(29)商教日七初月正午庚麿雯
1990 中學會考资管專欄
MILL & BALE PRESS
the
{x √2-5x dx.
-(2-5x)+号
Additional Mathematics (18)
報日僑
五期星
日二月二(〇九九一年九十七國民華中
日七初月正年午康廚
incefinite
integral
The equation of the curve is
y = x + x = 2.
dx
(Ans.)
Zvdy
[Hint: x = -
Solution to Exercise 18
4. (a)
(x - 1)
dy
=
2tan-1y
分類廣告 熱綫電
546258
1. (a) (xsinx)
टे
(Ans.)
(Ans.)
546445
W. S. So
Revision Exercise 18
Integration -- Indefinite integral
Horked Example
1. Show that if [f(x)dx = {x) + then
if(ax+b)dx=
Flax+b)+e.
(Proved)
=
= sinx Xxx
sinx
= sinx + xCOSX
(Proved)
(b) {
dx
{b) d(xsinx} = (sinx+xcosx}dx
/dxsinx) = sinxdx fxcosxdx
xsinx = -c95x + { xcosxdx fxcosxex = 20% + ㄨㄥˋㄨˊ C
Exercise 18
1. (a) Show that
xsinxi
- sinx + XCOSX.
2. 12sinx
integral
(b) Hence find [xcusxrx.
indefinite
2. find
[zsinx - 3cosx)dx.
3cosx)'
=
dx
Sin Xcos x
cos2x+sin2x
dx
sin xcosx
咋
=
| csc7x + sec7XGK
-cotx + tanx + C
(Ans.)
Let = x -
y
7.jx 256 dx
Schition:
Since ff(x)dx = F(x) c
F*{x} - {{x}
Differentiate F(ax+b) with respect;
to x-
3. To stone at any moit x, y) of a
curve is given by
想
4sin x 17sinxcosx cos x
ajlsys2x) - 6sin2x+ qq1+cos2x;
13. 5c052x - 65:n2x
+
j(251ax - 3cosx) idx.
2/17 + 5c052x. - 6sin2x dx
孿+手sin2x+3cos2x + C
dx
F(ax+b)]
F!{ex+b}
dtaz+b}
X
=
Flax+b) (ak
= f(dx+1}}
2. Fax+bidx = Flax+bi-.... (hours)
2. Snow that
· sinxicosx dx = 33-sïn«r
2510X-COSK
Solution:
sinxcost do
1990 48#ERROR
ZUR DA BANAN
MILE & DALE PRESS
English Language (18)
IDIOMS & SHORT COMPREHENSION
J. Wu
Choose the best answer from the dig, co given.
1 "really do not know what to do with, this gift. It is certainly a white elephant se mej",
From this we know than the gift, 14
A. large in size and attractive.
8. valuable but useless.
C. very rare or oven tekanan,
D. beautiful but to big hot korea.
רומה?
2. John
starts 你们 revision until the eleventh hour.
This means What John .....
A. likes to work as 11 0.0%
8. does his revision very
aigne
his
ate at
C. does his revision only at the
last possible moment.
D. spends devan hours aim is
revision.
3. T shoute
not worry
Well, ''} leave it th chanUP! From this we know that the speaker
A. thinks that he has a chance.
6. is sure that something tragic is
going to happen.
C.is reiy
Something cannot be dec,fnd by himself,
D. thinks that his worry
necessary.
nt
4. There is nothing he will but do
to get his money back.
This menos trat Colin
AMG MOMO
A. will do nothing
B. will no anything
C. does not want
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13
餐館頂讓
dv
1 2jx
1.
X1,
Curve.
Curve cuts the x-axis at Find the equation of the
4. (3) Tim (x-4)
1
3.
+1
(b) Find
the indefinite integral
dk.
1
dy =
+1 dx
X-1
dx
5. Finc / dujy, use the substition
x = y2.
6. Find
A
x
B. and aothing
5. Ta trguld not Cry
milk.afts do tohethins." Toas that you .....
A. should not concerned over a situation which cannot he
3. shrid becke careful
ririnking Whe
C. should have worked färder and
achievi sone Wing. 0.hould put your milk bottles, in
A Base, Ask any mas
The para sek trian in
ans .....
A. wise ma
Ce teache
Dag average verson
the street!
Westw goliceman caught the thief red-
hauded.
cans that the thie!
were as hard and was bleeding
worse the policamar caught him, 8. someone and was caught. Cards daught ia the act of
D. was caught
wikstad hands.
by
包 policeman
B. Con't be to optimistic in this case. The niley Powson's choice." Dis means that we
A. have no choice åt „ak
craice.
ask Babson to fake'
C. have a choice given by Hobson." D. are sure that Henson's choice 15"
not good one.
