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1、PastExaminationPapers2008/2009,2009/20102009/2010學年入學考試試題ADMISSIONEXAMINATIONPAPER第一部份PartIWriteyouranswersinthespaceprovidedforeachquestion.Answerswrittenelsewherewillnotbemarked.將答題步驟及答案寫在每題所提供的空間內,,寫在該空間以外的答案不會被,寫在該空間以外的答案不會被評分。PartI1.(a)(3marks)Solvethefollowingequationforx:(3分)對以下方程求
2、解x:2x+12−2=x2(b)(3marks)Letf(x)=3−x−2.Forwhatvaluesofxisf(x)arealnumber?2(3分)設f(x)=3−x−2。求所有使f(x)為實數的x值。2x+5x+22.(4marks)Expressassumofpartialfractions.2(x+1)(x+)12x+5x+2(4分)將化為部分分式和。2(x+1)(x+)13.(6marks)Thefollowingdatashowthesellingpricesof9modelsofmobilephones:(6分)以下數據所示為9款不同型號手提電話的售價:
3、$2,130$3,250$4,760$1,800$2,770$6,050$2,340$1,980$1,560Findthe(a)mean,(b)median,and(c)standarddeviationofthesetofdatalistedabove.求該組數據的(a)平均數,(b)中位數,(c)標準差。4.Themarkedpriceofatelevisionis$7,500.Acustomermaychooseoneofthefollowingthreemethodsofpayment:一部電視機的標價是$7,500,有三種付款方法可供顧客選擇﹕84Syllabu
4、s2010/2011Method1:Paybyonesinglepaymentwitha5%discount.方法一:以現金一次付清所有款項,可享標價的九五折優惠。Method2:First,pay20%ofthemarkedpriceasinitialpayment.Thenpaytheremaindertogetherwitha7%simpleinterestby12monthlyequalinstallments.方法二:先以現金支付標價的20%,餘額要另加7%單利息,可分12個月每月支付相同的款項清還。Method3:Atfirst,noinitialpaymen
5、tisneeded.Afterwards,paythemarkedpricetogetherwithan8%simpleinterestby12monthlyequalinstallments.方法三:開始時不用付款,所有欠款要另加8%單利息,可分12個月每月支付相同的款項清還。(a)(4marks)WhatisthepercentageincreaseofthetotalamountpaidbyusingMethod2insteadofMethod1?(4分)以方法二付款,比以方法一付款,所需款項增加的百份比是多少?(b)(4marks)Whatisthediffere
6、ncebetweentheamountofamonthlyinstallmentwhenusingMethod2andthatwhenusingMethod3?(4分)方法二和方法三每月支付的分期款項相差多少?5.Asquadofsoldiersaremarchingfromabarrackstoamountainarea.Theycarryaloadof4,800kganditissharedequallybyallsoldiers.Inthemiddleofthejourney,22soldiersleftandbroughtaway320kgofload.There
7、stofthesoldierscontinuetheirjourneyandtheloadcarriedbyeachremainingsoldiernowis3kgheavierthanbefore.一隊軍人奉召由軍營出發前往一個山區。每人背負相同重量的物資,全隊攜帶了4,800kg。在途中,22人離開大隊並帶走共重320kg的物資,其餘軍人繼續前往該山區,每人須背負的物資比出發時重了3kg。(a)(4marks)Letthenumberofsoldierssettingoutfromthebarracksbex.Inthec