CITY HALL
買一第張五第
日一廿月二十年午丙感夏
WAH KIU YAT PO
英文中學會考試題預習專欄
欧眼英文中學會考試題預習專欄理
#
英文科
(十四)
·許籓芳·
數學科
【十四)
·歐陽鬣女·
MATHEMATICS (4)
LESSON 14 INDICES & LOGARITHMS
We are all familiar with the following"laws:) (1) a": a". a2 = a
"GENERAL" ENGLISHT(IZ)
Answers to, the previous, exercise
1.a)The people were not '111-prepared for war since every man had been trained once in his life, in accordance with the law of the country.which wasifaithfully observed.
b)A band of well armed ruffians, some of whom werel
escaped prisoners, entered the village in the night' to steal the cattle of the villagers while they wera sleeping.
c)Getting angry at the ingratitude of the "snake which turned upon him, its benefactor, who warmed it to life when he found it half dead of cold, the woods - man killed it, without giving it time to bite him, [2.a)with; 0; b) under; on;' c) to; to;d) at;,
ejon; by;
g) to; to;. n) by;[by: (k) from.
1)of:
f) under; toi j) in;
3.a) Compound complex sentence, containing.two main clauses
and two subordinate clauses)
(1) He left the cottage-- Main clause.
(2) and after crossing the river he returned "almost immediately, accompanied by the five young men. Main clause, co-ordinate with(1)
(3) whom he had met on the road. --Adjective clause
qualifying "men" in (2)
(4) and who had arrived there with a boat-load or
commodities collected from the jungle.--Adjective clause, qualifying "men" in (2) and co-ordinate with clause (3).
་་
b)Compund Complex sentence, containing two main clauses
and three subordinate clauses.
(1) A negro woman stopped to observe me -- Main clause. (2) and, "perceiving my weariness and dejection, inquired
into my situation --Main clause, co-ordinate with(1). (3) At sunset, as I was preparing to pass the night in
a tree.--Adverb clause modifying "stopped" in (1) (4) who was returning from the labour of the field. --
Adjective clause qualifying "woman" in (1)
(5) after my explanation of which she told me, with a
look of compassion, to follow her.--Adiective clause qualifying "situation" in (2).
4.amisinformation;
g) immeasurable
b) misconduct;
c) incredulous;
r) inconsiderate
1) incorrigible 1) dissimilar
dinarticulate
e) untimely
h) refundable
Junmindfull
k) nonpayment
m)unfold
1
n) disfigure
plunreadable-
q) nonsense İADAN IL/
o) irreligious r) insensitive
SA) Indices & surda
(2) a* a"="
(3)
(4) at = 1/at = (1/a) (5) a = a; {a to!
EXAMPLE 1 Simplify (a)]
(b)
Solution:(a)Exp!•
(B)TEXD=
If x=8
"If x = a And,
prove that x2+ x” 2alka*
then, I'=(a+,
Read the following passage and then answer the questiong
elow:z
An absorbing afternoon can be spent in the fishing age of Aberdeen. One need not go there merely to have al at the Floating Restaurants or to buy fish; it is th Just to have the opportunity to take a leisurely
around and, if one is a keen photographer, there is ty of material to provide original and unusual snap-
-l
The harbour itself is always crowded with vease be of Shapes sizes and ages: large fishing Jurks, accommo ing 60-70 people and with gay pennants flying, are seen cheek by jowl with tiny sampans, each of which 1 poled by a solitary woman. Here, a big junk 19 a hive of activity for its owners are preparing for the night's fishing expedition. From every available mast and draped over the sides can be seen huge nylon trawling nets. The men are busy with various tasks, some examining the sails or inspecting the engine. Two of them are sand-papering the anchor-chain to rub off the rust before giving it a new coat of paint. The younger men are scrubbing down the decks while those women not not engaged in cooking or tending babies are mending the rents in some of the older nets. The children move about quite freely and are as surefooted as we are on land rosy-cheeked, dark-eyed mischievous faces peep out at us as we pass
We have just noticed a sea-hawker. She is a wrinkled old lady in a small sampan, laden with inexpensive plastic goods, sewing needles, reels of cotton, bunches of safety- pins, assorted buttons and everything needed by the woman. with nimble fingers as she makes clothes or patches and mendattorn garments. Opposite. the Trade School, one begins to wonder if the water really exists, for it can hardly be seen Here, packed as tightly together as sardines in a tinare the small boast which are no longer seaworthy but are still used as homes by hundreds of families. What a contrast these unpainted, dilapidated vessels make when compared with the highly-decorated, vividly-coloured Floating Restaurants with their luxurious decor- and yet these people seem very contented with their lot and wave cheerfully to us as we send our way back to the bus terminus for the homeward journey. 11.Answer the questions:
What kind of person would enjoy a visit to Aberdeen? b) Is there any difference between a pennant and a_flag?
