澳门大学2011-2012入学考试数学B卷

P a s t E x a m i n a t i o n P a p e r s 2 0 1 0 / 2 0 1 1 , 2 0 1 1 / 2 0 1 2 S y l l a b u s 2 0 1 2 / 2 0 1 3

4. The total cost of producing a certain brand of watches ($C) is the sum of two

2011/2012 學年入學考試試題ADMISSION EXAMINATION PAPER 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) 是兩部份之和。一部份是常數，而另一部份

第一部份Part I 隨手錶生產的數目(n) 正變。當製造 100 隻手錶時，每隻手錶的平均成本是

$24。當製造的手錶數目增加至300 隻時，每隻手錶的平均成本減至$14。

Write your answers in the space provided for each question. Answers written a. (3 marks) Find C in terms of n.

elsewhere will not be marked. (3 分) 以 n 表示 C。

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評

分。 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

1. Solve each of the following equations for x: same as originally formulated. Will the average cost per watch increase by

對以下方程求解 x：more than 20%, less than 20%, or exactly 20%? Explain your answer.

(3 分) 設一次經濟危機只會令生產總成本的常數部份增加了 20%，而

a. (3 marks) (3 分) e2x 3e x 10 0 ；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。

b. (3 marks) (3 分) log log log 0

5 x .

3 2

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。

2. (4 marks) Find integers a and b such that 11 6 2 a b 2 .

(4 分) 求整數 a 和 b 使11 6 2 a b 2 。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,

1

3. Let r 0 and r 7 . Find the exact values of the following, and express

r

your answer in its simplest form.

1

設r 0 及r 7 。求以下的真確數值，並把答案化至最簡。

r

find the number of sides of the polygon.

(3 分) 若每隻內角是每隻外角的 4 倍，求正多邊形的邊數。

6. In a quiz there are three multiple choice questions, each with four possible

a. (3 marks) (3 分)

b. (2 marks) (2 分)

3 1

r ；

r

3

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

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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

少兩題方可合格。嘉敏温習了測驗範圍的70%，所以她懂得作答一道題的

第二部份Part II 概率是 70%。若她懂得作答，她大意犯錯的概率是 10%。若她不懂得作答，

她會隨意選擇一個答案。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

a. (2 marks) Find the probability that Carmen answers a given question given on that page.

correctly. 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

(2 分) 求嘉敏答對某一道題的概率。該頁內的指示填寫答案。

b. (4 marks) Find the probability that Carmen passes the quiz.

(4 分) 求嘉敏在測驗中及格的概率。 1. If f (x) 2 3x and g(x) 2x 3,f ind f g(x).

若 f (x) 2 3x、 g(x) 2x 3，求 f g(x)。

7. In the figure below, L1 is a straight line

with x-intercept 4 and y-intercept 2. A. 6x 7 B. 6x 7 C. 6x 7 D. 6x 11 E. 6x 11

L2 has y-intercept 10 and is

p erpendicular to L1. L3 is a vertical line

with x-intercept 1.

2. Let f(x) be a polynomial in x. When f (x 1) is divided by 2x – 3, the

在以下圖中，L1 是一條 x 截距為 4、y 截距為 2 的直線；而 L2 的 y 截remainder is

設 f(x) 為 x 的多項式。當 f (x 1) 除以 2x – 3 時，餘數是

距為 10，且與 L1 互相垂直。L3 是一條 x 截距為1的垂直線。

3 1

1

A. f

B. f

C. f

2

2 2

a. (2 marks) Find the equation of

L1.

(2 分) 求 L 的方程。

1

3

5

D. f

E. f

2

2

b. (2 marks) Find the equation of L2. 3. The running speeds of three people A, B and C are in the ratio x : y : z . The

(2 分) 求 L2 的方程。times taken by them to complete a 1000 m race are in the ratio

A、B 和C 三人跑步的速度之比是x : y : z。那麼他們完成 1000 m 賽跑所c. (4 marks) Hence or otherwise, find the area of the region bounded by the 需的時間之比是

lines L, L and L.

