二期星日一十月二年九六九一層公年八十五國民華中
"KNGLISH (15):
強志試題預習
數學科 (十五) 歐陽路文
育教僑華
1969
頁三第張六第 日五廿月二十年申戊园复WAH KIU YAT PO 日橋
135 A train travels 120 ml. at uniform rate; if
the rate had been 5 mph more, it would have taken 20 min. less for the journey. Find the rate of the train.
1969
會考試題預習
VATHEMATICS
LESSON 15 : SOLUTION OF SQU-
SOLUTION: Let the train's speed be x apn
then, the original time taken And the time taken, at (x+5)mph is (20
-120 hr =(22° - } ) Ar
英文科
(十五)
hr
hence
SKAPLE
Solve 3h+kmilḥk
26. 3k-4
120
120
1360
[x) (x+5)
It is obviously that hek 0 is one solution Suppose that ' £) (ie, both A and £ are non-ten)
[x-40)(x+45.
40 or 45 (rejected)
Ex(1) hx
Jet A=z
The train's or
al speed is 40 mon
Ba then fird
3A+B=11
Similarly, Eq. (2) becomes: 2A-3B=-L
9A+1?B=33
·BA-128-10
174.
17
Subst
into Bal(3); 3(1)+40=11,
or 3xx
x20why
(x+3)(x-2)
Tx+316x-21
5 TL 6 A number of two digits has x for its tens-
digit and y for its units-digit; also the sum of the digits is more than 10 What are the
digits of the sum of the number and the
obtained by reversing the digits 7, Show that the tens-digit of this sun is always equel to the sun of the other two digits.
*** 10 SOLUTION: Let 10x+y be the req'd no. s.t.
Then, there exists two nos. u,vs.t. x+y=10uty here u49, 59, and way €9 (" +€ 949=18)
the original no 10x+y the reversed no. 10y+x Arid, their sum = (10x+y)&(10y+x)
±, 10(x+y)+(x+y)
100+10(*7)*7
x+y=10u+v U+Y≤ 9
Which is the three-digit no. form by the sun. And, the sum of its 100-digit and unit-digit U‡V Which is exactly equal to the 10-digit (w/v).
EXP
HINTS &
TO EX. 14
for
non-zero number
the given equations
+2='49
Cube the given equation:
By subs
Divide all romerators resp. by their denominators. Then!
-(3 + ——- ) + (5+ ---
(b)
=(3+247) +(3−2/2)*
TX-8)(x-4)
2x-12
2x-12
[ ( x − 1 2x+3 5 ) = {(x2 - 12x+32)) = 0
EXPLE 3 Solve
Solution: From E.(2)*
= 8
50 (3) inté Eo.(1):
-(x-5)
=(2)
NOTE: When the pair of simultaneous ecu is formed by
one liner together with one quadratic, we usually solve the equ, by substituting the linear into the quad
(3x+5)* +4x==
((3x+8)= 7x7464xxx+64 (7x+6)(x+8),
then
16(x*47x48)
Note: (1) In writing down the solution, care must be]
taken to pair the values correctly.
-3
or (-8,-4); (-14, 14). It should noT be written as x=-8 or -14; y= -4 or 14 The work may be much simplified, if the. quadratic has factors. As in the Abou- example:
Eg.(1) can be written as {x*-*)+4x+4y
(x+y){x−y+l}, eitherx+y=0 Tor x-y mo
y=-xor
Subst.Evex into Eo.42):
•··=x+4
Substa yx+4 into] Eq÷(2):4(x+4)=3x = 8
(mem)(m2en* -mni)
=[(3+22}+(3-242)] [34-1 ]=198
(a) x2 +8=(x+2)2
(x+2}{{x^=2x+4)-(x+2) ] =0
(b) So the given ernation!
(6x" +22x312)-2(4x2 +17x+15) (2x2+5x-
(x2+17x+15)(2x+5x-3) = -2(4x*+17x415) (4x2+17x+15) [(2x2+5x=3 ) = ( 4x2+17x+15)] = 0
(4x+5)(x+3)(x+3)==0
-—or -3(trebled)
6) (a) log 2.5= log 10- log 4-1-2 log 2 = 0.39794
log 2log 3-10g 2+10g 10
1.1761
(b) 108 15 = log: 30
f) log. 0.12 lög 12
7) 10F(x-y+log(7x-Ry)=
105(x3tv3)-10R()
From Ea.(1
From Fc (2)
log 100 og 342 10g 2-2
1.07918
2
7x-8y) 10-100
x2-xy+y*
•= x+y=20' on
x into the quad ecuation: (x-(10-x)] [(7x-2(10-x))=100
(3-5)(3x-16)=10 (x-7)(3x-10) ≈ 0.
