真二第張六第日五十月五年亥癸歷夏
R
初中成績評核預習
雄風出版社
中一英文(一)
F. ENGLISH
EXERCISE T
Select the best of the choices offered for each of the following situations. All respon ses must be polite.
1. You meet a friend who says, 'How are you? You
are reply:
A. How are You?
B
How do you do?
с
Very well, thank
you.
I'm not very well today?
Your friend intro-
WAH KIU YAT PO
Allow do you do? B. How are you? C. I am a driver,
3. You have dialled a
number but you ar
not sure if you
have done it
correctly. When
someone answers
the telephone, you may ask:
A. Is the number.
234567?:
報日僑華
please? If she is in, you may answer:
Yes, please hold
on.
Yes, please hold .out.
Yes, please wait for her."
Yes, hang up please
However if Mrs War is not in, you may say:
B. Did I dial 234567 C. Is this 234567? D. It must be 234567
A.
I'm sorry. Please ring again.
B.
No, she is not here at all.
I'm sorry. out.
V. She's
D. Oh dear, away
,she's
4. If you want to
duces you to someone 5.
who says How do you
đó ? You reply:
-1983
中學會考試題預習專欄
speak to Mr Chan on the telephone, you say:
I want to speak to 7. When you answer the Mr Chan?--
telephone, you may
B. May Mr Chan speak
to me please? % C. It would be nice if I could speak to Mr Chan, D. May I speak to Mr
Chan, please?
You pick up the receiver and hear this:!Is Mra Van in
6(9-24-8)=-42.
is 6
(Ans.)
|x(x-2)|<
<x(x-2)
附加數 <試卷一)
and
明德出版社提供資料
-2x < 1
want to tell people your name. Suppose your name is Jimmy Tam. You say:
A. Hello, Jimmy Tam
speaking.
Hello, I am Jimmy Tam.
C. Hi, this is Jimmy
Tam.
3
4cos esine-4cogesin
4
coa B-6cosesin 0+8in ¿cos3esine 4cosesin
4
.COB O
·C08
cos e бcos Osiz sin
and
COS
COB
4sine 4sin e
COBO
-21-1
and
(x=a) (1−ß) where
Osin 0 sin Gsing
2.
cos o cos 0
Atang-4tan"@
2
1-6tan 0+tan
SUGGESTED SOLUTIONS
ADDITIONAL MATHEMATICS
Paper 1,1983.
1. x +4x+2= {2x+1)x0
- 2 + ( 2 ) + 4 ) x + ( 2 + 1)=0
Since tliisiras no
real roots,
(2^44) −4 ( 1 ) ( 2+ 1) <0
.2
4+16+16-8-410
+31+2×0
(1+1) (142) <0
can be any value except. 1 1-72
and 142
{And...)
(c) Let x-tane
2
六期星 日五廿月六年三八九一曆公年二十七國民華中
A.
Hello, Mr Jimmy is
speaking.
Your good friend
tells you that he cannot come to your party. You reply:
A. What a pity! B. I'm so sorry for
your absence C. Too bad.
D. Well, I feel So
"sorry.
9. Your grandfather is preparing to go out for a walk. When he looks out of the window, he finds that it is raining, You feel quite sorry for him and say:
A. That's no good. D. Ah, it's unlucky. C. What a shame! D. I'm so sorry about
the weather,
10. 'I think I have
Shame on you. B. It doesn't matter. C. Don't mention it.
D. Don't worry, They
may reappear sooner or later.
You visited a friend in the hos- pital. When you see him, you say to him:
A. What a pity! B. Bad luck!
c.
Don't worry, You will recover soon D. This is nothing.
12. You see your
suggest to
育僑華
your
friend that it is
about time to go. home. You say:
A. Come on, let's home. D. It is too late to
go home.
C. It is so late that
we go home. D. Shall we go home
now?
1.4.
Your hostess offers you some more biscuits. You are very full already, so you say
'm sorry that's enough.
B. I've had enough
alread
No, thank you.
teacher carrying a pile of books the corridor. want to help her. You say:
in
You
C. No, please. D.
Do you want me to help you?
B. Want me to help
you? Can I help you? D. Should I help you?
C
lost my old photo- graphs. I can't find them anywhere says grandmother. You reply:
13.
It is already very late. You want to
a from
Time taken for one.
ball min
{x−6)(x2-6x+12}=l}
or
x2-6x+12=0
---4(1)(12)
or
(Ans.)
(c)
(3.55)
Time taken for al1 balls in the rth Layer
-22r(r+1)
«(r+1) min (Ans.)
Total time taken for all balls of 10 layers
£16,0)
10
8 (3-3)
Σ
r+1)
3-31-4
$10
·10-
arg
(Ans,)
r-1
arg
10
(1+10) 65 min
(Aus)
10.
x +4x-6x-4x+1=0
3
tan 9+4tan 0-6tan
4tan0+1×0
ANSWERS
1C 4. D
7. A 10.D 11. C 13.D 14.
12
0.000
(c) Volume of solid
formed by LMN when x=r is
∙12
2 2ch-b(r)
Volume of solid form formed by ALMN
when *
is
2-(4)-
2rh-b(5)
()
2. Since
A.P. c-b
2b-a
(Ans.)
in
are in G.P
Logz-logy-logy-log*;
21ogy=log=+1og2
(b−c)logx+(c-a)logy+
(a=b}logz=(a−b)(logx+
Togz)+2(b-a)logy
(a−b),21ogy-2(a−b)logy
(ins.)