94 95

4. What will the original principal $P amount to in two years’ time if interest is 8. Which of the following is/are geometric sequence(s)?

compounded monthly at 12% per annum? 以下那項是等比數列?

若複利息每月計算一次，且年利率為12%，本金$P 在兩年後的本利和是

多少？

A. $P(112%)

B. $P(112%)

C. $P(11%) 2 24 2 I. x7 , x5 , x3 , x, …

II. sin90,sin 270,sin 450,sin 630, …

I II. 1, 1.1, 1.11, 1.111, …

D. $P(11%)24

E. $P(16%)4 A. I only 只有I

B. III only 只有III

C. I and II only 只有I 和II

5. The marked price of a toy is $180. If the toy is sold at a discount of 20%, the D. II and III only 只有II 和III

profit percentage will be 20%. What is the cost of one toy? E. I, II and III I、II 和III

某件玩具的標價是$180。若玩具以20%的折扣售出，則盈利百份率是20%。

每件玩具的成本價是多少？

9. If the point (1, 2)i s rotated 90° about the origin in the clockwise direction to

A. $115.2

B. $120

C. $125 the point P, write down the coordinates of P.

D. $160

E. $180 若點(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。

6. The total height of four people A, B, C, D is 644 cm. A is the tallest, D is the A. (2,1) B. (2,1) C. (2, 1)

shortest and the difference in height between A and D is 22 cm. The height D. (2, 1) E. None of the above 以上皆不是

difference between A and B is the same as difference between C and D. Find the

height of A.

A、B、C、D 四人的總高度為644 厘米。A 為最高，D 是最矮。A 和D 高10. Find the median of the following five numbers:

度的差異是22 厘米。A 和B 高度的差異與C 和D 之間的差異相同。求A 求以下五個數的中位數:

的高度。

x 2 4,x 2 7,x 2 4, x 2 2,x 2

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 A. 0 B. x 2 4 C. x 2 1

D. x 2 4

E. x 2

7. Suppose that x varies directly as y and z2 . Find the percentage change in x

when y is increased by 10% and z is decreased by 10%.

假設x 隨y 和z2 正變。當y 增加10%，z 減少10%時，求x 改變的百份率。

A. 10.9%

B. 1%

C. 0%

D. +4.2%

E. +8.9%

11. In the figure, a circle with radius r and centre O rests on the ground. D is a point 13. The rectangular block as shown below has base dimension 8 cm by 16 cm, and

on the circle such that COD x. Find the height of D above the ground AB. a surface area of 496cm2 . What is the volume of the block?

圖中，一個半徑為r、圓心為O的圓與地面相切。D是圓上一點使得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。

COD x。求D和地面AB的距離。

它的體積是多少？

O

A. 12800 cm3 立方公分

B. 2560 cm3 立方公分x

D C. 1280 cm3 立方公分 D. 640 cm3 立方公分E. 512 cm3 立方公分

A B

C

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 A. r(1sin x)

B. r(1sin x)

C. r(1tan x)

placed in the right tray to have balance in Figure 3?

D. r(1cos x)

E. r(1cos x)

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？

12. A sequence has general term 3n+ 3 (n1,2, 3,).W hich of the following

is/are true?

某數列的通項是3n+ 3 (n1,2, 3,)。以下那項是正確的？A. 12

B. 10

I. Every term of the sequence is divisible by 3. C. 8

數列的每項皆可被3 整除。 D. 6

II. Every term of the sequence is positive. E. 4

數列的每項皆是正數。

III. The 1000th term of the sequence is greater than 1000.

數列的第1000 項大於1000。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

A. I only 只有I

B. I and II only 只有I 和II the value of m.

一組n個數的平均數是m。若從這組數據移走1、4、12 三項，餘下的

C. I and III only 只有I 和III n– 3 個數的平均數不變。求m的值。

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16. If M and N are both positive integers, which of the following equations have

