Grade 7 Math Released Test Questions – Standardized Testing and

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CA L I F O R N I A S TA N DA R D S T E S T                                             G R A D E


 Released Test Questions                                                                                                           Math           7
                   Introduction - Grade 7 Mathematics 

The following released test questions are taken from the Grade 7 Mathematics Standards Test. This test is one
of the California Standards Tests administered as part of the Standardized Testing and Reporting (STAR)
Program under policies set by the State Board of Education.

All questions on the California Standards Tests are evaluated by committees of content experts, including
teachers and administrators, to ensure their appropriateness for measuring the California academic content
standards in Grade 7 Mathematics. In addition to content, all items are reviewed and approved to ensure their
adherence to the principles of fairness and to ensure no bias exists with respect to characteristics such as
gender, ethnicity, and language.

This document contains released test questions from the California Standards Test forms in 2003, 2004, 2005,
2006, and 2007. First on the pages that follow are lists of the standards assessed on the Grade 7 Mathematics Test.
Next are released test questions. Following the questions is a table that gives the correct answer for each question,
the content standard that each question is measuring, and the year each question last appeared on the test.

The following table lists each strand/reporting cluster, the number of items that appear on the exam, and the
number of released test questions that appear in this document.

                                                                                         NUMBER OF                        NUMBER OF
     STRAND/REPORTING                                                                   QUESTIONS ON                    RELEASED TEST
         CLUSTER                                                                           EXAM                           QUESTIONS
     Number Sense  Rational Numbers                                                                 14                               17
     Number Sense  Exponents, Powers, and Roots                                                     8                                11
     Algebra and Functions  Quantitative Relationships
     and Evaluating Expressions                                                                      10                               14
     Algebra and Functions  Multi-step Problems,
     Graphing, and Functions                                                                         15                               17
     Measurement and Geometry                                                                        13                               16
     Statistics, Data Analysis, and Probability                                                      5                                 5
     TOTAL                                                                                           65                               80


In selecting test questions for release, three criteria are used: (1) the questions adequately cover a selection of
the academic content standards assessed on the Grade 7 Mathematics Test; (2) the questions demonstrate a
range of difficulty; and (3) the questions present a variety of ways standards can be assessed. These released
test questions do not reflect all of the ways the standards may be assessed. Released test questions will not
appear on future tests.

For more information about the California Standards Tests, visit the California Department of Education's
Web site at http://www.cde.ca.gov/ta/tg/sr/resources.asp.
                                                                      -- 1 --
              This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projected
                         based on performance on released test questions. Copyright  2008 California Department of Education.
G R A D E                                               CA L I F O R N I A S TA N DA R D S T E S T



   7        Math                                                                                                 Released Test Questions


THE NUMBER SENSE STRAND
In Grade 7, there are two reporting clusters within the Number Sense strand: 1) Rational Numbers and
2) Exponents, Powers, and Roots. This booklet contains released test questions for each of these clusters.

The following seven California content standards are included in the Rational Numbers reporting cluster of the
Number Sense strand and are represented in this booklet by 17 test questions. These questions represent only
some ways in which these standards may be assessed on the Grade 7 California Mathematics Standards Test.


              CALIFORNIA CONTENT STANDARDS IN THIS REPORTING CLUSTER

            Number Sense
            Standard Set 1.0 Students know the properties of, and compute with, rational numbers
                             expressed in a variety of forms:
            7NS1.1                   Read, write, and compare rational numbers in scientific notation (positive and
                                     negative powers of 10) with approximate numbers using scientific notation.
            7NS1.2*                  Add, subtract, multiply, and divide rational numbers (integers, fractions, and
                                     terminating decimals) and take positive rational numbers to whole-number
                                     powers.
            7NS1.3                   Convert fractions to decimals and percents and use these representations in
                                     estimations, computations, and applications.
            7NS1.4*                  Differentiate between rational and irrational numbers.
            7NS1.5*                  Know that every rational number is either a terminating or repeating decimal and
                                     be able to convert terminating decimals into reduced fractions.
            7NS1.6                   Calculate the percentage of increases and decreases of a quantity.
            7NS1.7*                  Solve problems that involve discounts, markups, commissions, and profit and
                                     compute simple and compound interest.


            * Denotes key standards (Mathematics Framework for California Public Schools)




                                                                      -- 2 --

              This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projected
                         based on performance on released test questions. Copyright  2008 California Department of Education.
                                                       CA L I F O R N I A S TA N DA R D S T E S T                                             G R A D E


 Released Test Questions                                                                                                          Math           7
The following five California content standards are included in the Exponents, Powers, and Roots reporting
cluster of the Number Sense strand and are represented in this booklet by 11 test questions. These questions
represent only some ways in which these standards may be assessed on the Grade 7 California Mathematics
Standards Test.


