1984-11-02 — Page 26

頁二第張七第 日十初月十年子甲曆夏

1985

中學會考試題預習專欄:

數學

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·明德出版社 盧雄國提供資料

MATHEMATICS

I.K. LO

MILL & DALE PRESS LTD.

Test 3

Answer ALL questions in Section A and any FIVE in Section B. Section A (405)

1. Find the area of the

V-shaped polygon in figure 1.

Figure 1

. If the area of a face

of a cube is increased

by 96%, find t

(i) the % change in

length of the

1985

中學會考試題預習專欄

地理

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•藜基施

GEOGRAPHY (7).

Y.Y. LEE & K.C. CHOI

MILL & DALE PRESS LTD,

Questions for Revision, 17. Below is a photo-

graph taken on Cheung. Chau Island, Hong Kong. The features shown on the photo resemble a certain landscape found in limestone area.

Name the type of landscape that ïa found in limestone area and explain its formation.

On what type of

rock do you think

features of similar

appearnace may

WAH KIU YAT

報日僑

longest diagonal,

(ii) the change in

volume.

6. In L, Bare

the roots

of the equation

2

3. If the nth term of an

A.P. is 5n-3,

(i) find the first

term and the

common difference.

of the A.P., (ii)find the sum of

first 10 terms of A.P.

In figure 2, a circle is inscribed in AABC.

of FDE=55° and [DEF=60°, find ACB.

Figure 2

5. In figure 5, 1D | BC, /ABC=50°, [ACB=30°

and BC-10 cm, find the length of AD.

Figure 3

develop in Hong Kong. Give a reasoned account of it.

Suggested Answers: 1. In the limestone

regions, Such a type of landscapé is known as Karren landscape, which is marked by deep and narrow grooves separated by round or flat topped ridges. The deep and narrow grooves are often produced by solution along joints since joints in limestones are generally well- developed and the rock, which is made up of calcium carbonate is easily dissolved in dilute carbonic acid formed when rain water absorbs.carbon. dioxide, as it falls through the atmosphere the joints are thus gradually opened up. or widened as rain-water seeps through them. Grooves, which are known as grikes, are. therefore resulted. They are separated by the flat or round- topped ridges called clints.

Limestone is absent in Hong Kong and there- fore we cannot see at first hand the results. However, similar features can be found on granitic areas, e.g. on Cheung Chau Island. It is because granite is also a kind of well- jointed rock. On the rock where parallel joints are well deve- loped, rain-water, humid air or salt

spray from the sea

3x-8x+2=0

2

find (i) +82

(16)

7. Simplify

1-a

L1+a

1+a 1-a

1-a

+a

Section B (60%).

8. If the sum of firstn

terms of a progression

(2n+1)

is

(a) (i)

find the first term of the

progression,

(ii) find the second

and the third term of the

progression,

(iii)what kind of

progression is it? why?

(b)Find the smallest

number of terms must be taken of the series such that the sum is greater thau 171.

9. (This question is for

Syllabus A only).

As shown in figure 4. L'

is a straight line of equation 4x+3y+k=0. C is a circle which touches the y-axis and centred at 0. P is a

will remove the

soluble material such as feld-spar along the joints, Weathering which concentrates. along joints gradually enlarges them and deep and narrow grooves resulted. They are found separated by the remaining parts which look like flat topped ridge. Such

a type of landscape on granite is known as Pseudo-Karren,

14. Landslides Care very

common in Hong Kong. Give an account of all the factors responsible for their occurrence and

suggest some possible ways to prevent them.

Suggested Answers: CAUSES OF LANDSLIDES IN HONG KONG:

Landslides are very common in Hong Kong, especially in the rainy summer months. The factors responsible for their occurrence are:

1. Types of Rocks.

common

Granite is a rock in Hong Kong and it is easily subjected to weathering, expe- cially under the moist and warm climate which encourages active chemical weathering. Thick layers of weathered materials are usually found on slopes. The weathered mantle may have a depth of 200 feet. These loosened materials are very likely to slide down steep slopes whenever there is a change in the environmental factors, e.g. heavy

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五期星

parabola with vertex

at the origin and focus at E.

