1975-05-01 — Page 19

育教僑舖,買三第張五第9十二月三年卯乙歷夏

育教 僑華

1975.

中鬧蕾污專櫃

新數學 ®

(廿五)、國興

LODERN MATHEMATICS (#25)

1. Juven gxdy+4

value of ant gx=3x-9; the

A. 18 B. 21 C. 24 EX300

Di 27%

2. Which of the following 19 the regation of the statement: For all

x of a certain est,

A. For all I, I<0

E. For all xx÷?

0. For do x, x2 0.

E. For some

3. A pirole is inscribed in a tri- angle with aides of lengtha 8, 13,. and 17 at the segments of the side of length 8, medy by pointiate tangency bar and a, with ra. Ther the tio 18 les

A. 1.3

8. 2:50. 1.02 D. 2:3

P. 7. B. 08.-20/17 T. -2 10 The sum of tile cumèrical Ou-

efficients of all the terme in the

: expansion of (x-2y)18 18

P..0 0.1 R. 19 S-1 T.-19 11. If 10812(x)+108,2(0) = 1; 0>0;

Exi, x, then x equals

A. 1/8, 1/b 0. b2 D. b B.E 12. Givon parallelogram ABOD with E the midpoint of diagonal BD. Point E Le connected to a point. Pin D& so, that DP DA. What is the fatio of the area of triangel DFE to the

area of quadrilateral ABER 7

A 1:2 B. 30. 1:5 D. 1:6

13. Two numbers are such that theiz

WAH KIU YAT PO

A. 1:1 B. 1:6

報日僑華

- 1 MAY.1975

D.37

n+1:n+11

e

+b

23. The expression:(台1}-(2-2)

the same value as:

1

A

D. 81 E.814 24. Line 12 Intersecte line 1, and line 1, is parallel to 1. The thra lines are distinct and ide in a plana. The number of points equili stant from all three lines ist A. E. 10. 2. D. 4. E. 8 25%

3636 the reporting decimal

***** is written in

simplest fractioral fam, the sup

of the numerator and denominato ris

15 B 450 114 D. 135 E15

difference, theid, and theirĽ975:

Product are to one another sa 1:7:24

The product of the two mambers ist

A. 6. E. 120. 24 D., 48 B. 96.

24

14. Let y(x-a)+(x−b), a, b

constants. For what value of x 18 y a minimum? -

A

B. a+b C. Jab

?

15. The set of values of n for whic +3xy+x+my-m has two factors, with integer coefficients, which are linear in x and y, is precisely:

A 0,12,12 3.0, 12 C. 12, -12 D. 12. E. O

heep He 16. In a famer bought 749 sheep.

pold 700 of them, for the price paid for the 749 sheup. The remaining 49| were sold at the same price per head as the other 700 Based on the coat: the percent gain on the entire transaction is

ten-mile race first beats, Second by 2 miles and First beats Phini ty 4 miles. If the runners the isce, by how many miles does: maintain constant speeds throughout Second test Thirl?

P. 2 Q. 24 R. 24 S. 24 T. 3

A. 6.5 B. 6,75 C. 7-0 D. 7.517. It is a real number anu

B

8.0.

5. A line through the point (-6,0)

evts, from the second quadrant a 41iangular region with area T. The equation of the line ist

1A, 24x+y+ 2a7-0

C.21x+sy-24 = 0

D. 27x-ay-2αT=.0

E none of these.

6. Let f(x)=x+3x+2 and let 3 be

the set of integers 10,1,2, ... 251 The number of members. s of S suot that f(e) nas remainder zero when divided by 6 19:

P. 250. 22. R. 21 S. 18

7 Given the distinct points

17

+y) Line segment are drawn cor- necting these points to each other ak to the origin o. of the three possibilities: (1) parallelogram (2)straight Line (3) trapezoid figure OPEQ,

upon the location of the

Q, and it, pan

only 1 none of the possibilities mentiored

Lat n be the number of mirs of valves of b and c such that 3x+by+b=0 and ex-2y+12=0 the same graph, Then D is:

P001R, 200

lave

5. finite but more than 2 1. greater than any finite mumber 3- 2x-3y-2=0 and x+3y-14=0, (the minerical value of N

x=b[+l-31 $ a who ea30, the

F. 0442.01 0.01<<1:: .E.

18. The sum of a teme of an

arithmetic progression is 153, and the common differense 1s 2. If the first: team is an integer, and n>1, then the mmber of possible values

F. Q34 8. 5. 6 19.

In this figure. [RPS = /FD, FD = 4 inches, DR-6 Inches, FR 5 inches, FS = 7+ inches. The Length. of RS, In inches

Q4 51

Pundetermined

S

20. The larger root minus the small er vot of the equation (7+483)2 + (2+√3)x-2=0 is P. −2+3/3 Q. 2-·√3 R. 6+3.5.

56-3/3 1.3√342

21. The number of real values of satisfying the equation

022~7x45=148

G. 2 DL. 4

E more than 4.

