1970-05-19 — Page 22

頁二第張六第日五十月四年戌庚屬夏 WAH KIU YAT PO

英中會考附加數學(二)答案

學英文院撰答

B.K, Certificate of Education Examination (English)

Additional Maths. Paper II

的到

SOLUTION

Section A

2,ab

報日僑華

ohsina

排課

九一外活動就不同了。 :: 有之。可贴在學(正在學校求學)的靑少年對 【境癌的關係,財不能參加的有之,或自我维修的 一時參加壐校外程,或因時間,經濟和滑 公、工商管理等),破對於某維學術有興趣,鐦臨 的。阿如某些人需要某種竪識(如電腦、新數學 一以需要,也可以不需要,但是就者是不可以不要 | 基斯于木門瑷抑的遇,在需要上設,後者是可 薇育,上說,前者是屬于學控教育,後者 的,在性質上說-前者是屬於理校, 活对等都是:它和校外森程足不同 上課之外而作其他有教育性的一切 所鹋跳外活動刨除正式在課室

動應怎樣安排

·青少年的課外活

二期星「日九十月五年〇七九一屋公年九十五國民華中 育教僑華

鹽的

外有

是藥

論來

[冖 J 演習,其野营,野癸合批 [:])郊外旅行(琉際誠校際):朗利用禳

動的幾個例子來談談吧, 且可以加强教育的效果。現在雞蛋出關於課外活

日少年教育的進行,不整可以究實發育的内容,而 ,也没有心神去接受了。所以外活動,對於實 「總有很寶貴的知識和道域,皃眾們到了這個時候 一的話,那就會因體力上的疲乏,心理上的壓心, 月· 其學習興趣,啓發其營梦思想:加强其體力發展 上和心理上)丙方面,正在發展,如果一天對

● - 爲每一個少年,在求學時期,身心一生 ,則他們的殺許就會滿生毛病了,有鷸腳不醚發

一張常識和技術。 ,如西傷、沿街、菜、推等,以共狂收 時明或其他寇茲的時機,訓科總生育率狀體工作 〔四JH包含救傷等)習:利用餘

芋 時間,演習安通安全服務,

識別證號,怎麼通過馬路,以灈凇安法做 交叉路口或操出將處,假帶種種米,而神

,多訓姊學生防火演習,以卅逛其防火常識和技 丶Cu在郊外行滴當的時撼,說可以一些有甄 (二)防火数智,可以利用課餘成放班時間 一地的事物,指示學生硏究功課有關的各磺開價

·魔宗斯年行龍橋、

|游泳以及各種如暢的比賽。。 一、六必要時可利用機會舉行、阿步、 脞報、環境的潸聖靈課金的佈置,爬山、撈

,實帶的主觀條件,去學自運用了。」

到兒還心散,以致荒度他们的學業,的岔路上法 ||館」。(若沒有限制的玩號、鋸戰,也很容易使 如果不然的話,也就會走入「玩物寶志,梁荒於 而運用的妙站,就靠你的心靈了。總之, 「活動,能够運碼得識,就可以促進教育的成功, ,,上而的無吮例子,亦不過忍略那大嫻罷了i

12,6 – 2√216 - 2 √√18 ± 12

30 – 12,√6 - 18 2/18 x 12 + 12

(√√18 – √12)2

Positive square root of 30 - 12√6 1 No18 or 0.779.

2

From (1) & (2)

8

k (say)

From (3) 5(3k) + 3(−2k) - 7(k)

2rd

12,

英中會考附加數學(三)試題

HONG KONG

CERTIFICATE OF EDUCATION EXAMINATION (ENGLISH)

1870-

ADDITIONAL MATHEMATICS

PAPER III (MECHANICS)

Time allowed Two hours

Answer ALL questions in-Section A, and THREE questions from Section B, taking NOT MORE THAN TWO from each of the two groupin.

Untess otherwise swisted. irradonal umbers tee v2亣n the avrwers aped not be replaced by zciet approximations

Take gas 9-8 metres/sec in the metric system, or 32 ft/sec in the British system.

SECTION A (40 marks)

Answer all questions in this Section.

In the differentist wheel and axle shown in Fig.1, the

diameter of the wheel is 2 ft, and the diameters of the

two partions of the axle are 5 in and 4 in, respectively.

t effort (in ib wr) is required to raise a load of 1 too. wt,

If the efficiency in this case is 70% ?

(4 marks)

Effort

Loud

SECTION

(60

marks. ALL questions

carry

equal

sacks.)

•Answer THREE questions from this Section, taking NOT MORE THAN TWO from each of the two groups,, -All working must be shown. Whenever necesary, explanation must be given.

Group I

10.

A uniform bu AB of weight 10 kg wt and length 100 m is hinged to a vertical wall at so that it can turn freely in a vertical plane. It is kept in squilibrium by a light and inextensible rope fastened to B and to a fixed polat C, 60 cm vertically above A. If angle-BAC =60°, And, by a graphical method, (a)' the lansion in the rope, and (b) the magnitudc and the direction of the reaction at A

If the tension in the rope cannot exceed 200 kg wt, what is the maximum load that can be suspended from the mid-pdint of the bar?

Three coptic forces are acting on a rectangular- lansina OABC placed in a coordinate system, ar *shown in Fig.6.

Find (a) the components of the resultant force tr Waha ̈OX and the OF, direction; all

(b) the moment of the resultant about (9)

(c) the co-ordinates of the point at which

the line of action of the resultant cuis the Yaxis.

