10 Practice Test 2 - Focus On Learning

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PSAT 10 Math TestsPractice#Test 2Make time to take the practice test.It’s one of the best ways to get readyfor the PSAT 10.After you take the practice test, score it right awayat collegeboard.org/psatscoring.5LPT01

33Math Test – No Calculator2 5 M I N U TES, 1 7 QUESTIONSTurn to Section 3 of your answer sheet to answer the questions in this section.For questions 1-13, solve each problem, choose the best answer from the choicesprovided, and fill in the corresponding circle on your answer sheet. For questions 14-17,solve the problem and enter your answer in the grid on the answer sheet. Please refer tothe directions before question 14 on how to enter your answers in the grid. You may useany available space in your test booklet for scratch work.1. The use of a calculator is not permitted.2. All variables and expressions used represent real numbers unless otherwise indicated.3. Figures provided in this test are drawn to scale unless otherwise indicated.4. All figures lie in a plane unless otherwise indicated.5. Unless otherwise indicated, the domain of a given function f is the set of all real numbers x forwhich f(x) is a real number.rhwA pr 2C 2prb1A bh2A whrwV whac 2 a2 b 2rh2xcb60 xs 45 s 230 45 sx 3Special Right Triangleshhwr4V pr 33V pr 2h1V pr 2h3V 1 wh3The number of degrees of arc in a circle is 360.The number of radians of arc in a circle is 2p.The sum of the measures in degrees of the angles of a triangle is 180.Unauthorized copying or reuse of any part of this page is illegal.42CO NTI N U E

33Which of the following is an equivalent form of theexpression 15x 24ax ?A) 39ax 2B) 39(a 2x)C) (5 8a) xD) (15 24a) x2The formula d rt is used to calculate the distancean object travels over a period of time, t, at aconstant rate, r. Based on this formula, what is therate, r, in terms of d and t ?dtA)r B)r dtC)r tdD) r d tUnauthorized copying or reuse of any part of this page is illegal.1433Which of the following ordered pairs (x, y) satisfiesboth equations y x 2 3x 4 and x y 4 ?A) (0, 4)B) (2, 6)C) (3, 14)D) (5, 9)4Which of the following is a solution to the equation2x 2 4x 3 3x 2 ?A) 1B)0C)3D)6CO NTI N U E

33 3x 4y 20x 10y 16If (x, y) is the solution to the system of equationsabove, what is the value of x ?A) 14B) 12C) 4D)166The equation y 36 18x models the relationshipbetween the height y, in inches, of a typical goldendelicious apple tree and the number of years, x, afterit was planted. If the equation is graphed in thexy-plane, what is indicated by the y-intercept of thegraph?A) The age, in years, of a typical apple tree when itis plantedB) The height, in inches, of a typical apple treewhen it is plantedC) The number of years it takes a typical apple treeto growD) The number of inches a typical apple tree growseach yearUnauthorized copying or reuse of any part of this page is illegal.5447Giovanni wants to buy shirts that cost 19.40 eachand sweaters that cost 24.80 each. An 8% sales taxwill be applied to the entire purchase. If Giovannibuys 2 shirts, which equation relates the number ofsweaters purchased, p, and the total cost indollars, y ?A) 1.08(38.80 24.80p) yB) 38.80 24.80p 0.92yC) 38.80 24.80p 1.08yD) 0.92(38.80 24.80p) y8A line is graphed in the xy-plane. If the line has apositive slope and a negative y-intercept, which ofthe following points cannot lie on the line?A) ( 3, 3)B) ( 3, 3)C) (3, 3)D) (3, 3)CO NTI N U E

3A parachute design uses 18 separate pieces of rope.Each piece of rope must be at least 270 centimetersand no more than 280 centimeters long. Whatinequality represents all possible values of the totallength of rope x, in centimeters, needed for theparachute?A) 270 x 280B) 4,860 x 4,870C) 4,860 x 5,040D) 5,030 x 5,04010A carpenter has 60 with which to buy supplies. Thecarpenter needs to buy both nails and screws. Nailscost 12.99 per box, and screws cost 14.99 per box.If n represents the number of boxes of nails and srepresents the number of boxes of screws, which ofthe following systems of inequalities models thissituation?A)n 14.99s 60{1n2.99 s 1B)n 14.99s 60{1n2.99 s 1 12.99n 14.99s 60 C) n 1 s 1 12.99n 14.99s 60 D) n 1 s 1Unauthorized copying or reuse of any part of this page is illegal.934511B28 28 ADCIn the figure above, which of the following ratios hasthe same value asA)BDDCB)BCACC)ADBDD)DCBCAB?BCCO NTI N U E

