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Past Examination Papers 2010/2011, 2011/2012 92 2011/2012 學年 入學考試試題 ADMISSION EXAMINATION PAPER 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，寫在該空間以外的答案會被評 分。 1. Solve each of the following equations for x: 對以下方程求解 x： a. (3 marks) (3 分 ) 0103 2 xx ee ； b. (3 marks) (3 分 ) 0logloglog 235 x . 2. (4 marks) Find integers a and b such that 22611 ba . (4 分 ) 求整 a 和 b 使 22611 ba 。 3. Let 7 1 and 0 r rr . Find the exact values of the following, and express your answer in its simplest form. 設 0r 及 7 1 r r 。 求以下的真確值，並把答案化至最簡。 a. (3 marks) (3 分 ) 3 3 1 r r ； b. (2 marks) (2 分 ) 6 6 1 r r . Syllabus 2012/2013 93 4. The total cost of producing a certain brand of watches ($C) is the sum of two parts. One part is constant while the other part varies directly as the number of watches produced (n). When 100 watches are produced, the average cost per watch is $24. When the number of watches produced increases to 300, the average cost per watch can be reduced to $14. 製造某牌子手錶的總成本 ($C) 是部 份 之和。一部 份 是常，而另一部 份 隨手錶生產的目 (n) 正變。當製造 100 隻手錶時，每隻手錶的平均成本是 $24。當製造的手錶目 增加至 300 隻時，每隻手錶的平均成本 減至 $14。 a. (3 marks) Find C in terms of n. (3 分 ) 以 n 表示 C。 b. (3 marks) Suppose an economic crisis has only caused the constant part of the total production cost to be increased by 20%, the other part remains the same as originally formulated. Will the average cost per watch increase by more than 20%, less than 20%, or exactly 20%? Explain your answer. (3 分 ) 設一次經濟危機只會生產總成本的常部份增加 20%，而 餘下部份則和之前的相同 。 問每隻手錶的平均成本增加會大於、等於、 或是小於 20%？ 解釋你的答案 。 5. In a regular n-sided polygon, let each interior angle and each exterior angle measure x and y respectively. 在某正 n 邊形內，設每隻內角及每隻外角的大小分別為 x 和 y 。 a. (2 marks) Write down the values of x and y in terms of n. (2 分 ) 寫下 x 和 y 的值，答案以 n 表示。 b. (3 marks) If each interior angle is 4 times as large as each exterior angle, find the number of sides of the polygon. (3 分 ) 每隻內角是每隻外角的 4 倍，求正多邊形的邊。 6. In a quiz there are three multiple choice questions, each with four possible answers, exactly one of which is correct. Students can pass the test if they answer at least two questions correctly. Carmen has studied 70% of the materials, so there is a probability of 70% that she knows that question. If she knows a question, the probability that she makes a careless mistake is 10%. If she doesnt know a question, she will guess an answer randomly. Past Examination Papers 2010/2011, 2011/2012 94 某次小測共設三道選擇題，每題有四個選擇，只有一個選擇正確，答對最 少題方可合格。嘉敏温習測驗範圍的 70%，所以她懂得作答一道題的 概是 70%。她懂得作答，她大意犯錯的概是 10%。她懂得作答， 她會隨意選擇一個答 案。 a. (2 marks) Find the probability that Carmen answers a given question correctly. (2 分 ) 求嘉敏答對某一道題的概。 b. (4 marks) Find the probability that Carmen passes the quiz. (4 分 ) 求嘉敏在測驗中及格的概。 