1978-02-10 — Page 23

12.A piece of wire 3 long" is bent into the form an isosceles triangle, of which one angle is 100° Find the longest side. 13.A cask contains only wine at first... litres are drawn and replaced by

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育教僑華

210x

Py+ NOJ

−(m + Z)i+(n + }}}

2

3x+3y= 60

(1)

2

+ y

-20 (Ana.)

n

+

(2)

1978

1 is a circle with centre

From (1) and (2)

「中學會考試題預習專欄

(0,0) and radios (20,

(I)

(II)

(III)

D

end a

(111) The equation of a

Therefore,

Mit & Data Peti

straight line passing through

4(2,1) and

(8,4)

BAE AT

(AE

+

AF) (Ans.)

數學十九

2 y

The circle

X " +

20

(2)

Exercise, 9.

(2)

20:

4

新數學 三十九 魯榮家

MODERN MATHEMATICS (19)

Answers to Test 7 (cont.)

11, Let the first teru and

the common ratio of the

be a and r respectively.

Since the second term is 27.

ar 27

()

The sum to infinite is 121

Substitute (1) into

(2x)2 y

y = 2 o'r ym-2

➡4 or x

herefore, C, D are (4,

1214

and (-4,-2).

2 am 243 2430 (2)

(iv) CD =

From (1

-J80

2ar

Ska (3)

Substitute (2) into (3).

243 243r)x54

2√20

-2 times the radius.

of the circle,

Therefore CD is one of the

*8, ap

diameters of the circle,

文長波

Mathematics 19

Answer All questions in

Section A and any Six questions in Section B. Section A

1. If

2P find p' in

terms of x and

Write down the a

of the series

1+3/1+3+5

1.1+4 1+447

th

term

3. If the surface area of a sphere increases by 44%, what is the percentage increase in its radius?

4 litres of water. 4 more litres are next drawn and replaced the same by water. If the volume of water is now 19%, how many litres of wine were in the cask first?

14. Water is discharged at

5500 Litres per min from a reservoir of surface area.

7200. ភk » រៅ + inta with surface area

one

5bud (sq.m. The sides of

both reservoirs are vertical planes. By how much does the difference of the levels of the two surface alter in 15min? (Correct to 3 sig. figure)

(1) What are the above

methods called usually? (11) Suprose air being con-

posed of 80 nitrogen and 20 oxygen by volu ume, try to estimate the average relative

ass of air.

(iii) Comvinte the following

tables (one method for each gas):-

Kases

molecular

ABS

suitable method

02 NO2

HC1

N2

ន

243r

- 243r+ 54.

14% (i)

9 +2 1)(3r

Marks less than or equal to

cumulative fréquency

20

ཆབ་

3&m

In the figure, if ABLUC

and DCLBC, find the length of. AD.

5. ABCD is a trapezium in

which AB, DC are parallel.

If AB-7cm, DC-3cm and if

the area of ABCD is

In the figure, ACLAB, ANLBCBX and AY ere bisectors of LABC and DAC respectively. Prove that: XY//AC MAR 16.The side CD of the aquare

ABCD is produced to E; P is any point on CD; the line from P perpendicular to PB cuts the bisector

of LADE at Q. Prove that a)8, P, P, Q are concyelfs

BP-PO.

16

36

When r

27

27

·61

(Ans.)

76

When

18 sq.em. find the area of ABCD..

7.1.

HO

If 3sine +4e089-5, find

化學

40%

the value of tane.

(Ans.

Therefore the first term

and the common ratio of the G.P. are 81 (or 404) and 1/3 (or 2/3) respectively.

12. (1) ZCAX + LACX 90

since ZACB 90°

(11) tan 2CAX -

LBCX + ACX

ZCAX ZBCX

CX

-90

AX

tin BCX

From (1)

ACAX

2 BCX

XH

AX

AX XB

iii)

If AB.

9cm

AX-

X

Then XB = (9

From (ii),

2

CX AXXH

Area of the squar

CX2

+ 9x

(iv) The expression -x“

will have maxinnu value

when x =

Therefora

-2

2-15

0

(11) According to the graph

above,

32

(80% of the total

number of candidates) students with marks less than or equal to H therefore, the pass

(above)38, 15, the probability for Lett

ing a preen marble for each drawn is 2/5 and that for

mark is

a red marble is 3/5.

(1) The required probability

H

125

(ABM).

(ii) The required probability

(蛋)(修)(号)+(蛋)(号)(音)

2

+9x

30

6

(Ann,)

the maximuEL

area of the square

2

~(4.5)2 + 9(4.5). -20,25

13,(i) ar = √(x =

BP -

(11) TE AP

Then

+

(iii) The probability that at

en marble

In the figure, AP is the tangent at A to the circle, centre @ - Find P in terms

of a (Geometry theorem

·

need not be quoted when used.)

