1977-12-06 — Page 27

1978

「中學會考試題預習專欄

明德社主編

數學(十)

(十) 女長波

Kathematics. 10

4

日六月二十年七七九一圈公年六十六國民中

育教儒 : 頁三第張七第日六廿月十年巳丁屦复

WAH KIU YAT PO

報日僑

二期星

11

(11)

教僑華

rt, 4 POD

(iii) Volume of the larger

In the figure, AB and CD are ares of Concentric circles, centre 0, cut off by radii. ODA and OCB, If AP=BC=Fem. Al}=5cm, 6-3cm,

calculate

(a) the length of the radii (a) the

the circlesl

(b) the area of the shaded shaded part,

Area of rt

*(OD) (DP)

Pr

(tan300) (PD)

*( tan300) (4) 8/3 em

Area of quad,OEP

2 x (8√3)

16/3 cm

Area of sector DEP

360

: 120

X

(π )(4)2

2

Tcm

16

Area of the shaded region

16√3 - 16

10.96 cm2

(Ans.)

-3 b

2

соле

-}()(4)2 (6)

32 T. cm3

Volume of the smaller

cone

-4(1)(2)2 (3)

Volume of the frust tum

32 T

28 T

87.96 cm3.

brown

157 10%

13.(0,-3) is on the curve,

-3-b (0+a)2

is on the curve

(i) The required probability

15%

40%

(1+a)2

(2)

(Ans)

d. exclude irrelev-

ant comenta

exclude any repet- ition.

never include your own opinion in your precis whether you agree with what the author says or not,

Arrange all the points in the order that you consid- er appropriate..

5. Write the precis from the

notes,

6. Check to see that your

precis îs of the correct length. Do not write mere than required or too short.

7. Check your grammar,

Read the fair copy. Make sure that there is no spelling mistake.

There are other important points which you should note:

Answer: All questions

Section A and any Six

questions Section 8.

Section A

Simplify

--> * - · ( x + 2 -~-~).

Find ? and q if (x+2) and (3-3) are factors of

32

•* ́*p* ̈+qx=18-

X, Y, Z can do a priesØF- work in 12, 5, 10 days: respectively. All work for 2 days and X and leave, Jow long will Y then take

to finish the work? \n Amen borrowed $320o und repsid it hy two equal annual instalments at 6% compound interest. Find the amount of each.

instálient correct to the nearest 8.

In the figure, B, C are

altitude of A^PC, LAFF=67. Find ABCF (Geometry theorem need, not he quoted when used,}}

16.

In the figure, AB is tangent to circle AUNT "AE-EB, and CFED is a

straight line. Prove that Arno is a parallelogram.

In the figure, Af is the

bisector of ¿DAB,

ZABC=ZACD, CX-XB, CY-YD.

Prove that A, X, C, Y are cancyelic,

新數學 (十) 魯榮家

MODERN MATHEMATICS (10)

Answers to fest Four (cont

11.

(2) -(1).

-12a

(Ans.)

Sub, into (1)

1 (Ans.)

The equation of the

curve is

+ 2)2

3 or

(3.9) and (1,0) are on

the x-axis and the curve.

c = 3 (Ans.)

(11) The greatest value of

occurs at x = 2.

The greatest value of

· 2)2

(ii) The required probability

-25%

251 → 15%

- (Ans.)

(iii) The required probability

1/25% 15% + 10%

100%

(Ans.)

.16.Since a + bi is one of

the solutions of

Px.

Therefore,

pfarbi)2+q(n+bi); r = 0

0

+2abi)+(q8+qbi )er - (pa2-pb=+qa+r) +(2pah+gh)1 −0

'pa

+q&+r ̈ ̈= 0.

2 pab qb 0 p(a−bi)2+q(a−bi)+r

(1)

(2)

-p(a--b2-2ahi)+q(a−bl)er

•{pa

a+r)~(2pab+qb)i

1. Use your own words

This does not mean that you should avoid using any wards or expressions that have appeared in the original passage. You just aumarize the passage or the part that is asked for in your own words as far as possible. You can do the following

a. Change the construction

of the sentence,

b. Use different parts of,

speech of the word; Use

another word or expression.

But you should not change the meaning or ideas intend- ed to convey in the origin- al

passage.

If the writer writes in the first person, you have to use the third person. For examples

in the original

In the figure, BE bisects ZABC and DE//EC. ® AR=5cm BC=7ca, Calculate the

length of AD.

(Geometry

theorem need not be quoted

when used.)

