1977-04-07 — Page 26

報日僑華

四期星

M is the mid-point of" AD." Find BM:BC. (Geometry

theorem neednot be quoted when used.).

In the figure, AT and BP are the tangants to the circle, AT=35°,4BOT=115°, Find BPT. (Geometry theorem need not be quetëd when used.).

7. The present population of

a distinct is 164500. IE it has increased at the rate of 14 der 1000 per · year for the last 3 years: find correct to 3 figures, what it was 3 years ago.

4 8. =

If x = -- and y=

find x in terms of z in as simple a form as possible; also find z in terms of x.

Section B. (Fach question

carries 10 marks) 9. In the figure, A and B

are two places on the earth's surface with the same latitude 67°30°N and with longitudes 10°F and 70°F respectively. 0 is the centre of the earth and C is the centre of the parallel of lati tude 67°30'N.

Calculate the distance From A to B along the latitude. 67°30′N.

b). Calculate ZAOB.

If a circle is described on the surface of the earth. with centre 0; passing through A and B, find: the distance from A to B along the arc of this circle.

(Take the radius of earth

be 3960 mi)

10. A has $5000 engaged in a

concern, and B $7500. The gross profit For year is $3200. 1 of

F

which is spent in salariés and $30 in insurance of the premises. A then receives 8% of his captical, and B 4% on his, and the remainder of the profit is divided between them in proportion of their capital. Find the net recerpts of A and B. respectively.

11. 1 man, 3 women and 4

boys can do a piece of work is 96 hours; 2 men and 8 boys can do it in 80 hours, 1 boy and 2 men and 3 women in 120 hours; in how many hours can it be done by 5 men and 12 boys ?..

12. A stone thrown into the

air with velocity um/sec, at an angle of 0° to the › horizontal will hit the

ground at a distance

u2singe

29

m, where 10,

if u=40, draw a graph to show the distance reached for 'values of 9 from 0- to 90°, and read from it (a) the greatest distance

that can be reached. (b) the values of for

which the distance is 60m.

13. Two circles intersect at

A and B. The tangent at A to the first circle meets the second circle at P andthe tangent at A to the second circle meet the first circle at. Q.

Prove that: (a) the

As PEA, ABQ are equiangular. (b) If PBQ is a straight line, ¿PAQ=90°.

then

14. P is any point on the

cireumference of a circle deseribed vith

日七月四年七七九一展公年六十六國民華中育教儒三

centre 0 and radius oct

also A is a point on

OC and B is a point on

你

OC produced, such that

OA.OB.=

Prove that

(a) OP touches the circle

APB at P.

(b) bisects the LAPS.

the ratio PA PB is constant for all positions of P. 15. 1 (x+1)(2x-3) and (x-1)

(3x-5) are either consecutive even numbers or consecutive add numbers, find all possble pairs of numbers they can be.

st th

16. The 1

8th

terms and of an A.P. are in G.P.

and the 1st

term is 9.

Find the 2nd term of the A.P. and the sum of an terms of n.

化(廿一)

Chemistry (21)

Question 35

A.

朱宏林

Several simple experiments were carried out on five metala deno- ted by letters A,B,C,D and E and the observations were recorded as follows:-

Experiment 1- Action with water:

D reacts vigorously; A reacts slowly; while B, C and do not react. Experiment 2- C displaces B from

an aqueous solution of the nitrate of B. Experiment 3 -The oxides of B and C are reduced by heating with carbon; the oxides of the other metals are not. Experiment 4 A, D and E react with dilute hydrochloric acid while C and B. do-not.

A

L

From the 1st experiment only, write down the relative react- ivities of the metals, p From the 2nd experiment only, write down the relative react ivities of the metals,

c) From the 3rd experiment only,

write down the relative react- ivities of the metals.

d) From the 4th experient only,

write down the relative react- ivities of the metals.

Place the metals in order of decreasing reactivity.

f) At which position in this or-

der can hydrogen occupy?

f) Only one of these metals gives rise to a strong alkali. Which one is it?

g) When the nitrates of these metals are heated only one decomposes to give the metal. Which one is most likely to do so?

D.

An experiment was carried out to determine the relaive(vapour)den- sity of a gaseous hydrocarbon ha- ving a formula of type CH2n+2° The results were:-

mass of an evacuated flask=26.31g mass of flask full of hydrogen

=26.52€ mass of flask full of hydrocarbon -32.40g

a) Calculate the relative(vapour density of the hydrocarbon. Find its molecular formula. Hence, what is the value of n? What is its molecular formula?

d) Write down the possible stru

ctural formulae of the hydro- carbon.

Question 36

A.

Solution C contains 10 g of sodium hydroxide per 250 cm of solution. Solution D contains 90 g of a sol- id acid with a formula of HA per 500 cm of solation. The formula mass of the acid is 90. It is found that 20 gm of solution C requires 10 cm of solution D to react completely.

a) What is the molarity of the

solutions C and D respectively?

b) How many moles of sodium hydro-. xide in.20 om of solution C?

3

c) "How many moles of HA in 10 om?

of solution D?

d) How many moles of sodium hydro-

xide react with one mole of HA?

e) Hence, calculate the value of n

in HA

f) Write an equation for the reac-

tion between sodium hydroxide and the acid,

B.

Hard water is water which does not easily give a stable lather with soap becatise it reacts with soap to form a precipitate or boun. There are two types of hardness:

temporary hardness and permanent hardness'. The temporary hardness can be easily removed by boiling. When a temporarily hard water is boiled, a deposit is left in the

boiler.

Another simple way of softening water(1.e. removing the hardness) is to add washing soda (sodium carbonate) to it; this method can remove both temporary and permanent hardness.**

a) What fons are responsible for

the hardness of water? b) Name the substances which are

resposible for the temporary hardness..

c) Name the substances which cause

permanent hardness.

d) What are the chemical names of

Boaр;

ii) scum;

iii) the deposit left in the

boiler?

e) Give the equation for the form ation of the deposit in the boller.

Give the equation for the reao- tion in softening water by add- ing into it washing soda.

Question 37:

A.

0.048 g of a divalent metal with symbol X were added into 10 cm (an excess) of 1M HCl in a suita- ble apparatus at 20°C and atmosp here pressure. The volume of hy drogen liberated was noted every half minute. The graphy of plot- ting the volume of g28 against time from the start of the exper iment was shown below:-

Total volume of i2 in on3

B

When was the reaction most rapid?

b) How many seconds had elapsed:

before all the metal had re- acted?

c) What was the volume of hydrogen

gas obtained when all the metal had reacted?

How many moles of hydrogen had been obtained when all the met al had reacted? (Molar volume at 20°C and atmospheric press- ure is 24 d.)

R

Give the equation for the rea- ction between the metal X and hydrochloric acid,

f) Hence calculate the relative

atomic mass of the metal X.. g) How many seconds had elapsed before half of the metal had reacted?:

h) What volume of IM HC1 would be

required to react completely with 0.048 g of the metal X?

B.

In the experiment as shown below, a mixture of lead(II)oxide and carbon is strongly heated in a hard test-tube and the gas liberw ated, if any, fs passed into the aqueous calcium hydroxide in an other test-tube.

༢

carbon + lead(II)oxide.

heat

tube A

tube B

calcium hydroxida solution

A grey substance is obtained

in the hard teat-tube. A. is it?

What

b) Give the equation for the rea ction inside the test-tube A.

a) What happens to the solution in

the test-tube B? Name the sub stance observed.

d) Write down the equation for the

formation of the substance you observe in test-tube B.

#

e) which property of carbon is 73

shown in this experiment? What would you observe if cal

cium oxide is used?