### Transcription

Unpacking the Math HiSET TestPart 2: Overview & Pre-Test SolutionsKim HansonSummer 2014

HiSETTM Mathematics OverviewThe Mathematics HiSETTM test is one of five subtests students must take and pass to earntheir high school credentials. This test requires students to answer quantitative mathproblems by applying mathematical concepts, and by using reasoning and critical thinkingskills.The test is offered either on the computer or by pencil and paper. Each testing center hasspecific dates/times for each of these forms.Students have 90 minutes to complete 50 multiple-choice questions and are allowed to usea Casio-cfx260 scientific calculator for all questions. Scrap paper is also available. Eachquestion is in the form of a word problem or a visual graphic and includes 5 answerchoices. Students should be encouraged to answer ALL 50 questions. Only correct answersare counted toward scoring. Although there are leveled questions easy-medium-hard, thequestions are NOT ordered by difficulty.The following mathematical topics are covered throughout the Math HiSET subtest: Numbers and Operations on NumbersMeasurement/GeometryData Analysis/Probability/StatisticsAlgebra ConceptsStandard scores will be represented on a 0-20 scale.To pass the Math HiSETTM subtest students must earn a score of at least 8.To pass the full HiSETTM exam students must attain all three of the following:1. Achieve a score of at least 8 on each of the 5 subtests2. Score at least 2 out of 6 on the essay portion of the writing subtest.3. Have a total combined score on ALL 5 subtests of at least 45. (an average score of 9per subtest)On the scoring sheet all questions are grouped into one of the 4 mathematical topiccategories: Numbers & Operations on Numbers, Measurement/Geometry, DataAnalysis/Probability/Statistics, and Algebra Concepts. The report shows the “numbercorrect” in each category.Paper-based test scores will be delivered 3-5 business days after the test center submitsanswer sheet.Official computer-based test scores are posted within 3 business days of completion.Unofficial scores are displayed immediately after completion of the test.

HiSETTM Mathematics Test1. The HiSETTM test can be taken on paper or computer.2. It is available in English or Spanish.3. The mathematics test is 90 minutes long.4. There are 50 multiple choice questions.5. Each question has 5 answer choices.6. A calculator may be used on the entire test; it will be provided by the testing center.All centers will have the Casio cfx260.7. Questions are based on realistic situations.8. The questions are designed to integrate knowledge of mathematics, so any questionsmay involve content from more than one content category.9. Test-takers will need to make inferences or predictions based on data or information.10. There are up to 6 questions based on one set of given information.11. The test does not include a formula page. Some needed formulas are included withthe question; perimeter, are, volume and Pythagorean Theorem are not.12. Candidates will need to know basic linear measurement facts: 12inches 1foot, 3feet 1 yard.13. Most questions using metric measurement include the information in the question.Examples: 3.3feet ͌ 1meter, 1,000m 1km. Candidates should have a basicunderstanding of the metric system.14. Computer based tests will be scored immediately after completion. Paper basedresults will be available to the test taker online 1 to 2 weeks after completion.15. Scores will be reported on a scale of 0to 20 for each of the 5 subtests. Passing thewhole test will require a total of 45 points (average of 9) with no single subtest scoringbelow an 8.16. Candidates are allowed to test 3 times in one calendar year.17. Six new practice tests will be available in 2015.18. AZTEC will be providing computer based HiSETTM prep. (Fee based)19. McGraw-Hill will be releasing HiSETTM prep materials in fall 2014.20. Accommodations are available and need to be requested Directly from ETS. Someaccommodations are allowed without formal permission.21. Find more information and practice test samples at hiset.ets.edu

14A used motorcycle can be purchased for 500 cash or on credit with a 200 downpayment plus payments of 70 per monthfor 5 months. How much would be savedby paying cash?The following graph shows the salesfigures for a toy company since itopened 10 years ago.Toy Sales0.9 50 150 200 350 550Dollars in MillionsABCDE0.80.70.60.52A solution of salt water is made bydissolving 2 grams of salt in 1 liter ofwater. Which of the following would yielda solution with the same concentration?145 6Year78910approximate dollar value of sales inthe company’s 9th year of business?A Dissolving gram of salt in 2 litersof water 2A 75,000,000B 7,500,000C 750,000D 75,000E 7,5001B Dissolving gram of salt in liter2of water 21C Dissolving 1 gram of salt in liter2of water5D Dissolving 1 gram of salt in 2 litersof waterConsider the graphs below.1yE Dissolving 2 grams of salt in liter2of water33According to the graph, what was the112UTSAn appliance store uses the followingformula to set its selling prices.Price (actual cost) (25 percent of actual cost)RQIf the actual cost of a refrigeratorxis 800, what price will the store setfor the refrigerator?Although the numbers are not includedon either axis, it is possible to determinefrom shape and location that the equationy 1.2 x 4 corresponds to graphA 200B 600C 800D 1,000E 1,400ABCDEQ.R.S.T.U.GO ON TO THE NEXT PAGE-5-

