1988-11-01 — Page 16

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二期星日一月一十(八八九一年七十七國民華中( 16 )

7-25 = -1

2r= 8

(Ans.)

283

3 - 12

(Ans.)

(a) (+x+axZjim

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1-28x+4x+6x-122x2+12a2x2+

The teacher, with his students, (bg) going on a picnic. Everyone in the class

Exercise (B)

A blue and red scarf this dress.

with

15.

The

Choose the best answer from the choices givent

A gons wel!

go well

(read)

gets well

13.

get well

aloud.

The committee

having

1989 中學會考預習專欄

discussion.

age n

411 th equipment

A. has

3. have

明德出版社

are

installed.

raise

16.

10.

One

to learn

3. Nu

gun.

majority (like) leisure.

hate and neighbour

The leader of rioters

佢 group

"easons

interest group everyone who Treeting.

are...have 8.

C. is...have

The Tumber

having a

7%.

obvics 1 attended the

are....

D. is...has

students

great in this school and a numurs

of them

to oat around for

sact dead.

your lesson every

classes.

g abroad.

was

the man with a

D. XXX.

D. ways...is

A. 15...has.

C. were

Nobody knows that you are lying, 11. Many single

D. ways...are

C. dre...has

0. 15...hove

D. are...have

......?

teenag

about too

Answers

лу

classmates

(A) 1.

has

名

aren't you do they

is fl J. don't they

There .... a lot of information contained in this book.

parent...hig

parents... his

6. reeds

parents... their

7. is

parent...their

B. have D.

10. Tike

12. John, David and Henry ................

given a piece of paper to write

each

1i.

quenches

12.

已

12. "How do you do?"

(be)

Where

the rest

of the

on.

13. is

14. are / were

usually the first words we say people whom we meet for the first

students gone?

A. has

B. hage

函 nas

E. have

C. 13

C. is

D. are

13. Collecting

stamps

Lime.

There

more than one way to

(be)

13. There

{be} every reason to

solve the problem.

favourite hobby but M find

interesti

believe in his words.

A. his

6. have

is...it

C. 18

D. are

a are...it

No news

be good news.

On the table

(be)

vase

Neither of my two friends

14.

This is one

and some cups.

Neither my parents nor my brother coming.

Four

tines

four

(be)

coming to one party.

nas

that

... ever Beer reduced.

have

A. movie..

C. is

D: are

movie

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七十七國民華中

日二十二月九年戊夏

=1+4ax+ a2x2+.....

4a=8

a=2

Coefficient of x is azi

1989 中學會考預習專欄

明德出版社

Revision Exercise 5

Section A

MILL & DALE PRESS

Additional Mathematics (5)

W. S. Su

Revision Exercise 5 Binomial Theorem

Worked examples:

(Ans.

In the expansions of (ax+1)8 and (xia), their ccefficients or x4 ere equal, find the value of a. 2. In the expansion of (1+x)2+(1+x)2+

the coefficient of x2 in the expansion of (1+x+x*) is 15 and n

is a positive integer, find the value of 0.

Solution:

( 1 − x + x + ) = ( 2 - { x - x ? } ]′′

<t-nix-xz;+1(y-1)qx.

= 1-8x+(a + (-1) x2

+higher powers of x

Coefficient, or x:

rị

r2n-30-0

(n-5) (-6)=0

n=~6 (rejected}

2. [xparo 11+2ax)>(1-ax)* in ascending powers of x up to and including the tera containing x. f the coefficient of x is 8. evaluate the cocfficient of x:.

Solution:

(1+2ax) (1-ax!2

_{1+6ax+12d*x?+833x3)(1-2ax+x*)

find the

coofiicient of x in Leis ofn,

In the expansion of {1+x}", the

coefficients of the

term .

che`(ri1)th term and (r+2jtn

tern are a, 53, 15a respectively, find the values of a, n, e.

4. Expand (1-x)(H+6x) in ascending Dowers of x as far as the term containing x2.

5. Find the value of d, if the term

independent of x in the wincnt... expansion of (x2+)" is -

6. Find the coefficient of

expansion of (+2)7.

IA EN

i: Ta

The coefficient of x expansion of (a+x)" are in the rat o 5:4. Find the possible values o a.

Section 0

8. (a) Expand (1+x+ax?" in ascending

powers of x as far as the term in x2, where n is a positive integer.

報日僑華

(b) If the coefficients of x and xz

are Sand 25 respectively, find

the values of n and a.

x in the above expansion.

(d) Apply the expansion to evaluate

(1.0103)5 to 4 decimal places.

Solutions to Revision Exercise 5

1. Coefficient of x4 in (ax+1)* is

Coefficient of x in-(x+a) is 955-1264.

Dd2=12bd5

= 5

(r=1) {0-r+1)!

Tha (r+1)th term of the expansion

Flin-r)!

in = 6r+1

ㄓ

(6+1)! (n=7-1}!

15a

% = 3

n = 4+3 €r+1=4m+3

-2 n-11

(1-3x)(+5x)3

=[150,3x+2(3x) 24.... . ][1+3(5x)

+3{5x)?+(3x}*]

= (1-15x+90x2 + ... } { 1+15x+75x2+125x*)

=1+15x+75x2-15x-225x2(90x2+.....

Ccefficient of

= 70

7. Ccefficient of.

= 7024

Coefficient of x3-

70a

28a

36ix9

=1-50x2+Rianar power of x

The (r-1) term of the expansion

9-r

(Ans.)

+nigher

power of x (n-1),2

=1+nx+max2 + nán=12x? shigher power

of x

=1+nx+Ena+m[n+1ljx?enigm

nigher oewer.

af x

18-2-

The term is indepent of x. i.e. 18-2r-r=0

(b) Cagfficient cf x = n 日

Coefficient of x?

alg-i

50-10

- 25

3r=18

= 3

Coefficient of

322 _n(n-1)(n=2), nta-1) +0 _ain-1)(0-2)+n2 (Ans.)

3. Coefficient of the En term=

Coefficient of the (rath

term

643 21

(Ans.)

Coefficient of the 2) term

= 6(10)+10 =70

(d) (1.0103) = (1+0.01 +3(0.013215

= 1+5(0.01)+25(0.01) 7010.0113

= 1.0526

(Ans.)

股市

MILL & DALE PRESS

English (5)

Dear Students,

Today's issue is designed to give

practice

SCRE }}}}}

agreement

subjeft- concerning

found

are

often

compositions written by stardents. Mos of the time these mistakes can avoided if you work with more care and apply your knowledge of Uis aspect.

Complete the following sentences with the correct form of the word given

in brackets:

Exercise (A)

1. One of my friends

lost his purse.

to read novels during

11. I prefer a drink to cakes.

former (quench) ray thirst.

Mistakes

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1988-11-01 — Page 16

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