(a)(i). Find the value

of k

(ii) Find the centre

of the circle. (ii)Find the equation

of the circle. (iv) Find the

(b) Find

日二月一十年四八九一展公年三十七國民華中 育教僑華

of students. For 105 students the cost is

$955 and for 92

students the cost is $844.

(a)Find a formula relat-

ing the cost and the number of students.

(b)Find the cost of

picnic for 320 students..

a

(a)Find the values of

f, g and c.

(b) Find the centre and

radius of the circle.

15. The following table shows the result of 100 candiates in a Mathematics test.

Frequency

Mark's

coordinates of A and B.

20-30

4

2.

30-40

11. In figure 5, VABC is

40-50

10

an isosceles tetrahed

50-60

20

ron.

.60-70

28

70-80

20

80-90

9

90-100

4

(1) the coordinates of the focus F. (ii) the equation of

the parabola P.

Figure

10.(This equation is for

Syllabus A only)..

The cost of a school picnic is party constant and partly varies as the number. rainfall removal of support or weight added above. In some cases, landslides take place where the more. resistant volcanic rocks overlying weathered granite. In these cases, land- slide happen by under- cutting, i.e. the weathered granite is removed first leaving the volcanic rock to stump down.

Climate

The uneven

tribution of fall

is also an important contributing factor. From May to September, Hong Kong may be affected by stationary trough which may bring continuous and. intensive. rainfall. The record of 375-500. mm a day is not. surprising. The soaks into the ground and may act és a lubricant or destroy. the cohesiveness of soil. All these render. the slope unstable. Moreover, the heavy rainwater may add weight to the slope and make the whole mass become more susceptible to down- slope movement.

3. Structural Condition

The hilly nature of Hong Kong is also a

favourable factor. The abundance of steep slopes provides an ideal condition for the occurrence of

landslides,

4. Vegetation Cover

Since it has been believed that veget ation can provide a protective cover,

the

VA=VB÷VC=10 cm, AB=BC÷CA÷6 cm. Calculate

(a)the angle between

planes VAC and ABC.

(b)the area of AABC, (c)the volume of the

solid.

Figure 5

2 2

12. If x+y^+2fx+2gy+c=0

represents a circle passing through (1,1), (1,3) and centred at 2x-3y+6=0...

scarcity of a binding vegetation cover is. considered as a contributing factor,

too.

5. Human Activities

Due to the rapid increase of population and the limited supply of flat land, high buildings have been constructed on hill- slopes. It is already. accepted that the existing natural hillside slopes, where "made up of culluvial"

material, are in state of limiting equili- brium, since they are not the final slopes of these hillsides, Excavation or cutting of those slopes auto- matically increases the slope angle and this increases the risk of landslips.

PREVENTIVE MEASURES:

In an attempt to prevent landslides the following ways are. suggested:

1. The Government should

limit intensive development of those mid-level areas where the soil is of colluvial origin and the hillside slopes are in excess of 35°.

The Government should immediately review its current land policy with a view to decent ralizing the urban areas and utilizing some of the flat land in the New Territories for the purpose. This to be preferred to further exploitation of hilly torrain involving large scale cuttings and

is

(4) Find the mean

score in the test.

(ii) Construct the

corresponding histogram of the above frequency

distribution. (iii)If 75% of

candidates passed in the test, from your histogram, determine the

pass mark.

14.If 3x-4y-14z-0 and

2x−y+4=0,

(a)find the ratio x:y:2, (b)In addition, if

4

-3x3-3+8z3×16,

find the values X, y and z.

excavations.

More carefully survey should be done before construction.

Surface drainage channels or conduits can be constructed to. drain the water on the slope. In all ground susceptible to soil creep, water service mains, particularly those carrying water under high pressure, should be constructed of materials which are not of brittlë nature and thus particularly libale to fracture arising from differential movement of the soil,

5. The laying of a layer

of 'Chunam plaster of cement on the surface of cutting is also effective in pre- venting large quantity of water: from seeping into the slope.

6. As some light

preliminary movements. probably take place before the rock mass breaks loose, suspected slopes should be detected oftenly. Both the Resettlement and the Public Works Department should continue to act on complaints about possible dangers in existing squatter areas. In addition, regular inspections of these areas should be made by experienced engineers to watch out for possible danger spots and to take

action when necessary

to alleviate such danger.

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