1970-05-19 — Page 23

ENCE LIBRARY

19 MAY 1970

CITY HAL

育教儒華 頁三第張六第

英中會考附加數學(二)試題

日五十月四年戌庚醫夏 WAH KIII YAT FO

報日僑華

二期星

ADDITIONAL MATHEMATICS

PAPER

Time allowed - Two hours

Answer all questions in Section A and any THREE questions in Section B

Mathematical tables will be suppiled.

All working must be clearly shown.

SECTION A (40 marka)

Answer ALL questions in this section. Emphasis should be placed on accurate working

(4 marks,

Expand

Hence, or otherwise, find the positive aquara moot of

(4 marks]

Solve the simultaneous equasons

4 marks)

alculate the gradient of the curve

at the point (1.1).

4 marks)

Dettererisante

(30

knd expend the minit

itt smolest form.

[4 marka)

Given that 4 cos:@

identity in 9, and that is posit

-z and tan'a

using the rubstitutionsin, find the value of

(5 marki)

Find the distance from the origin to the perpendicular bisector of the line segm

A (1,3), and B (4, 7)

Given that

By using the remainder theorem, prove that

Find also the remaining factor of F (x)

Joining the point

3c) x2 - (b)

− (b + 25 × 34) x − 2 (1 − b);

2) is a factor of ̈ F(x). "

10英文中學會考試題預習專欄

道英文書院主編

英文科(廿九)

ENGLISH LANGUAGE (29)

ine were to Exercise 26

13. (C)

14. (A)

3.

15. (C)

27

4.

16. (0)

28. (A

17(E

29. (A)

18.

30

(B)

19.

31

(c)

20. E

32

(0)

21. (E

33

22.

34

23% (D) 24. (D)

35

две

This is the Last Revision Exercise we til go througn; together before the examination comes. Patterns of very common sentenoda ara given with all the key WOL

underlined and fmplications maña, Answers to preko patterns are alse supplied at the end of the exercièe And before we say good-bye, may I draw your attentior to the writing of letters.

According to the syllabus for the General angiisu Paper 1969, candidates may be asked to write a short letter. It le likely that a test of letter writing. will be get in the 0.E. Paper I this year, especially when the duration of the Papar is extended to 24 hours (with 15 extra minutes added to the Paper), Iz is auggested that candidates should pay special attention to the writing of formal Invitation letteri and Apply letters.

Pick out the best answer to complete each of the following sentences -

35 far as I can remember, the boy three monska ago.

(A) cones. (B) came (C) had com (D) was coming (E) would come

"I don't often see Kary now. She

(A) or busily. (B) worked busily

(C) had worked busily. (D) has been busy working

E) is busy working

Recently, she *... Binging very hard,

(A) practises (B) practised (0) is practising (D) has been practising (F) will practise

Before we moved to our new house w

old one for ten years.

日九十月五年〇七九一层公然九五剑民莖中

I could haver agree with her nor

(A) was Kary (B) Mary was

(D) Mary could (B) did Mary

(C) could Mary

16. We all agree that Mary is not foolish nor

(A) does Susan (B) doesn't Susan (C) in Susar (D) isn't Susan (F) Susan is

17 He used to

sing when he was bathing. still used to ... when he bathe.

(A) Bing (3) being sing (0) singing

(D) having sung (E) be singing

I can never get used to ... bread and butte for breakfast.

(A) have (3) has (C) having (1) being having

(B) having had

19. No sooner halo.

the house than ne skoutÖG TOR

4) did he enter (B) he did enter-

(C) had he entered (D) he had eatore.

(F) was he entering.

20. Hardly *****, one house when he shouted for help.

(A) did he enter (B) he did enter (C) had he entered (D) he had enterou

E) was he entering

wiik kis father, he left the house angrily¡ (Note the arguing case before he left the houssi

Argued (B) Being argund (C) Arguing

(D) Having argued (E) Having been arguing

••ue thought of her beauty. (He was thinking of her when he was lying in bed.) (A) Lying in bed (B), Have laid in bea (C) Laid in bed (D) Being lain in bar (B) Having lain in bed

(The man

proceeded with great care, chased the tiger.) (A) Chased the tiger (C) Having shased the tiger (D) Being chased the tiga. (E) Having been chased

the

(3) Chaning the Tiger

man shouted for help. (The tiger chased the man.)

Chased by the tiger (B) Chasing the tiger

Having shamed the tiger

Having been chasing the tiger

Having Been chased by the tige

AT. 198 Mʊvea intu a*. (Nosinatawi

Absolute).

(A) Being newly painted".

