selecting random sample........................ 34 Question 5 - Make a prediction based on data in scatterplot ......................................... 35 Question 6 - Calculate probability of indepenent events ................................................ 36 Question 7 - Determine the type of graph to best represent a situation ........................ 37 Question 8 - Determine conditional probablity from two-way table .............................. 37 Question 9 - Solve a data-related problem and justify the answer ................................. 39 Question 10 - Use survey results to make an inference................................................... 39 Question 11 - Solve a problem involving color patterns .................................................. 40

Mathematics Common Core (MACC) State Standards (CCSS) Domains

EE = Expressions and Equations F = Functions G = Geometry MD = Measurement and Data NBT = Number and Operations in Base Ten NF = Number and Operations Fractions NS = Number Systems OA = Operations and Algebraic Thinking RP = Ratios and Proportional Relationships SP = Statistics and Probability

F-BF = Building Functions A-SSE = Seeing Structure in Expression A-APR = Arithmetic with Polynomials and Rational Expressions A-REI = Reasoning with Equations and Inequalities G-SRT = Similarity, Right Triangles, and Trigonometry G-CO = Congruence S-ID = Interpreting Categorical and Quantitative Data

3 NAEP Grade 12 Mathematics Answers to Sample Questions Florida Department of Education Division of Accountability, Research, and Measurement; Office of Assessment July 2013

NAEP GRADE 12 MATHEMATICS

Alignment to Mathematics Common Core (MACC) State Standards (CCSS) and Answers to NAEP Sample Questions

NAEP GRADE 12 NUMBER PROPERTIES AND OPERATIONS

Question 1, MACC.6.NS.2.3

Description: Multiply a 3-digit number by a decimal number Difficulty: Easy Complexity: Low

Correct answer is B

Answers *B A C D E Omitted

Percent chosen by Florida's participating students 63% 12% 12% 5% 7% 1%

Question 2, MACC.6.RP.1.3c and MACC.7.RP.1.3

Description: Estimate amount of time for problem in context Difficulty: Medium Complexity: Low

Correct answer is D

Answers *D A B C E

Percent chosen by Florida's participating students 52% 14% 12% 15% 7%

4 NAEP Grade 12 Mathematics Answers to Sample Questions Florida Department of Education Division of Accountability, Research, and Measurement; Office of Assessment July 2013

Question 3, MACC.6.EE.2.6

Description: Find the cost of mailing a letter, based on its weight Difficulty: Easy Complexity: Low

The correct answer is C

National Data1

Question 4, MACC.6.RP.1.3c

Description: Calculate an expected value, given a percentage Difficulty: Easy Complexity: Low

Correct answer is C

National Data

1 Grade 12 mathematics state-level results for Florida are only available for 2009. Only national-level results are available for the other assessment years.

5 NAEP Grade 12 Mathematics Answers to Sample Questions Florida Department of Education Division of Accountability, Research, and Measurement; Office of Assessment July 2013

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