solutions? 19. If is in Quadrant II, then cos may be equal to

若位於第二象限，那麼cos可能等於

若 M 和 N 都是正整數，下面那一個方程式有解? I. 0.7

I. 14123 M 2 N 2II. 0.8

II. 40000 M 2 N 2 III. 1.1

III. 75643 M 2 N 2

A. I only 只有 I

A. I only 只有 I

B. II only 只有 II B. II only 只有 II

C. III only 只有 III

D. I and II only 只有I 和II C. I and II only 只有 I 和II

E. II and III only 只有II 和III D. II and III only 只有 II 和III

E. I, II and III I、II 和III

1

x y

2

y x

17.

x y

y x 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。例外的一項是

A. x y 3x 7y 1 0 2 2

A.

x

x y

y

B.

x

x

y

y

C.

x

2

x

y

2

y

2

B. x 2 y 2 3x 7y 10 0

C. x 2 y 2 3x 7y 1 0

D. x

2

x

y

2

y

2

E.

x

2

x

2

y

y

2

D. 18x 2 18y 2 54x 126y 497 0

E. 2x 2 2y 2 6x 14y 1 0

18. If the simultaneous equations (with unknowns x, y)

若聯立方程(x、y 未知數)

y y

x

2

x 2

x h

have only one solution, find the value of h.

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2011/2012 學年參考答案MODEL ANSWER

Part I

1. a. e2x 3e x 10 (e x 5)(e x 2) 0 e x 2 0, o r e x 5 0 . The first

equation leads to the root x ln 20.6931.There is only one real root.

Candidates will also receive full credit if complex roots are given.

b. log [log (log x)] 0 log (log x) 1log x 3 x 2 8.

3 5

3 2 3 2 2

1500 9n 4. b. The average costs per watch before and after the crisis are , and

n 1500(120%) 9n

, respectively. Thus, the average costs per watch is increased

n

by

1500(20%)

, and the corresponding percentage change is

n

1500(20%)

1500(20%)

n.

20%n .

1500 9n

1500 9n

n

Hence the overall percentage increase is less than 20%.

2. 11 6 2 (a b 2)2 a2

2b

2

2ab 2 . Equating terms leads to

a

2

2b 2 11

ab 3

…………. (*)

180(n 2) 360

5. a. x , y180 x .

n n

4

180(n2) 360

b. x y 4 n10. So there are ten sides.

n n

B y elimination it was found that there are four values of b satisfying (*), namely,

1, 1,3/ 2, a nd 3/ 2 . However, since both a and b are integers, and ab 3,

so b is either 1 or 1. It cannot be 1, otherwise a 3,c ontradicting

11 6 2 a b 2 0. T hus b1,and a 3 .

6. a. There are two scenarios under which Carmen may answer a particular

question correctly: (i) she has studied the materials, and doesn’t make

careless mistake; she hasn’t studied the materials related to that question,

3

3. a. 1 1 3 1 3 1 7 3 1 7 7 3 7 4 7

r 3 .

r

3

r r r

2

r

3 2

r r r r

and guessed the answer correctly. The required probability is

(0.7)(10.1) (10.7)(0.25) 0.705.

b. Carmen passes the quiz if she answers either two or three questions correctly.

2 2

b. 1 1 2 1 1 2 4 7 2 110

r 6 .

r r

3

The required probability is .705) (0.705) (1 0.705) 0.7902

(0 3 2

.

r r r

7. a. As L passes through the two points (0,2) and (4, 0) , its slope is

1

4. a. Let C x y n, where x and y are constants.

When n 100 , C 24100 2400 , so that

x 100y 2400 (1)

When n 300 , C 14300 4200 , so that

x 300y 4200 (2)

Solving (1) and (2), we found that a 1500, and b 9 . Thus C 1500 9n.

(2)

1

2

1

x

. The equation of

L is y 0 (x 4) , or y 2 .