(B) Having been newly painted

(0) The house was newly painted

(D) The house being newly painted

(E) The house having been newly paintED 26 He went to the barber this morning, ne

(The cutting

ng of hair was not done by him. Someone else did thie for him)_

(a) cut his hair (8) had out his hair (C) would have cut his hair

(D) has his hair cut. (B) had his hair cu

marks):

25 nd 5-27, find, without using tables

the value of xy.

the value of (log 25) (log, d)

SECTION D: (50) marks)

Answer my THREE questions in this

10

In the figure, all the marked angles are right angles

Figure

Express OB, UC, UD, O in terms of and hence show that OF: 0416. (H) Show that the lengths 48 BC, CD, DE: forma geometrical progression. (H) Find in terms of a, the

the perimeter of DABCDE, leaving your answer in surds (iv). Show that the areas of ▲ DAR, OBC, OCD, ODE form geometrical progression.

Find in terms of a, the of ABCDE, leaving your answer in ads

(3)-D is the mic-poun of a uno segimas An ur lengin 4, XY the perpendicular bisector of AB

and XD = 36, YD 2 By finding the values of fan AXB, tin AYB, show that SAXB + LAYB * "90",

Comtuar une equanon zan 34 # out 24.

Show that 18 in Dot of this equation,

By expressing each side of the equation in tezona of tand and substituting x for zhat.tan 18′′ in a root of the equation 5x 10x + 1 =

Deduce that an 18",

equations of two curves C, C2 are

PRATNATALIE KEN İSKAANN ir ne turning points of C and C2

Find the equations of the tangents to Cat the three points where Cs and intersect. (1):Sketch, in one diagram, the curves C. and Co

(A) livet (B) were living (C) woula nave lived (D) had lived, (E) have lived

the end of this month, wẹ examinations.

all

our

(A) shall finish. (B) finished p (C) would have finished (D) are finishing (E) shall have finished

a letter at twelve o'clock tomorroWA shall write (B) wřite (©), am writing. shall be writing (E) have written

Kacco.

last month for he had been stayin

bad not some (B) wouxu not come (C) was not coming (D) did not mame

(B) has not cons

as not com

He said that he would have been robbed 15 tam strong young man

(A) did not come

B) could not come

C) was not coming

în time.Y

(D) had nos ouse

ware not some

John wishes that his mother, t him to

A) allows (B) is allowing (C) has allowed. D) will allow · (E) would allow

Mary Wishes that her mother yesterday

(á) does not eve

(B) did not stop.

c) has not stopped.

ker going

(D) had not stopped.

(E) would not stop

11. I think that it is time you .... working.

(4) begin (3) are beginning (C) will begi (D) began (5) have begun

12. Either the naughty boys or the youngest girl

among tkan ........ taken away my umbrella. (A) have (B) has (C) in (D) will be

Neither the youngest girl nor the naughty boyi

... escaped punishment.

(4) have (3) has (C) is (D) are (E) will

27. He went to the tailor again for he

He wanted the tailor to make the coat for his

wanted to make a new cont

made a new coat (C) had made a new cost wanted to have a new coat gade

(F) was going to make a new coat

We

mus ucen for the accident

(As a matter of fact, we bad not been there,}

(A) were (B) would be

(5) would have been

29. He *****

(C) went (D) had been

in that case, he would not have bee caught. (In fact, he had not left and he was caught.)

(A) should leave (B) had left (0) lerv.

to leave (B) ought to have left

(B) ought t

30 Mary Bald sne would never cons again,

the harshness of the boys. (Afte

for the (A) owing to (B) due to (D) on behalf of(E) coming from

Answers to Szer4168 29

ZD)

11. D 12. (B)

22.

3. (D

13. (A)

237

4(D)

14. C

24.

5(E)

15.

16

17.

18.

20.

Correction

кже

The correct answer to Sentence. I should be

(E) are

Economie &CPMULEOVAffairs Answers to Exercise No. 27

9. D

215%

16 1

10. E

37. B

11 E

18.

12. D

13. B

·14

19. E

20.

I did not think that he would come and Mary did not expeat of his coming....

too (B) nether (C) either (D) also as well

calculate the angles and

(i) calculate the length of the track, BCDF (correct to. 2 significant figures).

is the

ligh prove th

to the figure, ABCDEF (u v teilway uzik 2.Qare the centres of the equal circles each of radius nile. With the notation and measurements (in miles) marked in the figure)

show that P235/2 miles,

it a variable straight line passing through the point (8,0) and with gradient

Is another variable straight ine passing through the origin, making an angle of 45" with Zy and

with gradient ma (O< my €1)^{

is the point of intersection of Land Eg

Find the relation between wid my

"Using a diagram, show that (8, 8) is one possible portion of ♬

Using (1) et otherwise, Lid the equation of the circle on which P. must less, and a

iv) The circle in (1) intersects the line, y=-* (x - 8) at 4 and 8. If the mid-point of AB

(a) Given that tan

prove that siri.

show that the equation à cos 0 +6.sin 6

251 (c+= 0,⋅

(ii) the general solution us sue équation 18 cos 0

are the solutions of the equation

show, without solving for 4 and 2, that