育教僑華頁三第張五第日三初月五年辰丙歷駸
WAH KIU YAT PO
報日僑華
-期星
Section B
Total amount of salary she receives.
9. Let the lengths of AB and BC be x cm and
= $[2x6600+(10-1)x420] = $84900
中學會考數學科(題解)
葉柏芳。
Modern Mathematics (27)
y cm respectively
3x+2y= 38
4+*+7y =97
(1)x39x+6y=114 -(3)
(2)x2 9x+14y=194--(4) (4)-(3) 8 - 80
(2)
9.
=
1331323
Jy 10
Subst.
V10 in 3x+20=38
x=6
D
The lengths of AB and BC are em. and 10 cm. respectively.
Solution to H.K.C.E.E. 1976 (
Section A
10. (1) AŘ = 2. AP
≈ 2(AC+OP)
=
2(1 + 2) AP- AB
ARAB
ince ABCD is a rectangle
ACB350
AB 20 sin35 cm
11.472 cm.
BC. = 20 cos 35o "em
16.384 cm
The length and breadth of the rectangle are 16.384 cm and
11.472, em respectively.
Let N = 10.5678
log N
log0.5678
x 1.7542
1.9181
0.8281
Let the co-ordinates of D be (x,y)
ADBC BC
2)-(33)
=7.
The co-ordinates of
Dare (3,7).
Since ABC
2 6. +3
1+ 1
ABC 90°:
17.
ABCD is not a rectangle.
x) (x-2)
2x(x-2)+ (x − 2) ≤0
2)(2x+1)≤ 0.
The solution set of x is
[x = -< x < 2 }
Since AB-AC = CB = AD = BD
AABC and AABD are equilateral triangles:
CAD CBD-120°
The perimeter of the shaded area = 2 x r x --- units
4T
Tr units
6. Volume of cylinder
π(5) 10 = 103-210
Line
790 250 3.16
A
Suppose it is true for nk
1+2+3+...+k=k(k+1) Line (5) the statement is true when n = 1 and if n = k is true then n k+1 is also true; hence, by the Principle of Mathematical Induction the statement is true for all positive integers n.
Ans. $2.80
Distance travelled in miles
Figure 4
BR
29.
(ii) Since BR - 2CP
28
(BR)=2(CP)= diameter of
the given circle
The magnitude of BR is constant
The locus of R is a circle, centre B and its radius is twice of the radius of the given circle.
(iii) AB = √(6-2)2+(0-3)2 = 5 units The equation of the locus of Ris (x-6)2+ y2 = 25
2
+y^-12x+1)
Modern Mathematics (28) Solution to H.K.C.E.E.1976 (Paper
11. (i)(a)Since O is one of the roots.
of the eruation *. £(0) = −10+2k = 0
k =
(b)Since k = 5
10)+5(x+2)=0
x(x-6)= 0
x=0 or 6
The other root is 6.
(ii)(a)Since (x2-11x-10)+k(x+2)=0 → x2+(k−11)x+(2k−10)=0
The sum of the roots is
equal to the product of. the roots
-(k-11) - 2k-10
k 7.
(b) The given equation becomes
2
-4x+4
(x-2)2 = 0
x= 2 (repeated)
QC-2-cot25°m=4.289m
„". The area of the shadow of the
wall on the
=4.289x10xsin60o sc.¤
horizontal ground
37.14 sa.m.
13. (1)
(ii) x = 103- (iii) When x = 0
2
4asino boo90° b = 4
When x = 90
3 asin90° + beoa90°
A = 3
14. (a) Mary's yearly salary in the
first year = $550 x 12
= $6600
Mary's yearly salary is increased by $35 x 12 =8420
(b)(i) The sum to infinity of the
series
日一卅月五年六七九一曆公年五十六國民華中
The sum of the first 6 terms of the series
9[1 − (−)6]
His error
=
1.3 글루
137-1323-54
(ii) His percentage error
#
* 100%
0.14%. (correct to 2
significent. figures)
15. (1) Mean number of fire incidents
in a day
1x15+2x1
224
1.9
60
(11) The average damage per fire
incident
2280000
114
= $20000
The number of days in one year when there are 5 or more fire incidents
360 x
= 18.
16. (a) The probability that the sum
of the two numbers shown is
8 =
(b) The probability that both dice show odd numbers.