Directions: Questions 6 through 11 are based on the information below.A city is going to build a new swimming pool at the recreation center. The illustration below shows the plans forthe pool.70 m30 m20 m50 mTile68Assuming that the pool is 10 feet deep,approximately how many cubic metersof water will this pool hold when filled?( 3.3 feet 1 meter )A1,000B3,000C 10,000D 30,000E 100,0007ABCDEIf one box of tiles covers 10 squaremeters, which of the followingrepresents the number of boxesrequired to cover the designatedarea around the pool with tile?ABCDEThe Recreation Department wantsto put in swim lanes along the lengthof the pool. If each swim lane mustbe 8 feet wide, which of the followingrepresents the best estimate for thenumber of swim lanes there can be inthe pool ( 3.3 feet 1 meter )?920 8(20 3.3) 820 (3.3 8)50 (8 3.3)(50 3.3) 8To maintain water purity, each week11kilograms of a certain chemical(70 30) 1070 30 10(50 20) 10should be added for each million liters[(70 30) (50 20)] 10[(70 30) (50 20)] 102.5 million liters of water, how many2of water. If the pool containskilograms of the chemical should beadded each week?ABCDE1.52.252.53.03.75GO ON TO THE NEXT PAGE-6-

10ABCDE1112It is estimated that construction ofthis pool area will cost 75,000. A largecorporation donated 35,000 towardthe construction of the pool, and anadditional 2,000 was earned duringa local fund-raising activity. If 20 localbusinesses agree to donate the restof the money, which of the followingrepresents the average amount eachbusiness will have to contribute?r dtIf rate remains constant, which of thefollowing must be true?ABCDE 75, 000 37, 000( 75, 000 2, 000) 2020 ( 75, 000 37, 000) 75, 000 20( 75, 000 37, 000) 2013A larger diagram of the proposedswimming pool area will be presentedto the city council. If each inch onthat diagram represents 5 meters ofactual distance, what are the overalldimensions of the pool area (includingthe tile area) in the diagram?ABCDEThe relationship between rate ofspeed (r), distance traveled (d), and timetraveled (t) is given by the followingequation.Consider the equation 2 3 4.To solve the equation for x, what wouldbe the most logical first step?ABCDE4 inches by 2 inches10 inches by 4 inches14 inches by 6 inches250 inches by 100 inches350 inches by 150 inches14When t remains constant, d increases.When t decreases, d remains constant.When t decreases, d increases.When t increases, d decreases.When t decreases, d decreases.Add 3 to both sides of the equation.Subtract 3 from both sides of the equation.Divide both sides of the equation by 2.Multiply both sides of the equation by 2.Subtract 4 from both sides of the equation.A tank for mixing chemical solutions is1.5 meters long, 0.6 meters wide, and1.5 meters deep. Which of the followingrepresents the maximum number ofcubic meters of solution this tankwill hold?A (1.5 0.6) 1.5B (1.5 1.5) 0.6C 1.5 0.6 1.51.5 1.5D0.6E 1.5 0.6 1.5GOGO ONON TOTO THETHE NEXTNEXT PAGEPAGE-7-

Directions: Questions 15 through 17 are based on the graph below, which shows the percentages of theEarth’s surface at various elevations.Percentage of Earth’s Crustal Surfaceat Various Elevations5,0004,0003,000Elevation (meters)2,0001,000Sea 0Level-1,0005101520Percentage of Earth’s pproximately what percentage of theEarth’s surface is at or above sea level?A 22%B 30%C 50%D 60%E 100%16A 12 kmB 8 kmC 7 kmD 5 kmE 2 kmWhich of the following elevationintervals contains the highestpercentage of the Earth’s crustalsurface?ABCDEWhich of the following bestapproximates the difference betweenthe highest elevations and the lowestelevations of the Earth’s crustalsurface? (1, 000 m 1 km)0 to 1,000 1,000 to 0 4,000 to 3,000 5,000 to 4,000 6,000 to 5,000GO ON TO THE NEXT PAGE-8-