7. In the figure below, L 1 is a straight line with x-intercept 4 and y-intercept 2 . L 2 has y-intercept 10 and is perpendicular to L 1 . L 3 is a vertical line with x-intercept 1 . 在以下圖中， L 1 是一條 x 截距為 4、 y 截距為 2 的直線；而 L 2 的 y 截 距為 10，且與 L 1 互相垂直。 L 3 是一 條 x 截距為 1 的垂直線。 a. (2 marks) Find the equation of L 1 . (2 分 ) 求 L 1 的方程。 b. (2 marks) Find the equation of L 2 . (2 分 ) 求 L 2 的方程。 c. (4 marks) Hence or otherwise, find the area of the region bounded by the lines L 1 , L 2 and L 3 . (4 分 ) 由此，或以其他方法，求直線 L 1 、 L 2 和 L 3 所圍成的面 積。 Syllabus 2012/2013 95 第二部份 Part II This part contains 20 multiple choice questions. Please select the desired answers on the answer sheet appeared on the last page of Part I. Please follow the instruction given on that page. 本部份有 20 條選擇題，請在本試卷第一部份尾頁的答案紙上選擇答案。請依照 該頁內的指示填寫答案。 1. If xxf 32)( and 32)( xxg , find )(xgf . xxf 32)( 、 32)( xxg ，求 )(xgf 。 A. 76 x B. 76 x C. 76 x D. 116 x E. 116 x 2. Let f(x) be a polynomial in x. When )1( xf is divided by 2x 3, the remainder is 設 f(x) 為 x 的多項式。當 )1( xf 除以 2x 3 時，餘是 A. 2 3 f B. 2 1 f C. 2 1 f D. 2 3 f E. 2 5 f 3. The running speeds of three people A, B and C are in the ratio x : y : z . The times taken by them to complete a 1000 m race are in the ratio A、 B 和 C 三人跑步的速之比是 x : y : z。那麼他們完成 1000 m 賽跑所 需的時間之比是 A. x : y : z B. z : y : x C. zyx 1 : 1 : 1 D. xyz 1 : 1 : 1 E. None of the above 以上皆是 Past Examination Papers 2010/2011, 2011/2012 96 4. What will the original principal $P amount to in two years time if interest is compounded monthly at 12% per annum? 複息每月計算一次，且為 12%，本 $P 在後的本和是 多少？ A. 2 %)121($ P B. 24 %)121($ P C. 2 %)11($ P D. 24 %)11($ P E. 4 %)61($ P 5. The marked price of a toy is $180. If the toy is sold at a discount of 20%, the profit percentage will be 20%. What is the cost of one toy? 某件玩具的標價是 $180。玩具以 20%的折扣售出，則盈百份是 20%。 每件玩具的成本價是多少？ A. $115.2 B. $120 C. $125 D. $160 E. $180 6. The total height of four people A, B, C, D is 644 cm. A is the tallest, D is the shortest and the difference in height between A and D is 22 cm. The height difference between A and B is the same as difference between C and D. Find the height of A. A、 B、 C、 D 四人的總高為 644 厘米。 A 為最高， D 是最矮。 A 和 D 高 的差是 22 厘米。 A 和 B 高的差與 C 和 D 之間的差相同。求 A 的高。 A. 178 cm 厘米 B. 176 cm 厘米 C. 174 cm 厘米 D. 172 cm 厘米 E. 170 cm 厘米 7. Suppose that x varies directly as y and 2 z . Find the percentage change in x when y is increased by 10% and z is decreased by 10%. 假設 x 隨 y 和 2 z 正變。當 y 增加 10%， z 減少 10%時，求 x 改變的百份。 A. %9.10 B. %1 C. 0% D. +4.2% E. +8.9% Syllabus 2012/2013 97 8. Which of the following is/are geometric sequence(s)? 以下那項是等比 ? I. , 357 xxxx II. ,630sin,450sin,270sin,90sin III. 1, 1.1, 1.11, 1.111, A. I only 只有 I B. III only 只有 III C. I and II only 只有 I 和 II D. II and III only 只有 II 和 III E. I, II and III I、 II 和 III 9. If the point (1, 2 ) is rotated 90 about the origin in the clockwise direction to the point P, write down the coordinates of P. 