I ntroducing the R E L E S E D T E S T I T E M S Virginia Standards Learning The complete set items that appeared on the Spring Standards Learning test taken b most public school students in Virginia is presented in the following pages. The intent this release these test questions is to provide parents and teachers additional information to accompan the Student Performance Report and/or the Parent Report. The information accompaning each test question is broken into several components: Reporting Categor: Matches the score report and allows for identification strengths and weaknesses indicated b student scores. Standard Learning: Presents the SOL used in developing the assessment question. uilds On: Indicates what the student has studied in previous course work. Instruction: Provides information for teachers to use as the SOL is incorporated into instruction. The answer to each question can be found in the back the booklet. Commonwealth Virginia Department Education
lgebra I Reporting Categor: Epressions and Operations R E L E S E D T E S T I T E M S. Standard Learning:. The student will represent verbal quantitative situations algebraicall and evaluate these epressions for given replacement values the variables. Students will choose an appropriate computational technique, such as mental mathematics, calculator, or paper and pencil. uilds On: Work with variables and representation verbal epressions begins with the mathematics SOL in fifth grade and continues through the sith, seventh, and eighth grade SOL. The stud Order Operations occurs in the seventh and eighth grade SOL. What is the value a b if a and b b? 6 6 Which epression correctl represents the area the rectangle above? 8 6( ) C ( )( 6) D C D What is the value a b ab if a and b? F 6 G H J 6 Instruction: Provide students opportunities to evaluate epressions for a given replacement set. Verbal quantitative situations should also include pictorial analsis. Commonwealth Virginia Department Education
lgebra I. Standard Learning:. The student will appl the laws eponents to perform operations on epressions with integral eponents, using scientific notation when appropriate. uilds On: Work with eponents begins in the mathematics SOL in fifth grade and continues to be studied through the sith, seventh, and eighth grade SOL. Scientific notation and computation with integers is found in the seventh and eighth grade SOL. R E L E S E D T E S T I T E M S. Standard Learning:. The student will add, subtract, and multipl polnomials and divide polnomials with monomial divisors, using concrete objects, pictorial representations, and algebraic manipulations. uilds On: Work with the Order Operations and computation with integers occurs in the mathematics SOL in grades 7 and 8. If a /, (a )(a ) F 6 The area a rectangle is given b 6 and the width the rectangle is w. What is the length, l, the rectangle if l w? G H F l G l 6 H l J l J SESSION: PGE: 7 /6/ 9:8 LOGIN IS-pam PTH: @sun/disk/cl SESSION: PGE: /6/ 9:8 LOGIN IS-pam PTH: @sun/disk/cl The sun is about. 8 kilometers from Earth. If light travels about kilometers per second, about how man seconds does it take light from the sun to reach Earth? 7 Which epression is equivalent to 6? C C D, D SESSION: PGE: 8 /6/ 9:8 LOGIN IS-pam PTH: @sun/disk/cl 8 Which epression is equivalent to (a b)(a b)? Instruction: Provide students an opportunit to perform operations on epressions using the laws eponents. Problems with scientific notation are seen as an application these laws. F a b G 6a b H a ab ab J 6a ab b Instruction: Provide students an opportunit to eperience the various representations polnomials and work with polnomials presented in contetual situations as well. Commonwealth Virginia Department Education
