Grade12 Algebra (2)

7/30/2019 Grade12 Algebra (2)

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Grade 12 Algebra

Sample Questions and Answers

This booklet contains sample items from the National Assessment of Educational Progress

(NAEP). Additional items can be accessed atwww.nces.ed.gov/nationsreportcard/itmrls.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center forEducation Statistics (NCES), National Assessment of Educational Progress (NAEP)

1NAEP Grade 12 Algebra Practice TestFlorida Department of EducationDivision of Accountability, Research, and Measurement

Office of Assessment
http://www.nces.ed.gov/nationsreportcard/itmrlshttp://www.nces.ed.gov/nationsreportcard/itmrls


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NAEP Grade 12 Algebra

ContentsNAEP Grade 12 Algebra........................................................................................................ 2

Contents............................................................................................................................... 2

Introduction ......................................................................................................................... 3Question 1............................................................................................................................ 4

Question 2............................................................................................................................ 5

Question 2, continued........................................................................................................... 5

Question 3............................................................................................................................ 6

Question 3, continued........................................................................................................... 6

Question 4............................................................................................................................ 7

Question 5............................................................................................................................ 9

Question 6.......................................................................................................................... 11




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Introduction

This practice Algebra test includes a sample of publicly released items from NAEP.

Included with each item are the correct answer (indicated by an asterisk) and thedistracters; the percentage of Floridas responses to each of the possible answers;

and the Description, Difficulty, and Complexity of each item.

Additional publicly released items and item data may be accessed through the

NAEP Questions Tool (NQT) at

http://nces.ed.gov/nationsreportcard/itmrlsx/default.aspx . The NQT is an

interactive tool that provides access to over 2000 released questions from NAEP

assessments in all NAEP subject areas. It is also used to access NAEP assessment

items, their correct answers and distracters, and their scoring results by subject,grade, item type, difficulty, content classification, frameworks, year, and key

words.

For more information about NAEP results, go to the NAEP Data Explorer (NDE) at

http://nces.ed.gov/nationsreportcard/naepdata/ . The NDE is an interactive tool

that provides access to a wide variety of data about what students know and can

do, as well as demographic and contextual factors that may affect their

performance. The NDE produces charts, customized tables, and graphics based on

NAEP results by year and jurisdiction; significance between jurisdictions, within

variables, and across years; and gap analyses between jurisdictions or acrossyears and between groups, between years, and between groups and years.

Additional information about the knowledge and skills the mathematics

assessment is designed to measure can be found in the 2011 Mathematics

Framework, http://www.nagb.org/publications/frameworks/math-2011-

framework.pdf. The current NAEP Mathematics Framework guided the

development of all Mathematics assessments since 2005. The previous NAEP

Mathematics Framework guided the development of the mathematics assessments

between 1990 and 2003.


http://nces.ed.gov/nationsreportcard/itmrlsx/default.aspxhttp://nces.ed.gov/nationsreportcard/naepdata/http://www.nagb.org/publications/frameworks/math-2011-framework.pdfhttp://www.nagb.org/publications/frameworks/math-2011-framework.pdfhttp://nces.ed.gov/nationsreportcard/itmrlsx/default.aspxhttp://nces.ed.gov/nationsreportcard/naepdata/http://www.nagb.org/publications/frameworks/math-2011-framework.pdfhttp://www.nagb.org/publications/frameworks/math-2011-framework.pdf


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NAEP GRADE 12 ALGEBRA

SAMPLE QUESTIONS and ANSWERS

Question 1Which of the following expressions is NOT equivalent to (a + b)(x + y) ?

a. (a + b)x + (a + b)yb. a(x + y) + b(x + y)

c. (b + a)(y + x)

d. ax + by

e. ax + bx + ay + by

Answers

Percent chosen by Floridasparticipating students

*D 57%

A 14%

B 10%

C 5%

Description: Determine a nonequivalent expression

Content Area: AlgebraDifficulty: Easy

Complexity: Low




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Question 2

The first four terms in a sequence are shown below.