4 0

1

2 2

1

b. Slope of 2 2

L. As it passes through the point (0,10) , its

1/ 2

equation is y 10 2(x 0) , or y 2x 10 .

24 2

c. It was found that L and L meet at A( , ) , L and L meet at

1 2 1 3

5 5

5

B(1,) , and L and L meet at C(1,12) . The base of the

2

2 3

right-angled triangular region bounded by these three lines has base equal to

29

5 24 29 . Therefore the area of

BC . The height is

12 1

5 5

2 2

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1 29 .

2010/2011 學年入學考試試題ADMISSION EXAMINATION PAPER

29 841

the triangular region is 42.05

2 2 5 20

Part II

第一部份Part I

1. A

2. E

3. C

4. D

5. B

6. D

7. A

8. C Write your answers in the space provided for each question. Answers written

9. A 10. E 11. D 12. E elsewhere will not be marked.

13. D 14. B 15. D 16. B 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評

17. B 18. A 19. B 20. C 分。

Part I

1. A straight line L passes through the origin and is perpendicular to another straight

2

line L : 2 4 0.

x y L and L intersect at point A.

1

1 2

一直線 1 x y L 和L 相交

L 穿過原點，且和另一直線 L : 2 4 0 互相垂直。

2 1 2

於點 A。

a. (2 marks) Find the slope of L .

2

(2 分) 求L 的斜率。

2

b. (2 marks) Find the coordinates of point A.

(2 分) 求點 A 的坐標。

2. a. (2 marks) Express cot(A B) i n terms of cot(A) and cot(B).

(2 分) 以cot(A) 及 cot(B) 表示cot(A+B) 。

Hint 提示: tan(A B) tan A tan B

1tan A tan B

b. (3 marks) If and are acute angles such that45 , find and

(3 分) 若及均為銳角且45 ，求(1cot)(1cot ) 並化至

最簡。

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3. The marked price of a digital camera is $8,450. If it is sold at the marked price, 5. When f (x) ax 3 13x 2 bx 60 is divided by3x 2 14x 5, the remainder is

the percentage profit is 30%. 7x 35 .

一部數碼相機的標價是$8,450。若以標價售出，可獲得 30%的盈利。當 f (x) ax 3 13x 2 bx 60 除以3x 2 14x 5時，餘式是7x 35 。

a. (3 marks) Find the cost of the digital camera. a. (4 marks) Find a and

b.

(3 分) 求該數碼相機的成本。(4 分) 求a 及 b。

b. (3 marks) If the digital camera is sold at 10% discount, find the percentage b. (2 marks) Factorize f(x).

profit then. (2 分) 因式分解 f(x)。

(3 分) 若以 10%的折扣百分率出售該數碼相機，求此時的盈利百分

率。

6. (6 marks) The average monthly salary of a factory’s workers would have

increased by $1,000 either if three additional workers each of $18,000 monthly

4. Mr. Lei works in an electronic company. His total monthly income ($I) is the sum salary had recruited, or if three workers, each of $12,000 monthly salary had

of the basic salary and the bonus. The former is constant while the latter varies been sacked. What was the original number of workers in the factory?

directly as the profit of the company ($V) in the particular month. When V = (6 分) 若額外招請三名月薪各$18,000 的新工人，或解雇三名月薪各

100,000, I = 7,000. When $12,000 的工人，某工廠僱員的平均月薪會增加$1,000。問工廠原來有僱員V = 200,000, I = 8,000. 多少人？

李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

數，而後者隨公司的每月盈利($V)正變。當 V = 100,000 時，I = 7,000；當V =

200,000 時，7. Jenny will have a Mathematics test in this week. If she passes, she will go to a

I = 8,000。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

a. (3 marks) Find I in terms of V. choices also have equal chances. The table below shows the expenses for her choices.

