白緻頁四第張三第日四十月二年子壬雇夏 WAH KIU YAT PO
【 1972英文中學會考試題預習專欄-
堅道英文書院主編
數學科
(#)
Mathematics
(Lesson 22)
Solution to exercise 21
(1) Lot - -
(yk)2
(wk)?
(wk)?
1)
eight or the disca
radius of the diso,
thickness of the dis
Constant
WILBIL
報日僑華
二期星:日八十月三年二七九一年一十六國民華中
Let d be the common difference The 3 sumbeza are
1972英文中學會考試題預習專欄 3
5. Who wants to go for a valk
A.
堅道英文書院主編
(a - ¿) + a + (a + d) - 27 Ja 21
英文科
(#)
(LED (1-0)2 + + + (a + 1)* • 293
the three numbens are 4, 9, 14
Prove that the sum of the terms with in the n bracket of the serier 1) + (3 5) + (7 + 9 + 11) +
*
1315 +17 + 19) + ***** 18 2° and that the sum of the terme ini
the first n bracketa i8 2x2( n + 1)2
solutions. The first term
bracket
-32 x 1 → 1
The first term in the bracket.
73 x 2 +
The first term in the 4th bracke
- 4 x 3 + 1
first term in the nth bracket (n-
+1 = n
number of terms in the
bracket
The sum of terma in the nth bracket
- |2(n − n + 1) + (n − 1) x 2]
the common difference in
21 + 2 +
Sum of terme in the first n bracketi
- (a + 1) - (• the first bracket has tera second bracket has 2, etc.)
Sum of terms in the first a brackets
플(n
constant
..w = kr) - where k is a constant】
Lot w1r 2, and hq be the weight, radius
and thickess of the first diac,
Let W and h2 be the weight, radius. and thicmess of the escond discs
Geometrio progression
A number of quantities are said to
when they be in geometric progression increase or decrease by a constant factor.
The constant factor is called a Dommon ratio,
We have the following formulası
株
~~ fiv
The ratio of their radii i8 41
Series
A series is a succession of quant
ities which are arranged in order accor ding to Bom definite law.
Each quantity in the serien is cal➡ led a term of the Bezien./
the e
The term written in a fora de- pending on a fe usually called the gen- eral term. This general term must be such that by substituting particular values of ʼn we may obtain any particular term which is required.
Arithretical progression
An arithmetical progression is series in which successive terms increase or decrease by a common difference.
We have the following formulas:-
where
(= a + (n-1)d
lant term
n no. of terms
(3) Find 3 numbers in G.P.. whose sum ia
19 and whose product is 216. Solutions
Denote the numbers by
When
Thus the nu
or 2/3
are 4, 6, 9
(4) Insert 4 geometric means between
160 and 5
Solutions
We are going to find 6 terms. G.P. of which 160. is the first and
the las
Let x be the common ratio
Then
160%
Taglish Language (22)
Answer to Isthe 21
There are different ways in which an Adverb Clause of ConcERRION CAN be expressed
Examplest
A. By though* or sitnough" i
Though the weather was bad, we ge- cided to go on our journey.
notwithstanding that (in spite of the fact that)'
We decided to go on our journey “ notwithstanding that the weather was bad,
By
'however, followed by adject ive (or adverb)
However bad the weather was, we decided to go on our journey. By as with an adjectiva
(or an verb) going before it?
Bad as it was, we decided to go on our journey.
By all the same " I
The weather was bad, all the same, we decided to go on our journey. Answer to Question 1-8 of the last issue:
a. R
It 18 always possible to change the Degree of Comparison of an Adjective or an Adverb in a sentence, without changing the meaning of the sentence': Examples.
A, Tokyo is the biggest city in Asia
No other city in Asia is as bi as Tokyo..
C. Tokyo.ia bigger than any other
city in asia.
Answer to Questions
10 and
10. S
3. Causative Use of
Interchange of Aotive and Passive
17. R
18. B
Anewer to (20)1 - R
19.