9. Nee you surprised? The Principa!
TAS THEN the new teacher the axe
分 that the 些
teacher
A. has been given a present. 8. has received an axe from the
Principal.
D. has been pronoted.
10, can assure you that from now on
立信
(提防穀餐
【搬運有限公司 £7701199
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i
機
(Ans.)
= { x
dx
xyz + 2x2 =
OX
-/l-(2-5x) + 3 /2-58-dx
dx
+
212-5+12+12=512
5{4}{2-5x)
-1
tan
(Ans. }
375
2X
+x+
x - isy = J
T. + 1 = 0
C-2
5. a = y:
dx = 2ydy
everything
should
be
plain
sailing.
This means that fitm now on
A the speaker will become a Diain
sailor.
A. I could not know when the lesson
began and ended.
Bould not understand what the
teacher had been saying.
Telt bored because the teacher Abad been speaking for too long. Bthere should not be any trouble D. 1 could see the head of the
or obstacles,
C. thore should be some risks.
D. travelling at sea should involve
no risk.
11. Af
a student is under a cloud,
A. he is standing in the open air. B. he is sick on that day. Che
experienced
has unpleasant.
something
D. he is suspected of having done
something wrong..
12. i would not believe that.. Kitting below the belt is not John's way of doing things."
This means that .....
never
AJON
advantage.
takes an unfair
B. John seldom hits the others. C. John always takes advantages of
others.
D. John knows how to hit others.
tbacher.
16. Though the whole family sweat blood. they can hardly support
themselves.
This means that
A. the whole family work
slaves.
8. the whole family are killed
Like
C. the whole family are working"
dangerous jobs.
D. the whole family are having "an
easy life.
17. When I lost mall wy money, 1
discovered that John was e weather friend.
This means that John
fair-
A. refused to have anything to do
with me.
B. brought nice weather for me.
C. helped me out of my trouble.
D. WAS a friend of mine who was
13. The foothaii match last year ended 18. When someone is robbing Peter'
in a draw.
This means that
A. there was a lucky draw after the
football match.
B. they drew lots to decide which
side won the match.
C. the football match was boring. D. neither side won the match.
14 "Next Thursday is a red-letter day
For de
This means that ..
A. the speaker 4111 tedet vara red
lotter next Thursday.
R. next Thursday is a public
holiday.
C. next Thursday is an important
day for the speaker.
D. next Thursday is a miserable day
for the speaker.
15. The Leacher had been speaking for an hour already, but I could not make head or tall of his lesson. This means that
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pay Paul, this means that
Aa has committed a crime of
robbery.
B. Peter is the victim and Paul
benefits. Che is
by paying his debts borrowing em another person.
D. his debts to Raul drive him to
commit a crime.
19 mother was rather put out by
Dawid's manne".
This means that
A
mother
David's behaviour.
about
B. David did not like my mother.
C. David's manner made my mother
rather angry.
(-8-30x) (2-5x) 2
A. The
situation
favourabic.
375
(Anse}
d(2-5x)
(Ans.)
verv
B. We could not think of any other
decision.
C. We are faced with many other
choices ..
D. We could follow their suggestion
alternately.
21. I'm afraid 甭
birthday party.
can't attend your
This means that .....
A. do not want to attend the
Darty,
B. The birthday party must be quite
threatening.
I's sorry for mot going to the party.
Q. I'm afraid of attending the
party.
22. She can't make head or tail of the
Tctter he has written to her. this.means that .....
A. She cannot understand what he care has written.
By She
doesn't
know where, the letter begins and ends.
C. There is no beginning or end in
the letter.
D. The etter is written in an
exotic language.
23. Jack is a man of letters.
This means that Jack
A. is a postran.
B. loves writing letters.
Cikes learning the alphabet.
D. is a writer.
24. David is going to follow, in his
father's factsteps.
This means that
A. David is behind his father's
back.
B. David will take up his father's
profession.
C. David will walk near his father.
D. David will do what his father
tells him to.
D. My mother had d very good
impression of Davia.
Answers.
20. In view of the situation, we had no
1. B 6. D
2. C 3. 0
11. D
· 16. A
4. B 7. C .8. A 9.C 12.. A 13.0
14. C 17. A 18. C 19. D
5. A
10. B
15. B
20. B
21. C
22. A 23. D 24. B
alternative but to follow their suggestion.
This means that .....
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