1973-12-20 — Page 14

頁二第張四第日六廿月一十年丑癸歷夏

WAHKIU YAT-PO

報日僑

四期星

日十二月二十年三七九一年二十六國民中育教儒望

Elementary Laws:

If a,b,c,and d are real numbers.

1974 中學會考試題預習專欄

堅道書院主

数學科(課程甲)(七)輿

真方程式・従早一財條 例え請求過小西真

決定文値

3 x + 2y + 1 = 0; X-9 -3 = 0

1. If ayb, then atc sbtc

1874 中學會考試題預習專欄

2.If aybandex, then axyb or 3.If ab. and c=0, then scbc

堅道書院主纇

数料(課程乙)(七)交長波

MATHEMATICS (7)

4. If an and cco,

5.If ab and b>c,

6.If a>b and c>d, then a+c>b+d

7.If a>b and c<d, then a-c>b-1

Solution to exercise.

Let a be the first term of the progression,

a be the common difference,

·a + 60

1o [ 28 + 9å] = 320

Example 1 If a and b are real

numbers and abo, prove. 2.2.

that (ab) (a−b) 4

Solution: (a2-b2)2-_(8-b) 4

-(a+b) (amb)/-(a-b)4

- (a-b)[(a+b)-(a−b)2)

(amb)(a+b+a-b)(s+dwa+b)

社講韮線株式

(程式

(A)通式:Ax+by+cco

(B)黒斜式 10,t)為り軸距

y=mx+f

iCray | Polk, y1). Pr(x+,4+)

77-7 7-42-J

該品直線交無線株式

then a bo

then ac

Ad+Big+2

A1 1+ B2Y +12=

X: 3x+x+1+k(α-Y->) - 0 - 11

4ab(8-b)

from (2) 10a + 45d320

(2)=2(3)

20+ 9d64 2a+ 124 88

3d 24

8

·Example Find the solut. set of:

Subatdn8 Into (1) B+4844

Sum of the first 18 teras

Solution:a) Method.18

3メータ++ (メーリーコ)

(エ) ショ

P1 ! X, Y), P, (Xx Jr) Px (xy).

何が各共値

(DBA)

戴式音(90) 110,f)

(0.0) 12 (0, +)

常事()時

試

女通過集一度町並木

ネート

截距式

-182(-4)+17(8)

9(−8+136)

1152

The perimeters of the sucess- ive triangles are f0cm,5cm,

Sun to infinity -

-200m

The area of the sucosesive triangles are 30sq.om., 7284.

Sum to infinity - 30.

40 sq.cm.

-5x+2>0⇒(2x−1)(x-2)

(2x-10. and

x-20) or

(2x-140 and

x-2x(0) -

orand

x<2}

yor x

(x>t and x>2

(1:12

The solution set is:

or k

Method 2: Tabular ananpis

(法線式:AB程式内田

OABO

PAB法線OL長

昔AxtBy+co為化試

4x+54 +20-0 側) (43) 黒(カラー)求

= 緑方程式

(黒式)

A

If 2x -5x+2 - 08x=1 or 2

A

c = 0.

+2

照明同号

例

313,3) M2. 株式

・

y-x+>(kx-1)=0.

び開の値は、必通過

{x: %<x<2}

Let n bt the number of even numbers between 14 and 200 inclusive-

200

14+ (-1) (2)

Sum of the all-aven.numbers between 14 and 200 inclua per ive -

(14+200)

10058

(1-2)(x-3)>2

(x-2)

(x-2) (x−3)>2(x-2

ovided

x=-5x+6>2x ~8x+8

x-3x+2<0

(x-1)(x+2)<O

(x-120 and x-2(0) or

< and x-2>0) 20

→(x1 and x42) 'or (x and

x>2)

(KX<2) or (a false stat-

ement) 1x2

The solution set is

(F)直無虹之垂直距離

P1 = {}=x, Co-O+

Demo-p

2=263)+4

1400 1x15x-129+8=0.

為法爆式,並求其與切。

三角形三中線照

2試通過み+=0

31-412-2

5412

三直線

4. Let N be the numbers of multiples

of 10 between 14 and 200 Andlusi

1ve.

200 - 20+(N-1)(10)

200 - 20 .10

N19

Sum of all multiples of 10 between 14 and 200 Inclusive®

- 12 (20+200)

2090

Example 3 Calaulate the limiting values of x and y fron

11x+yx35

(2)-(1)10x25

x2

(1)x1111x+1.1ý<110

P若原野 10,0診で知

厳正昔P無 10,0 三黒側 介袗知耳同側d恣

+

株式

P=

緑間

the Simultaneons inequan

若も通過原10)

3-9-4

x+y410

五:赤黒1-312) 豆直線

向上時為正商

(3)-(2)→10yz75

若草

The limiting values of I

and y are x>25 and y<7k

Ax+ By + C INA+B?

21+39 +8=0P8Fate.

4-43 41-38 +4=0

1 51+ by-pol

Sum of all even numbers from 14 to 200 inclusive excluding the those which are multiples of 5

10058

7968

Inequalities:

2090

A quantity p is said to be grea- ter than another quantity q if (p-q)| is positive.«(ice/ a>b)

We have two kinds of inequalit- 1881

1. Consider x+120

This is true for all values of x becsuse x2=2x+1=(x−1)2 which is non-negative.It is called an alsolute Inequality..

2. Consider x2-4x-50

It is true for some values of x only and it is called a condit- ional inequantity.

Exercise 7

1. If a,b and carg rgal numberoy

at prove that a2+b2+c22ab+be+qa

2. Find the solution set of

a) 12x2-23x+1020

b) x-4x-330

a) —— - 1>0

4)| 2x-1 <5

3. A rectangular board is Construct← ed in such a way that its area must not be less than 18 sq.ft, its length must not exceed 6. ft. and its width must not 'excess Bft. If its width must not exceed twice its length, find

a) the minimum.Length possible

b) the minimum width possible

形式表示 則

A = Ad By

In A2+B*

(G) 直系15ieTone 7

Rtraight lines)

若通過 改直線に立黙

※軸証(0)

2 (2, c) = 2x + 34-5=0

Aidt.Biy+cit ke(Asat Boy+ca)

RA

= cosgo"=

136=Rin190-540)=60054

所三間距離

10

み)+300)+f.

A =

精酒

Rin 548 00036

fum 70=00011 = ANIC + DAT

0

X A1d + B1 1) + C1 =0 / A 2 d + B x y + Cz

設目黒(32)主直線

3d-q= −4, 1-0 1 - y = 0

d=

+(-3)-3(2)+12

-9

1

而該點

題解答

2 Kb kir 18

130