52 lb wt:

2

sind

29 It we

:hs stationary or la motion),

In Fig.7, the block ABCD of weight W, lies on the inclined plane. A force P acting through the centre of gravity of the block and parallel to the plane is used to pull the blocks the plane. If the coefficient of friction,, between the block and the plane is (whether the i find the frictional force F between the block and the inclined plane when',

a) is just large enench to rauca motion:

By calcurating the values of ♬ corresponding to a few convenient values of P (ebe £ 'w0, 9

or otherwise, sketch the graph showing the relationship between Find P ́s P. increased from 0 to B

2.

Show that if P is increased beyond. Wising + icca)1

and

the bigck will overturn before slipping.

2008 13

(+ 2x) − sin(3 + 2x).2sin(3=2x)

2x)

A particle of mass

moving with constant velocity 2 collides with another particle of mass 2 moving with velocity in the same straight line and the same direction as the first particle. If the two particles stick together after the impact, find the velocity of the combined ma

What is the loss of kinetic energy due to the impact?

(5 marks)

A garden roller of weight, W and radhus is to be pulled

`up a rep of height h (Ev ) by a force of magnitude. P acting through the centre of gravity of the roller and . perpendicular to its axis. The direction of the pulling force is as shown in Fig. 2. Find the least value of required.

(5 marks)

(since

2003

4com

3 ing

G05 ∞ – raingsind

- – 2001 ∞ )0089 - (3 – reind ) sinė - 0

since sing and cose are independent (or more correctly, linearly independent) trigonomet functions

and:

In Fig.3, the block 4 has mass 4 kg, and the suspended.

articles and have inasses 2 kg and 3 kg, respectively, The horizontal table is smooth; the pulleys are light and frictionless the string is light and inextensible with the portion setween the pulleys horizontal. Find the net force acting on the block.

(6 marks)

Smooth horizontal fabio

Fig.3

A shell is projected from a point P with a speed of metres/sed at an elevation of 30". It explodes when it reaches the ground on the same horizontal level as P. A1 P the sound of explosion is heard sec after projection. If the speed of sound is 'e metres/sec, show that

*Neglect the resistance of the air.

((8 marks) (d

A boat crosses a river from a pioint A to another point B. downstream on the opposite pink of the rivery the banks being paralle. The length of AB 1:200 actres, and AB makes an angle of 60" with the banks, as shown in Fig.d. The river cunent has a uniform velocity of 2 meiros/sec. parallel to the bariks.. In order to follow the course along AB all the time, and to reach in 2 minutes, the boat must sail at a velocity of u metres/se, at an angle of a with AB. Calculate the values of and sine

2.metrewsee

A motor car of mass 4,000 15 activorat the bottom of an incline with a speed of 30 m.ph, starts to go

up the incune, and reaches the top with a speed of 15 mph. The faciine is half a mile long, and makes an angle of sin with the horizontal, If the frictional alatanos against the motion of the car le

constant and soul

to 10 lb wi, calculate....

(1) the retardation of the car,

(b) the tractive (pulling) force on the car;

the work done by this force in going up the tricline,

Find also, in ft Is wt,

(d) the Thus of civetic energy of the car;

(e) the gain of potential energy of the cas,

(f) the work done against the resistance,

rolng up. the inicline.

Hence, use the principle of conservation of energy to check the remali to (c).

A particle 4 of mass 1 kg is connected by a spring 04 to a fixed point 0. When 04, is rotating about O in a horizoutal cincle of radis vide the agrime exerts = force of 25kg wt on the particle towards O

·Find the angular speed of DA ARG

If now the system is enclosed in a fixed horizontal rough circular ring, centre and internal adjun

20 cm, as in Fig.8, and if the angular speed of OA. is increased to 63 radians/sec (with the spring QA remaining straight), find.

(a)

the normal reaction of the ring on the particle:

the moment about O of the Irictional force between ths article and the ring, given that the coefficient of friction in 0-25; Agent

the power (in metre-kg wt/sec. ) required in overcoming tha friction in this mation.

■2e a(sine))} Let

Gradient of the line AS AF

Gradient of the perpendicular bisso

Midpoint of AB i (24, 51

of the perpendicular bisector as

distance from (0, 0)

A uniform circular plate of mass 200 gm and radius 12 cm? has two small masses of 300 gm and 500 gm fixed to it at

and respectively, as shown (Fig. 5). If: G is the centre

of gravity of the system, find the values of arid 04.

.5000n

spring

Horisontal

Félag,

A track of 101a) mass M; Mfg is moving on smooth horizontal rails al a uniform velocity . The

mas My is projected from the truck with a velocity a relative to it and in the same direction as V

(s)

Udag the principle of conservation of linear momentum, find the new velocity of the truck.

(b) If the projection of the mind hnnies.The Ihich to test, and Vainterins or:

is projected from the truck with velocity relative to the truck junud in the opposite direction as V; find the velocity of the truck after projection.

(Centre of circle)

If the mass

(11) 2.5

¥10825

HOW

2(a-b)

P(1) - (b-0)

(2)

* - (a+2b-30)x~

(b+20-3

(a+2b−3c) – (b+20-38) — 2(a-b)

(b−6)o – (a+2b–30).4 ~ (b+20−3a)•2 (8b-8b-2b+2b) + (-86+120-48) + (−4a+68−28)

Since:(x-1) RU YA Y VA LOUVOIR DIF(X) the produet (x-1)(x-2) is also a product of P(x) ***** p(x) by (x2-3x+2) by long division to Divide the other factor. It is (b−c)x + b

and 5 -

310552 105521

310852

210g 5