ANS. (7,3) or (365)
x = 7 or 33
Taking logarithm:
log 1.832. Tog 0.93
Tog 0.93"-log 1.832
0.2630 0.2530 T-9685-0.0325
-8.35
***
Note: If it is desired to do the last step by taking'
Care must be taken forse cannot find the
(to base 10) of a negative number
log log.
EXERCISE 15
1) Solve the following simultaneous equat.
(a)
y+6x=3xy
(b) rax+by c
Ixtay
2) Solve (a) 2x-3.
x-1 x+2
-=2÷
EXAMPLE AS Solve
(2)
SOLUTION:] 56.(1)+] Eq. (2)x2; (x+y)** 16
x+y
Eq. (1)-Eq. (2)x2:] (xy)* 36,
From Eq. (3) and Eqs(4), we find the solutions] (+1,+3);' (-1,-3); (+3,+1); :( -3)-1) -|
(b) f(x
3x + 1 27. }) = x2 + y2 − 6(x − y) *
3x
X-9
・メーム
Solve the following pairs of simultaneous equator
(a) (x2- 5xy + 3y2 + 3 =
Answer to rapor XIV.
Poverty is a relative term applicable equally to peer or peasant who cannot maintain the standard of comfort prevailing in his particular social class,
(24 words)
faper XV
Complete these sentences by adding words opposite in meaning to the ones underlined;
1. Three months after the manager had engaged the
cashier, he
his for dishonesty.
2. The magistrate praised the bravery of the boy who
tried to save the child from burning and criticized the
of those that ran away.
Ons of the boys, is very silent all the time, but the "other is very
and hardly stops to breathe."
One of his uncles is very mean and gives him nothing for his birthday, but the other one is extremely
John was sound asleep by ten o'clock, but George remained all night;"
He wanted to know not only the time of the ar
of the train but also of its.
A philanthropist is a lover of mankind and a
is a hater of mankind.
Honesty is a virtus but dishonesty is
person is a
A credulous person is a person who believes anything he is told while a person who doubts everything.
10. The ascent of the mountain was difficult but tha
was easy
Fill in the missing words in the following sentences The meaning of the word and number of letters in it, and the initial letter are given:
He spent half of his money and then garbled and lost the other half so that he was soon (9, without money.)
The huses began to shake during the earthquake and several of them ca 19. fell down in a heap), burying the people inside them.
The driver was de
07. Blinded) by the bright head-lights of the approaching car and couldn't see where he was going
She liked the home-made cake very much and so ane asked her landlady for the r
(6, instruction:
for making something to eat.
When he reached home after walking the last eigno miles he was absolutely e
(9, worn out).
He is the most e: (9, active) person I have ever met, for he never seems to rest for a
moment.
Although the boy couldn't swim he made a very p. (6, courageous) attempt to save the drowning child.
No one showed any o
(8, pity or regret) when
He lost his money because he had always been such a miser.
His wife died six years ago and he has remained (7, a man whose wife has "aled) ever-
since.
10. The parents became extremely a⠀
(7, worried
when their son had not returned by eleven o'clock,
C. Complete these sentences with the correct tense of
the verb in brackets:
1. His arm that had been (a))
was very badly (b)
Although he had been (a),
he (b)
(to be),
He had (a)
isting) by the wasp
(swell) the following day.
(offer) another post,
(prefer) to stay where he (0)__
(118) in the sun for two hours and then he suddenly (b) (spring) to nis feet and (o);
(run) home
Last week the hangman first (a) (hang) his hang)
coat on a peg and then went and (b)
the murderer in the prison yard.
She told me that he had (a)
(tread) on the (bita)
dog a foot and that the dog had (b). him.
3. Rewrite the following sentences, replacing each
group of underlined words by a clause of equivalent maning-
1. I got up early with the object of seeing tha
sunrise.
2. We do not know the reason for his acsence,
3. Watching the train go out, we saw him waving to us.
4. I have very little hope of your success..
5. That is undoubtedly the answer to the problem,
but I cannot understand the method of your solution.
6. In spite of his eminance, he was an approachable
persor
There is no likelihood of his arraying tonight. 8, We do not know the time of his arrival.
9. We took every precaution against being seen by
the enemy:
10. Every man was treated according to his deserts.
4) X starts to cycle from Fat 10 a.m. and reaches Qat
2 nm. Y leaves G at 10:45 am and reaches P at 1:15 pa Find when they meet
5) A garden path, bounded by two circles, is gravelled
the cost being 6 12s. Along both edges.
at 28 per yd
T
of the path is a stone edging at 3s per yd., the cost. being£19 168. Find the width and the inner radius of the path.
6) Find a number consisting or two digits such that one.
sum of twice this number and three times the number formed by interchanging the digits is 183 and such that the number exceeds by 5) twice the préduct of, its dicits,
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