育教僑華頁三第張六第一十二月十年申戊曆夏
WAH KIU YAT PO
育敎僑華
1969 文中學會
1969
日僑華 二期星
題預習
日十月二十年八六九一屉公年七十五國民華中
(1) remove
(11) abolish
(iii) lessen
英文科 (木)
桂枝
iv) lightens
(v) cancel
ENG3:13H (6)
數學科
歐陽鉅女
MATHEMATICS (6)
Answer to Paper
Besides reading about the miseries of life in tragedy, we also feel a sense of "satisfaction" as WO enjoy every incident of a tragedy. Why do we feel this enjoysut? It is certainly not because we enjoy the triumph of evil over virtus – we feel a sense of estisfaction" because to all, and a debitum that triumphs oær evil
accomplish: (1) to bring to pass
material
(li) to carry on
(iii) to make known
(iv) to complete
(v) to finish:
ei (1) take shape
(11) accumulate. (iii) become true
(iv) be controlled (v) be completed
dismantle 17 (1) store up
(11) hide away (ii) break up-
LESSON 6: THE SIX TRIGONOMETRICAL RATIOS
It is important to note that:
(1) The trigonometrical ratios of an angle are numerical quantities. Each of them, represents the ratio of ens length to another, and they must themselves never be regarded as lengths.
(11) Each trigonometrical ratio of an angle depends only en the magnitude of the angle, and not upon the length of the lines which bound the angle.
(iii) The sins and cosine of an angle can never de gina-.
ter than unity; the secant and cesecant of an angle can never be less than unity, while the tangent and cotangent are unstricted by any value.
EXAMPLE 1
ABCD 18 8 square; C is Joined to N, the mid- point or AD. Find all the trigonometrical ratios of the angle NCD.
SOLUTION: Let NCD =
Hende
and that DN 1, then DC - 2
By Pythagoras
TADOR VI
Rasa the following passage carefully............
In an effort to obviate the fear of another outreak of a global war, there are pacifists like Bertrand Russell, who endeavour to establish international understanding among the great powers of the world. Ruseall believes that this is quite s difficult tank to accomplish, as long as each nation lives under the threat of the deadly weapons of the other. Unless each country is willing to get dom to
conference table on an equal footing, the ides of paaceful co-axis tence among dii, nations will never
Materis 1320. But is it possible ro nations to confer on an equal footing, as long as they do not feel obliged to dismantle their nuclear weapons? It may on a long time before permanent disarmament is observed by the powers. In the mantins, any discussion on world peace is fruitless; and if each country attempts to surpass the other in this nuclear race, and if rockets and bombs are continually perfected for warfare, will the world not one of these fine days be annihilated without warning?
(iv) break open
() break into
fruitless
(1) prevented
(11) without success (111) impossible
(iv) unimportant
(v) disastrous
annihilated: (1) completely destroyed
(11) partly destroyed (111) slightly destroyed (iv) greatly affected (v) partly affected
7. diabolical: (1) very wicked
(11) powerful (111) alarming
(iv) strong
(v) irrational
stupendous ?.
(1) stupid (ii) silly (iii) great
EXAMPLE 2. Prove that tan 60.
SOLUTION: Let ABC be an equias ahem.
Draw AD BC, then 4 ABD ACD (AAS er RHS)
BD = DC — BC
Let BDX, then AB BC2X
By Pythagoras, AD=√18"-43" =√fix
Ha ABDI
ALL other ratios of 30" 60" 45" may be found by the same method. Bare we tabulate the values as in below!
RATIO
YALUF
PE.
Since Con tan a cotec SSC
O
A
20
1
2
前
Russell argues that the only solution to world paace is the probihition of nuclear tasting for other than for the good of the world. The dropping of the atomic bombs for the first time in the history of civilization, on August 6th and 9th, 1945 at Hiroshima and Nagasaki respectively, eloquently testified to the diabolical ruthlessness of the capabilities of the boobs. The aftermath was stupendous; so much property and so any lives were obliterated in one devastating blow, the fact defied imagination. But what were regarded as disastrous weapons are now but miniature bomba. Under the menace of this horrible shadow, how can we expect nations to conduct peace talka when at a moment's notice, one of them could turn round and deliver a fatal blow, even greater thân Santicipated? In this respect, the british philosopher contends that there should be only one military force in the world to take charge of these deadly weapons. Apart from this, he is of the opinion that there no other course open to the muclear powers.