If so, explain the différence.
Where are the fishing-net's put to dry?
What is sand-paper being used for?
e) What is meant by the word trawling!?..
f) How are the women helping the men?
Why does one wonder if water exists opposite the
Trade Scnoo17,
2.Explain the meaning of:
遊
a leisurely walk: b) cheek by jowl: c) engaged in:]
d) no longer seaworthy:e) tururious decors
3.Give the Noun from each:
a) original: b) gay:
c) various:d inspect:
d) mischievous: f) assorted: g) compared: h)contented: 4.Change the voice in each sentence from Active to Passive;
or from Passive to Active:
a) An absorbing afternoon can be spent at Aberdeen..
o) The harbour is crowded with vessels.
c) Huge nets can be seen.
d) We are giving it a new coat of paint.
e) The water can hardly be seen.
The men are examining the sails.
Note: a reel of cotton". Complete the following:"
a) a...kof envelopes: b) a of keys:.
of servants:
a
[}..**... of china?
8) a wreath of..
a suite of ARME
d) a... of matches:
h)'a'nack of
f) a hand of..
a canteen of
• yên?».
"=(a=√a^-T)*.
Ega » + Eqt2) 3.
a* − i ) + ( a − fa2 -ï }′) (39)(√a^=1)"},
KXAMPLE 3 : Solve
Solution:
(2 + 6)+(X)
Check
Lif" when
U
-67+7
62+7
+fX
期
日一册月一年七六九一年六十五國民華中
共有二于三百卅九人。 設立志學校或補習學校修珀職熱教育者,他 在私立學校方面,本活瞵生在私人所
·工教育,五一人。
及商科課程洇,共有三千三芦六十一人。 至於以部份時間在私校攻體工鸯職
XPN-UGELAKKAKEL- (*)NKEGESKE
學生人數續誌
工業職業教育
商嚣教育:一六六五人。 職業教育:一一八五人。
有下列之統計數字 校及私立搫校修醌中等工農業發宵者,牡 除上述之外,在各官立學校、津貼學
C112EKAIT -
禕貼學校:六八二人。 官立學校:四六六三人。
私立慕校,一五八人。
-(1)#PHRX-
K-11
津貼盡談「七十六人。
(11)+EASE-
-私立學校:六四二天。
私立學校:一三五四人。〔
then, x is called
NOTATION:
the logarithm of the number N, to the bass a
xlog.N
1s
The following are the main properties of logarithm: 1: If a is a non-negative number such that al, then, a
always positive, for all x (1.e. x may be negative, zero, or positive). Hence, it is meaningless to say log of negative. number or log. of zero.
2°: logal=0, for any non-zero a.
3°: log.al, for any non-zero a.
14 • 102,MN=10g ̧M+10gN
(5° log 108,
=
M log N
6":"log ̧N➡k log, N; for any keve,"
www
[NOTES (1) 10g ̧‡ 10g, # 10g ̧(M±N }
‚'ve,integer, fraction,0)
My log. M
(2) log
Toga M
(3)
lego
M
log - log N
?
Tog. N
(4) From property 5, when 1, then, log-leg Macolog_N. (5) Logarithm to base 10 is called common logarithm. NOTATION: log.. N=x, or more general log N=x. Which is most used in practical calculation, and was introduced by English mathematician Briggs(1556-1631); (6) Logaritha to base e
where
e=1++++ 2.71828 18264 ...
is called Natural Logarithm.Natural logarithm is used. in theoretical mathematics, and was introduced by English mathematician Naple (1550 - 1617).