點 (1, 2 ) 以原點為旋轉中心，依順時鐘方向旋轉 90至點 P，寫出點 P 的座標。 A. ( 2 , 1 ) B. ( 2 , 1) C. (2, 1 ) D. (2, 1) E. None of the above 以上皆是 10. Find the median of the following five numbers: 求以下五個的中位 : 4 2 x , 7 2 x , 4 2 x , 2 2 x , 2 x A. 0 B. 4 2 x C. 1 2 x D. 4 2 x E. 2 x Past Examination Papers 2010/2011, 2011/2012 98 O x D C A B 11. In the figure, a circle with radius r and centre O rests on the ground. D is a point on the circle such that xCOD . Find the height of D above the ground AB. 圖中，一個半徑為 r、圓心為 O 的圓與地面相。 D 是圓上一點使得 xCOD 。求 D 和地面 AB 的距。 A. )sin1( xr B. )sin1( xr C. )tan1( xr D. )cos1( xr E. )cos1( xr 12. A sequence has general term 3n + 3 ) ,3 ,2 ,1( n . Which of the following is/are true? 某的通項是 3n + 3 ) ,3 ,2 ,1( n 。以下那項是正確的？ I. Every term of the sequence is divisible by 3. 的每項皆可被 3 整除。 II. Every term of the sequence is positive. 的每項皆是正。 III. The 1000 th term of the sequence is greater than 1000. 的第 1000 項大於 1000。 A. I only 只有 I B. I and II only 只有 I 和 II C. I and III only 只有 I 和 III D. II and III only 只有 II 和 III E. I, II and III I、 II 和 III Syllabus 2012/2013 99 13. The rectangular block as shown below has base dimension 8 cm by 16 cm, and a surface area of 496 2 cm . What is the volume of the block? 以下圖中長方體的底部尺寸為 8 公分乘 16 公分，表面積為 496 平方公分。 它的體積是多少？ A. 12800 3 cm 方公分 B. 2560 3 cm 方公分 C. 1280 3 cm 方公分 D. 640 3 cm 方公分 E. 512 3 cm 方公分 14. There are three types of weights, , and . These are put on the scale as shown in Figures 1 and 2 to have balanced weights. How many need to be placed in the right tray to have balance in Figure 3? 有三種砝碼 ， 和 ，把適當的砝 碼放在天秤上會使秤平衡，如圖 1 及 2 所示。在圖 3 右面的秤內需放置多少個 才會達至平衡？ A. 12 B. 10 C. 8 D. 6 E. 4 15. A group of n numbers has mean m. If the numbers 1 , 4, 12 are removed from the group, the mean of the remaining n 3 numbers remains unchanged. Find the value of m. 一組 n 個的平均是 m。從這組據移走 1 、 4、 12 三項，餘下的 n 3 個的平均變。求 m 的值。 A. 2 B. 3 C. 4 D. 5 E. 6 Past Examination Papers 2010/2011, 2011/2012 100 16. If M and N are both positive integers, which of the following equations have solutions? M 和 N 都是正整，下面那一個方程式有解 ? I. 22 14123 NM II. 22 40000 NM III. 22 75643 NM A. I only 只有 I B. II only 只有 II C. III only 只有 III D. I and II only 只有 I 和 II E. II and III only 只有 II 和 III 17. 1 2 x y y x x y y x A. yx yx B. yx yx C. 2 22 yx yx D. 2 22 yx yx E. 22 2 yx yx 18. If the simultaneous equations (with unknowns x, y) 方程 (x、 y 未知) 2 2 xy hxxy have only one solution, find the value of h. 只有一個解，求 h 的值。 A. 3 B. 1 C. 1 D. 3 E. 5 Syllabus 2012/2013 101 19. If is in Quadrant II, then cos may be equal to 位於第二象限，那麼 cos 可能等於 I. 0.7 II. 8.0 III. 1.1 A. I only 只有 I B. II only 只有 II C. I and II only 只有 I 和 II D. II and III only 只有 II 和 III E. I, II and III I、 II 和 III 20. All of the following circles have the same centre except 以下除一項外，各圓的圓心皆相同。