XV. Mathematics, Grade 10

XV. Mathematics, Grade 10

Grade 10 Mathematics TestThe spring 2015 grade 10 Mathematics test was based on standards in the 2011 MassachusettsCurriculum Framework for Mathematics that match content in the grade 9–10 standards from the 2000Massachusetts Mathematics Curriculum Framework. The standards in the 2011 Framework on thegrade 10 test are organized under the five major conceptual categories listed below. Number and Quantity Algebra Functions Geometry Statistics and ProbabilityThe Massachusetts Curriculum Framework for Mathematics is available on the Department website atwww.doe.mass.edu/frameworks/current.html. More information and a list of standards assessable onthe spring 2015 test are available at www.doe.mass.edu/mcas/transition/?section math10.Mathematics test results for grade 10 are reported under four MCAS reporting categories, which arebased on the five Framework conceptual categories listed above.The table at the conclusion of this chapter indicates each item’s reporting category, the 2011 Frameworkstandard it assesses, and the 2000 Framework standard it assesses. The correct answers for multiplechoice and short-answer items are also displayed in the table.Test SessionsThe grade 10 Mathematics test included two separate test sessions, which were administered onconsecutive days. Each session included multiple-choice and open-response items. Session 1 alsoincluded short-answer items.Reference Materials and ToolsEach student taking the grade 10 Mathematics test was provided with a grade 10 MathematicsReference Sheet. A copy of the reference sheet follows the final question in this chapter.During Session 2, each student had sole access to a calculator with at least four functions and a squareroot key. 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.241

Grade 10 MathematicsSession 1You may use your reference sheet during this session.You may not use a calculator during this session.DIRECTIONSThis session contains fourteen multiple-choice questions, four short-answer questions, and threeopen-response questions. Mark your answers to these questions in the spaces provided in yourStudent Answer Booklet.ID:307945 C Common1 ID:292919 WDN10 phi.eps B Common3 The first five terms in a geometricsequence are shown below.4, 12, 36, 108, 324, . . .The length, in centimeters, of arectangle is represented by anexpression, as shown in the diagrambelow.What is the next term in the sequence?A.432B.648C.972D. 12962 45ID:281580 A Common2 Based on the diagram, which of thefollowing is closest to the length, incentimeters, of the rectangle?Which of the following is equivalent tothe expression below?x 2 1 7x 2 60A. 8.3A. (x 1    12)(x 2 5)B. 8.7B. (x 1    10)(x 2 6)C. 9.1C. (x 1    15)(x 2 4)D. 9.5D. (x 1    20)(x 2 3)242

Mathematics Session 1ID:303380 CCF28 Laundry.eps [opt a0 D CommonGiselle surveyed 10 students at random about the number of people in their household and thenumber of times laundry is washed in their household each week. The results of her survey areshown in the table below.Weekly Laundry WashesNumber of Peoplein Household2323653434Number ofWashes1225551633Which of the following scatterplots best represents the data in the table?Weekly Laundry Washes77665432101234565432107Number of People in Household66Number of Washes754321123456234567Weekly Laundry WashesD.701Number of People in HouseholdWeekly Laundry WashesB.Weekly Laundry WashesC.Number of WashesNumber of WashesA.Number of Washes4 5432107Number of People in Household1234567Number of People in Household243

Mathematics Session 1ID:306536 C Common5 ID:308031 C Common6 What is the value of the expressionbelow?What are the solutions of the equationbelow?(5 1 4) 2 2 (5 1 4 2)(x 2 2) (x 1 9) 5 0A. 20A. x 5 22; x 5 29B. 52B. x 5 22; x 5 9C. 60C. x 5 2;x 5 29D. 92D. x 5 2;x59ID:308716 NEE055 revised.eps B Common7 The line plot below shows the fuel efficiency, in miles per gallon, for the vehicles owned by arental car company.XXXXXXXXXXXXXXX27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43Fuel Efficiency (miles per gallon)Based on the line plot, what is the median fuel efficiency, in miles per gallon, for the vehicles?A. 32B. 33C. 34D. 35244

Mathematics Session 1ID:258813 B Common8 ID:287445 A Common10 Jay and Kalani graphed lines ona coordinate plane. Jay’s line isrepresented by the equation below.2xy452 5236Kalani’s line is parallel to Jay’s line.Which of the following could be anequation of Kalani’s line?A. 418 25B. 436C. 402 103A. 2xD. 402 253B.D.5y2xC. xy2yx2y555ID:294024 B Common9 Which of the following is equivalent tothe expression below?The first 2,450 people to attend abaseball game received a free hat.A total of 19,544 people attendedthe game.Which of the following is closest tothe fraction of people attending thegame who received a free hat?A.120B.18C.15D.1424532033

Mathematics Session 1ID:294676 CMC537 sales.eps C Common11 ID:279245 B Common12 The scatterplot below shows therelationship between the total monthlysales, in millions of dollars, at a retailstore and the monthly commissions, indollars, earned by one salesperson.12 A. 0Retail Store SalesB. 15000C. 24D. ��s MonthlyCommission (in dollars)Which of the following is equivalent tothe expression below?Total Monthly Sales(in millions of dollars)Based on the line of best fit for thescatterplot, which of the following isclosest to the monthly commission thatthe salesperson could expect to makewhen the total monthly sales at the retailstore are 0.8 million?A. 1500B. 2500C. 4500D. 6500246112

