SAT数学考试问答题
1.145 3006101230
In theabove sequence every term after thefirstis formedbymultiplyingby xand then addingy,where x andyarepositive integers. Whatis thevalue of x+y?
2.A confectioner has 500 mint,500 orangeand500strawberryflavored sweets. Hewishes to make packets containing 10mint,5orange and 5 strawberrysweets. What is the maximum number ofpackets of this typehecanmake?
3.IfSisthesum of 8,6,4,2 and x,what must bethevalueofxfor xto equal 1/5S ?
4.25per cent of 600is equal to 15per cent ofwhat number?
5.What is themaximum number ofpoints of intersection offour distinctlines ina plane?
6.Ifone edgeof a 6-inch ruleris to bemarkedin 1/10 inch units,howmanymarkswilltherebeon the edge includingthe0 and 6 inch marks?
7.If thearea of therighttriangleaboveis 72, what is thevalueof x?
8.Giventhatthesum of theodd integers from 1 to 99 inclusive is 2500,whatisthesum of theeven integers from 2 to 100inclusive?
9.In a certain gameof 50questions, thefinal score is calculated bysubtracting twice thenumber of wronganswersfromthetotalnumberofcorrectanswers.Ifaplayerattemptedallquestionsandreceived a finalscore of35,howmanywrong answersdidhegive?
10.Family1 comprising mother, father andsonareto be seated ata table with family2 comprising mother, father anddaughter. Thelayout of the table is showninthediagram. Frepresentsone ofthe fathersandMrepresents oneofthemothers.Xrepresentsanyfamilymemberbutwiththeconditionthat a malefamilymember must sit opposite afemale oftheother family.Howmanydifferent seatingplans arepossible?
参考答案:
1.CorrectAnswer:12
Explanation:
Look for a simple relation between thenumbers.Soifwe trymultiplyingby2, then 145becomes 290,to whichweneedtoadd10tomake300.(If wetriedmultiplyingby3thenumber wouldbetoolarge.Check with thethird term;doubling 300gives 600 andadding10 gives 610. So this is therelation, andx=2 , andy=10.x+y=12
2.CorrectAnswer:50
Explanation:
Since everypacket musthave10mints,this is thelimiting factor since themintswillbe usedupfirst.
500/10 gives thenumber ofsetsof mints = 50 packetscanbe made.
3.CorrectAnswer:5
Explanation:
Ifx=1/5 of thesum,then 8+ 6 +4 +2=4/5of thesum. So20=4/5 of S,and 20/4is1/5of S =5
4.CorrectAnswer:1000
Explanation:
Express inmath language
(25/100) x600=(15/100) n
25x(600/15) =n n =1000
5.CorrectAnswer:6
Explanation:
Two lines haveone point of intersection.A third linecan cut through theother two to give two newpoints of intersection. (Total =3).A fourth linecan cutthrough the other threegivingthree newpoints of intersection(Total 3 +3 =6)
6.CorrectAnswer:61
Explanation:
Therearesixtytenthstobemarked.Thiswillrequire61marks,because youwillneedamarkforzero.(If youstilldonotunderstand,drawoutarulerandcounthowmanymarksfortwoinches,whichwillbe20+
1).
7.CorrectAnswer:45
Explanation:
Areaof a triangle is ½basex height. ½xb x 12=72
Therefore base =12
This means this is anisosceles right triangleandx=45
8.CorrectAnswer:2550
Explanation:
Ifyouwrite out partof each series likethis
1,3,5,7...
2,4,6,8...
Youwillseethat everyterm in thesecondseries is onemore than thecorrespondingterm in thefirst series. Since there are 50 terms,thesecond sumwillbe 50more than thefirst=2500+50=2550
9.CorrectAnswer:5
Explanation:
Letthenumberofwronganswers =x
Right answers=50 - x
Subtracting twicewrong from rightwill give 35 (50- x) - 2x=35;50 - 3x=35
15=3x;5 =x
10.CorrectAnswer:16
Explanation:
AssumeFather1andMother2areseatedasshown.Nowselectoneoftheremainingfourpeopleforthe firstvacant seat. We canonlychoose oneof thetwo peoplefrom theother familyto sit opposite them (to ensure thatthe personis of the opposite sex).For theone vacantseat on thesamesideofthetablewe have achoice ofone out of two,and the finalpersonwillhaveto sit opposite. Sowith Father 1 and Mother 2seated firstwe havea totalof 4 x2x2 =16arrangements.