3312 3 212 3 3a a(x y ) (x y ) x 3 y 2If the equation above, where a is a constant, is truefor all positive values of x and y, what is thevalue of a ?A) 2B) 3C) 5D) 6Unauthorized copying or reuse of any part of this page is illegal.124613If the equation y (x 6)(x 12) is graphed in thexy-plane, what is the x-coordinate of the parabola’svertex?A) 6B) 3C)3D)6CO NTI N U E

337Answer: 12For questions 14-17 , solve the problem andenter your answer in the grid, as describedbelow, on the answer sheet.1. Although not required, it is suggested thatyou write your answer in the boxes at the topof the columns to help you fill in the circlesaccurately. You will receive credit only if thecircles are filled in correctly.2. Mark no more than one circle in any column.3. No question has a negative answer.4. Some problems may have more than onecorrect answer. In such cases, grid only oneanswer.Writeanswerin boxes.7 / 12.123456789Grid inresult.2as 3.5 or 7/2. (If 3 1 / 2 is entered into the/21234567892 / 3. 666201201.6. Decimal answers: If you obtain a decimalanswer with more digits than the grid canaccommodate, it may be either rounded ortruncated, but it must fill the entire grid./ /. . .0 0 01 1 1 12 2 2 23 3 3 3.Unauthorized copying or reuse of any part of this page is illegal./ /. . .0 0 01 1 12 2 23 3 34 4 45 5 56 6 67 7 78 8 89 9 9Decimalpoint. 667/ // /. . . . . .0 0 00 0 01 1 1 11 1 1 112 2 2 22 2 2 223 3 3 33 3 3 334 4 4 44 4 4 445 5 5 55 5 5 556 6 6 66 6 6 667 7 7 77 7 7 778 8 8 88 8 8 889 9 9 99 9 9 99Answer: 201 – either position is correctgrid, it will be interpreted as 31 , not 3 1 .)2Fractionline2 . 52Acceptable ways to grid 3 are:5. Mixed numbers such as 3 1 must be gridded// /. . .0 0 01 1 12 2 23 3 34 4 45 5 56 6 67 7 78 8 89 9 9Answer: 2.547/ /. . .0 0 01 1 1 12 2 2 23 3 3 3./ /. . .0 0 01 1 12 2 23 3 34 4 45 5 56 6 67 7 78 8 89 9 9NOTE: Youmay start youranswers in anycolumn, spacepermitting.Columns youdon’t need touse should beleft blank.CO NTI N U E

3321x 14 7(3x a)In the equation above, a is a constant. For whatvalue of a does the equation have an infinite numberof solutions?15Juliene practiced her dance routine for twice as manyminutes on Monday as she did on Tuesday. Shepracticed her routine those two days for a total of2 hours and 15 minutes. For how many minutes didJuliene practice her dance routine on Monday?.1416In the expression below, a is an integer.12x 2 ax 20If 3x 4 is a factor of the expression above, what isthe value of a ?17(ax by)(cx dy)In the expression above, a, b, c, and d are non-zeroconstants and ad bc . If ac 18 and bd 50, whatis the value of the coefficient of the xy term whenthe expression is multiplied out and the like termsare collected?STOPIf you finish before time is called, you may check your work on this section only.Do not turn to any other section.Unauthorized copying or reuse of any part of this page is illegal.48