(3 分) 以 V 表示 I。

Test Result Choice Expense

b. (3 marks) In a certain month, the bonus constitutes 40% of Mr. Lei’s total Movie $80

income. Find the profit of the company in that month. Passed

Concert $250 (3 分) 李先生在某個月的花紅佔他的總月薪 40%。求該月份公司的盈

New Dress $120 利。

Failed Reading group Free of charge

Reference books $150

.

4

5

The probability that Jenny passes the Mathematics test is

珍妮在本週將有一個數學科測驗。若成績及格，她會去看一齣電影或一場演

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測驗成績選擇費用D. 2a 2b

b a

及格

電影$80

演唱會$250

新裙子$120

E. 2

a 2b

b a

2. The axis of symmetry of the parabola y x 2 6x 7 is 不及格

讀書小組免費

拋物線 y x 2 6x 7的對稱軸是參考書$150

珍妮在該數學科測驗成績及格的概率是4

5

。

A. x = 3

B. x = 3

C. y = 2

a. (2 marks) Find the probability that Jenny buys a new dress.

D. y = 2 (2

分) 求珍妮會購買一套新裙子的概率。

E. y = 7

b. (5 marks) Find the probability that Jenny spends no more than $140.

(5 分) 求珍妮用不多於$140 的概率。 4

3. If log x denotes log x , and log(5x2 ) a , then log

10

4

x

4

若log x 表示log x , 且log(5x2 ) a ，則log

10

4

x 第二部份Part II

A. 2 a

B. 2 2a

This part contains 20 multiple choice questions. Please select the desired answers on C. 2 a 2

the answer sheet appeared on the last page of Part I. Please follow the instruction given on that page. D. 4 a2

E. 4 2a

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

4. Two sides of a triangle have lengths 5 and 8. The third side may have length 該頁內的指示填寫答案。

某三角形的兩條邊的長度為5 和 8。第三條邊的長度可能是

1. If f 1 a b

( , then

x) x

f f I. 3 II. 8

x) f

f

x

b

a

A. I only 只有 I

B. II only 只有 II A. 0

B. 2b

a

C. I and III only 只有 I 和III

D. II and III only 只有 II 和III

C. 2a

b

E. I, II and III I、II 和III

108 109

5. Which of the following is/are identity/identities? 8. In the sequence ,a, b, c, d, 0, 1, 1, 2, 3, 5, 8,each term is the sum of the

以下那項是恆等式？previous two terms to its left. Find a.

數列,a,b, c, d, 0, 1, 1, 2, 3, 5, 8,的每一項為其左面前兩項之和。求a。

I. cos2 x 1sin2 x

II. x 2 4x 4 0 A. 0

I II. x 2 1 (x 1)2

B. 1

C. 3

A. I only 只有I D. 1

B. III only 只有III E. 3

C. I and II only 只有I 和II

D. I and III only 只有I 和III 9. At the start of 2004, John invested $500 in a fund that doubles every seven years.

E. I, II and III I、II 和III If interests are compounded continuously, in what year will he have $1,200 in his

account?

6. Given distinct positive real numbers x, y and z such that 由2004 年年頭開始，約翰在某基金投資了$500。此基金每七年翻一翻。若利

給定同的正實數x、y 及z 使息以連續複利計算，他的户口在何年將會有$1,200？

x z y y ,

z x

y x z

A. 2010

which of the following is true? B. 2011

下面那一項正確？ C. 2012

D. 2013 A. x

y z

E. 2014

B. x z y

C. y x z

D. y z x

E. z x y 10. If x is a real number, the value of 2x2 4x 9 i s

若x 是實數，2x2 4x 9 的值

7. In an n-sided polygon, one interior angle is x and the sum of the other (n – 1) A. at least 5 最小是5

interior angles is2006. 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。B. at most 5 最大是5

C. at least 7 最小是7

D. at most 7 最大是7

A. 12 E. at least 9 最小是9

B. 12 or 13 12 或13

C. 14

D. 14 or 15 14 或15

E. 16

11. Let f (x) ax 2 bx c ,where a, b, c are constants. If the equation f (x) 0 13. If the graph of y 2(1x)2 3 is translated upward by 1 unit and then leftward

has a positive real root and a negative real root, which of the following must be by 2 units, find the equation of the new graph.