lgebra I R E L E S E D T E S T I T E M S. Standard Learning:. The student will factor completel first- and second-degree binomials and trinomials in one or two variables. The graphing calculator will be used as both a primar tool for factoring and for confirming an algebraic factorization. uilds On: Work with developing number sense and the understanding mathematical facts necessar to be successful with factoring occurs throughout the K-8 mathematics SOL. 9 Which is the complete factorization the trinomial? ( )( ) ( )( ) C ( 6)( ) D ( )( ) Which is the complete factorization the trinomial 8? F ( )( ) G ( )( ) H ( )( ) J ( )( ) Instruction: Provide students an opportunit to factor second degree polnomials with integral coefficients and a positive leading coefficient less than four.. Standard Learning:. The student will estimate square roots to the nearest tenth and use a calculator to compute decimal approimations radicals. uilds On: Work with square root begins with the mathematics SOL in grade 6 and increases in compleit through grade 8. In kilometers, the approimate distance to the earth s horizon from a point h meters above the surface can be determined b evaluating the epression h. bout how far is the apparent horizon to a person looking out to sea from the top a cliff meters above sea level? km 6 km C km D km Which is closest to the value 7? F.8 G. H.7 J.6 Instruction: Provide students with opportunities to use the calculator to find square roots and make reasonable interpretations the displaed values for a given situation. Word problems with square roots and the use square roots in formulas should be included in instruction. Commonwealth Virginia Department Education 6
lgebra I Reporting Categor: Relations and Functions R E L E S E D T E S T I T E M S. Standard Learning:. The student will analze a given set data for the eistence a pattern, represent the pattern algebraicall and graphicall, if possible, and determine if the relation is a function. uilds On: Work with patterns begins with the mathematics SOL in Kindergarten and progresses in difficult through grade 8. Emphasis on a graphic interpretation patterns occurs in the sith, seventh, and eighth grade SOL. Which the following tables represents a function? Which table most likel matches this graph? F C G D 6 8 H J Instruction: Provide students with opportunities to analze a table ordered pairs and sets ordered pairs to identif a pattern; to determine if a relation is a function from a table ordered pairs; and to determine the table ordered pairs for a given graph. Commonwealth Virginia Department Education 7
lgebra I R E L E S E D T E S T I T E M S. Standard Learning:. The student will analze a given set data for the eistence a pattern, represent the pattern algebraicall and graphicall, if possible, and determine if the relation is a function. uilds On: Work with patterns begins with the mathematics SOL in Kindergarten and progresses in difficult through grade 8. Emphasis on a graphic interpretation patterns occurs in the sith, seventh, and eighth grade SOL. (, ), (, ), (, ), (6, ),... These ordered pairs follow a pattern. If (, ) is in this pattern, what is the value? C D 6 7 9 Using the same relationship between and as the table, what is the value when is 8? F G H J Instruction: Provide students with opportunities to analze a table ordered pairs and sets ordered pairs to identif a pattern; to determine if a relation is a function from a table ordered pairs; and to determine the table ordered pairs for a given graph. Commonwealth Virginia Department Education 8
lgebra I R E L E S E D T E S T I T E M S. Standard Learning:. The student will determine the domain and range a relation given a graph or a set ordered pairs and will identif the relations that are functions. uilds On: Work with the terms domain and range begins with the seventh grade mathematics SOL and continues in the eighth grade SOL when work with relations begins. 7 What is the domain the set ordered pairs {(, ), (, ), (, ), (, )}? {,,, } {,,, } C {,,, } D {,,, } 9 Which the following is not a graph a function? 8 C D What is the domain the function shown above? F ll integers G ll real numbers H ll natural numbers J ll whole numbers Instruction: Provide students an opportunit to determine the domain and range a function for a given set ordered pairs or from a graph, and to determine from a graph if a relation is a function. Commonwealth Virginia Department Education 9
lgebra I. Standard Learning:.6 The student will, given a rule, find the values a function for elements in its domain and locate the zeros the function both algebraicall and with a graphing calculator. The value f() will be related to the ordinate on the graph. uilds On: Work with the terms domain and range begins with the seventh grade mathematics SOL and continues in the eighth grade SOL when work with relations begins. R E L E S E D T E S T I T E M S. Standard Learning:.9 The student will analze a relation to determine whether a direct or inverse variation eists and represent it algebraicall and graphicall, if possible. uilds On: Work with relations begins with the mathematics SOL in grade 8. a varies directl as b and a when b. What is the constant variation? 8 What is the range the function f() 8 when the domain is {,, }? C D 8 F {7, } G {7,, } H {,, } J 8, 8, 7 8 SESSION: PGE: /6/ 9:9 LOGIN IS-pam PTH: @sun/disk/c a varies directl as b and the constant variation is. Which equation represents the relationship? SESSION: PGE: /6/ 9:9 LOGIN IS-pam PTH: @sun/disk/c F a b Input f() = Output f() G a b H a b Using the function machine in the diagram, what is the output when is input? J a b 7 8. C 9 D 9 SESSION: PGE: /6/ 9:9 LOGIN IS-pam PTH: @sun/disk/c If f() 6, what is f()? F G 8 H J 7 Instruction: Provide students with an opportunit to write an equation for a direct variation based on a set data and to determine the constant variation based on a set data. Instruction: Provide students with an opportunit to calculate the functional values (range) for a given function, in a variet contets, when provided values for the domain. Commonwealth Virginia Department Education
lgebra I Reporting Categor: Equations and Inequalities. Standard Learning:. The student will solve linear equations and inequalities in one variable, solve literal equations (formulas) for a given variable, and appl these skills to solve practical problems. Graphing calculators will be used to confirm algebraic solutions. uilds On: Work with equations begins in the mathematics SOL for grade when students complete numerical sentences involving basic facts for addition and subtraction and becomes more formal in the sith, seventh, and eighth grade SOL. R E L E S E D T E S T I T E M S. Standard Learning:. The student will justif steps used in simplifing epressions and solving equations and inequalities. Justifications will include the use concrete objects, pictorial representations, and the properties real numbers. uilds On: Work with the properties real numbers begins with the mathematics SOL in grade 7. 8 The statement If (a ), then 6a 8 is justified b the F ssociative propert multiplication G Multiplication propert equals H ddition propert equals J Distributive propert Using the distance formula, d rt, what is the value t when d, and r? 6.,97 C,7 D,96, SESSION: PGE: 9 /6/ 9:9 LOGIN IS-pam PTH: @sun/disk/c 9 If, which the following statements cannot be true? SESSION: PGE: 6 /6/ 9:9 LOGIN IS-pam PTH: @sun/disk/c 6 What is the solution to 6? F G H J C C C C C C C D SESSION: PGE: 7 /6/ 9:9 LOGIN IS-pam PTH: @sun/disk/c 7 rectangle has a perimeter 6 inches and length inches. What is the width the rectangle? 76 in. 6 in. C in. D 8 in. Instruction: Provide students an opportunit to solve multi-step inequalities in one variable; to solve a literal equation (formula) for a specified variable; and to appl skills for solving linear equations to practical situations. Instruction: Provide students an opportunit to identif a propert real numbers used in simplifing epressions and solving equations and inequalities. Questions that require students to identif what CNNOT be done to simplif an epression or solve an equation or inequalit based on the properties real numbers should also be included in instruction. Commonwealth Virginia Department Education
lgebra I R E L E S E D T E S T I T E M S. Standard Learning:.6 The student will select, justif, and appl an appropriate technique to graph a linear function in two variables. Techniques will include slope-intercept, - and -intercepts, graphing b transformation, and the use the graphing calculator. uilds On: Work with graphing coordinates begins in the mathematics SOL in fifth grade and progresses through grades 6 and 7 to graphing lines in grade 8. Which equation is represented b this line? Which line on the graph below has -intercept and -intercept? F G H J C D Instruction: Provide students with an opportunit to determine the graph a line when given the - and - intercept. Commonwealth Virginia Department Education
