XIV. Mathematics, Grade 8

XIV. Mathematics, Grade 8

Grade 8 Mathematics TestThe spring 2015 grade 8 Mathematics test was based on standards in the five domains for grade 8 in theMassachusetts Curriculum Framework for Mathematics (March 2011). The grade 8 standards can befound on pages 65–69 in the Framework, and the five domains are listed below. The Number System Expressions and Equations Functions Geometry Statistics and ProbabilityThe Massachusetts Curriculum Framework for Mathematics is available on the Department website tics test results are reported under five MCAS reporting categories, which are identical to thefive framework domains listed above.The tables at the conclusion of this chapter indicate each released and unreleased common item’sreporting category and the framework standard it assesses. The correct answers for released multiplechoice and short-answer questions are also displayed in the released item table.Test SessionsThe grade 8 Mathematics test included two separate test sessions. Each session included multiplechoice, short-answer, and open-response questions. Approximately half of the common test items areshown on the following pages as they appeared in test booklets.Reference Materials and ToolsEach student taking the grade 8 Mathematics test was provided with a plastic ruler and a grade 8Mathematics Reference Sheet. A copy of the reference sheet follows the final question in this chapter.An image of the ruler is not reproduced in this publication.During Session 2, each student had sole access to a calculator with at least four functions and a square rootkey. Calculator use was not allowed during Session 1.During both Mathematics test sessions, the use of bilingual word-to-word dictionaries was allowedfor current and former English language learner students only. No other reference tools or materialswere allowed.221

Grade 8 MathematicsSession 1You may use your reference sheet and MCAS ruler during this session.You may not use a calculator during this session.DIRECTIONSThis session contains eight multiple-choice questions, one short-answer question, and one openresponse question. Mark your answers to these questions in the spaces provided in your StudentAnswer Booklet.ID:298201 D Common1 ID:301684 WTJ030functiontablechoice D Common2 A store sells white scarves and redscarves. A white scarf costs 3.Which of the following tables shows arelationship that is not a function?A. A red scarf costs 5.On Monday, the store sold 12 scarvesfor a total of 50.What is the total number of red scarvesthat the store sold on Monday?A. 4B.B. 5C. 6D. tOutput34563456InputOutput3344481216

Mathematics Session 1ID:307389 C Common3 ID:297520 C Common5 Which of the following numbers isirrational?A. 25B.Each soft drink at the first restaurant hasthe same price. The table below showsy, the total price of one large pizza andx soft drinks at the first restaurant.23C.7D.9Richard wants to purchase one largepizza and some soft drinks for a clubmeeting. He compares the prices at tworestaurants.Prices at theFirst RestaurantID:307563 B Common 4A tree in Oakland has a mass ofapproximately 3 10 6 kilograms.A tree in Mapleville has a mass ofapproximately 6 10 4 kilograms.The mass of the tree in Oakland isabout how many times the mass of thetree in Mapleville?A.20B.50xy1 19.252 20.503 21.754 23.005 24.25At the second restaurant, the totalprice, y, of one large pizza andx soft drinks can be represented bythe equation below.C. 200yD. 5001.5x18Which of the following statements is true?A. The price of one large pizza is moreat the second restaurant than at thefirst restaurant.B. The price of one large pizza is moreat the first restaurant than at thesecond restaurant.C. The price of one soft drink is moreat the second restaurant than at thefirst restaurant.D. The price of one soft drink is moreat the first restaurant than at thesecond restaurant.223

Mathematics Session 1Question 6 is a short-answer question. Write your answer to this question in the box provided in yourStudent Answer Booklet. Do not write your answer in this test booklet. You may do your figuring inthe test booklet.ID:307400 Common6 What value of x makes the equation below true?x2169224

Mathematics Session 1Mark your answers to multiple-choice questions 7 through 9 in the spaces provided in your StudentAnswer Booklet. Do not write your answers in this test booklet. You may do your figuring in the testbooklet.ID:307512 MJB002 number lines.eps B Common7 Points K, L, M, and N are shown on thenumber line below.KLMN–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6Which point on the number line bestapproximates the location of 2 3 ?A. point KB. point LC. point MD. point N225

Mathematics Session 1ID:303341 CCFBAM002 lines.eps [stem D Common8 A scatterplot is shown below.yxWhich of the following most closely approximates the line of best fit for the data in thescatterplot?A.yC.yxB.xyD.yxx226

Mathematics Session 1ID:303787 CCFBAM017 segment.eps A Common9 Quadrilateral RSTU is shown on the coordinate grid below.1 unity1 unit9876UR5TS4321–9 –8 –7 –6 –5 –4 –3 –2 –1 0–1–2–3–4–5–6–7–8–91 2 3 4 5 6 7 8 9xThe quadrilateral will be reflected over the y-axis. What will be the length, in units, of theimage of TU after the reflection?A. 2B. 3C. 5D. 6227

Mathematics Session 1Question 10 is an open-response question. BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION.Show all your work (diagrams, tables, or computations) in your Student Answer Booklet.If you do the work in your head, explain in writing how you did the work.Write your answer to question 10 in the space provided in your Student Answer Booklet.ID:307588 SL016 reading graph.eps [ CommonKate is reading a 500-page book. The graph below represents the relationship between thenumber of hours Kate has spent reading and the number of pages she has read.Reading Ratey450400Number of Pages Read10 350300Kate’srate250200(5, 200)150100500123456xTime (in hours)On the grid in your Student Answer Booklet, copy the x-axis, the y-axis, and the linerepresenting Kate’s reading rate exactly as shown. Be sure to label the line “Kate’s rate.”a. At what rate, in pages per hour, is Kate reading? Show or explain how you got your answer.b. What is the total amount of time, in hours, it will take Kate to read the entire 500-page book?Show or explain how you got your answer.Edward is reading the same 500-page book. The equation below represents the relationshipbetween y, the number of pages he has read, and x, the number of hours he has spent reading.y50xc. On your grid, graph the equation that represents the number of hours that Edward has spentreading and the number of pages he has read. Label the line “Edward’s rate.”d. Edward thinks he will finish reading the book in less time than Kate. Is he correct? Show orexplain how you got your answer.228