外的一項是 A. 0173 22 yxyx B. 01073 22 yxyx C. 0173 22 yxyx D. 0497126541818 22 yxyx E. 0114622 22 yxyx Past Examination Papers 2010/2011, 2011/2012 102 2011/2012 學年 參考答案 MODEL ANSWER Part I 1. a. ,020)2)(5(103 2 xxxxx eeeee or 05 x e . The first equation leads to the root .6931.02ln x There is only one real root. Candidates will also receive full credit if complex roots are given. b. 823log1)(loglog0)(logloglog 3 223235 xxxx . 2. 222)2(2611 222 abbaba . Equating terms leads to 3 112 22 ab ba . (*) By elimination it was found that there are four values of b satisfying (*), namely, 1, 2/3 and ,2/3 ,1 . However, since both a and b are integers, and 3ab , so b is either 1 or 1 . It cannot be 1 , otherwise 3a , contradicting 022611 ba . Thus 3 and ,1 ab . 3. a. 747377 1 37 1 3 1 3 11 3 2 2 3 3 3 r r r r r r r r r r . b. 1102742 11 2 11 2 2 3 3 3 3 2 3 3 6 6 r r r r r r r r . 4. a. Let nyxC , where x and y are constants. When 100n , 240010024 C , so that 2400100 yx . (1) When 300n , 420030014 C , so that 4200300 yx . (2) Solving (1) and (2), we found that 1500a , and 9b . Thus nC 91500 . Syllabus 2012/2013 103 4. b. The average costs per watch before and after the crisis are n n91500 , and n n9%)201(1500 , respectively. Thus, the average costs per watch is increased by n %)20(1500 , and the corresponding percentage change is %20 91500 %)20(1500 91500 %)20(1500 n n n n . Hence the overall percentage increase is less than 20%. 5. a. n n x )2(180 , n xy 360 180 . b. 10 360 4 )2(180 4 n nn n yx . So there are ten sides. 6. a. There are two scenarios under which Carmen may answer a particular question correctly: (i) she has studied the materials, and doesnt make careless mistake; she hasnt studied the materials related to that question, and guessed the answer correctly. The required probability is 705.0)25.0()7.01()1.01()7.0( . b. Carmen passes the quiz if she answers either two or three questions correctly. The required probability is 7902.0)705.01()705.0( 1 3 )705.0( 23 . 7. a. As 1 L passes through the two points )2,0( and )0 ,4( , its slope is 2 1 04 )2(0 . The equation of 1 L is )4( 2 1 0 xy , or 2 2 x y . b. Slope of 2 2/1 1 2 L . As it passes through the point )01 ,0( , its equation is )0(210 xy , or 102 xy . c. It was found that 1 L and 2 L meet at ) 5 2 , 5 24 (A , 1 L and 3 L meet at ) 2 5 ,1( B , and 2 L and 3 L meet at )21 ,1(C . The base of the right-angled triangular region bounded by these three lines has base equal to 2 29 2 5 12 BC . The height is 5 29 1 5 24 . Therefore the area of Past Examination Papers 2010/2011, 2011/2012 104 the triangular region is 05.42 20 841 5 29 2 29 2 1 . Part II 1. A 2. E 3. C 4. D 5. B 6. D 7. A 8. C 9. A 10. E 11. D 12. E 13. D 14. B 15. D 16. B 17. B 18. A 19. B 20. C Syllabus 2012/2013 105 2010/2011 學年 入學考試試題 ADMISSION EXAMINATION PAPER 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，寫在該空間以外的答案會被評 分。 