WIXLIB

XV. Mathematics, Grade 10

Grade 10 Mathematics TestThe spring 2019 grade 10 Mathematics test was a next-generation assessment that was administered in two primary formats: acomputer-based version and a paper-based version. The vast majority of students took the computer-based test. The paper-basedtest was offered as an accommodation for students with disabilities who are unable to use a computer, as well as for Englishlearners who are new to the country and are unfamiliar with technology.Most of the operational items on the grade 10 Mathematics test were the same, regardless of whether a student took the computerbased version or the paper-based version. In places where a technology-enhanced item was used on the computer-based test, anadapted version of the item was created for use on the paper test. These adapted paper items were multiple-choice, multiple-select,or short-answer items that tested the same Mathematics content and assessed the same standard as the technology-enhanced item.This document displays released items from the paper-based test. Released items from the computer-based test areavailable on the MCAS Resource Center website at mcas.pearsonsupport.com/released-items.Test Sessions and Content OverviewThe grade 10 Mathematics test was made up of two separate test sessions. Each session included selected-response, short-answer,and constructed-response questions. On the paper-based test, the selected-response questions were multiple-choice items andmultiple-select items, in which students select the correct answer(s) from among several answer options.Standards and Reporting CategoriesThe grade 10 Mathematics test was based on high school standards in the Massachusetts Curriculum Framework forMathematics (2017). The standards in the 2017 framework are organized under the five major conceptual categories listedbelow. Number and Quantity Algebra Functions Geometry Statistics and ProbabilityThe grade 10 test assessed standards that overlap between the Model Algebra I/Model Geometry and Model Mathematics I/ModelMathematics II courses. The Massachusetts Curriculum Framework for Mathematics is available on the Department website tics test results for grade 10 are reported under four MCAS reporting categories, which are based on the five frameworkconceptual categories listed above.The table at the conclusion of this chapter provides the following information about each released operational item: reportingcategory, standard covered, item type, and item description. The correct answers for selected-response and short-answerquestions are also displayed in the table.Reference Materials and ToolsEach student taking the grade 10 Mathematics test was provided with a grade 10 Mathematics Reference Sheet. A copy of thereference sheet follows the final question in this chapter.During Session 2, each student had sole access to a calculator. Calculator use was not allowed during Session 1.During both Mathematics test sessions, the use of bilingual word-to-word dictionaries was allowed for current and formerEnglish learner students only. No other reference tools or materials were allowed.351

Grade 10 MathematicsSESSION 1This session contains 21 questions.You may use your reference sheet during this session.You may not use a calculator during this session.DirectionsRead each question carefully and then answer it as well as you can. You must recordall answers in this Test & Answer Booklet.For some questions, you will mark your answers by filling in the circles in yourTest & Answer Booklet. Make sure you darken the circles completely. Do not makeany marks outside of the circles. If you need to change an answer, be sure to eraseyour first answer completely.For other questions, you will need to fill in an answer grid. Directions for completingquestions with answer grids are provided on the next page.If a question asks you to show or explain your work, you must do so to receive fullcredit. Write your response in the space provided in this Test & Answer Booklet.Only responses written within the provided space will be scored.352