40, 8, 24, 16

Each term after the first two items is found by taking one-half of the sum of the

two preceding terms. Which term is the first odd number in this sequence?

a. The 5th term

b. The 6th term

c. The 7th term

d. The 8th term

e. The 9th term

Question 2, continued

Answers


*C 61%

A 7%

B 14%

D 13%

E 5%

Description: Solve problem involving numerical sequence

Difficulty: Medium

Complexity: Low




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Question 3

Which of the following expressions is equal to ?

a.

b.

c.

d.

Answers


*D 21%

A 34%

B 10%

C 29%

E 5%


Description: Subtract rational expressions

Difficulty: Hard

Complexity: Low




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Question 4

What is the solution to the system of equations ?

Answer: x = ______________________ y = _____________________

Solution:

Answer: ,

Solution (not required in response):




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Score & Description

CorrectBoth values correct

PartialOne correct value only

IncorrectIncorrect response

Description: Solve a system of linear equations

Difficulty: Medium

Complexity: Low




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Question 5

The population P of a certain town is given by the equation P = 50,000(1 + r)t,

where ris the annual rate of population increase and tis the number of years since1990.

a. What was the population in 1990?

Answer: ____________________

b. In 2001 the population was 100,000. What was the annual rate of population

increase?

Answer: ____________________

Solution:

(a) Answer: 50,000


In 1990,

(b) Answer: 6.5% (or 0.065) (Accept responses from 6% to 7%, inclusive)


In 2001,

Score & DescriptionCorrectBoth parts correct

Partial 1




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Part (a) correct only

Partial 2Part (b) correct only



Description: Find annual rate of population growth

Difficulty: Hard

Complexity: Moderate




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Question 6

The graph above shows distance versus time for a race between runnersA and B.

The race is already in progress, and the graph shows only the portion of the race

that occurred after 11 A.M.

The table on the next page lists several characteristics of the graph. Interpret

these characteristics in terms of what happened during this portion of the race.

Include times and distances to support your interpretation. (A sample

interpretation of they-intercepts is given in the table.)




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Solution:

There are three components in this response.

Note: Sample responses for partial credit.




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Score & Description

Part A:

CorrectAcceptable response

PartialAcceptable interpretation without numerical values for slopes

OR

Numerical values without acceptable interpretation for slopes


Part B:

CorrectAcceptable response

PartialAcceptable interpretation without numerical values for point of intersection

OR

Numerical values without acceptable interpretation for point of intersection


Part C:

Correct




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Acceptable response

PartialAcceptable interpretation without numerical values for x-intercepts

OR

Numerical values without acceptable interpretation for x-intercepts





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Composite Score:

Student response received one of five possible composite scores (Extended,Satisfactory, Partial, Minimal, or Incorrect) based on the student's combinedperformance on Parts A, B, and C of the item. For example, a student response ofCorrect for Part A, Correct for Part B, and Incorrect for Part C received a compositescore of Satisfactory.

Composite Score Part A Part B Part C

Extended Correct Correct Correct

Satisfactory

Correct Correct Partial

Correct Correct Incorrect

Correct Partial Correct

Correct Incorrect Correct

Partial Correct Correct

Incorrect Correct Correct

Partial

Correct Partial Partial

Correct Partial Incorrect

Correct Incorrect Partial

Partial Correct Partial

Partial Correct Incorrect

Partial Partial Correct

Partial Partial PartialPartial Incorrect Correct

Incorrect Correct Partial

Incorrect Partial Correct

Minimal

Correct Incorrect Incorrect

Partial Partial Incorrect

Partial Incorrect Partial

Incorrect Correct Incorrect

Incorrect Partial Partial

Incorrect Incorrect Correct

Incorrect

Partial Incorrect Incorrect

Incorrect Partial Incorrect

Incorrect Incorrect Partial

Incorrect Incorrect Incorrect




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Description: Interpret characteristics of graph in a context

Content Classification: Algebra

Difficulty: Hard

Complexity: High


Documents

Grade12 Algebra (2)