These words from the passage could have one of the meanings A or B or C or D or E. Choose the correc meaning
(iv) ridiculous! (v) immending
fatal (1) astonishing
(ii) horrible iii) deadly (iv) fading
10. contenda z
B. Explain:
hard.
(1) disagrees (11) maintains (iii) refrains
(iv) contesta
(v) tends to say
1. outbreak of a global war
2. on an equal footing
3. permanent disarmament
4. prohibition of nuclear testing
5. the impact of defied imagination
C. Make a precis of the passage, using your own words
as far as possible. Do not use more than 100 words.
EXAMPLE 3: If tán »
find the value of
2
Saturday was
64.8.
SOLUTION From th By Pythagoras,
, as shown)"
Note: We may express the exp. in terms of tane by?
dividing the exp. by case
EXAMPLE 4: ABC is a triangle such that ABC = 24′′
AC8-1100 is the mid-pt. of BC and draw)
·AD LBC před; Prove that
BOLUTION
tan OAD (tan BAD + tan CAD).
and calculate AOC
BD + CD (OD +BO) + CD)
OD Divided by AÐ:
By definition,
B-24
2.00
(BD+CD)
A
tán DAD Tên rt,^ OAD)
fan BAB (this is BAD).
for CAD
OAD(tan BAD + tan CAD)
BAD 90°- -24" - 66*
„CAB=110′′ X - CAD = 110 – 90m:
tan OAD=(tan 66+ tan 20′′) 1.3050).
OAD tan 1.3050 a 2A0C=90 - 52°32′ 37228'
EXAMPLE 5 AB-3 com, BC-
SOLUTION OF
Fram
ABP
2.3333
4. RÁG 186:48:
Ronce
= 5.0.2 Cl
1) Let X mi
- BAP = 3; OR = BAG — 33′′ 24 tan BAP
AB
RINTS & ANS. TO EX
I3 van 33′′ 24 3x0.6594. 1.9782
the distance of the town from the ho the time taken at 10 moh
Is mon har
Total time taken to cover 2X mi is (147) k=
1. h19 av. speed
which is independent with X (the distance)
Suppose that the grocer aixes 6 lb, of tea at 19 od per il with 1 to of tea at 15. per this and sells the 7 lb of mixture at 1s 6 per lb.
6 lb of tea at is 6d per lb cast 19 6d x 698% 11b"
1s
No 19 x 1-19. -the cost of 7 lb of mixture is 109.A But the selling price of 7 lb of mixture is 1874 x 7.
- 10a 60
the gain
108:64—193-5%%
10%.
Total no, or hours of sunshines for the first 6 daya. Was
11.2 x 6 = 67.2
Total no. of hours of sunshines for the last 6 days
was
AP bigests BAC, Find PC.
10.8 x 6ble. 8.
Na. of more hours at sunshines on Sunday than on
the water, (containing 0 or alcohol) ➡ the liquid containing 65% of alcohol.
the mixture containing 45% of alcohol. The gain er L, in Lm is 45% - 0% 45% The less of L. in L. 18 65% -45% - 20% The ratio, LFT 12 = 20% 45% - 29 If 36 gall of L2 is mixed with Lị, then.
← of 36 gall = 16 gall.
ANS. 16 gall of water must be added to L
5) (1)
- 90% of the pupils taks Mathematics *10%
" do not take Mathematics. Similarly (11) 15% of the pupils de not take Phy
((111)35% of "
1. Chem.
the greatest % of pupila who do not take the three subjects 10%+15% +35% 60%
the 1-<st % that take all the three subjects i
60% van 40%
EXERCISE &
1) Find by drawing and measurement, the values of
sin 35 and-cot-35
2 Given cos
find all the other
ratios in terms of þig. 3) (a) Find the value of 3. tan 45
30 +5 cot 45′′
(b) If-tari 45° find X.
cos"60"X3ain 45 ces 45 tan
·4) Find the area of an equilateral triangle whose
base is 6 cm.
5) An aeroplane flying horizontally passes, vertically
above a man's head › ten seconds later he notes that its elevation is 60", when will it be 30% ?
6) me base of a tank is 2 ft square, and contains water to a depth of 1 ft. It is filled about ano edge as shown, through 15′′. imhat is the length of AP