              CALIFORNIA CONTENT STANDARDS IN THIS REPORTING CLUSTER

            Number Sense
            Standard Set 2.0 Students use exponents, powers, and roots and use exponents in working
                             with fractions:
            7NS2.1                  Understand negative whole-number exponents. Multiply and divide expressions
                                    involving exponents with a common base.
            7NS2.2*                 Add and subtract fractions by using factoring to find common denominators.
            7NS2.3*                 Multiply, divide, and simplify rational numbers by using exponent rules.
            7NS2.4                  Use the inverse relationship between raising to a power and extracting the root
                                    of a perfect square integer; for an integer that is not square, determine without a
                                    calculator the two integers between which its square root lies and explain why.
            7NS2.5*                 Understand the meaning of the absolute value of a number; interpret the
                                    absolute value as the distance of the number from zero on a number line; and
                                    determine the absolute value of real numbers.


            * Denotes key standards (Mathematics Framework for California Public Schools)




                                                                     -- 3 --

             This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projected
                        based on performance on released test questions. Copyright  2008 California Department of Education.
G R A D E                                               CA L I F O R N I A S TA N DA R D S T E S T



   7         Math                                                                                                Released Test Questions


THE ALGEBRA AND FUNCTIONS STRAND
In Grade 7, there are two reporting clusters within the Algebra and Functions strand: 1) Quantitative
Relationships and Evaluating Expressions and 2) Multi-step Problems, Graphing, and Functions. This booklet
contains released test questions for each of these clusters.

The following seven California content standards are included in the Quantitative Relationships and
Evaluating Expressions reporting cluster of the Algebra and Functions strand and are represented in this
booklet by 14 test questions. These questions represent only some ways in which these standards may be
assessed on the Grade 7 California Mathematics Standards Test.


              CALIFORNIA CONTENT STANDARDS IN THIS REPORTING CLUSTER

             Algebra and Functions
             Standard Set 1.0 Students express quantitative relationships by using algebraic
                              terminology, expressions, equations, inequalities, and graphs:
             7AF1.1                  Use variables and appropriate operations to write an expression, an equation,
                                     an inequality, or a system of equations or inequalities that represents a verbal
                                     description (e.g., three less than a number, half as large as area A).
             7AF1.2                  Use the correct order of operations to evaluate algebraic expressions such as
                                     3(2x + 5)2.
             7AF1.3*                 Simplify numerical expressions by applying properties of rational numbers (e.g.,
                                     identity, inverse, distributive, associative, commutative) and justify the process
                                     used.
             7AF1.4                  Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality,
                                     expression, constant) correctly.
             7AF1.5                  Represent quantitative relationships graphically and interpret the meaning of a
                                     specific part of a graph in the situation represented by the graph.
             Standard Set 2.0 Students interpret and evaluate expressions involving integer powers and
                              simple roots:
             7AF2.1                  Interpret positive whole-number powers as repeated multiplication and negative
                                     whole-number powers as repeated division or multiplication by the multiplicative
                                     inverse. Simplify and evaluate expressions that include exponents.
             7AF2.2                  Multiply and divide monomials; extend the process of taking powers and
                                     extracting roots to monomials when the latter results in a monomial with an
                                     integer exponent.


             * Denotes key standards (Mathematics Framework for California Public Schools)




                                                                      -- 4 --

              This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projected
                         based on performance on released test questions. Copyright  2008 California Department of Education.
                                                       CA L I F O R N I A S TA N DA R D S T E S T                                             G R A D E


 Released Test Questions                                                                                                          Math           7
The following six California content standards are included in the Multi-step Problems, Graphing, and
Functions reporting cluster of the Algebra and Functions strand and are represented in this booklet by 17 test
questions. These questions represent only some ways in which these standards may be assessed on the Grade 7
California Mathematics Standards Test.


              CALIFORNIA CONTENT STANDARDS IN THIS REPORTING CLUSTER

            Algebra and Functions
            Standard Set 3.0 Students graph and interpret linear and some nonlinear functions:
            7AF3.1                  Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems.
            7AF3.2                  Plot the values from the volumes of three-dimensional shapes for various values
                                    of the edge lengths (e.g., cubes with varying edge lengths or a triangle prism
                                    with a fixed height and an equilateral triangle base of varying lengths).
            7AF3.3*                 Graph linear functions, noting that the vertical change (change in y-value) per
                                    unit of horizontal change (change in x-value) is always the same and know that
                                    the ratio ("rise over run") is called the slope of a graph.
            7AF3.4*                 Plot the values of quantities whose ratios are always the same (e.g., cost to the
                                    number of an item, feet to inches, circumference to diameter of a circle). Fit a
                                    line to the plot and understand that the slope of the line equals the ratio of the
                                    quantities.
            Standard Set 4.0* Students solve simple linear equations and inequalities over the rational
                              numbers:
            7AF4.1*                 Solve two-step linear equations and inequalities in one variable over the rational
                                    numbers, interpret the solution or solutions in the context from which they arose,
                                    and verify the reasonableness of the results.
            7AF4.2*                 Solve multistep problems involving rate, average speed, distance, and time or a
                                    direct variation.


            * Denotes key standards (Mathematics Framework for California Public Schools)




                                                                     -- 5 --

             This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projected
                        based on performance on released test questions. Copyright  2008 California Department of Education.
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