true? 若把y 2(1x)2 3的圖像向上平移1 單位，然後向左平移2 單位，那麼新設f (x) ax 2 bx c ，其中a、b、c 是常數。若方程f (x) 0有一個正實根

的圖像的方程是

和一個負實根，以下那項必定是正確的？

A. y 2(1x)2 4

I. a 0 B. y 2(2 x)2 1

II. c 0 C. y 2(3 x)2 2

III. b 2 4ac D. y 2(3 x)2 4

E. y 2(x 1)2 4

A. II only 只有II

B. III only 只有III

C. I and III only 只有I 和III 14. If the sum to infinity of the series k k 2 k 3 ... i s

1

2

, find k.

D. II and III only 只有II 和III

E. I, II and III I、II 和III 若數序k k 2 k 3 ... 的無限項之和是

1

2

，求k。

12. In the figure below, AB is a straight line and P is a point on AB. If the coordinates A. No solution 無解

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。若P 的坐標是(0, c)，求c B.

1

3

的值。

C. 1

2

B(4, 6) D. 1

or 1

2

1

或 1

2

E. 1

3

or 1

1

3

或 1

P(0, c)

A(-2, -6)

15. Given that ( 2 , 2), (4, 2) and(3, 5) are three points on a circle. The radius of

A. 4

B . 2 that circle is

已知( 2 , 2)、(4, 2) 及(3, 5) 為一圓上三點。圓的半徑為

C. 0 A. 3

D. 2 B. 10

E. 4 C. 15

D. 4

E. 5

16. The top of a ladder A resting against a vertical wall is 24 feet above the ground. 18. In the given three by three sub-squares, the three entries in each row, column, or

By moving the base of the ladder 8 feet farther out, the ladder slides down resting diagonal added up to the same number. The figure shows four of the entries. What

against the wall at a point A' 20 feet above the ground. How long is the ladder? is x?

有一把梯子倚着一道垂直的牆壁，梯子的頂部A 離地面24 英尺。若把梯子在一個3×3 格的正方形格子內，每一行每一列及每條對角線上三個數字之和的底部再向外移8 英尺，則梯子頂部向下滑至離地面20 英尺的點A' 。梯子都相等。圖中顯示其中四個數字。x 為多少？

有多長？

x 7

A. 2

A. 25 feet 英尺

B. 6

10 3 B.

27 feet 英尺 C. 7

C. 28 feet 英尺

D. 8

D. 30 feet 英尺

E. 9

E. 32 feet 英尺

19. A line passing through the origin with slope m is tangent to the circle

x 2 y 6x 8y 20 0.F ind m.

2

一條穿過原點，且斜率為m 的直線與圓x 2 y 2 6x 8y 20 0相切。求m。

A. 3

4

17. Let f (x) a nd g(x) b e polynomials. If f (2) g(2) , then which of the following

must be true?

設f (x) 和g(x) 為多項式。若f (2) g(2)，則以下那項必定正確？B.

C.

1

2

4

3

I. f (x) and g(x) are both divisible by x – 2

f (x) 和g(x) 皆可被x – 2 整除D.

1

2

or

11

2

1

2

或

11

2

II. f (x) g(x) is divisible by x – 2

f (x) g(x) 可被x – 2 整除

III. f (x) g(x) is divisible by x – 2 E.

3

or

4

11

4

3

或

4

11

4

f (x) g(x)可被x – 2 整除

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

A. I only 只有I standard deviation are respectively

B. II only 只有II 一組數據的平均數和標準差分別為m 和s。若把該組數據全部乘以正常數k，

C. I and II only 只有I 和II 則新的平均數和標準差分別是

D. I and III only 只有I 和III A. m2 and s m2 和s

E. I, II and III I、II 和III

B. km and k s km 和k s