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.Download Link: