Introduction - Grade 5 Mathematics

Transcription

1 LI FOR N I ST N R S TE ST G R E Released Test Questions Math Introduction - Grade Mathematics The following released test questions are taken from the Grade Mathematics Standards Test. This test is one of the alifornia Standards Tests administered as part of the Standardized Testing and Reporting (STR) Program under policies set by the State oard of Education. ll questions on the alifornia Standards Tests are evaluated by committees of content experts, including teachers and administrators, to ensure their appropriateness for measuring the alifornia academic content standards in Grade 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 alifornia Standards Test forms in 00, 00, 00, 006, and 007. First on the pages that follow are lists of the standards assessed on the Grade 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. NUMER OF NUMER OF STRN/REPORTING QUESTIONS ON RELESE TEST LUSTER EXM QUESTIONS Number Sense Estimation, Percents, and Factoring 6 Number Sense Operations with Fractions and ecimals 7 9 lgebra and Functions 7 Measurement and Geometry 9 Statistics, ata nalysis, and Probability TOTL 6 80 In selecting test questions for release, three criteria are used: () the questions adequately cover a selection of the academic content standards assessed on the Grade Mathematics Test; () the questions demonstrate a range of difficulty; and () 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 alifornia Standards Tests, visit the alifornia epartment of Education s Web site at This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

2 G R E Math LI FOR N I ST N R S TE ST Released Test Questions THE NUMER SENSE STRN In Grade, there are two reporting clusters within the Number Sense strand: ) Estimation, Percents, and Factoring and ) Operations with Fractions and ecimals. This booklet contains released test questions for each of these clusters. The following five alifornia content standards are included in the Estimation, Percents, and Factoring reporting cluster of the Number Sense strand and are represented in this booklet by 6 test questions. These questions represent only some ways in which these standards may be assessed on the Grade alifornia Mathematics Standards Test. LIFORNI ONTENT STNRS IN THIS REPORTING LUSTER Number Sense Standard Set.0 NS. NS.* NS. NS.* NS.* Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents. They understand the relative magnitudes of numbers: Estimate, round, and manipulate very large (e.g., millions) and very small (e.g., thousandths) numbers. Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number. Understand and compute positive integer powers of nonnegative integers; compute examples as repeated multiplication. etermine the prime factors of all numbers through 0 and write the numbers as the product of their prime factors by using exponents to show multiples of a factor (e.g., = = ). Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers. * enotes key standards (Mathematics Framework for alifornia Public Schools) This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

3 LI FOR N I ST N R S TE ST G R E Released Test Questions Math The following five alifornia content standards are included in the Operations with Fractions and ecimals reporting cluster of the Number Sense strand and are represented in this booklet by 9 test questions. These questions represent only some ways in which these standards may be assessed on the Grade alifornia Mathematics Standards Test. LIFORNI ONTENT STNRS IN THIS REPORTING LUSTER Number Sense Standard Set.0 NS.* NS.* NS.* NS. NS. Students perform calculations and solve problems involving addition, subtraction, and simple multiplication and division of fractions and decimals: dd, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results. emonstrate proficiency with division, including division with positive decimals and long division with multidigit divisors. Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of fractions and mixed numbers (like and unlike denominators of 0 or less), and express answers in the simplest form. Understand the concept of multiplication and division of fractions. ompute and perform simple multiplication and division of fractions and apply these procedures to solving problems. * enotes key standards (Mathematics Framework for alifornia Public Schools) This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

4 G R E LI FOR N I ST N R S TE ST Math Released Test Questions THE LGER N FUNTIONS STRN/REPORTING LUSTER The following five alifornia content standards are included in the lgebra and Functions strand/reporting cluster and are represented in this booklet by test questions. These questions represent only some ways in which these standards may be assessed on the Grade alifornia Mathematics Standards Test. LIFORNI ONTENT STNRS IN THIS STRN/LUSTER lgebra and Functions Standard Set.0 F. F.* F. F.* F.* Students use variables in simple expressions, compute the value of the expression for specific values of the variable, and plot and interpret the results: Use information taken from a graph or equation to answer questions about a problem situation. Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution. Know and use the distributive property in equations and expressions with variables. Identify and graph ordered pairs in the four quadrants of the coordinate plane. Solve problems involving linear functions with integer values; write the equation; and graph the resulting ordered pairs of integers on a grid. * enotes key standards (Mathematics Framework for alifornia Public Schools) This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

5 LI FOR N I ST N R S TE ST G R E Released Test Questions Math THE MESUREMENT N GEOMETRY STRN/REPORTING LUSTER The following seven alifornia content standards are included in the Measurement and Geometry strand/ reporting cluster and are represented in this booklet by 9 test questions. These questions represent only some ways in which these standards may be assessed on the Grade alifornia Mathematics Standards Test. LIFORNI ONTENT STNRS IN THIS STRN/LUSTER Measurement and Geometry Standard Set.0 MG.* MG.* MG.* MG. Standard Set.0 MG.* MG.* MG. Students understand and compute the volumes and areas of simple objects: erive and use the formula for the area of a triangle and of a parallelogram by comparing it with the formula for the area of a rectangle (i.e., two of the same triangles make a parallelogram with twice the area; a parallelogram is compared with a rectangle of the same area by cutting and pasting a right triangle on the parallelogram). onstruct a cube and rectangular box from two-dimensional patterns and use these patterns to compute the surface area for these objects. Understand the concept of volume and use the appropriate units in common measuring systems (i.e., cubic centimeter [cm ], cubic meter [m ], cubic inch [in ], cubic yard [yd ]) to compute the volume of rectangular solids. ifferentiate between, and use appropriate units of measures for, two- and threedimensional objects (i.e., find perimeter, area, volume). Students identify, describe, and classify the properties of, and the relationships between, plane and solid geometric figures: Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools (e.g., straightedge, ruler, compass, protractor, drawing software). Know that the sum of the angles of any triangle is 80 and the sum of the angles of any quadrilateral is 60 and use this information to solve problems. Visualize and draw two-dimensional views of three-dimensional objects made from rectangular solids. * enotes key standards (Mathematics Framework for alifornia Public Schools) This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

6 G R E LI FOR N I ST N R S TE ST Math Released Test Questions THE STTISTIS, T NLYSIS, N PROILITY STRN/REPORTING LUSTER The following five alifornia content standards are included in the Statistics, ata nalysis, and Probability strand/reporting cluster and are represented in this booklet by five test questions. These questions represent only some ways in which these standards may be assessed on the Grade alifornia Mathematics Standards Test. LIFORNI ONTENT STNRS IN THIS STRN/LUSTER Statistics, ata nalysis, and Probability Standard Set.0 PS. PS. PS. PS.* PS.* Students display, analyze, compare, and interpret different data sets, including data sets of different sizes: Know the concepts of mean, median, and mode; compute and compare simple examples to show that they may differ. Organize and display single-variable data in appropriate graphs and representations (e.g., histogram, circle graphs) and explain which types of graphs are appropriate for various data sets. Use fractions and percentages to compare data sets of different sizes. Identify ordered pairs of data from a graph and interpret the meaning of the data in terms of the situation depicted by the graph. Know how to write ordered pairs correctly; for example, (x, y). * enotes key standards (Mathematics Framework for alifornia Public Schools) 6 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

7 LI FOR N I ST N R S TE ST G R E Released Test Questions Math What is rounded to the nearest ten? SM0 The total land area for the United States is,7,8 square miles. What is this value rounded to the nearest thousand square miles?,00,000,7,000,8,000,0,000 What is the decimal 0.7 written as a fraction? SM company donated 00 books to a local library. If 70 of them are fiction, what percent of the donated books are fiction? What is 0% of 0? What is written as a percent? 8 6.7% 0% 7.% 0% SM097 SM07 % 0% 60% 6% SM0 7 In a parking lot, out of every 8 cars is blue. What percent of the cars in this lot are blue?.% 7% 9%.% SM00 SM0 7 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

8 G R E Math 8 What decimal is equal to? LI FOR N I ST N R S TE ST Released Test Questions What is the prime factorization of 6? 9 9 = What is the prime factorization of? 9 What is the prime factorization of? SM07 SM009 SM08 SM07 Which of the following shows the number 60 factored into prime numbers? P Q R S - 0 SM076 Which letter on the number line best identifies the location of 6? P Q R S SM06 SM0 8 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

9 LI FOR N I ST N R S TE ST G R E Released Test Questions Math Which point on the number line best represents.? 6 Which number line appears to show the dot placed at? SM = SM088 SM07 8 Javier bought 9 pounds of ground beef. He saved $8.7 by using a store coupon. How much did he save per pound of ground beef? $0.89 $0.9 $.08 $7. SM7 9 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

10 G R E Math 9 Veronica can type 8 words per minute. t this rate, how many words can Veronica type in. minutes? LI FOR N I ST N R S TE ST Released Test Questions Maria has $7.0 to buy lunch. If she buys a turkey sandwich that costs $.7, how much money will she have left? $.7 $. $.7 $0. SM076 SM08 0 Tony had a rope 8. meters long. He cut off.6 meters. How long was the piece of rope that was left?.6 meters.7 meters 6.6 meters = 6.7 meters SM SM00 SM6 Robert wants to buy notebooks that cost $. each. How much do the notebooks cost all together, without tax? $.8 $.0 $.7 $ , 70 7 = SM06 6 t a school, there are 70 desks to place into classrooms. If the same number of desks is placed in each classroom, how many desks will be in each room? SM09 SM08 0 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

11 LI FOR N I ST N R S TE ST G R E Released Test Questions Math 7 What is the answer to this division problem? ) 6 SM000 8 Maurice talked on the telephone to two friends. He talked to Sherry for hour, and to Gabriel for hour. How much time did Maurice spend on the telephone? hour 6 hour 7 hour = 0 It takes Suzanne hour to walk to the 6 playground and hour to walk from the SM7 playground to school. How much time does it take Suzanne to walk to the playground and then to school? 7 hour 9 hour SM00 hour hour hour SM0960 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

12 G R E Math LI FOR N I ST N R S TE ST Released Test Questions = 9 0 = 9 SM00 SM007 Hector can throw a ball 0 feet. Lee can throw the same ball 8 feet. How much farther can Hector throw the ball than Lee? feet feet feet = SM feet SM09 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

13 LI FOR N I ST N R S TE ST G R E Released Test Questions Math i = c + SM079 Which situation could be described by the expression above? Lia jogged c miles yesterday, and miles farther today. Lia jogged c miles yesterday, and miles fewer today. Lia jogged miles yesterday, and c miles fewer today. Lia jogged miles yesterday, and c times as far today. SM007 7 The table below shows the average number of lunches bought in a cafeteria each day over a period of years. Lunches ought afeteria Lunches ought Year The greatest decrease in the number of lunches bought occurred between which two years? from 998 to 999 from 999 to 000 from 000 to 00 from 00 to 00 8 If N =, what is the value of 6 N? SM9 SM000 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

14 G R E Math 9 If k = 6, what is the value of 7k? LI FOR N I ST N R S TE ST SM096 Released Test Questions Sophie caught twice as many fish as her dad. If her dad caught F fish, how many fish did Sophie catch? F + F F F 0 If n =, what is the value of 6 n? 7 7 SM00 SM079 hn has 6 crayons. This number is 8 more crayons than ill has. Which equation should be used to find b, the number of crayons ill has? b = 6 8 Which expression represents the product of n and? n n + n n 6 b = 8 b = 6 +8 b = 6 8 SM If z =, what is (6z)? 0 7 SM SM06 What value for z makes this equation true? = ( + 8 z 7 8 0) ( ) SM000 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

15 LI FOR N I ST N R S TE ST G R E Released Test Questions Math 6 What value for w makes this equation true? w = ( 0 ) + ( ) 8 The map below shows the location of different stores. 0 0 SM007 7 The map below shows the starting positions of two scientists studying plants in a rain forest. Scientists in Rain Forest N Shoe Store y Toy Store Hardware Store - Grocery Store x W Hallie 0 - E Which store is at the point (, )? Hardware Store Grocery Store Shoe Store Toy Store - - Joe SM - - S Which ordered pair best names Joe s location? (, ) (, ) (, ) (, ) SM006 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

16 G R E Math 9 The map below shows the locations of rides at an amusement park. Maria was at the point (, ). musement Park Rides N (north) Ferris Wheel 6 Water Slide LI FOR N I ST N R S TE ST Log Ride (west) W Little - ipper - - Giant Sky oaster - Train - -6 E (east) Released Test Questions 0 What is the ordered pair for point? y x S (south) She walked units west and units north. Which ride did she walk to? Giant oaster Little ipper Sky Train Ferris Wheel (, ) (, ) (, ) (, ) SM09 SM00 6 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

17 LI FOR N I ST N R S TE ST G R E Released Test Questions Math Which point represents (, 6)? Q y P S R x Which equation could have been used to create this function table? x y = y = x x y 9 8 point P point Q point R point S y = x y = x + SM00 SM7 7 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

18 G R E LI FOR N I ST N R S TE ST Math Released Test Questions Line m is represented by the equation y =. y Which table represents values of x and y such that y = x +? m Which ordered pair is located on line m? x x y - 0 x y x y 0 x y 0 SM (, ) (0, 0) (, ) Which equation shows the relationship of all the values in the table below? (, 0) SM09 x y y = x x = y + y = x + x = y SM0 8 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

19 LI FOR N I ST N R S TE ST G R E Released Test Questions Math 6 Joaquin charges $.00 per hour to baby-sit. What equation could Joaquin use to find the number of hours (h) he needs to baby-sit in order to earn $0.00? h = 0 h = 0 h = 0 + h = 0 SM8 7 In the figure below, WXYZ is a parallelogram. W Z 8 In this parallelogram, triangle has an area of 7 square feet. What is the area, in square feet, of the parallelogram? SM06 9 The trapezoid below can be divided into identical triangles. X Y If the area of triangle WXY is square inches, what is the area of WXYZ? square inches square inches square inches square inches SM070 If the area of the shaded parallelogram is 6 cm, what is the area of the trapezoid? 8 cm cm cm 8 cm SM00 9 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

20 G R E Math 60 What is the area, in square meters, of the parallelogram below? 9 m LI FOR N I ST N R S TE ST 6 Released Test Questions in. 8 in. 7 m in SM09 6 What is the surface area of the box formed by the pattern below? This rectangular prism has a length of inches, a height of 8 inches, and a width of inches. What is the volume? cu in. cu in. cu in. 6 cu in. SM07 6 What is the volume, in cubic inches, of the school locker below? cm cm cm cm cm cm cm 9 0 in. cm cm 8 cm cm cm 8 cm SM in. 8 in. SM0 0 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

21 LI FOR N I ST N R S TE ST G R E Released Test Questions Math 6 What is the volume of a cube that measures 0 inches on each edge? 0 cubic inches 00 cubic inches 000 cubic inches 0,000 cubic inches SM00 6 store has a rectangular parking lot that is 00 feet by 0 feet. What is the perimeter of the parking lot? 67 Which is closest to the measure of the angle shown below? 0 o 0 o 0 o 0 o 0 o 0 o 60 o 0 o 70 o 00 o 80 o 90 o 90 o 0 o 0 o 60 o 0 o 0 o 60 o 70 o 70 o 0 o 0 o 80 o 0 o 80 o 0o 80 o 00 o 0 o 70 o 0 o 60 o 0 o 0 o 0 o 0 o 0 o 0 feet 0 feet 00 square feet,000 square feet SM8 66 The area of a backyard would most likely be measured in square inches. cubic inches. cubic feet. square feet. 68 Which of the following best describes the figure below? SM0 SM acute angles obtuse angles parallel lines perpendicular lines SM8 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

22 G R E Math 69 What is the approximate measure of this angle in degrees? LI FOR N I ST N R S TE ST 7 Released Test Questions M L N 0 0 SM97 Triangle LMN is a right triangle, and angles L and N are equal. What is the measure of angle L? SM06 z What is the measure of angle z in the figure above? 0 80 SM06 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

23 LI FOR N I ST N R S TE ST G R E Released Test Questions Math 7 Nina made a triangle by cutting the corner off a sheet of paper. 7 ndrew constructed a triangle so that and were the same size and measured o o? One angle is. What is the measure of the third angle of Nina s triangle? 0 60 SM What is the measure of? What is the measure of angle R? R SM9 9 o 9 o Q S SM0 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

24 G R E Math Released Test Questions 7 The figure below is made of small cubes. Top Side Front Which best shows the side view of the figure? LI FOR N I ST N R S TE ST 76 Sharice scored the following numbers of points in dart games. 88, 96,,, What is the median of these numbers? 6 88 SN0066 SM00 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

25 LI FOR N I ST N R S TE ST G R E Released Test Questions Math 77 Students were asked how they traveled to school each day. The table below shows these results. Travel to School Type of Travel Percentage us 0% ar 0% Walk % ike % Which graphic correctly displays these data? Travel Type Travel Type ar us ar us ike Walk ike Walk Travel Type Travel Type Walk ar ar us ike Walk us ike SM0 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

26 G R E Math Released Test Questions 78 group of people went fishing for four days. Together, they caught 0 pounds of fish each day. Fish Tuna Snapper Flounder Mackerel ay LI FOR N I ST N R S TE ST Part of Total Pounds Fish Tuna Snapper Flounder Mackerel ay Part of Total Pounds ay ay Fish Tuna Snapper Flounder Mackerel Part of Total Pounds Fish Tuna Snapper Flounder Mackerel Part of Total Pounds On which day was tuna 0% of the total catch? ay ay ay ay SM098 6 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

27 LI FOR N I ST N R S TE ST G R E Released Test Questions Math 79 Regina s piano teacher kept this record of Regina s progress on a song she is memorizing. Percent Memorized Piano Practice Number of ays Practiced How many days of practice did it take for Regina to memorize half of the song? 6 8 SN Which point represents (, ) on this graph? 7 6 y M N - 7 point K point L point M point N K L x SM99 7 This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

28 G R E Math LI FOR N I ST N R S TE ST Released Test Questions Question Number orrect nswer Standard Year of Release NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS. NS This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

29 LI FOR N I ST N R S TE ST G R E Released Test Questions Math Question Number orrect nswer Standard Year of Release 6 F F F F F. 00 F. 00 F. 006 F. 006 F. 007 F F F F F F. 006 F. 007 F. 00 F. 00 F. 00 F F MG MG MG MG MG MG MG MG MG MG MG MG MG MG This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.

30 G R E Math LI FOR N I ST N R S TE ST Released Test Questions Question Number orrect nswer Standard Year of Release 7 MG MG MG MG MG PS PS PS PS PS This is a sample of alifornia Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. opyright 008 alifornia epartment of Education.