百二筅弘匹第
E六初月正戌庚醫
WAH KIU YAT PO
日僑華
三期星日一十月二年〇七九一曆公年九十五國民華中 育教僑華
一名的歌頭 中文中學會考試題預習專欄
僑
70英文中學會考試題預習專欄
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數學科
MATHEMATICS (15)
(十五)
„dadratio. Expressions and Equations ja one or MOTS Variables
Before proceeding to algebraio methods it is 'necessary to bacome conversant with the various typan
of numbers with which mathematical reasoning is ¡concerned.
Consider a straight line that can be extended Pindefinitely in either direction. On this line choose
a point 10' to represent zero and mark off to the right to represent the positive numbers, The negativi: numbers will be similarly marked to the left of "01: along this line.
Any point on this line will represent a number according to the chosen scale, and any such number is known as a real number.
Real numbers are subdivided into two groups, (i) rational numbers (11) irrational sumbera.
A rational number is any number that can be expressed as the quotient of two integers (whole numbers) Thus t, 4/3, -22 eta,, are all rational numbers.
An irrational number is a real number that cannot be expressed as the quotient of two integers,
Thùn No3,7. L are examples of irrational numbers,
Consider the equation à s
+ 2x +
(x + (x +
(-1)
(-1)
480)
2A
From this formula it can be usen that the roots
of the given quadratic will bei
∙ (1) real ir b2
(11)
> 480,
compler numbers if b2 4 480
(iii) coincident af b2 - 480
(iv) rational if b2 - 4ac be a complete square,
Example 2 (1) Find to two decimal places the roos
of the equation 2x - 7x + 4 = 0
(11),Find the roots of the equation
5x 4*
In this cage
-(−1) ±√/ [(-7)2 - 4.x 2 x 4] 7±√(49
32)
-7=127 7± 4.123
11.123 or 2.877
(using square root tables.
2.78 or 0.72
(11) In this case
--(-4) = ~
4 (6-4)*
4-1 [10-40] 4 = N (-24)
10
2
10
2 = No6 x Fl
226
英文科 (+) 王淑方。
LESSON. FIFTEEN
CHAPTER TWO.
GENERAL ENGLISH
(G) VOCABULARY TESTS · (The Choice of the
EXERCISE 18
Complete each of the following sentences by underlining the best of the alternatives given. DO NOT write the answer in the blank space. (C.S.C. EXAMPLE:
1966)
The man feared his wife would die that night, because the doctor had described her condition as
fair, moderate, critical, unsafe. | doubtful.
rambled,
strolled,
Of all the books in the library this to my most likable, most likely. favourite. favourable, preferable.
[(b) He down the street looking at the goods dia
played in the shop windową.
loitered,
journeyed, travelled
(c) The boy was asked to give a brief,
he had been doing that morning.
history, anecdote, story, tale, acco
the police that he had lost his wallet. reported, announced, stated, informed, declared
((d) He
made,
of what
Note: Since the result in (11) involves √-2 cennot be worked any further,
Theorem If of and ♬ be the roots of the equation
0, to prove that ɗ-
dB -
He finally:
success.”
achieved, performed, became.
I had a noiiqay to-morrow. hope, like want, with desire
(g) He was, so
recover.
severely, deadly
11 that they thought-
seriously fatally,"
badly..!
(h) He paid quite a lot of money for the prec atone but found later that it was not true, good, invaluable. genuine.
(1) The teacher observed that the class had mad
that term both in Mathematics
little
English.
advancement; step
progress:
Improvement
sae quantity (-1) found in this result is usually denoted by the letter 1, which is the first latter of the word "imaginary!.
Definitions:
(1) A quadratic expression in x is an expression of the form az2 + bx + ☺ where a, b, o are constants. (2) A quadratic equation in a single variable x 18. an equation of the second degree in I of the type
ebze om 0, where a, b, c are constants, oF an equation that can be reduced to this form.
Example 1 Solve the equation
(x = 4)
Multiplying through the given equation by (x − 1)(x = 3)(x – 4) to clear fractions.
3(x-4)(x-1) — 4(x-1)(x-3)+5(x-3)(x-4)=U 3(x2=5x+4)=4(x2~4x+3)+5(x2=7x+12)
3x - - 151 + 12 - 4x2+162~12 + 5x
34x + 60 -0
17x+30
From the previous formula
-b + √(x2 - 400), ß
480)
480)
XB-|-0 + √(B2 - 400)} {~D~~(6′′ - 440)
20
(-b)2 - [^[p2 - 4x0)]2
(2
· 12 - (12 - 400) - 423 - 1.
Otherwisi the equations
(x − α )(x − ẞ) - 。.
(1) (2)
and
The man told the days to get out of his garden because it was his private.
dodanian, ownership
(k) When I was a DOY by brother.
üse
He
cate. property,
possession,
to go tor long walka with
was using
was use, used.
- on the bed with a sigh or relief.]
land, lie,lied, lain-
(a) The paper had been
into small pieces. Tom, Forned, teared, tored
No one would believe the story because it was
credible
credulous, incredib
was so bad that it was complete
(2x
(x-6)=0
or 6
4. second-degree (quadratio) equation in one. variabis alwaye has two roots, a third-degree equation (cubic) in one variable always has thres solutions, and so on.
when the roots of an equation involve i -((-1) they are said to be complex numbers, and otherwise they are real roots, if awo roots of an equation are equal they are said to be coincident.
--
Thus the roots of a quadratic equation in one unknown can be real, coincident, or complex numbers. and it is to be noted that complex number roots can be shown to occur in pairs.
When a quadratic equation, which has been manipulated into the form ax + bx + c = 0, cannot be solved by factorisation it will be solved by means of the formula obtained as follows s
Dividing through by
Completing the square of the L.X.S. by adding th @quare of kalf the coefficient of x to each side.
4a
2
430)
24
- 400
will have the same roots and are known as equivalený équationé, and the coefficients of the various powers of x in the two equations must be proportional.
Expanding equation (2) it becomes
x2 - ( d + B)x + dB mo Comparing equations (3) and (1)
d.ß-- dB-
Example Form the equation whose roots ars
(1) (11) of
giving the
coefficients in each cana in terms of ap 5. 0.
Les ; and, be the roots in each care. Then the required equation is
(1) dirß) - I
Lißin
therefore required equation is
(11) α
+B
nand úr it.
illegal,
illegible
igible.
ǝhe decided to join the teaching
proffession,
affesion
legible,
profession, profesion, prófessian,
The visi at Her Royal Highness was an gettable
occassion,
occasian
ocassio
occasion;
(未完轉入第四張第三頁)
d. B. - (d+ }) (B • }) -α.g. 22.
B
2.
1.aB. dj + ह
x2 + b2 • o2 - 280 .
'herefore required equation in
blate)(x
AB
0163