22. A regular hexagon is inscribed in a ofrole. The ratio of the lang- th of a side of the hexagon to the 【length: of the shorter of the arca

intercepted by the side. fas

中鬧會考專機

數學科 (廿五),文長波

ADDITIONAL MATHEMATICS (#25)

Solution to exercise 24

• n+1n+] 1 Det k

Then k

升中試中文科題解

注意:由第3至第旧题(即由第五至第40)

湾生必須在試意中作备。

̇聞每篇文字,然後把最通常的答案填寫在題

以人們現在愈來愈注重居住的環境生个 香港人来说吧,許多人而来都過慣了購 使. 的生治,可是近年來也開始注意到和生活熱器 有關的室内設

關於室←設對一般人認為那只是富有人家

家具其實我們是將室內設持並不一定要有钱 家具的,只不過是说明心思,把宝內佈置得著 用,美觀,染舒適

和怨我們把一套沙發便放在客廳襄這可 能浪费了許多空間,而且也不好。相反地,我們得 動動腦筋,把它適當地并站起來,再加上一些小擺

·設洲麼,整個客点就會更美觀和舒適 作者藐近年果香港人也意室内設計,因為他們. 愈來愈注重居住的環境

3.作者泥画设有寬敞的住宅和名贵的家具也可以进行

室內設計,不要運用心思便可以了 3.作者不赞成把一套沙發随便安社,因為這可能

浪費了許多空間而且也不好看

有些人點守時不大整纯男人约定了時間伊 往往道了半小時甚至一小時才忍的,卻看作 常又和安宮本来是了明代時入席的好有失賓,

门

201

HALII

【四期星

日一月五年五七九一层公年四十六國民華中

Tu

= 7 (8 ~ 2x) = 27) ( 4 − r).

2.a) x cos y sin à cos 20 and x sin e- y obs: » 2a sin 29

sin & cos. 26

ទ

2 sin, 28 28in 20

sine

ain oncos

sine-tain30

-30066 – 2cose 280-3sine

by Let k=

2sin7日-3日inG

3(cose-sine)-2(

3(cose+sine)-2(009"ersin20):

有些人的字迹游不自己的地址,常常故意遲到 讓進人的其他客人空,這是绝型必不得的,

光隆通寶青的妖然定了的夺的時間為

·們只有特別事情

6.作者認為有些人路常不守時是因為

孟顯示自己的地位

∵婚的意我你不必依照每组詞語的先後次序。

齕家带来了量的雨水,因此水箱的放花?含水 的触感

逆強迫

興類的發生是自然而然的,不能送

激烈的、賺利

經過一場激烈的競案後我隊終於 韓得線利之

在政府當与蔬意建設之下,不通短越南

拟战报出下面約附圖在所路與的字句;靖寫成一段 九十至一百個字的还噁文字(包括德點舒建亚所瑨

*想的字句),但必須符合附图所表示的意思

......不守時刻不但會給人家壞印象;更重要的。

值得您認但許多人不守時制已经等陪慣他 過高、何學克突策解云足年歌新九並見代學及院粗院時 如要 道嘗院小

[(cose-dine)2(1-2ainesose)

[(coss eine) (1+2sinecose)

10. (bry) + (x=y)

3. Let you am, ren and a chi: be the volume, the radius and the haight of the cone respectively then

V="r2h and r+b= 12

where V=1>r2(12-r}

_a [37 (12x2 -2)]

(24r-3r)

Ar(8

Let

=0 or 8

--877-30

25677

r gives a maximum V Hence the maximum volume of the

256.7 Done is.

Exercise 25

cu..

x

1 For a certain curve 6x+4 and y has a minimum value 5 when x=1. Find the equation of the curve and the maximum value of y. 2. The centre of two circles of rad R and r ere

ant(a, 0) where a and bare positive. The # "equation of the direct common tanm gent is x cos x + 7 sinx =& 008 §.

where and are souts. Prove that

R 008+ b con

and show that, 4 = 2r

•a• 008 ♬ = (b + 2a) con X 品

3. If tan x tan Attan B

1+tan tan show that Bin 21 + sin 20 sin 2x-1+gin 2A sin 2B3

4. Find the sum of the seriss

(1)+(1+2)+(1+2+3)+***. to n tems.

5. If the roots of x-porq = 0 are two consecutive integers prove that

(每行楼克十楼,每格一字) 我帶弟弟從天橋過馬路 1格 突然看見 個孩子越:20格 過欄干,向馬路的那面30格 跑去,就在這時候,一40格 輛貨車正疾駛而來眼50格

在

70格 面部生車的司機

眼明手快,

80格

平生熊但那孩子 格

已嚇得臉色發青面

100+

0000

下氛均秘和

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