1819Consider the circle graph below.Land and Water Areas on EarthIndian OceanLand AreaIf the temperature at 8:00 a.m. was 22 F,and at 4:00 p.m. the same day, it was – 2 F,what was the average temperature decreaseper hour during this period?ABCDEAtlanticOcean2 F2.5 F3 F5 F6 FOtherWater20Pacific OceanIf the measure of the arc associatedwith the Pacific Ocean is approximately125 , which of the following representsthe proportion of Earth’s surface that iscovered by the Pacific Ocean?125A360 125BCA Exactly 80% of the lawns sprayed lastmonth have 5 or fewer weeds.B At least 80% of the lawns sprayed lastmonth have exactly 5 weeds.C More than 80% of the lawns sprayed lastmonth have 5 or more weeds.D It is very likely that more than half ofthe lawns sprayed last month have 5 orfewer weeds.E It is very likely that more than half ofthe lawns sprayed last month have atleast 5 weeds.360 125360360 125125360DEEach month a lawn-care companysprays for weeds in 500 differentyards. Last month, to determine theeffectiveness of its herbicide, thecompany randomly selected 50 lawnsfor inspection. Of the lawns selected,40 showed 5 or fewer weeds. Which ofthe following could the lawn companyconclude with the greatest certainty?12512536021Which of the following correctlyexpresses x yards, y feet, andz inches in terms of inches?ABCDE36x 12y zx 12y 36z36x 36y zx 36y 36zx 36y 12zGO ON TO THE NEXT PAGE-9-

2224A fence encloses a rectangular fieldmeasuring 300 feet by 100 feet. A cow istied to a fence post at one corner of thefield. If the rope is 50 feet long, whichof the following represents the grazingarea of the cow inside the fence in squarefeet?The diagram below shows a coordinategrid. What are the coordinates of thepoint where the graph of y 4 x 8intersects the x-axis?y8Area of a circle π( radius) 2Area of a rectangle length times width64A 300 1002B (300 50) (100 50)CD–8–6 –4 –2π 50 50–24π 50 50–4ABCDE2 1010 eV8 1011 eV25How many more electron volts areproduced by the new model as comparedwith the original model?A7.8 1011B7.8 1010C7.8 109D6 101E4 10168–8The unit of measurement used to describethe energy produced by an atomic particleaccelerator is the electron volt (eV). Shownbelow are the amounts of energy producedby two versions of a particle accelerator.Original ModelNew Model4–62E (300 100) (50 50) π232(2,0)(8,0)(0, 2)(0, 4)(0,4)Kyle purchased a padlock with aresettable combination that uses 3 digitsfrom 0 through 9 that must be entered inthe proper order. A digit may be repeatedin the combination. Which expressionshows the total number of possiblecombinations for the padlock?A 310B 10 3C 10 9 8D (10)(9)(8)E 10 10 10-10-x

Mathematics Practice TestAnswer E11C12E13A14C15B16D17A18E19C20D21A22C23A24A25B-11-

Solutions1. ACash 500vs.Credit 200 5( 70) 200 350 550 550 - 500 502. C Method #1: The salt content of the solution yields a 2:1 ratio. Meaning that thesalt is double what the water content is. Read through the answer choices tofind where the salt is double the water.Method #2: Set up each answer choice into a proportion and solve. Definition ofa proportion: cross products are equal.a. b. c. d. e. (actual cost)800800 10001 4 1 1 1 4 1 2 3. DPricePricePricePrice (25% of actual cost)(.25)(800)2004. CFind the value along the y-axis(vertical axis)The answer choices are expanded while the values along the y-axis(verticalaxis) are shortened and written as decimal numbers(they have been divided by1,000,000).Expand each of the values:0.5 1,000,000 500,0000.6 1,000,000 600,0000.7 1,000,000 700,0000.8 1,000,000 800,000

The years lie along the x-axis(horizontal axis) and are in increments of 1 year.Matching year number 9 and finding the data plan falls between 0.7 and 0.8the estimation is 0.75.0.75 1,000,000 750,0005. B 1.2 4 1.2 Negative slope: line heads up into Quadrant II and down into Quadrant IV.Line R shows negative slope6. BFind the volume of the pool. % ℎ ' ( ) ℎ ' ℎ %ℎ *50-*20-*10 10,000 / 0Convert from feet to meters: use the given ratio (3.3ft 1 m) and a proportion.3.3 / 10,000 / 1 Cross multiply and solve for x.10,000(1) 3.3x10,000 3.3 x3,030 0 3,000 0 (approximate)7. DThe pool is in the shape of a rectangle.Formula for the area of a rectangle is 2 ( .Method #1: Whole Area