Complete the following sentences with the most suitable answer
you fond
1. Ara:
A. Yes, I do
B. No, I don't
C. Yes, I an
D. No, I ghan
Were you at the cinema last night?
A. Yes, I did
B. No, I wasn't
C. Yea, I were
D. No, I am no
Must I go by train?
A. Yes, you need
E. Yes, you are
No, you needn't
No, you mustn't
Need you leave all your papere
all over the floor?
4. Tea, I'm afraid I must.
E. Yes, I need
C. No, I need not
D. No, I mustn't
The proof of this theorem is avak1- able in any standard textbook Discriminant of quadratic equation
gome want to
B. No, no one wants
C. Yes, someone docą
D. No one does
3. Nat do I
There is a hole in youF COAT,
P. Of course there íá...
Q. Yes, it does
R. Yes, it is
S. So there ju
T. So it is.
Why didn't you weita to me?
I didn't
P. NO
Q. Yes, I did H. So I didn't S. But I did
Of course I did.
I feel sure this dog vill bite ne,
P. Yes, I feel
Q. So I feel
R. But I don'
S. Of course I don't
• You couldn't undexatauk a gorg
No, I could t
No, I couldn
R. Yes, I couldn'
9. So I couldn't
10. It wasn't mê,
P. Yes, it wasn't
Q. No, it was
R. But it was
S. So it was
11. The
The situation couldn't be much A. Hoj
could
B. So it could
C. Yes, it couldn't
D. But it could
12. The train never used to stop her
A. Yes, It did
B. Yes, it didn't.
G. No, it did
D. So it did.
I have never been to Berlin.
A. So does he
B. So hasn't he
C. Nor hasn't he
D. Nor he has
14 Ee-
always makes flatākons
A. But you too
B. So you ão
C. No, you don't
D. But you don't
Bis shoes didn't fit him well.
A. So didn't his shirt
B. So his shirt didn't
C. But his shirt did
D. But his shirt didn't as well He wasn't late last fine.
P. No, he wasn't, wasn't he "Q, Yes, he was, was he
R. No, he wasn't, was, he 8. Yes he wasn
HAB he
didn't come early encuch No, I didn't, did I
Yes, I did, didn't I
R. No, I did, didn't I
T: (P) and
18. The chair wasn't broken yesterday.
P. Now it was, want t
Q. Yes, it wasn't, was 1s
was it R. No, it wasn't.
3. Yes, it wasn t wasn't 1. (P) and (B)
19. You are rather late.
P. Yes, I an, aren'
Q. Yes, I am, an I
B. No, I am not, am I not
S. No, I am, an I
They gave us a
a lovelý teav Yes, they did, did they Yes, they didn't, they did, R. Yea, they did, dim't they
No, they didn't, did they T. (A) and (s)
Let and be the roots of the
common dif:
ference
first term
sum to n term
When 3 quantities are in arithmetical progression the middle one is said to be the arithmetical mean of the othar two.
The arithmetic mean
Examples
The sum of 3 numbers in A,P. 18 27 and the sum of their square is 293. Find then, Solution Let a be the midale ora
160
32
** The means are 80, 40,
Theory of quadratic equatio:
Theorem".
where 8,
constante and a is called a quad- ratic equation' in
à quadratic equation in x cannet have more than two distinct roota. (In general an equation of nth degree cannot have more than ʼn roots)
— 480 is called the disorining ant of the quadratio equation
Coneider, the following
(AV)
4a070, there are two distinct
real roots..
there are two equal real roots
<0, there are two imagina
sry roots and they
are conjagate of each other.
perfect square, there aze two rational roots
Relation between the roots and coeffic~ ients of the equation
Exercise 22.
(1) For what alues of n has the squa➡
tion
equal roote?: (2) Let and be roots of the equation
fana tie value of
(2) ∞ B2
(3) Given
(111)d-f
are roots of (1
0, find the equation whose roots are 13 and K.
(4) Prove that the sum of n terms of in
"series 5 +55 + 555 + 5555
+1
10
11