lgebra I R E L E S E D T E S T I T E M S. Standard Learning:.7 The student will determine the slope a line when given an equation the line, the graph the line, or two points on the line. Slope will be described as rate change and will be positive, negative, zero, or undefined. The graphing calculator will be used to investigate the effect changes in the slope on the graph the line. uilds On: Work with graphing coordinates begins in the mathematics SOL in fifth grade and progresses through grades 6 and 7 to graphing lines in grade 8. What is the slope the line represented b? C F G H J D Which line on the graph has undefined slope? F G H C J D SESSION: PGE: /6/ 9: LOGIN IS-pam PTH: @sun/disk/c Which describes the slope the line that passes through (7, ) and (8, )? Positive Negative C Zero D Undefined Instruction: Provide students an opportunit to determine the slope a line and to determine if the slope is positive, negative, zero, or undefined when given a graph, two points, or an equation. Commonwealth Virginia Department Education
lgebra I R E L E S E D T E S T I T E M S. Standard Learning:.8 The student will write an equation a line when given the graph the line, two points on the line, or the slope and a point on the line. uilds On: Work with graphing coordinates begins in the mathematics SOL in fifth grade and progresses through grades 6 and 7 to graphing lines in grade 8. Which is an equation a line that has a slope and contains the point (, )? 7 Which is an equation for the line that passes through (, ) and (, )? C D C D 6 Which is most likel an equation for the line shown? F G H J Instruction: Provide students with an opportunit to write an equation a line given the graph a line, two points on a line, or the slope and one point on a line. Commonwealth Virginia Department Education
lgebra I. Standard Learning:.9 The student will solve sstems two linear equations in two variables, both algebraicall and graphicall, and appl these techniques to solve practical problems. Graphing calculators will be used as both a primar tool solution and to confirm an algebraic solution. uilds On: Work with equations begins in the mathematics SOL for grade when students complete numerical sentences involving basic facts for addition and subtraction, and it becomes more formal in the sith, seventh, and eighth grade SOL. 8 One competitor in a -mile biccle race took a total hours to complete the course. His average speed in the morning was miles per hour. His average speed in the afternoon was miles per hour. How man hours did he ride in the morning, and how man hours did he ride in the afternoon? F Morning -. hours, afternoon -. hours G Morning - hours, afternoon - hours H Morning -. hours, afternoon -. hours J Morning - hours, afternoon - hour R E L E S E D T E S T I T E M S. Standard Learning:. The student will solve quadratic equations in one variable both algebraicall and graphicall. Graphing calculators will be used both as a primar tool in solving problems and to verif algebraic solutions. uilds On: Work with equations begins in the mathematics SOL for grade when students complete numerical sentences involving basic facts for addition and subtraction, and it becomes more formal in the sith, seventh, and eighth grade SOL. Work with developing number sense and understanding mathematical facts necessar to be successful with factoring occurs throughout the K-8 mathematics SOL. The number seconds to complete a chemical reaction was determined to be given b the equation s T T where s is the number seconds and T is the temperature in degrees Celsius at which the reaction occurred. If a chemical reaction was complete in seconds, what was the temperature at which the reaction occurred? SESSION: PGE: 9 /6/ 9: LOGIN IS-pam PTH: @sun/disk/c 6 9 C 7 C C C D C What is the solution to this sstem equations?,, C, D, SESSION: PGE: /6/ 9: LOGIN IS-pam PTH: @sun/disk/c 6 Which is the solution set for the equation above? SESSION: PGE: /6/ 9: LOGIN IS-pam PTH: @sun/disk/c The length a rectangle is centimeters longer than its width. The perimeter is 6 centimeters. What are the length and width the rectangle? F 7cm,cm G 6cm,cm H cm,cm J cm,cm F {, } G {, } H {6, } J {, 6} Instruction: Provide students an opportunit to write and solve a sstem linear equations in two variables, either algebraicall or graphicall, and use these techniques to solve practical problems. Instruction: Provide students with an opportunit to solve quadratic equations both algebraicall and graphicall and solve problems using the appropriate technique. Commonwealth Virginia Department Education
lgebra I Reporting Categor: Statistics R E L E S E D T E S T I T E M S. Standard Learning:. The student will use matrices to organize and manipulate data, including matri addition, subtraction, and scalar multiplication. Data will arise from business, industrial, and consumer situations. uilds On: Work with matrices begins with the mathematics SOL in eighth grade. The matrices show the membership b grades in the Science Club (S) and the rt Club () at eacon Hill, Rockwood, and Whitne middle schools. [] 6 eacon Hill S Gr 6 Gr 7 9 Gr 8 7 Rockwood S Gr 6 Gr 7 8 Gr 8 8 Whitne S Gr 6 Gr 7 8 6 9 Gr 8 Which shows the total number students in each club at each grade level at the three schools?.[]? F. [ 9 ] 8 9 C 7 G.. H 6. D 9 9 8 J. Instruction: Provide students with an opportunit to add matrices and use scalar multiplication with a given matri. Commonwealth Virginia Department Education 6
lgebra I R E L E S E D T E S T I T E M S. Standard Learning:.7 The student will, given a set data points, write an equation for a line best fit, using the median fit method, and use the equation to make predictions. uilds On: Work with analzing data and making inferences and work with median begins in the mathematics SOL in sith, seventh, and eighth grades. Using the median fit method, which scatterplot most likel has a line best fit represented b? 6 9 8 7 6 9 8 7 6 6 7 8 9 6 7 8 9 9 8 7 6 9 8 7 6 6 6 7 8 9 Which equation best represents the data shown on the scatterplot? F G 7 8 9 H C 9 8 7 6 9 8 7 6 6 7 8 9 6 7 8 9 J 9 8 D 7 6 9 8 7 6 6 7 8 9 6 7 8 9 Instruction: Provide students an opportunit to write an equation for the median fit line from a scatterplot; and to identif a scatterplot when given the equation for the median fit line. Commonwealth Virginia Department Education 7
lgebra I R E L E S E D T E S T I T E M S. Standard Learning:.8 The student will compare multiple one-variable data sets, using statistical techniques that include measures central tendenc, range, stem-and-leaf plots, and bo-and-whisker graphs. uilds On: Work with stem-and-leaf plots begins in the fifth grade mathematics SOL, and with bo-and-whisker graphs in sith grade. Work with the measures central tendenc begins in fifth grade, progressing in difficult through the sith, seventh, and eighth grades. 7 Mari and Marc are bowling a -game match to determine the top bowler for their league. Marc averaged 6 for his three games. Mari bowled 7 and for her first two games. What is the least she must bowl for her third game if she is to win the championship? 6 C 7 D 8 9 In which data set is the median value equal to the mean value? {,,7,9,} {7, 9,,, 6} C {6,, 8,, 7} D {,, 6,, 9} SESSION: PGE: 8 /6/ 9: LOGIN IS-pam PTH: @sun/disk/c SESSION: PGE: /6/ 9: LOGIN IS-pam PTH: @sun/disk/c 8 Stem Leaf 6 8 7 779 8 67 9 6 This is a stem-and-leaf plot a group test scores. What is the median score? F 7 G 76 H 77 J 77. This is a bo-and-whisker plot a set scores. 6 7 8 9 In which quartile would a score 76 fit in this set? F st G nd H rd J th Instruction: Provide students an opportunit to compare measures central tendenc using numerical data; and to work with data displaed in a stem-and-leaf plot and/or a bo-and-whisker graph. Commonwealth Virginia Department Education 8
Correct nswers R E L E S E D T E S T I T E M S LGER I TEST.. J.. G. C 6. J 7. C 8. J 9.. J.. G. C. H. 6. H 7. 8. G 9. D. G. C. F. C. F. 6. G 7. D 8. J 9. D. H.. G.. G. 6. G 7. 8. H 9. D. H.. G.. G. C 6. G 7. C 8. H 9. D. J b the Commonwealth Virginia Department Education, James Monroe uilding, N. th Street, Richmond, Virginia, 9. ll rights reserved. Ecept as permitted b law, this material ma not be reproduced or used in an form or b an means, electronic or mechanical, including photocoping or recording, or b an information storage or retrieval sstem, without written permission from the copright owner. Please contact the Commonwealth Virginia Department Education at (8) -, Division ssessment and Reporting, to request written permission. Commonwealth Virginia Department Education 9