Mathematics Session 1Directions for Completing Questions with Answer Grids1.Work the question and find an answer.2.Enter your answer in the answer boxes at the top of the answer grid.3. Print only one number or symbol in each box. Do not leave a blank box inthe middle of an answer.4. Under each answer box, fill in the circle that matches the number orsymbol you wrote above. Make a solid mark that completely fills thecircle.5.Do not fill in a circle under an unused answer box.6. Fractions cannot be entered into an answer grid and will not be scored.Enter fractions as decimals.7. If you need to change an answer, be sure to erase your first answercompletely.8.See below for examples of how to correctly complete an answer grid.EXAMPLES– 1 4–\ \ \ \\ \ \ \0000000\\\\\\\1 \11 \1 \1 \1 \1 \\222222\\\\\\\ 23 \33 \3 \3 \3 \3 \\444444\\\\\\\ 45 \55 \5 \5 \5 \5 \\666666\\\\\\\ 67 \77 \7 \7 \7 \7 \\888888\\\\\\\ 89 \99 \9 \9 \9 \9 \\65 . 34 8 3 1 6–\ \ \ \\ \ \ \0000000\\\\\\ \1 \11 \1 \1 \1 \1 \\2222222\\\\\\ \3333333\\\\\\ \4444444\\\\\\ \5555555\\\\\\ \6666666\\\\\\ \7777777\\\\\\ \8888888\\\\\\ \9999999\\\\\\ \–\ \ \ \\ \ \ \0000000\\\\\\ \1 \11 \1 \1 \1 \1 \\2222222\\\\\\ \3333333\\\\\\ \4444444\\\\\\ \5555555\\\\\\ \6666666\\\\\\ \7777777\\\\\\ \8888888\\\\\\ \9999999\\\\\\ \3539 . 5 5 5 5–\ \ \ \\ \ \ \0 \00 \0 \0 \0 \0 \\1 \11 \1 \1 \1 \1 \\2 \22 \2 \2 \2 \2 \\3 \33 \3 \3 \3 \3 \\4 \44 \4 \4 \4 \4 \\5 \55 \5 \5 \5 \5 \\6 \66 \6 \6 \6 \6 \\7 \77 \7 \7 \7 \7 \\8 \88 \8 \8 \8 \8 \\9 \99 \9 \9 \9 \9 \\

Mathematics MA302104qOPSession 1BWhich of the following is equivalent to this expression? 5x( 6x2 1)A30x3 4xB30x3 5xC 11x3 4xD 11x3 5xMA713469914 PA OP CwConsider this function.f (x) x(18 x)What are the values of f (0), f (5), and f (18)?Af (0) 18f (5) 90f (18) 36Bf (0) 0f (5) 90f (18) 324Cf (0) 0f (5) 65f (18) 0Df (0) 18f (5) 450f (18) 36354

Mathematics Session 1MA308750 OP BeThis diagram shows a circle with an inscribed right triangle and some of itsmeasurements, in units.86Based on the diagram, what is the circumference, in units, of the circle?A5πB10πC14πD25πMA728439252rOPA,B,COn a coordinate plane, a single transformation will be performed onsquare RSTU.Select three transformations of square RSTU that would result in acongruent figure.Aa translation 3 units up and 8 units to the rightBa rotation of 270 counterclockwise about the originCa dilation by a scale factor of 1 with respect to the originDa dilation by a scale factor of 1.5 with respect to the originEa dilation by a scale factor of 2 with respect to the origin355

Mathematics MA281616OPSession 1XConsider this system of equations.th c 2.25h c 1.75What value of h makes the system of equations true?Enter your answer in the answer boxes at the top of the answer grid andcompletely fill the matching circles.–\ \ \ \\ \ \ \0 \00 \0 \0 \0 \0 \\1 \11 \1 \1 \1 \1 \\2 \22 \2 \2 \2 \2 \\3 \33 \3 \3 \3 \3 \\4 \44 \4 \4 \4 \4 \\5 \55 \5 \5 \5 \5 \\6 \66 \6 \6 \6 \6 \\7 \77 \7 \7 \7 \7 \\8 \88 \8 \8 \8 \8 \\9 \99 \9 \9 \9 \9 \\MA301428yOPBWhich of the following is equivalent to this expression?4k4 16k3 10k2A4k2(k2 4k 2)B2k2(2k2 8k 5)C2(2k4 14k3 8k2)D2k2(2k2 16k 10)356

Mathematics MA713459721 PAuOPSession 1DConsider this inequality.y x 4Which of the following graphs represents the solution set of the inequality?AyB654321-6 -5 -4 -3 -2 -1 0-1-2-3-4-5-6C6543211 2 3 4 5 6xy-6 -5 -4 -3 -2 -1 0-1-2-3-4-5-6D1 2 3 4 5 6xy654321654321-6 -5 -4 -3 -2 -1 0-1-2-3-4-5-6y1 2 3 4 5 6x357-6 -5 -4 -3 -2 -1 0-1-2-3-4-5-61 2 3 4 5 6x

