1979-06-11 — Page 15

有教僑華 買三第張四第日七十月五年未己服

1979

WAH KIU YAT POI

邹日僑

●期星

cos20c082-0

Let

日一十月六年九七九一层公年八十六闔民鑒中

́. A(t, 2t) lies on (1)

中學會考試題預習專欄

n2+1

Differentiate

(1)

in20

2yy

附加數學科

建議參考資料(二)

明德出版社提供

ADDITIONAL MÄTHIS, (II)

2

COS: X

→ sin x

f'(x) ■(1+sin3z){2cosx)(-ainí)

(1+sin

x)(2sinx)cos7

(14sin x)

Bin2

2-27sin20

(1) is $20c

(sing+18) cos2k+1

2*ain20

(2winga cong+18)

√(2sing

sin20

†(20) du

Whe

Wher

# [1 − ( })"]

2+),

(21)

du

equation of tangent

A 18 ven hy

17.

- }]

(ii) Comparing

1-

with ty

(Ang.)

the sl

(Ans.

(2x)()

(1+(---)2)° /2

(-1)-(0)

2. (2x

The 5th term

°C, (2x2)^~^(-2x)

2n-12

Since this is constant

5th term

(Ans.)

be (h, k)

Pch,k)

sin20

•k+2

sin2

k+1

sin20

Putting k+1,

the last exp, s

cos20cos2

sin2+1

ain20

Since the statement holds

and if it holds

also holds

hence,

by mathematical induction,

it holds for all positive

integral values of a. (Ans.)

(i)

Lin (1

(1)

dz (x + 2y)

(Ans

dy

dx

·(2) (As)

(2) .(3)

dx

(x+2y)*

(1) and

-[(x+2y) (2+)]

[(2x+y) (1+2)]

(x+2y)

-2x-4y-xx-2y

(x-2)(x

require

- √

|x(2 - x)| dx

x) dr

(x+2y)2

(1) and (2) intersect at P(2,

(Ans,)

(x+2y)

3x dx – 3ý

(x+2y)

(2) and (3)

and (3)

(Ang.)

(** Py)3 ***

(2) and (3) intersect

at Q(1, 1),

(3x 11⁄2 – 3y)

+ 28 )3

(1) and (3) intersect at R(1, 11).

(Ans.)

2y

(3x dx - 3y)(x+2y)

3x(x+2y) dx - Jy(1+ 2y)

3x(x+2y) (-2)-3(x+2y)

(ii)

(2)

-6(x2+ xy + y2)

rom (1) (Ans.)

Q(12.03

The co-ordinates of M. are

(2x-12)2 + (2y)? 48x+144+4y2-16

-12x+32

which is the locüs

12-

2y

sq. units, (Ans.)

(cost,

.(1)

·(2)

cose, co

icose sing

80

ine cose

+25–10x+x: −80

é, sinė

2x

of roots.

~~(~2)

Where X X are the

x-co-ordinates of A and B

respectively¿

x-co-ordinate of M,

the mid-point of AB

cos(9, + 8,)+isin(0 +82)

cose1 +isine

+ isī

(cose, + isine,)

[com(-2)+1sin(-8)]

cos(0,-

(iii) Volume of the solid

generated by the 3 curves

Volume generated by the region PRS

Volume generated by the

egion PSQ

- xf" [(12- y)- 1] dy

-x" (11- y)dy

dy

In20

Whe

os28:

sin2

sinze

2sin20cos20

2 in20

cos20

is true for n

Assume that the statement

is true for n

cist -qis¤

From (1)

Mis (1, 4)

Now, slope of AN

slope of the line LAB-1

the line through MLAB

is given by

0

(1)(x - 1).

(Ans.)

x dx

7.(i) Let

cise, cise

cia(0

cia

- (@2+

(11) The argument of the

last expression is given by

Y

- 2x + 2x

16.12

10

cubic units.

(Ans.,)

4x

(i) Substituting

(t2, 2t) into (1),

(92

$20)

(1%, }) (Ans.)

(s2,25)

(iii) The tangent

is given

slope of the normal

S

This is also the slope of

normal from (3, R(S, 2S)

(1,-2)

11.(i) (1+ ax✦

(11).

[1+ 2(a + bx)]*

=(a+hx)

x2(a+bx)2

4x(a + bx)

bx

4ax+ 4hx

(4h+ 6a2)x2

(Ans,)

A(1+ a2

[1440x4{4b+6a2)x2+...]

(4b4

(Ans.)

Since

(48~1)

+ (4b+ 6a2- a)22= 0 when

is very smal) 0

4a-1

2

6a-

-32

The approximate root: required is

(Ans.)

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