Part I 1. A straight line 2 L passes through the origin and is perpendicular to another straight line 042: 1 yxL . 1 L and 2 L intersect at point A. 一直線 2 L 穿過原點，且和另一直線 042: 1 yxL 互相垂直。 1 L 和 2 L 相交 於點 A。 a. (2 marks) Find the slope of 2 L . (2 分 ) 求 2 L 的斜。 b. (2 marks) Find the coordinates of point A. (2 分 ) 求點 A 的坐標。 2. a. (2 marks) Express )cot( BA in terms of cot(A) and cot(B). (2 分 ) 以 cot(A) 及 cot(B) 表示 cot(A+B) 。 Hint 提示 : BA BA BA tantan1 tantan )tan( b. (3 marks) If and are acute angles such that 45 , find and simplify )cot1)(cot1( . (3 分 ) 及 均為銳角且 45 ，求 )cot1)(cot1( 並化至 最簡。 Past Examination Papers 2010/2011, 2011/2012 106 3. The marked price of a digital camera is $8,450. If it is sold at the marked price, the percentage profit is 30%. 一部碼相機的標價是 $8,450。以標價售出，可獲得 30%的盈。 a. (3 marks) Find the cost of the digital camera. (3 分 ) 求該碼相機的成本。 b. (3 marks) If the digital camera is sold at 10% discount, find the percentage profit then. (3 分 ) 以 10%的折扣百分出售該碼相機，求此時的盈百分 。 4. Mr. Lei works in an electronic company. His total monthly income ($I) is the sum of the basic salary and the bonus. The former is constant while the latter varies directly as the profit of the company ($V) in the particular month. When V = 100,000, I = 7,000. When V = 200,000, I = 8,000. 先生在一間電子公司工作。他的總月薪 ($I)是底薪和花紅之和。前者是常 ，而後者隨公司的每月盈 ($V)正變。當 V = 100,000 時， I = 7,000；當 V = 200,000 時， I = 8,000。 a. (3 marks) Find I in terms of V. (3 分 ) 以 V 表示 I。 b. (3 marks) In a certain month, the bonus constitutes 40% of Mr. Leis total income. Find the profit of the company in that month. (3 分 ) 先生在某個月的花紅佔他的總月薪 40%。求該月份公司的盈 。 Syllabus 2012/2013 107 5. When 6013)( 23 bxxaxxf is divided by 5143 2 xx , the remainder is 357 x . 當 6013)( 23 bxxaxxf 除以 5143 2 xx 時，餘式是 357 x 。 a. (4 marks) Find a and b. (4 分 ) 求 a 及 b。 b. (2 marks) Factorize f(x). (2 分 ) 因式分解 f(x)。 6. (6 marks) The average monthly salary of a factorys workers would have increased by $1,000 either if three additional workers each of $18,000 monthly salary had recruited, or if three workers, each of $12,000 monthly salary had been sacked. What was the original number of workers in the factory? (6 分 ) 額外招請三名月薪各 $18,000 的新工人，或解雇三名月薪各 $12,000 的工人，某工廠僱員的平均月薪會增加 $1,000。問工廠原有僱員 多少人？ 7. Jenny will have a Mathematics test in this week. If she passes, she will go to a movie or a concert, or buy a new dress, and these choices have equal chances. If she fails, she will join a reading group or buy a set of reference books, and these two choices also have equal chances. The table below shows the expenses for her choices. Test Result Choice Expense Movie $80 Concert $250 Passed New Dress $120 Reading group Free of charge Failed Reference books $150 The probability that Jenny passes the Mathematics test is 5 4 . 珍妮 在本週將有一個學科測驗。成績及格，她會去看一齣電影或一場演 唱會或購買一套新裙子，各項選擇的機會均等。但成績及格，她會加 一個書小組或購買一套考書，這項選擇的機會亦是均等的。下表顯示 她各項選擇所需的費用。 