Mathematics MA274081iOPSession 1ALine w is represented by this equation.y 5x 3Which of the following equations represents a line that is perpendicular toline w?15Ay x 1By 5x 1Cy Dy 5x 11x 15358

Mathematics Session 1This question has four parts. Be sure to label each part of your response.MA298055 OPoXA line and a parabola are graphed on a coordinate plane. The equation of theline and the equation of the parabola are shown in this table.GraphLineEquationy –3x 5Parabolay –x2 2x 1A. What is the value of y for the line when x 4? Show or explain how yougot your answer.B. What is the value of y for the parabola when x 4? Show or explain howyou got your answer.C. The line and the parabola intersect at two points. The distance, in units,between the two points is represented by this expression.(4 – 1)2 (–7 – 2)2Simplify the expression to determine the distance, in units, between thetwo points. Show or explain how you got your answer.D. The area, in square units, of the region on the coordinate plane enclosedby the parabola and the line is represented by this expression.–22335(4)5(1)4– 4(4) – – 1 – 4(1)3232Simplify the expression to determine the area, in square units, of theenclosed region. Show or explain how you got your answer.359

Mathematics Session 1o360

Mathematics MA304304aOPSession 1CA waiter recorded the amount of money he earned in tips each weekday for atwo-week period. His data are shown in this table.Money Earned in TipsWeekMondayTuesdayWednesdayThursdayFriday1 25 44 48 63 752 35 35 48 62 75Which statement about the data in the table is true?AThe median and the range for week 1 are equal to the median andthe range for week 2.BThe median and the mode for week 1 are equal to the median andthe mode for week 2.CThe mean and the median for week 1 are equal to the mean andthe median for week 2.DThe mean and the range for week 1 are equal to the mean andthe range for week 2.361

Mathematics MA308767sOPSession 1BLine segment KL is shown on this coordinate plane.yK(–3, 5)xL(2, –3)What are the coordinates of the midpoint of line segment KL?1A( 1, 2 )B( 2 , 1)C( 2 , 1)D(1, 2 )111362

Mathematics Session 1This question has two parts.MA713808101 PAdOPA,DShayla and Carlos each have a bag that contains 5 green marbles,5 red marbles, and 10 yellow marbles. The marbles are all the same sizeand shape.Part AShayla will select two marbles from her bag at random. She will not returnthe first marble to the bag before selecting the second marble.Which expression represents the probability that Shayla will selecttwo red marbles?A5 420 19B5 420 20C5 520 19D5 520 20Part BCarlos will select two marbles from his bag at random. He will not return thefirst marble to the bag before selecting the second marble.The first marble Carlos selects will not be yellow. What is the probability thatthe second marble he selects will be yellow?A920B919C1020D1019363

Mathematics MA308033fOPSession 1AWhat are the solutions of this equation?x 2 7x 12 0Ax 3; x 4Bx 2; x 6Cx 2; x 6Dx 3; x 4364

Mathematics Session 1This question has four parts. Be sure to label each part of your response.gOPXThis double bar graph shows the amounts of time, in minutes, an athletespent on aerobic training and strength training each day for 5 days.Aerobic and Strength TrainingTime Spent Training (in minutes)MA2947026050403020100yyyyyda rsda ridadadassneeFuMoTudnTheWDay of the WeekAerobic trainingStrength trainingA. On what day did the athlete spend the longest total amount of timetraining? Show or explain how you got your answer.B. What is the median total number of minutes the athlete spent trainingeach day? Show or explain how you got your answer.C. What percent of the total number of minutes the athlete spent training forthe 5 days was spent on strength training? Show or explain how you gotyour answer.D. Determine whether the sum of the mean number of minutes spent onaerobic training and the mean number of minutes spent on strength trainingis equal to the mean total number of minutes spent training. Show orexplain how you got your answer.365

Mathematics Session 1g366

Mathematics MA281536hOPSession 1DA rectangular garden that is 16 1 feet wide and 11 3 feet long will be44covered with soil. If a bag of soil covers an area of 20 square feet, whichof the following is closest to the number of bags of soil needed to coverthe garden?A2B3C8D10367