A ball rests against a floor and a vertical wall as shown in the figure. A point P on the rim of rhi ballem antem

from the floor and the wall respectively. Calculate. the radius of the wheel. (Geometry Theorem need not be quoted when used.) Section B

9. The first term and the

common ratio of a G.P. is. x and y respectively. (a)Find the sum of the

(i)1st, 2nd and 3rd teras (ii)4th, 5th and 6th terms (iii)7th, 8th and 9th terms

in terms of x and y. (b)Hence, show that the result of (ii) 18 the geometric mean between the result" of (i) and (iii). 10.From the equations

least one

18 drawn

2

. (Ans,)

1- (probability that

11.

2) " + ( y − 1) ==

no green marble is

(y—4) 2

drawn)

1 -

98

(Ane.)

183

16.(1) AE

(11) A

AP-1 +3

I

FP

1:2

- 1)

= {(x - 8)2 + ( x = 4)2)

4x

2y)

(iii) Let-AČ - m(ÃË) + »(TP)

י.

where m¡n are acalars,

1 + J = m[I+ }5)+n(41 + 1)

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4x-2y-7x-0 and 3x+8y=29z', find x:y:2. Hence show

x2+4y2=3422.

a

In the figure, ACB is semicircle, `centre 0 its area is bisected by a line XY parallel to the diameter AB:

(a)If 4A0X=0<!, prove that

20-in20

(b)It 20-4, prove that

(十九)

Chemistry (19)

Question 28

(a) Diagram below shows

朱宏林

the apparatus used to pre- pare sulphur trioxide from sulphur dioxide; in school.

catalyst

oxygen

sulphu heat

dio-

xide

cone H2SO

4

Fek drying agent

sulphur trioxide

тесе iver

(1) Why are oxygen and sul- phur dioxide passed through cone H2SO? (11) Suggest a suitable

catalyst for the reaction.

(111) Give the equation

for the formation of sulphur dioxide. (iv) What does solid sul

phur trioxide look like?

(v) Why is a drying bulb

with drying agent att- ached to the receiver? (vi) What would you do if

you want to obtair some Sulphuric acid using sulphur trioxide?

(m) If 8 g of sulphur tri- oxide crystals are obtained, what is the volime of sulphur dio- xide used up during the conversion, méâTM

sured at s.t.p.7

(b) 200 cm3 of a gaseous com-

pound with molecular for ula NH is decomposed com-

pletely with electric aro, The products are then burned. with 200 cm oxygen. The volume of the mixture is 150 cm" when measured at the room temperature. However, ite volume is reduced to

on passing through alkaline progallol solution. (All volumes are measured at

room temperature and one atmosphere of pressure.) Calculate the values of x

100 om"

and y respectively. Question 29

(a) The diarram below shows

three methods commonly

used for collecting gases in laboratory.

(b), (i) wher

an infla-. mnable organic coupound Z were burnt in excess oxygen, 13.2 g of carbon dioxide and 8.1 g of water were obtained as the only products. Find the empirical formula of 2, (ii) Compound & reacts with phosphorus(V)chloride to give a colourless, steamy gas P which funes strongly with ammonia. On prolonged

heating with chromic acid, Z gives a substance Q which also reacts with phosphorus (V)chloride to give the same

colourless, steamy gas E. When Z is heated with concentrated sulphuric acid to 170°C or a little above this temperature, a colourless gas R is produced. R decolourises bronine water but has no reaction with anno niacal copper(I)chloride. R has a vapour density of 14. (1) Fame, giving structural

formulae where appropriate, the substances 1, Q, R and

(2) Give the equations for all the reactions involved.

Question 30

A, B and C are the three aqueous solutions, gach containing one solute only.

When a drop of C is added to 3, a white precipitate D is observed: which dissolves when an excess of C is added.

When C is added to A, a greenish precipitate E is formed which turns brown gradually on standing in air. A gives a white precipitate F with barium nitrate solution and F is insoluble in acid..

When A and B are mixed, there is no apparent change, but when con centrated sulphuric acid is run slowly down the side of the test- tube, a brown substance G is seen to form where the concentrated sul- phuric acid meets the mixed solu-

tion.

When C is evaporated there is no residue left.

When sodium hydrogen carbonate so- lution is added to B, a white pre- cipitate H' is formed. When this is washed, filtered and strongly heated, the residue K obtained is yellow but turns white on cooling. (a) Give the names of the solute

in solution A,B and C respec- tively.

(b) Give the names of the substan-

ces D, E, F, G, H and K res- pectively.

(c) Give the equations for the

following changes:→

(1) formation of D;

(ii) dissolution of D in an

excess of C;

(iii) formation of E;

(iv) turning brown of E on standing in air;

(v) formation of F;

(vi) formation of H;

(vii) formation of K.

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