EXAMPLE 5: Simplify (a) 2 log — - log 4 + 2 log 3 + £ Log 49. (b) ( Log 2)2 + ( Log 5)2 + (Logs) { (og 8) Solution : (a) Exp. = log (==)2 - Log = + log 32 + log, £49.
= log (35)(*)(9) 677
boy 100.
= 2
ibs Exp = {log 2)2 + { logs) +
(log 5) Log &
= (loy 2+ log 6 ) { Logs) * - ( Log 2 11 log >) + (log 5 } }
5
= { log(2 × 5 )][ (Logɛ }° - { Log. 2) ( Log 534 ( logs)]† 3logz legs
= { loge )* + 2 (log 2)log 5 ) + ( log 5.) *
Exp.
= (
Log 2 ~ ( log10)
с вод In which
EURLIC LIBRA
+6 + √3+1 = 3 + 2
solution
·L⋅ S = √-3 +6 + √ πT = A + / -
L.S
R.S.F
** L.S. # R. S! · 1=-3 is NOT a solution
ANS: =3
NOTE: As from part (il), we find that checking” is very im-,
portant. we
multiply oys introduce some roads when we
EXAMPLE : Rationalise+
Solutio
Exp =
5
the equation.
12-.22
4
- 8
NOTE:(1)ïf k' is a rational number and is NOT a perfect a power,
then, is called a SURD of the n order.(e.g.√ is
a quadratic surd.) Hence, surds are inexpressible either" as integers or as fraction, but the value of a surd can be obtained to any degree of accuracy.(i.e. an irrational
(2) A surd of any order may ha transformed into a surd of a
different order.
(3) Surds of different orders may be transiorudu luto suras oIļ
the same order, (4) Cab}* = a +
(5) A surd which is expressed so that the integer under the root
sign in as small as possible, is said to be in its simplest form.
§8) Logarithma. =,
If number can be expressed in the form a such that a*=N;
M
Log
51*
вод
fo*
/* = 1
12 log10
Vlog 10).. Log
102.
EXAMPLE 6 : Find x, y which satiary the following relation
108.(x*+ 1) 108x-108 4=1−10£{ $α)+1©B«>
Solution: Log (x2+1) - log x· log 4 = log. α- log_(y2+a^) + loga?
Loza yaz Кода
Or
водо
{x}{4)
4
HINTS & ANS. TO EX.11.
1) (a) 2xy(xy
(b) 3x(5x-4)
3)(x+1)
(c) Exp==(x*p<)^» {{*+a®)=(x*y*+f+m°}{x* - •g*• £= u*} (d) (a*- b`+ ab }{aa- b*~ ab }
(e) (x+1)(x+3)(x^- 3x+9)
(f) 2&*(3a+2) (3a-2) (4a2+1).
(g) 6x11x2- 37x- 70=(3x-7)(2x+5)(k − 2), (h) Exp. = (x+3)* −(2x)=(x*+2x+3)(x2+ 2x+3). NOTE: Apply Remainder Theorem to (e), (1) & (2),
10x*- 21x - 10=(5x42)(2x-5)
a) 1f 5x+2 is a common factor,
Then
5) IF 2x - 5 is a common factor,
Then 1001 +10($) +pno
+
ANS
P=-4 or -150
J Z + Z x 4 f g = ***
x + y = r
ence, zirgs+ay(1 2)=0 (und
2 (2+2)(1-2)=0 then. Lalor རྣཆ་རྣ ྃ 12=24 then 1 < = {* • j = xy → f}
EXERCISE 14
X
1)Find the meaning and value of a where a la ang non-zero no. 2)Simplify and express with positive indices:
(a) (0.4) (0.125)+(2.5)
(b)
(x2+
3) I x4.3, find the value of
4) Given A=3+2√2, n=3-2/2, find
(a) my (b) m2 m2, &. (c)‹ à3»n2;
5) Solve the following equations:
(a) X346 - x=2
(b)/2x37x+15 −√2x+5x- =-2x2-12x-18.
6) If a+b=7ab, then loga (lag at log b).
7) Sólve
Log(7x=873=3.
B) Given log 2=0.30103, log 30.47712, obtalo approximate values
of the logarithms to base 10 of:
(a) log 2.5; (b) log 15; & (c) log 0.12
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