44Math Test – Calculator45 M I N U TES, 31 QUESTIONSTurn to Section 4 of your answer sheet to answer the questions in this section.DI R EC T I O N SFor questions 1-27, solve each problem, choose the best answer from the choicesprovided, and fill in the corresponding circle on your answer sheet. For questions 28-31,solve the problem and enter your answer in the grid on the answer sheet. Please refer tothe directions before question 28 on how to enter your answers in the grid. You may useany available space in your test booklet for scratch work.1. The use of a calculator is permitted.2. All variables and expressions used represent real numbers unless otherwise indicated.3. Figures provided in this test are drawn to scale unless otherwise indicated.4. All figures lie in a plane unless otherwise indicated.5. Unless otherwise indicated, the domain of a given function f is the set of all real numbers x forwhich f(x) is a real number.rhwA pr 2C 2prb1A bh2A whrwV whac 2 a2 b 2rh2xcb60 xs 45 s 230 45 sx 3Special Right Triangleshhwr4V pr 33V pr 2h1V pr 2h3V 1 wh3The number of degrees of arc in a circle is 360.The number of radians of arc in a circle is 2p.The sum of the measures in degrees of the angles of a triangle is 180.Unauthorized copying or reuse of any part of this page is illegal.49CO NTI N U E

44A high school counselor conducted a study over16 consecutive quarters to determine the number ofstudents with part-time jobs. Each student in the2014 graduating class is surveyed once per quarterfor all four years of high school. The graph belowshows the data for each quarter the survey wasconducted.Number of studentsNumber of Students with Part-Time Jobs70605040302010002468 10Quarter121416During which of the following periods is the increasein the number of students with part-time jobslargest?A) Quarters 4 through 6B) Quarters 7 through 10C) Quarters 11 through 14D) Quarters 13 through 162Eli saves money each month to buy a new computer.The total amount he has saved, T, can be calculatedby the equation T 83 30m , where m is thenumber of months since he started saving. Whatdoes the number 83 represent in the equation?A) The amount of money Eli started withB) The number of months Eli has been savingC) The amount of money Eli saves each monthD) The total amount of money Eli wants to saveUnauthorized copying or reuse of any part of this page is illegal.1503According to the Department of Agriculture,consuming 100 grams of banana provides0.15 milligram of zinc. Which of the following isclosest to the number of milligrams of zinc providedby 140 grams of banana?A) 0.15B) 0.21C) 0.25D) 0.934When the equation y 5x p, where p is aconstant, is graphed in the xy-plane, the line passesthrough the point ( 2, 1). What is the value of p ?A) 9B) 2C)3D) 11CO NTI N U E

44The Number of Hitsand Times at Bat by Players ona Major League Baseball Team225200Number of hits17515012510075502500100 200 300 400 500 600 700Number of times at batThe scatterplot above shows the number of hits and thenumber of times at bat by each of 20 players on a majorleague baseball team. The line of best fit for the data isalso shown.Unauthorized copying or reuse of any part of this page is illegal.Questions 5 and 6 refer to the following information.515Which of the following statements about therelationship between the number of times at bat andthe number of hits is true?A) As the number of times at bat increases, thenumber of hits decreases.B) As the number of times at bat increases, thenumber of hits increases.C) As the number of times at bat increases, thenumber of hits remains constant.D) As the number of times at bat decreases, thenumber of hits increases.6For the player with 450 times at bat, the actualnumber of hits the player had is approximately howmany fewer than the number of hits predicted by theline of best fit?A) 10B) 20C) 30D) 40CO NTI N U E

4An advertisement states that the printing rate of acertain printer is 400 characters per second.According to the convention that 1 word consists of5 characters, what would be the advertised printingrate, in words per minute?A)2,000B)4,800C)24,000D) 120,0008Year01234Salary 38,000 39,140 40,314 41,524 42,769The table above shows the yearly salary, in dollars, ofan employee at a company. Which of the followingbest describes the type of model that fits the data inthe table?A) Linear, increasing by approximately 1,140 per yearB) Linear, increasing by approximately 1,245 per yearC) Exponential, increasing by approximately3% each yearD) Exponential, increasing by approximately9% each yearUnauthorized copying or reuse of any part of this page is illegal.74529(x 2y 3y 2 5xy 2) ( x 2y 3xy 2 3y 2)Which of the following is equivalent to theexpression above?A) 2x 2y 2xy 2B) 8xy 2 6y 2C) 2x 2y 8xy 2 6y 2D) x 4y 2 9xy 4 – 15xy 2104x 1 1 x 7 7 x 7 22Which of the following describes the solution to theequation above?A) x 0B) x 1012C) The equation has infinitely many solutions.D) The equation has no solutions.CO NTI N U E