Past Examination Papers 2010/2011, 2011/2012 108 測驗成績 選擇 費用 電影 $80 演唱會 $250 及格 新裙子 $120 書小組 免費 及格 考書 $150 珍妮 在該學科測驗成績及格的概是 5 4 。 a. (2 marks) Find the probability that Jenny buys a new dress. (2 分 ) 求珍妮 會購買一套新裙子的概。 b. (5 marks) Find the probability that Jenny spends no more than $140. (5 分 ) 求 珍妮 用多於$140 的概。 第二部份 Part II This part contains 20 multiple choice questions. Please select the desired answers on the answer sheet appeared on the last page of Part I. Please follow the instruction given on that page. 本部份有 20 條選擇題，請在本試卷第一部份尾頁的答案紙上選擇答案。請依照 該頁內的指示填寫答案。 1. If x xxf 1 )( , then a b f b a f x xxf 1 )( ，則 a b f b a f A. 0 B. a b2 C. b a2 Syllabus 2012/2013 109 D. a b b a 22 E. a b b a 22 2. The axis of symmetry of the parabola 76 2 xxy is 拋物線 76 2 xxy 的對稱軸是 A. x = 3 B. x = 3 C. y = 2 D. y = 2 E. y = 7 3. If log x denotes x 10 log , and ax )5log( 2 , then 4 4 log x log x 表示 x 10 log , 且 ax )5log( 2 ，則 4 4 log x A. a2 B. a22 C. 2 2 a D. 2 4 a E. a24 4. Two sides of a triangle have lengths 5 and 8. The third side may have length 某三角形的條邊的長為 5和 8。 第三條邊的長可能是 I. 3 II. 8 III. 12 A. I only 只有 I B. II only 只有 II C. I and III only 只有 I 和 III D. II and III only 只有 II 和 III E. I, II and III I、 II 和 III Past Examination Papers 2010/2011, 2011/2012 110 5. Which of the following is/are identity/identities? 以下那項是恆等式？ I. xx 22 sin1cos II. 044 2 xx III. 22 )1(1 xx A. I only 只有 I B. III only 只有 III C. I and II only 只有 I 和 II D. I and III only 只有 I 和 III E. I, II and III I、 II 和 III 6. Given distinct positive real numbers x, y and z such that 給定 同的正實 x、 y 及 z 使 z yx x zy y zx , which of the following is true? 下面那一項正確？ A. zyx B. yzx C. zxy D. xzy E. yxz 7. In an n-sided polygon, one interior angle is x and the sum of the other (n 1) interior angles is 2006 . Find n. 在某 n 邊 形中，其中一隻內角是 x ，而餘下 (n 1)隻內角的和是 2006 。求 n。 A. 12 B. 12 or 13 12 或 13 C. 14 D. 14 or 15 14 或 15 E. 16 Syllabus 2012/2013 111 8. In the sequence 8, ,5 ,3 ,2 ,1 ,1 ,0 , , , , dcba each term is the sum of the previous two terms to its left. Find a. 8, ,5 ,3 ,2 ,1 ,1 ,0 , , , , dcba 的每一項為其左面前項之和。求 a。 A. 0 B. 1 C. 3 D. 1 E. 3 9. At the start of 2004, John invested $500 in a fund that doubles every seven years. If interests are compounded continuously, in what year will he have $1,200 in his account? 由 2004 頭開始，約翰 在某基投資 $500。此基每七翻一翻。 息以續複計算，他的户口在何將會有 $1,200？ A. 2010 B. 2011 C. 2012 D. 2013 E. 2014 10. If x is a real number, the value of 942 2 xx is x 是實， 942 2 xx 的值 A. at least 5 最小是 5 B. at most 5 最大是 5 C. at least 7 最小是 7 D. at most 7 最大是 7 E. at least 9 最小是 9 Past Examination Papers 2010/2011, 2011/2012 112 11. Let cbxaxxf 2 )( , where a, b, c are constants. If the equation 0)( xf has a positive real root and a negative real root, which of the following must be true? 設 cbxaxxf 2 )( ，其中 a、 b、 c 是常。方程 0)( xf 有一個正實根 和一個負實根，以下那項必定是正確的？ I. 0a II. 0c III. acb 4 2 A. II only 只有 II B. III only 只有 III C. I and III only 只有 I 和 III D. II and III only 只有 II 和 III E. I, II and III I、 II 和 III 12. In the figure below, AB is a straight line and P is a point on AB. If the coordinates of P are (0, c), find the value of c. 在以下圖中， AB 是直線，而 P 是 AB 上的一點。 P 的坐標是 (0, c)，求 c 的值。 A. 4 B. 2 C. 0 D. 2 E. 4 A(-2, -6) P(0, c) B(4, 6) Syllabus 2012/2013 113 13. If the graph of 3)1(2 2 xy is translated upward by 1 unit and then leftward by 2 units, find the equation of the new graph. 把 3)1(2 2 xy 的圖像向上平移 1 單位，然後向左平移 2 單位，那麼新 的圖像的方程是 A. 4)1(2 2 xy B. 1)2(2 2 xy C. 2)3(2 2 xy D. 4)3(2 2 xy E. 4)1(2 2 xy 14. If the sum to infinity of the series . 32 kkk is 2 1 , find k. 序 . 32 kkk 的無限項之和是 2 1 ，求 k。 A. No solution 無解 B. 3 1 C. 2 1 D. 2 1 or 1 2 1 或 1 E. 3 1 or 1 3 1 或 1 15. Given that ( 2 , 2), (4, 2) and )5 ,3( are three points on a circle. The radius of that circle is 已知 (2 , 2)、 (4, 2) 及 )5 ,3( 為一圓上三點。圓的半徑為 A. 3 B. 10 C. 15 D. 4 E. 5 Past Examination Papers 2010/2011, 2011/2012 114 16. The top of a ladder A resting against a vertical wall is 24 feet above the ground. By moving the base of the ladder 8 feet farther out, the ladder slides down resting against the wall at a point A 20 feet above the ground. How long is the ladder? 有一把梯子倚着一道垂直的牆壁，梯子的頂部 A 地面 24 英尺。 把梯子 的底部再向外移 8 英尺，則梯子頂部向下至地面 20 英尺的點 A 。梯子 有多長？ A. 25 feet 英尺 B. 27 feet 英尺 C. 28 feet 英尺 D. 30 feet 英尺 E. 32 feet 英尺 17. Let )(xf and )(xg be polynomials. If )2()2( gf , then which of the following must be true? 設 )(xf 和 )(xg 為多項式。 )2()2( gf ，則以下那項必定正確？ I. )(xf and )(xg are both divisible by x 2 )(xf 和 )(xg 皆可被 x 2 整除 II. )()( xgxf is divisible by x 2 )()( xgxf 可被 x 2 整除 III. )()( xgxf is divisible by x 2 )()( xgxf 可被 x 2 整除 A. I only 只有 I B. II only 只有 II C. I and II only 只有 I 和 II D. I and III only 只有 I 和 III E. I, II and III I、 II 和 III Syllabus 2012/2013 115 18. In the given three by three sub-squares, the three entries in each row, column, or diagonal added up to the same number. The figure shows four of the entries. What is x? 在一個 33 格的正方形格子內，每一每一及每條對角線上三個字之和 都相等。圖中顯示其中四個字。 x 為多少？ A. 2 B. 6 C. 7 D. 8 E. 9 19. A line passing through the origin with slope m is tangent to the circle 02086 22 yxyx . Find m. 一條穿過原點，且斜為 m 的直線與圓 02086 22 yxyx 相。求 m。 A. 4 3 B. 2 1 C. 3 4 D. 2 1 or 2 11 2 1 或 2 11 E. 4 3 or 4 11 4 3 或 4 11 20. The mean and standard deviation of a set of data are m and s respectively. If all data in the set are multiplied by a positive constant k, then the new mean and standard deviation are respectively 一組據的平均和標準差分別為 m 和 s。把該組據全部乘以正常 k， 則新的平均和標準差分別是 A. 2 m and s 2 m 和 s B. km and sk km 和 sk C. km and ks km 和 ks D. km and sk 2 km 和 sk 2 E. 2 m and ks 2 m 和 ks x 7 10 3 Past Examination Papers 2010/2011, 2011/2012 116 2010/2011 學年 參考答案 MODEL ANSWER Part I 1. a. Slope of 1
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