1977-03-02 — Page 22

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頁二第張六第日三十月正年巳丁歷

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辦婦女節的新貢獻

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開價則分爲:廿元、四

正「四種,姬絲合唱團名盛。

As shown in the above figure,

1977中學會考試題預習專欄

明德社主鳊

40, 30 are the radii of the

circle

= 60

新數學(十七)·魯榮家

MODERN MATHEMATICS (17)

Answers to Exercise 7

Section A

1. Let the roots of the equa-

tion bed and ß.

since, angle

area of sector LOB

60 xx (70)2 cm2

360

2.

2566.b6cm"

Area of quad, OBTA

- 2 x ares of rt.A ATO

- 2 x x OAXAT

**

三期星

亞陸

米國

陸國鎮榮獲 歐!

特榮

獎獲

日二月三年七七九一公年六十六國民華中 育教聞港

事局主席黃合攝於酒會上市 FLEX- *BE/PRESKEPAGES 八蛋由左起:信昌集團執行董事樂財

KERK 專爲觀察森那美附屬機構伯昌集團屬下各公司之 招待本港工商界及財經界人士。陳氏此行來黹乃 主席嫌售假於日前假座香港希爾頓酒店裝置酒幸 (EKEREEKAKZOTKAFE.

會見港財經界政要

森那美董事局主席

本港新聞

*鍋三百七十九分記錄,榮獲米茄表

表一只。 安天時举行在該場館設立之韓別獎-獲頒重米茄

·示:米茄代孟梁士,且利眞頒予

a = 1 (Ana,)

substitute into (3) and (1)

Band. C - 3 (Ans.)

Section B

9. Since m

the roots

the equation

にx

1.e. 25x2 + 30x

2. Solution:

Since f(x)

"

·1.20

2x3-kx2+6x

3k is exactly divisible by x+2

£ (-2)=2(~2)3 -k(-2)2+ 6(-2)-3x

=0.

28

-7k

--4.

3. Solution:

tanix+cotx=2.

tanx +

tank

2

min

tan2x 2tanx 1

282

+

(161) 2

cm

32.5 cm

M

36CM Ń K.

DA. x, AT

Since one of the ro ceeds the other by

PX-

A OT

AT

DA tan30

'the qua

2k-

(2k

k

2k

(d~ß)?

(2).

(α-p)2 - rdp

4(2k.

Aera of quad. OBTA

DA = HA – tan 30 (cm)

70 x 70 x 0,5774

2899.26 cm

area of the shaded region.

2 (2829.26 2566.66) cm

k

or k

(Ans

262.6 em

22

5.

y-

(Ans.)

- 2mm

(-2)2 - 2 (?)

7 .-3

(ii). (m.

-(-2)2.

-10=4 101

n) (m - n) 10 i)

(Ans:)

(tanx

tanx

1

x = 45° or 225°.

Solution: Let AB-BC-CD- 2x units.

Area of semicircle AD = —m(3x)2 sq. units

9

2

TX2 sq. uni

Area of semicircle

AC = 1TM(2x)2 sɑ. units

2

=2x sh, units Area of semicircle

(y-3)2.

let the equation

2m+n and 2nim be

with roots:

AB

Sun ar

3(min) 3(-2)

Above, fig.

the radius of the circle

be rem. Since triangle ABC, is

equilateral, therefore HO is the angular Disector of LABC

and AD is the perpendicular bisector of pl

Hence B =

multiply both sides by

·2( y − 3)2 ≤ 4(y − 3) (y = 3)2 - 2(y• 3) <o

3)( y − 5)≤0

3< y < 5

solution set = {y : 36y65}

[

Note it is wrong

multi

ply both sides by y for we don't know whether

(y-3) is positive or not.

2y) b. ( x-3y +5) + k{x

(1+ k)x+(2k 3)x the slope is

fom

but

BC

2re os 30°

COB 300

300

= 2 × 3.464 (Ans.)

therefore, the radius of the

circle is 1,464en.

3. Let the numbers be

A and ar

their sum is 39

*A+AT" "39.

their product is 729.

(+) (a) (ar) -.729

from (2)

Я

-729

(2)

3729-9

substitute into (1)

+

3r3

(r

for r

9

9

yr

*.39

+

- 39x

-10r

3)(3r

3 or r

the numbers are

. 9, 9(3)

3 = 0

1)

ile. 3, 9, 27 (Aus.)

