1991-09-26 — Page 28

育教;日九十月八年未辛磨夏

國民華中

房

青籲

報日僑.

四期星日六七月九(一九九一)年十八國民華中(28);

(a) CĂ - OÀ - OC

11. (a) Since AACDA ADE-

(3x) (y +

(Ans.)

AD

1991中學會考試題建議答案

OB = OC- BC

明遷出版社

{Ans.)

IT

MILL & DALE PRESS-

OB - OA

9

Additional Mathematics (1)

- 10)† + y} . (Ans.}

公共房屋的居民不可

商空搆物,以免傷害、

長鴻通現正籲請所有

:[祗}斑屋署,

6 h

SUGGESTED SOLUTIONS TO ADDITIONAL MATHEMATICS, PAPER I

(b)(i):

4BC

• CA

Let zxy!

• [77 + 3] ± 4(7) + 3}•[(3 - x)i-(y+1)}]{

1x + (y = 3)1|= 2

x2+(y-3)

4%

It is a circle with centre (0, 3) and radius

7(x-10) +

=407(3x)

5y = 150 -35%

y = 30 7x

(Proved)

(13) (1) |BC|\ = √5|CA|

√4941 - √5 √13

10 = 9 - 6x

(x)? + (y + 1)

6x

2yk0

(Proved)

(b) p

2AB+ BC 2√h2 + t2 + 2t

2 h2+

2/h 6h2.

Jh 6.

249h

from (b)(i) x2 + (30- 7×)2

required complex number is 2 +

[Ans.)

Tim f(x) = f(x)

(2) AB = (4 - 10) + 21

Lin

0-0014

-n

n-0

[Ans.)

1x - 21

41

2)(x+2)

Jx

2-

•1) = Q

2||x

CA = (3-4) - (2 + 1)3

(-6)(-1)+(2)(

CALAB

(Proved)

(3) 08 (47) + (2-1)]

-31

OA 37 -

50x?

2(30-7x) 440x960 #0

(h - 6)2

-(rejected)

(Ans.)

(c) (i) op

བ

[Proved)

(h-6)

號

9:

(Proved).

Range of h; h..>

0'

when h=9

when h (9

:0:

2,

+3

(Ans.)

(a) g(x)

2cos2x

(Ans.)

(Aris.)

(b)

+ 2c052x

X-

maximum value of y = * + sin2*

2-3

251 25255)0

minimum value of y = 25

27.5

(b)(1)

港

妆

OB = -ÚA

A, B, O are collinear..

Olies on AB.

2x - 23

+ 6x) - 23

-2(x 3)* --5

心

(it) (

g(x)

+2x-2

2k)x2+(2

12k)

9) + 18-23

(Proved)

共圖

maximum.

real

-2x2 12x23)

12x)x-(2 + 2)

2k) (2 + 23k)

1027k - 3 (10k+3)(k-1) 0.

K2

Ans.

10

+.2x 2)

10x25

(2x2 + 12x 23)

21+

f(x) + k2g(x) = (x2 + 2x

(23)

(b) (1) 06

4k.

(11)00 = 25

(Ans.)

=

from (1)(ii)

+2mb)

for all

(Proved):

(c) k

-f(x) + g(x) 0

f(x) < -g(x)

9(x) = -1

NG KONG

20

(Ans.)

The least value of f(x)

when l >:D

is minimum at h.9.

The minimum value of.p

49, 18-31

PUBLIC LIBRARIES

The greatest value of

10. (a) (i), t2 + 1 + 1 = 0.

(it) Let

f(x) 3

9(x) 10

cos(24) + \sin{+21)

= cos(+24) + isin(± 2)

(Ans.)

(96)

18/3 (Ans:

(11) From the graph, range of p p 18/3

|12, (a) (i) ZGÓP = 90o Q

LOCP *90* (90°

(11) S

[cos(+ 2) + isin(± +25) 13

Slope of tangent at P(1, 2) is y'],"

cos[}{2kn± 2}] + ¡cos[}{2k** ?}}]

-1,0,1

Equation of tangent at P.is y a 2. Equation of normal at Ris

(Ans.)

cose + isine, where § = + 2x + 40+ (Ans.)

(b) (1)

(Ans.)

(b) (1) L,H.S. [2

cose-ising](z - cose

+ isine)

{z - cose) - {ising)2

(b) Slope of tangent at Q is y'

CP OCcose

CPOAC050

* 2cosé

.cose2cose

(Proved)

Area of sector CAB Area of ACAB

(2)(20) = (21) sínzá

4d2sind

cose = 2cosa

(Ans.).

differentiate with respect to @

-sine

גי

Equation of tangent at Q:

y

3x + y

Put A(0, 4) in (*)

310)+-4) 4 = 0

The tangant at Q passes through

(a) p + q = 2 -k

pq + k(q + p} = 1

pq 1-k(2-k)

(b) sum of roots

1 - 2k + k2 2-q

(Ans.}

The required equation is

product of roots 1- 2k + k2.

** - (2-k)x + 1 - Zk+ K2: Since the two roots p, q are real.

ΔΙΟ [-(2 - k}]2 - 4(1 - 2k + k? > 0 k(4 - 3k) > 0

*(3k -.4) 0

(Ans.)

z2 - 2zcase + cos10+ sin e

+2+1

2zcose + 1 = R.H.S.. (Proved)

[z-cos-1 - isin_^][z-cos(-2) - isin{- 201

(Proved)

(z-cos - isin ][z-cos(- ^^) - isin(- -)] Iz-cos - istn3][z-cos(- 1) - isin(- -)] [z-cos - isin2][z-cos + isin2()

[z-cos - isin2][z-cos + isima)

[z-cos-isin [z-cosisiny

[{z-cos)+sin(){2-cos)*+sin(2-cos}

Brt.

+sin?

(z2-2zcos + 1)(z2-2zcos + 1)(z2-2zcos + 1)

(Ans.)

(c) Put zi in (*)

=

(12-zicas2 + 1){i2-2icos-+-11112-2icos

-1-1+1 = (-2icos2)(-2icos)(-zicos)

x

Bicoscos cos

8T

(Proved)

(11)

(4-

2sing

4(1-cos28) sing

.4(25in2ø)

4sinesind

2sing

sing 2sing

4stne ...cos2d.

4sino

cos'0

(Ans.)

(c)

紫器·紫

•

(Proved)

When @= 3

T6

per second

(Ans.)

sing

(Ans.

25ing