44The table below shows the monthly electricity bills ofJoseph and Samuel for the first five months of a year.Electricity BillsMonthJanuaryFebruaryMarchAprilMayJoseph 184.66 193.12 175.99 145.30 180.33Samuel 188.99 181.27 176.35 149.23 185.66Based on the information in the table, which of thesestatements is true about the ranges and medians ofthe bills?A) Both the range and median of Joseph’s bills areless than the range and median of Samuel’s bills.B) Both the range and median of Joseph’s bills aregreater than the range and median of Samuel’sbills.C) The range of Joseph’s bills is less than the rangeof Samuel’s bills, while the median of Joseph’sbills is greater than the median of Samuel’s bills.D) The range of Joseph’s bills is greater than therange of Samuel’s bills, while the median ofJoseph’s bills is less than the median of Samuel’sbills.Unauthorized copying or reuse of any part of this page is illegal.115312Cars in Service on a RailroadIn service lessIn servicethan 10 years 10 or more yearsSingle level2154971682Double-deckerThe table above presents information about the810 train cars in service on a railroad.Approximately what percentage of the train cars inservice are double-decker cars that have been inservice for less than 10 years?A)2 percentB)7 percentC) 10 percentD) 16 percentCO NTI N U E

44A moving company uses plastic wrap to bundlegroups of boxes together. If a portion of plastic wrapthat measures 900 inches in length is used to bundleeach group of boxes, how many groups of boxes canbe bundled using 1,500 feet of the same type ofplastic wrap?A) 15B) 20C) 25D) 3014The table below shows the number of calories in acheeseburger at six different restaurants.Calories in a CheeseburgerRestaurantCaloriesBlue Jay810Clear Lake Cafe900Molly’s740Riverside Diner 1,120Maya’s Bistro1,050Tom’s Place700What is the difference in the number of calories in acheeseburger at the Riverside Diner and themedian number of calories in cheeseburgers at allsix restaurants?A) 190B) 233C) 265D) 390Unauthorized copying or reuse of any part of this page is illegal.135415A circle is graphed in the xy-plane. If the circle has aradius of 3 and the center of the circle is at (4, 2),which of the following could be an equation of thecircle?A) (x 4)2 (y 2)2 3B) (x 4)2 (y 2)2 3C) (x 4)2 (y 2)2 9D) (x 4)2 (y 2)2 9CO NTI N U E

4A high school developed a program called Propel, whichoffers extra guidance and support during the 9th-gradeyear. Before the school year began, 327 rising 9th graderswere selected at random to participate in a study; 109 ofthose students were randomly assigned to enroll in thePropel program and the remaining students served as acontrol group. A summary of the year-end grade pointaverages (GPA) for the 327 9th-grade students who werechosen for the study is shown in the table below.GPA for the 327 9th-Grade StudentsGPAEnrolled in Propel Not enrolled in Propel3.0 or greater6195Less than 3.04812316If a 9th-grade student at the high school is chosen atrandom, which of the following is closest to theprobability that the student will have a GPA of 3.0 orgreater?A) 0.64B) 0.48C) 0.33D) 0.19Unauthorized copying or reuse of any part of this page is illegal.Questions 16-18 refer to the following information.45517What is the difference, to the nearest whole percent,between the percentage of students enrolled inPropel who had a GPA of 3.0 or greater and thepercentage of students not enrolled in Propel whohad a GPA of 3.0 or greater?A)4%B)8%C) 10%D) 12%18Of the students enrolled in the Propel program, theratio of boys to girls is approximately 2:3. Which ofthe following is the best estimate of the number ofgirls enrolled in the program?A)44B)65C)73D) 131CO NTI N U E