Mathematics Session 1ID:306585 D Common13 ID:272630 D Common14 Leah took a 5-day car trip. The tablebelow shows the number of miles shedrove on each day of her trip.(xLeah’s Car TripDay ofTripMilesDriven1297217932034131Which of the following is equivalent tothe expression below?5192Of the total number of miles that Leahdrove on her trip, which of the followingis closest to the percentage she drove onday 1?A. 15%B. 20%C. 25%D. 30%247A. x27B. x212C. x23x7D. x27x123)(x4)

Mathematics Session 1Questions 15 and 16 are short-answer questions. Write your answers to these questions in the boxesprovided in your Student Answer Booklet. Do not write your answers in this test booklet. You may doyour figuring in the test booklet.ID:302058 ADJ35 escalator.eps Common15 The diagram below shows a right triangle and some of its measurements.18 mh30 What is h, the height in meters of the triangle?ID:306777 NEE074.eps Common16 A doctor recorded the resting heart rate, in beats per minute, of each of her patients.The distribution of the heart rates for this group of patients is shown in the box-and-whiskerplot below.Resting Heart Rate(beats per minute)405060708090100 110Based on the box-and-whisker plot, what was the median resting heart rate, in beats perminute, for this group of patients?248

Mathematics Session 1Question 17 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 17 in the space provided in your Student Answer Booklet.ID:306471 Common17 A student is approximating the locations of square roots and cube roots of integers on anumber line.a. Between which two consecutive integers on the number line isexplain how you got your answer.b. What is the value of55 located? Show or55 to the nearest tenth? Show or explain how you got your answer.m , where m is an integer, is located between 11 and 12 on the number line.The value ofc. What could be the value of m? Show or explain how you got your answer.The value ofnumber line.3n , where n is an integer, is also located between 11 and 12 on thed. What could be the value of n? Show or explain how you got your answer.249

Mathematics Session 1Questions 18 and 19 are short-answer questions. Write your answers to these questions in the boxesprovided in your Student Answer Booklet. Do not write your answers in this test booklet. You may doyour figuring in the test booklet.ID:294027 Common18 What is the value of the expression below ?1403 ( 2)44ID:268255 CMC226 slope.eps Common19 What is the slope of the line graphed below?y87654321–8 –7 –6 –5 –4 –3 –2 –1 0–1(–5, –1) –2–3–4–5–6–7–8(5, 5)(0, 2)1 2 3 4 5 6 7 8250x

Mathematics Session 1Questions 20 and 21 are open-response questions. BE SURE TO ANSWER AND LABEL ALL PARTS OF EACH 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 20 in the space provided in your Student Answer Booklet.ID:294530 CMC435 puzzle.eps Common20 A puzzle in the shape of a rectangle has six pieces. The puzzle and some of its dimensionsare shown in the diagram below.10 in.R5 in.BP8 in.YG4 in.3 in.12 in.O8 in.a. What is the perimeter, in inches, of the puzzle? Show or explain how you got your answer.The shape of each piece of the puzzle is listed below. Pieces R and O are trapezoids. Pieces Y and G are rectangles. Piece B is a parallelogram. Piece P is a triangle.b. What is the area, in square inches, of piece B? Show or explain how you got your answer.c. What is the area, in square inches, of piece R? Show or explain how you got your answer.d. What is the area, in square inches, of piece P? Show or explain how you got your answer.251

Mathematics Session 1Write your answer to question 21 in the space provided in your Student Answer Booklet.ID:296364 CMC275 pentagons.eps Common21 The first five figures in a pattern are shown below.Figure 1Figure 2Figure 3Figure 4Figure 5The pattern continues.a. What is the number of pentagons in Figure 6? Show or explain how you got your answer.b. Write an expression that represents the number of pentagons in Figure n.Figure 1 is one dot. Figure 2 is composed of five dots connected by line segments.c. What is the number of dots in Figure 6? Show or explain how you got your answer.d. Explain how the number of dots in Figure 8 and the number of dots in Figure 9 can beused to determine the number of dots in Figure 10.252

Grade 10 MathematicsSession 2You may use your reference sheet during this session.You may use a calculator during this session.DIRECTIONSThis session contains eighteen multiple-choice questions and three open-response questions.Mark your answers to these questions in the spaces provided in your Student Answer Booklet.ID:308918 C Common24 Ethan poured orange juice into eachof four glasses and estimated that eachglass contained 8 ounces, rounded to thenearest ounce.The line graph below shows thechange in the population of the stateof Ohio, in twenty-year intervals,from 1900 to 2000.Based on Ethan’s estimate, which ofthe following could be the actual totalamount of orange juice in the fourglasses?12,000,000A. 28.0 ounces10,000,000B. 29.6 ounces8,000,000Population of Ohio1900–2000Population22 ID:308723 NEE069.eps C CommonC. 31.6 ouncesD. 34.0 ounces6,000,0004,000,0002,000,000ID:306481 B Common23 0Four equations are shown below.effee feff1900 1920 1940 1960 1980 2000Yeareeff efeDuring which interval on the graph didthe population of Ohio increase at thefastest rate?A. 1900 to 1920How many of the equations are true forall real values of e and f ?B. 1920 to 1940C. 1940 to 1960A. 1D. 1980 to 2000B. 2C. 3D. 4253