Perimeter
2AC+2x=2
AC-1-x
In AACD
AD=√(1-x)2 -
Volume of solid formed, MI NA
=2[ 31(AD) (DC)] ==π(1-2x)x
(Ans.),
dy23(-2x+(1-2x). (1)]
(1-x)
Putting
1-4x=0
OR
[z~(3+1)} − |z×(5+51)|
| (x-3)+(y-1)i| 1(x-5)+(y-5)i| (x-3)2+(y-1)2 - (x-5)2+(y-5)2
2
-6x+9+y -2x+1
-10x+25+y^-10y+25
4x+8y=40
x+2y-10...(1)
(Ana.)
The perpendicular distance from 0 to the line is the
minimum value of 1z
Now, Slope of 1. Slope of oz
equation of OZ:y=21 Subilituting inte (1):x+2(2x)=10
have
when {z} is minimon
y=4
(Ans.
40
12-23(-4)
when x=1, the volume
is maximum
4. (1+ax)*(1—4x)3-
(coserisine):
=cos 0+4(cose) (isine)
4
+6(cose)(isine)
4(cose)(isine)3
(Ans, )
(isine)"
2 2
sin
+48x-488x
(1-12x+48x2+..
1-12x+48;
2.2
+8 x
=1+4(a-3)x+
6(a2 ~88 +8) x2
(Ans.)
Since the coefficient
of is. O
.3
Using-
4cosesin Equating the real and imaginary part,
cos40-
Scones
4cosesin 0.
รี
coefficient of.
(b)
sin40 cos40
4tang-tan 0=
1-6tan 6+tan
4tane-4tan 0 1-6tan p+tan e
-arg(-1+51) Ži)
-120
(ADS.)
Otan
-√3)
tanko-1
120°
(Ans.)
(a) P(n)
-1.2+2.
n(n+1)
(4n+1)
16
n-any
The ro
integer (Ang.)
of (1) are:
x-tau
(Ans.)
8. f(x)=x2+ex2+bx-72
(x)=3x2 +2ax+b Since f(x)=
+2ab+b=0 has equal
roots 4a.
of roots:
0-12 (Ans, Product of roots:
4
-.48
(Ans.)
(b).
+72m
(x+p}3+q
-x2+5px2 +3p x+p
Equating the coeffs.
of x
x and constant term: 3p--12 →→. p»-4(ing. 3p-48
+4=-72
(ans.)
Now, f(x)=0
. (x−4 ) 3—8-0
= n(n+1)(n+2)
Put 1, T.S.-1,2-2 R.S.=3(1)(2)(3) ×2×1 ̧ ̧§.
. P(1) is true
Assuming that n=k, 1.2+2.3+...+k(k+1)=
(k+1)(k+2)
Adding the n«(k+1)t} term on both sides of above,
1.242.3+...k{k+1}+ {k+1} (k+2)=
}k(k+1} (k+2)+(k+1)
(k+2)
_(k+1)(k+2) [k+3)
−={k+1) (k+2)(k+3) =P(k+1)
since F(D)is true for n=1 and if is true for nek, it is also true for n k+1 Hence by the principle of mathematical
induction, it is
true for all
positive integrs
No. of balls in r-h layer
1+2+3+6
-=(1+r)
(ii) The total no. of
balls of n layers
Σ, =(1+r)
1
$
PLM ABC (AAA)
hh-d
Put
|hx=2rh-2rd
2rh-hx 2F
Area of 4 LMN= 4 =-xd
--x(2rh-hr)
dx
Now, 142rh-hx+
x(-b)]
[2rh-2hx]
for stationary.
put
44.0
·dx... 2rh-2hx=0
x=r
127337
Using cosine
(Ang.)
-2хусон120°
xy-7-0(Ans.).
y2+2y-3-0 (y+3)(y-1)=0. y=-3 or
(ii) 2x+2yy1+xy
x+2y
(Ans.)
(b) When x-2, y=1
dx 1
dt
speed of B
dy
--(--)(-)m/
#)
dt
(Ans.)
4-(-2b)<
4is maximum when x-r (Ans.)
(b) Volume of solid
formed by 4 LMN=v
(c) Consider area of
AOB
2
2F
-(2rh-hx)
dv______ (2rb-hx)2x+ dx-24 r
x2(-n) putting
(2rh-hx)2x-x
(ing.)
4rhx-3hx✪ x(hrh=3hx)=0
Now, dv
dx
when
(x-4)3—(2)3-0
(x-4-2)((x-4)2+
~2(x-4)+(-2)=0
(x-6)(x2-8x+16+.x-8
+4)*0
tel
= (1.2+2.343. n(n+1)]
= [} (n+1)(n+2)}
==n(n+1)(n+2)
the volume is maximum
when xs
Ana
xysin120°-p(17)
}xy(3)-3p (/7) p-xy (AR)
dp
d-1/(xy)) 4/7/3
wilt it dx
dy 5
and
at
dx
-=[~({})+(1)(-)]
(Ans.)
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