44An artist is creating a sculpture using bendable metalrods of equal length. One rod is formed into theshape of a square and another rod into the shape ofan equilateral triangle. If each side of the triangle is2 inches longer than each side of the square, howlong, in inches, is each rod?A) 16B) 18C) 24D) 3020f (x ) 2x 422x 2x 4A rational function is defined above. Which of thefollowing is an equivalent form that displays valuesnot included in the domain as constants orcoefficients?x 2A) f (x) 2x x 22(x 2)B) f (x) 2(x 2)(x 1)C) f (x) D) f (x) 1x 112x 2Unauthorized copying or reuse of any part of this page is illegal.195621A landscaper is designing a rectangular fountainwith a 4-foot-wide path around it. The equationA 4p 64 will relate the area A, in square feet, ofthe path to the perimeter p, in feet, of the fountain.In the design, how many feet will the perimeter of thefountain increase for each additional square foot ofthe path’s area?A)164B)14C)4D) 64CO NTI N U E

4In the xy-plane the graph of the function q is aparabola. The graph intersects the x-axis at ( 1, 0)and (r, 0). If the vertex of q occurs at the point(2, 4) , what is the value of r ?A) 0B) 3C) 4D) 523Liquid going through a cooling system is chilled sothat its temperature decreases at a constant rate from100 C to 25 C in 5 seconds. Which of the followingfunctions represents the temperature C, in degreesCelsius, as a function of the time t, in seconds, afterchilling began, for 0 t 5 ?A) C 25 15tB) C 25 15tC) C 25 15tD) C 100 15tUnauthorized copying or reuse of any part of this page is illegal.22457244 3πr3The formula for the volume of a sphere with radius ris shown above. The radius of the planet Jupiter isabout 11 times the radius of planet Earth. Assumingthat planets are spheres, about how many timeslarger is the volume of Jupiter than the volume ofEarth?V A)11B)121C) 1,331D) 1,775CO NTI N U E

4The population of squirrels in a park has beendoubling every 15 years. Which of the followingstatements describes the type of function that bestmodels the relationship between the population ofsquirrels in the park and the number of 15-year timeperiods?A) Exponential growth, because the population ofsquirrels is increasing by the same amount each15-year time periodB) Exponential growth, because the population ofsquirrels is increasing by the same percentageeach 15-year time periodC) Linear growth, because the population ofsquirrels is increasing by the same amount each15-year time periodD) Linear growth, because the population ofsquirrels is increasing by the same percentageeach 15-year time period26If function f is defined by f (x) 3x 2 5x 4,what is f (x 4) ?A) f (x 4) 3x 2 5xB) f (x 4) 3x 2 5x 72C) f (x 4) 3x 2 29x 52D) f (x 4) 3x 2 29x 72Unauthorized copying or reuse of any part of this page is illegal.25458271y3154 4y 10xx The equations of two lines are shown above. If thelines are graphed in the xy-plane, which of thefollowing ordered pairs represents the point at whichthe lines would intersect?A) (1, 3)B) (3, 9)C) (5, 15)D) (7, 21)CO NTI N U E

447Answer: 12For questions 28-31, solve the problem andenter your answer in the grid, as describedbelow, on the answer sheet.1. Although not required, it is suggested thatyou write your answer in the boxes at the topof the columns to help you fill in the circlesaccurately. You will receive credit only if thecircles are filled in correctly.2. Mark no more than one circle in any column.3. No question has a negative answer.4. Some problems may have more than onecorrect answer. In such cases, grid only oneanswer.Writeanswerin boxes.7 / 12.123456789Grid inresult.2as 3.5 or 7/2. (If 3 1 / 2 is entered into the/21234567892 / 3. 666201201.6. Decimal answers: If you obtain a decimalanswer with more digits than the grid canaccommodate, it may be either rounded ortruncated, but it must fill the entire grid./ /. . .0 0 01 1 1 12 2 2 23 3 3 3.Unauthorized copying or reuse of any part of this page is illegal./ /. . .0 0 01 1 12 2 23 3 34 4 45 5 56 6 67 7 78 8 89 9 9Decimalpoint. 667/ // /. . . . . .0 0 00 0 01 1 1 11 1 1 112 2 2 22 2 2 223 3 3 33 3 3 334 4 4 44 4 4 445 5 5 55 5 5 556 6 6 66 6 6 667 7 7 77 7 7 778 8 8 88 8 8 889 9 9 99 9 9 99Answer: 201 – either position is correctgrid, it will be interpreted as 31 , not 3 1 .)2Fractionline2 . 52Acceptable ways to grid 3 are:5. Mixed numbers such as 3 1 must be gridded// /. . .0 0 01 1 12 2 23 3 34 4 45 5 56 6 67 7 78 8 89 9 9Answer: 2.559/ /. . .0 0 01 1 1 12 2 2 23 3 3 3./ /. . .0 0 01 1 12 2 23 3 34 4 45 5 56 6 67 7 78 8 89 9 9NOTE: Youmay start youranswers in anycolumn, spacepermitting.Columns youdon’t need touse should beleft blank.CO NTI N U E