.1/3

the numbers are

903)

27, 9 and 3 (Ans.)

-(2+)

(2k

since it is parallel to

swww

product of roots

(2n

4 m) (2m + n) 2(m2+

+5mn According to the

result of (

2

also ma

7

(2m+n) (2n+m)

? (-3)

k) = (2k -3) - 4 (Ans.)

therefore

the required

equation

To be cont

* 12x + 23 = 0

next week)

(Ans

As shown in the graph above, the optimal solution required is the point (7,10).

the maximum value required

3(7) + (10)

+ 50 281 (Ans.)

*

8. Since

5x^~1 = A(x2‍+x+2} + {8x+C; ) { x=1).

• Ax ̃+Ax+2A

5x

1

2

+

Bx +Cx -DI

C

2

(A

4

B. + C)x

+ 21

.. A + B = 5

數學(十七)·女長波·

Mathematics 17

Solution to exercise

Section A

1. Solution: Since and q

are the roots of

5x2 + 2x - 4 = 0.

D + Q. =

-

and Do The sum of the roots of

the required equation is. (2p+a)+(p+26) 3(D+q)

3(-)

= 3(-

=

The product of the roots of of the required equation is (2D+n)(D+2a)= 202+500+202

2

So. units

Area of shaded part

= (2x2 - mx2) sq. units

을까? sa. units

Since 2x2

Of

Area of shaded part.

is one third of the area of the whole figure.

Solution="

The total distance travel- led by the motorist

(2X32+ — x 42)Km

= 85 Km

the average speed of the motorist for the whole 85.

journey

=

1+ 3/2

Km Der hour

56 km per hour

Ans: The average speed of the motorist for the whole

journey is 56 km/hour.

6. Solution: The external

volume of the box =25 X 14 X 8cu.cm

2800 cu.cm

The internal volume of the box

= (25~1)X(14-1)x(8−0.5).

cu.cm

2340 cu.cm.

The volume of wood (2800-2340)cu.cm.

= 460 cu.cm.

Ans: The amount of wood

used to make the open box is 460 cu.cm.

7. Given: ACLBD AK=20cm,

KC=36cm, AB=25cm

To find the length of

KB,

KD and the radius of the circle

Solution: Since ACIED

KB =

$252-202

= 15cm

.AK. KC = BK.KD

20 X 36 = 15KD

cm

KD = 48 cm

From 0, the centre of the circley drav OMIBD and ON LAC

BM MD = X(15+48) cm

31cm.

KM -

=

(312-15) cm 162cm

ON KM is a rectangle

A

- B+ C

(2)

2A

C-

1

(3)

5.

(4)

x2 +

6.

0x - 글

O

2(D+C)2 + 21-룩)24 (-1)

+ Da

=

12

25

ON=KM = 161c.

Thus, the required equa- tion is

CN=NA

=

1X(36+20)cm

the 28cm

radius of the

circle

Toom

(1) (2)

(3)

+

(4)

LA

B

Given: AB is the common tangent of the circles. To Eind: the size of LAPB+LAQB

Solution: join rQ Since AB is the common tangent of the circles

LAFQ = LAQB

205B = 2CBA.

i.€. LAB = LQAB + QBA Since AQB+¿QAB+ LQBA = 180°

LAB LAQB 180°. Section B

9. Solution: Let x be the number of $1 coins,"

Then 2x is the number of 50g coins and 10x is the number of 10g coins.

210 < x+2x+10x < 230 21013x < 230

230

<x<

1.3

<x<17-

I.e. 15-2<

Since x must be an integer

X = 17

The total number of coins

13 X 17 = 221

10. Solation:

the least value of y = -1 the range of values of x such that y>0 is x <0.5 or x >1.5

c) Since the graph y=nx2+ax

+3 Dass through the points (3,0) and (1,0)

= 20+ 10+31

+ 24 + 12 = -(1).

+ 3:

1.E. 90+60+12=0.

(1)X3 3D+6c+36=0 8.

(2)-(3) 6-24 = 0 Subst.

D= 4

4 into (1) 4+20+12 Q

C = 8

d) Since the given graph is

..

4x + 1 = 0

8x +3 = 1.

The solution of

4x2

-8x + 3

and

2x2 or 4x2

2x2

·4x + 1 0 are 0.29

or 1.7

4x2 4x2

9x + 4 = 0

8x + 3 =

X

or

3

The solution of

4x2 - 9x + 4 = O are 0.62 or 1.64.

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