AE

BE BC

uni ts

units

also satisfies.

Hence, Bebi azad

the equation, therefore, it

is also one of the solutions

of the equation,

I think that all studenk should...

the precis

The writer thinks that

Simplify

COSA 1+sina

Solve the following equation, giving al of.x. from 0 to 360)

Section

AD // BC and AC

CBDA

values

Similarly

EB

- A

9. The daily cost of running

a summer camp for students. is partly constant and is partly proportional to the number of students. If the daily cost for 50 DA students is $321; and that For 75 students is $471- what would be the daily cost for 120 stiulents”

10.xy and k are three numbe numbers. The sum of x and Twice y is equal to five times k. The sum of the square of y and the product. of x and y is equal to four timas the square of kK.

Find x, y in terms of k.

(b) If x, y, k are e11 positive; find the value oť k such that X-y=4

Dirty water is pumped out from a pool through a pipe of em diameter at the rate of 1100 litres per minute, calculate the rate, in metres per second, at which the water flows through the pipe, 19. By selling eggs at 85 per

dozen, a man gained 20%. The cost price of the eggs. rines by 12%. If he mells at the same price as before, find his nev gain percent, By what percent should he raise his selling price to gain as much us formerly on every dozen?

*P is, #outh and Q is east

of a tower. The angle of elevation of the top of the tower from 1 and 9 are 24 and 30° respectively. If P is itim apart, find the height of the tower,

(a) DF = DÀ + AE

CE

-(—AD)+(--EA)

-(ABA) (Ang

CB+ BE

ZDA

+

3(EA

AD) (Ans.)

(h) DE CE

-(AD) + WX) [(3) (FA – AT) })} ~(AD·AÐ + AзEA – AÐ FA

EA · EA )

DE LICE

(Proved)

12.

(i) As shown in the figure,

P is the centre of the

circle inscribed, Let the radius of the circle ba

cw.

In rt. A OPD

PO 12 H

sin 4 POD

sin30"

Ans: The radius of the small

circle is 4 cm.

(i) Let the height of

original cone be h. cm.

Ans: The height is 6 cm. (ii) The

height of the nal cone

52 cm

The curved sufface area

of the cone

(1) (4) ( 152

8 13 T.

Slant height of the small

cone

13

3)222

Curved surface area of

small cone

( 1 ) (2) ( (13) = 2 √13T

the

Curved surface area of the

frustum

4813π - 2 13 TM

613T cm

* 67.97 cm

2

Area of the top and the

bottom of the frustum

π(2)2 + π(4)2

20 cm

2

62.83 cm2

Total Aurface area

67.97 130.62 em

62.83

(Ans.)

英文

十) 榮光

ENGLISH (10).:

Precis Raymond W.K.LO

In the Hong Kong Certificate of Education Examination, a paper on precis writing will be set, Candidates are expect- ed to sumarise either a part or the whole of the passage given.

The candidate will be given a prose passage of not more than 600 words afld one hour to write a precis not exceed ing 150 words.

PRECIS WRITING: Basic Steps

Before you read the passage, read the instruo tions very carefully. Read the question very carefully. Read every word of it, and read it at least twice,

Read the passage. It is important that you should read it over and over again. There are no hard and fast rules as to how many times you should read the passage since it all depends on the degree of difficulty of the passage,

Put down' all the import- ant points that are need- ed to mit the question. Every point should be relevant to what is asked for.

At this stage, you should also consider the follow- ing pointa's

a. exclude details ‘or

examples;

. exclude negative in-

formation;

exclude irrelevant points. This is in- portant especially when you are asked to give a summary of part

Think of the tenses you should use in your precia Pay attention to your grammar; agreement, plura forms, punctuation etc.

Your precis must be clear and concise. After writing the precis, compare it with the original and see that nothing important been left out.

6. Keep your fair copy clean

and tidy.

7. Your handwriting must be

legible.

Word of Warning

You mist refer to the question (or sometimes the instructions) from time to time since many candidates, under the pressure of time, vrite a precis summarizing the wrong part which is not asked for. Remember that you have only 1 hour's time to finish the precisi you vill not have time to re- write your precis.

In order to make your precis smooth, you should pay attention to the use of conjunctions or linking words. All the points must be linked proper]:

Remember: a precia is not

a list of things.

To A group of F.V. students': 1. Your question will be

ansvered when I deal with Problem Words -

2. Thank you very much for

your support and your let- ter.

Raymond W.K.LO