1975-03-20 — Page 19

Keraiance LIBRARY

2.1.MAR 1975

LAND OF THE UNDAUNTED

四期星

日十二月三年五七九一曆公年四十六國民中

3. The symbol al means. the absolu-

te value of a, and defined by

育教僑頁三第張五第日八初月二年卯乙

WAH KIU YAT PO

報日僑筆 CITY HALI.

育教僑華

Differentiating the now establish- ed expression for the volume as a product of functions of r..

point ia Pein

1075

中鬻會考專欄

堅道書院主編:

數學科(十九)·文長波

ADDITIONAL MATHEMATICS (#19) Solutian to exemiae 18

1in 2ton

and 1

Hence, A = (ra

李

行

COS

Equating this to zero and mutli- plying through. by

477

and provided A / 0, we have r2 A For finite positive rain di fand with held done fund the volume of the carie can he a small ás, W please but cannot obtain 0,

therarocer way correaponds te

477 maximum, and

4sine

4(2 + 200s 0)..

a

Thus the co-ordinates of the point satisfy +y2=4c:and the point..

lies on the circle.

The slope of the radius to this

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穷人人身

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的最代動 故激兒亂

事情女時

coa ·g = tain H The slope of the tangent is -cot 6, and its equation is y-2ain a X-2 2c0s.

-

Sicce both the circle though F and and through R and Shave their centies on the x-axis, the commos tangente PR and Q3 inser sect on the x-axio. at a point T:

TO-RO such that

問

The centrá mala

intersent. in

the circle PQSR lies on the perpendicular bianctor of its phord PR which also bisacta ON by symmetry the centrelies on the x-axis, and its co-o mine.tea

therefore 3, 0)

are n

PM

Consideration of the diagram,

* the squat or the aistиine of P from (1, 0) 1s 3 and the aquetion of the cirle PQRS is

· (x − 1)2 + y2 = 3 ⋅

Exercise 19.

** If the roots of the equation »2 −5x + 7 = U are o ant prove.

4:

¢4+34_5{x* +37) + 7{x? + ]=0}

2% Solve the equation

1083 (2 – 3x)= 10 Ég(6x2 = 19x +

秦林鄧王 鳳光

漢嬌榮引

崔隙

3. If a is a positive constant,

find the get of values of x for which a(x2 + 2x-8) is negatiys. Find the value of a if this function has a minimum value of -27.

4. Prove that

sin 3x sin x dx

27 = 7 (3/2)

5. If L, M and be the 1 mt: cand

n' tems of an A.?, prove that 1(K - N)+m(N-1)+n(LM) U

then

6. If a, a,c,d be an G.By

abtire ratio be

imiced the common

新數學 十九),謝國興·

MODERN MATHEMATICS (#19).

Vectors: (1)

Def: Any quantity which needs bota

magnitude and direction to repro- sent it completely, is called a vector. Such as Displacements: Force, Velocity.

1.

A vector is. by a line segment.

is usually representes The length of the line segment is represented the magnitude.of the vector and using an arrow-head to indicate. the direction of the vector..

2. The magnitude of a vector is the

positive:number which. ie the

measure of its length, and is de- noted by Talor OAL

4. Equality of vectors: 2 vectors

are said to be equal if they have aquel magnitude and the came direction".

5. Zero, vector: A vector whose

magnitude is zero is called a zero vector.

6. Addition of vectores Given

vectors a, b, and the sun offa, is e denoted

7. The negative of a vector Given e vector a, if a vector equals in magnitude to a but opposite. in direction then this vector is: written asend o8lled the ne gative of

vector

exists its additive inverse, such

8. Additive Inverse:

as @ + (-a) - ö.

Subtraction of vectors.

à- b=3+ (-5)

10. Properti (commutative).

of vector addition.

(associative).

111) ¤+0=¤, 0+8=0 (Jdentity)

北)亢+ (言)=(inverse)

11. Fultiplicetion of a vector by

scaler.

Given a vector à and a real number.

The product of a and k denoted by ka is also a vactor whose meg

nitude 13 k times of a direct- as if k is positive

ion is same

or oppositive direction if k 18 riegative

12. Properties of multiplication of

vector and scalar.

i)ka =ak (commutative)

ii) k(2+B) = kâ + kb (distributive), iii) if ka - then b 13. Vectors in the Cartesian

Coordinate plane,

Given 2 points A(x, y, en B, The magnitude and direction of A can be foued by the following formulae .LABL

EXAM

2.

(magnitude)

(section)

3., are the points of tsection.

AO or parallelogram ABCD.

IK

denoted by m and AC denoted by

1) BR-3-m

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