Pa st Examination Pape rs 2008 2009 2009 2010 84848484 2009 2010 學年 入學考試試題 ADMISSION EXAMINATION PAPER 第一部份第一部份第一部份第一部份 Part I Write your answers in the space provided for each question Answers written elsewhere will not be marked 將答題步驟及答案寫在每題所提供的空間內將答題步驟及答案寫在每題所提供的空間內將答題步驟及答案寫在每題所提供的空間內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 評分評分評分評分 Part I 1 a 3 marks Solve the following equation for x 3 分 對以下方程求解x xx 2122 b 3 marks Let 23 2 xxf For what values of x is xf a real number 3 分 設 23 2 xxf 求所有使 xf為實數 的 x 值 2 4 marks Express 1 1 25 2 2 xx xx as sum of partial fractions 4 分 將 1 1 25 2 2 xx xx 化為部分分式和 3 6 marks The following data show the selling prices of 9 models of mobile phones 6 分 以下數據所示為9款不同型號手提電話的售價 2 130 3 250 4 760 1 800 2 770 6 050 2 340 1 980 1 560 Find the a mean b median and c standard deviation of the set of data listed above 求該組數據的 a 平均數 b 中位數 c 標準差 4 The marked price of a television is 7 500 A customer may choose one of the following three methods of payment 一部電視機的標價是 7 500 有三種付款方法可供顧客選擇 Syllabu s 2010 2011 85858585 Method 1 Pay by one single payment with a 5 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 Method 2 First pay 20 of the marked price as initial payment Then pay the remainder together with a 7 simple interest by 12 monthly equal installments 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 Method 3 At first no initial payment is needed Afterwards pay the marked price together with an 8 simple interest by 12 monthly equal installments 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 4 marks What is the percentage increase of the total amount paid by using Method 2 instead of Method 1 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 4 marks What is the difference between the amount of a monthly installment when using Method 2 and that when using Method 3 4 分 方法二和方法三每月支付的分期款項相差多少 5 A squad of soldiers are marching from a barracks to a mountain area They carry a load of 4 800 kg and it is shared equally by all soldiers In the middle of the journey 22 soldiers left and brought away 320 kg of load The rest of the soldiers continue their journey and the load carried by each remaining soldier now is 3 kg heavier than before 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4 800 kg 在途中 22人離開大隊並帶走共重320 kg 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3 kg a 4 marks Let the number of soldiers setting out from the barracks be x In the context of this question establish a quadratic equation of x 4 分 設該隊軍人由軍營出發時有x人 根據題意 試設立一條有關 x 的二次方程式 b 4 marks After 22 soldiers have left how many soldiers remain in the squad What is the load that each remaining soldier must carry 4 分 當22人在途中離隊後 還剩下軍人多少名 餘下各人所攜物資 有多重 6 Box A contains 1 black ball and 3 white balls Box B contains 3 black balls and 2 white balls A ball is drawn out at random from A and put into B Then a ball is drawn out at random from B Find the probabilities of the following Pa st Examination Pape rs 2008 2009 2009 2010 86868686 events A盒載有一個黑球和三個白球 B盒載有三個黑球和兩個白球 若從A 盒中隨機抽取一球放入B盒內 然後又從B盒內隨機抽取一球 求以下 事件的概率 a 4 marks both balls drawn out are white in color 4 分 抽出的兩個球皆為白色 b 4 marks the second ball drawn out is white in color 4 分 第二個抽出的球為白色 第二部份第二部份第二部份第二部份 Part II This part contains 20 multiple choice questions Please select the desired answers on the pink answer sheet appeared on the last page of Part I Please follow the instruction given on that page 本部份有本部份有本部份有本部份有20條選擇題條選擇題條選擇題條選擇題 請在本試卷第一部份請在本試卷第一部份請在本試卷第一部份請在本試卷第一部份尾尾尾尾頁的頁的頁的頁的粉紅色粉紅色粉紅色粉紅色答案紙答案紙答案紙答案紙上上上上選擇答選擇答選擇答選擇答 案案案案 請依照該頁內的指示填寫答案請依照該頁內的指示填寫答案請依照該頁內的指示填寫答案請依照該頁內的指示填寫答案 1 If x x xf 1 1 then a faf 1 若 x x xf 1 1 則 a faf 1 A 0 B 1 C a 1 2 D a a 1 2 E a a 1 4 2 If the equation 052 2 kxx has no real roots find the range of the values of k 若方程 052 2 kxx 沒有實根 求k值的範圍 A 8 25 k Syllabu s 2010 2011 87878787 B 8 25 k D 8 25 k E 8 25 k 3 If 1 axx and bx 2 2 are identical find a and b 若 1 axx 與bx 2 2 相同 求a 及b A a 2 and b 0 a 2 及b 0 B a 3 and b 1 a 3 及 b 1 C a 3 and b 0 a 3 及 b 0 D a 3 and b 1 a 3 及 b 1 E a 3 and b 1 a 3 及 b 1 4 The figure below shows the graph of cbxaxy 2 The coordinates of the vertex are 3 5 With reference to the figure below which of the following must be correct 下圖所示為cbxaxy 2 的圖像 其頂點的坐標是 3 5 參看下圖 以下何者必為正確 I The y intercept of the graph 0 圖像的y軸截距 0 II 04 2 acb III The equation of the axis of symmetry of the graph is x 3 o x y 3 5 cbxaxy 2 Pa st Examination Pape rs 2008 2009 2009 2010 88888888 圖像的對稱軸的方程是x 3 A II only 只有II B I and II only 只有I及II C I and III only 只有I及III D II and III only 只有II及III E I II and III I II及III 5 What is the sum of all the different five digit integers formed by using the digits 1 2 3 5 9 without repetition 用1 2 3 5 9 組成數位不同的所有五位數總和為多少 A 5 333 280 B 4 666 640 C 3 999 960 D 3 555 520 E 2 666 640 6 Mr Chan has deposited a sum in a bank The interest rate is 6 per annum compounded monthly If the interest is 5 720 after 2 years find the original sum 陳先生把一筆款項存入銀行 年利率為6 每月計算複利息一次 若 兩年後他可得利息 5 720 求原來那筆存款 A 44 983 B 45 220 C 45 574 D 46 278 E 48 200 7 If a is greater than b by 20 and a is grea