Grade 8 MathematicsSession 2You may use your reference sheet and MCAS ruler during this session.You may use a calculator during this session.DIRECTIONSThis session contains eight multiple-choice questions, two short-answer questions, and one openresponse question. Mark your answers to these questions in the spaces provided in your StudentAnswer Booklet.ID:253764 CMH075 triangle.eps B Common11 ID:297649 CMC303 linear.eps [opt a0 D Common12 Dustin made a flag in the shape of atriangle, with the dimensions shownbelow.Which of the following graphs shows alinear function?A.yx inches3 inchesx10 inchesB.yWhich of the following is closest to thevalue of x ?A.x9.5B. 10.4C. 11.5C.D. 13.0yxD.yx229

Mathematics Session 2ID:253742 CMH068 triangle.eps C Common13 ID:297650 CMC304 increasing.eps D Common14 The diagram below shows n PQR,where /QRS is an exterior angle.A function is graphed on the coordinategrid below.yQ252 –6RSB.66 46x–6Based on the given angle measures,what is the measure of /QRS ?57 2–462 A.–2–2?P–4Which of the following statements bestdescribes the function?A. As the value of x increases, the valueof y increases for all values of x.C. 114 B. As the value of x increases, the valueof y decreases for all values of x.D. 118 C. As the value of x increases, the valueof y increases for positive values ofx only.D. As the value of x increases, the valueof y decreases for positive values ofx only.230

Mathematics Session 2ID:287601 AL981407 graph.eps C Common15 The graph below shows the number ofcalories Benjamin will burn over timewhile walking at a constant rate.Calories Burned While WalkingyCalories Burned2101801501209060(15, 60)300510 15 20 25 30 35 40 45xTime (minutes)Based on the graph, what isthe number of calories Benjaminwill burn after walking at aconstant rate for 42 minutes?A. 132B. 162C. 168D. 210231

Mathematics Session 2ID:307587 SL014 fruit stands.eps C CommonJulia and Tom each have a fruit stand. The information in the boxes below can be used todetermine the costs, in dollars, of cherries at the two fruit stands.Julia’s Fruit Standyy4.5x,where y equals the total cost, indollars, of x pounds of cherriesCost (in dollars)16 Tom’s Fruit Stand90807060504030201001 2 3 4 5 6 7 8 9xAmount of Cherries (in pounds)Based on the information, which of the following statements best compares the costs ofcherries at the two fruit stands?A. Cherries cost 1.50 more per pound at Julia’s Fruit Stand than at Tom’s Fruit Stand.B. Cherries cost 2.50 more per pound at Julia’s Fruit Stand than at Tom’s Fruit Stand.C. Cherries cost 1.50 more per pound at Tom’s Fruit Stand than at Julia’s Fruit Stand.D. Cherries cost 2.50 more per pound at Tom’s Fruit Stand than at Julia’s Fruit Stand.232

Mathematics Session 2Questions 17 and 18 are short-answer questions. Write your answers to these questions in theboxes provided in your Student Answer Booklet. Do not write your answers in this test booklet. Youmay do your figuring in the test booklet.ID:301708 Common17 A company makes hats with custom designs. For each custom order, the company charges aone-time fee of 25.00 for the design and 12.50 for each hat made.Write an equation that can be used to find c, the total cost, in dollars, of a custom order, interms of h, the number of hats made.ID:307546 MJB069 student heights an CommonThe scatterplot below shows the relationship between the height, in inches, and the shoe sizeof each of 10 students in a class.yHeight (in inches)18 Students’ Heightsand Shoe Sizes6968676665646362610567Shoe Size89xBased on the scatterplot, what ordered pair represents the outlier in the data?233

Mathematics Session 2Mark your answers to multiple-choice questions 19 and 20 in the spaces provided in your StudentAnswer Booklet. Do not write your answers in this test booklet. You may do your figuring in the testbooklet.ID:301697 A Common19 The formula for the volume of a cone isshown in the box below.Vr 2h3In the formula, r is the radius of thebase of the cone and h is the height ofthe cone.Which of the following is closest to thevolume of a cone that has a height of3.5 inches and a base with a diameterof 1.5 inches? (Use 3.14 for π.)A. 2 cubic inchesB. 5 cubic inchesC. 6 cubic inchesD. 8 cubic inches234

Mathematics Session 2ID:301685 WTJ033robotreports.eps A CommonThe students at a middle school want to hire a DJ for an end-of-the-year dance. The informationbelow can be used to find the total cost of hiring a DJ at each of four different companies.Awesome EntertainersTurntable TunesyCost (in dollars)20 30025020015010050(2, 160)x0123Numberof HoursCost(in dollars)12342002402803204Number of HoursCool BeatsRock-N-Sounds 300 plusan additional 35 per hourThe cost of hiring a DJ isrepresented by the equationc 45h 250,where c is the total cost, in dollars,and h is the number of hoursthe DJ works.Which company’s cost has the greatest rate of change?A. Awesome EntertainersB. Cool BeatsC. Turntable TunesD. Rock-N-Sounds235