(c) The probability that both
numbers shown are odd and their.
sum is ཐ་་ - 36 = 18
(a) Two dice are thrown and the sum of the numbers shown is 8. The probability that
these two numbers are both odd
END
中學會考經濟與公眾事務科題解
Section
文光
1) What is a limited company? Distin-
guish between a public limited company and a private limited
company, Why are limited companies becoming more popular nowadays?
A limited company is a business organisation registered under the Company Ordinance of 1948 and 1967. Its capital is divided into shares and the owners are called share- holders, A limited company is also a legal entity which can be sued and sue. The ownership of the company is divorced from the management, the latter is a aasigned to a board of directors.
public limited company is of much larger in scale. Its shares are listed in the Stock Exchange and can be traded and transferrable./The number of shareholders is unlimited. and the minimum directors are three.
A private limited company is much smaller in scale, Its shares are not quoted in the Stock Exchange and cannot be traded openly. The maximum number of shareholders is 50 and the minimum. directors are tro.
Limited companies are becoming more popular nowadays because of its nature of limited liability and transferrable ownership. It can raise capital much easier than other business organisations, e.g. sole proprietorship. It permits the average individuals to invest their saving in these companies without involving then the job of management. A limited company can also enjoy. permanent continuity which other
bus organisation cannot.
2) What are the conditions of perfect competition? Describe the main features of the product market structure of:
a) fashion shops, and
5) petroleum companies.
The conditions of perfect competition are that there are a large number of firms in the industry, so that no one can control the output and the price of the products. To maintain the permanent size of the industry, there is free entry of new.
firms to replace those closed down. The products of the perfect competi tion are homogeneous or identical and therefore the price de uniform
throughout the market. Above all, the consumers are well informed of the market conditions so that price discrimination cannot be practised.
The nature of the fashion shops is one of the imperfect market in which each shop tries to differentiate its products from the other shops. through special cuttings, designs, colours as well as trade marka Each shop also exerts some control over the market through price cutting and mass production. Consumers are discrimá- nated because of their ignorance of the market conditions of the various competitive products and their pre- ference for some particular brands. The fashion shops industry needs a lot of advertising to publicise one's products.
The petroleum companies are of oligapoly in nature in which there are fever firms. There is very little difference between the product of one firm and the other. Price agreement is, therefore, necessary in order to avoid price wars. Entry into the petroleum industry is much harder but not impossible. The demand of the product of any particular company depends on particular preference of the consumers. Advertisement as well. as extra free service, like washing a car for customers free, etc. tactics to attract more business.
are
3) What should the government do about:
a) profit tax.
b) salaries tar
c) expenditure on public housing, and d) expenditure on transfer payments
e.g. retirement pension, unemployment benefit, etc);
to deal with
I
unemployment and
11) inflation,
Give, reasons for your answer.
To solve enemployment, the government should reduce profit tax in order to leave firms more ready fund for expansion and other forms of investment. At the same time, it also increases the profit margin of the products. Better profit and greater expansion means more output and there- fore more employment of factors of production, including labour force.
The salaries tax should also be reduced to enhance the disposable income of the individuals who will ultimately increase their consumption. This mean more demand for goods and services which in turn will lead to increase in output and investment. The result is more employment.
The government should also, increase expenditure on public housing as this will ensure further expansion on similar lines of industries, like. construction iron and steel industries. More job opportunities will be created in all these related industries.
In time of unemployment, the government should also increase other expenditure like transfer payments, for this will replace the reductedn individual expenditure of those who become unemployed. Total demand for goods and services, will be regenerated and therefore output and investment will not be affected and employment maintains.
On the other hand, if the government is faced with an inflation the above policies will be reversed, Profit tax will have to be increased to reduce the total fund for invest- ment and expansion. Investment demand will be reduced and profit margin will fall. Firms react by reducing output and therefore unemployment. Wage and other costa of product will fall and hence a falling price will follow.
Salaries tax will also be increased in order to cut down personal disposable income, This will react on a similar reduct in personal consumption expenditure. Demand and price will fall.
The expenditure on public housing of the goverment should also be reduced in order not to exert an excess demand on the factor industries, like labour, iron and atsel. A fall in demand on these related factors of product will result in the reduction in investment. Labourers will be laid. off and therefore wage and price will fall.
Expenditure on transfer payments should also be cut, in order to effect 7 a reduction in consumption expendi túre ' of the people. The same chain effect will follow until price returna back to the pre-inflationary period. Inflation will thus be controlled.