4Type of mealFat (g) Carbohydrates (g)Stir-fry440Szechuan chicken535A grocer carries two types of frozen meals that havethe fat and carbohydrate content shown in the tableabove. John wants to purchase a combination of thetwo types of meals with no more than 350 grams offat and no more than 2975 grams of carbohydrates.If John purchases 10 Szechuan chicken meals, what isthe greatest number of stir‑fry meals he can purchaseso that the combination will satisfy the requirements?Unauthorized copying or reuse of any part of this page is illegal.2846029y x 2 4x 3y x 1If (x, y) is a solution to the system of equationsabove, what is one possible value of the productof x and y ?CO NTI N U E

44King Crab Supply from 2005–2012200180Pounds (millions)16014012010080604020005 006 007 008 009 010 011 0122 222 22 2Year20The graph above shows the supply, in millions of pounds,of king crab harvested and sold from 2005 to 2011. Theinformation for the year 2012 is not included in thegraph.Questions 30 and 31 refer to the followinginformation.30In 2006, the price of king crab was 8 per pound atthe beginning of the year and dropped to 7per pound toward the end of the year. If 60% of theking crab supply was sold at the higher price perpound and the rest was sold at the lower price perpound, what was the total revenue generated, inmillions of dollars, from the sales of king crab in2006 ? (Disregard the when gridding your answer.)31In 2011, the price of king crab was 17 per pound. In2012, x million pounds of king crab were sold at 16per pound. If the total money generated from saleseach year was the same, what is the value of x ?STOPIf you finish before time is called, you may check your work on this section only.Do not turn to any other section.Unauthorized copying or reuse of any part of this page is illegal.61

Take the Practice Test Resources to Help You PrepareResources to HelpYou PrepareYour PSAT 10 ScoreWhen you take the PSAT 10, you will receive anEvidence-Based Reading and Writing score anda Math score. In addition to the section scores,you’ll receive test scores, subscores, and cross-testscores that offer more detailed feedback about yourperformance.The College Board is committed to offering thebest practice—free, to the world—and to do so, wehave partnered with Khan Academy to help propelstudents to success. When you upload this booklet’spractice test answers to the Khan Academy website,we can offer you individualized instruction in theareas you need most. Learn more atcollegeboard.org/psatscoring.Taking the PSAT 10 in spring will give you a goodidea of what you will see on the SAT . Once youreceive your scores, be sure to start using theresources available through your online score report atstudentscores.collegeboard.org. In addition, findout how to use your PSAT 10 results to power yourstudy at satpractice.org.Make the Best Use of Your Practice TestPractice makes a difference! Take the full-length Practice Test #2 on the preceding pages, then find detailedinstructions on how to score the test at collegeboard.org/psatpractice. You will also find comprehensiveanswer explanations.Correct Answers Black letter after answer indicates difficulty level (e easy, m medium, h hard).READING 16.17.18.19.20.21.CBDBACBWRITING AND LANGUAGE .BADDBCCmmmehee15.16.17.18.19.20.21.MATH TEST – NO CALCULATOR1.2.3.DABmem4.5.6.CCBmmmMATH TEST – CALCULATOR1.2.3.4.5.62BABDBPSAT 10eeeme6.7.8.9.10.ABCADPractice Test #2mmmmm

PSAT 10 Practice Test #2Worksheet: Answer 37394142ABCBB43A45A444647ADC11D13C15D

PSAT 10 Practice Test #2 5LPT01 d 1 7/9/18 5:48 PM Math Tests. 3 3 Math Test - No Calculator 25 MINUTES, 17 QUESTIONS Turn to Section 3 of your answer sheet to answer the questions in this section.