1980-10-29 — Page 22

真二第張六第日一廿月九年申庚器室 ·WAH KIU YAT PO

1981

中學會考試題預習專欄

Figure

A

新數學(四) 明德出版社魯榮家提供資料

LODERM MATHEMATIOS (4)

W.K.LO.

(SILL & DALE PRESS LTD.)

Test 2

Answer All questions in

SectionA and any SIX in Section B. Section A

1. In figure 1, 0 is the centre of the circle,

and ZADE=70°,

Wind

Figure J

Pind the set of values.

of x B such that x25x+4≤0 and x-5x+6>0.

If x2-x-4=0, find the yalue of (2x-1)2.

In figure 2.0 is the céntre of the circle OA=0B=10cm wang

Find 'the area of

shaded revion.

take 丌=3.14)

Figure 2

In figure 3, LABC-90°, LCAB=30° /CDB=450 and

AD=10.

Find the Jength of 381

If -, prove that

(a+b)(c+d)=(b+c)2

Find the value of k if

2+y2+8kx+20y+125=0 represents a point cire

8. Prove the identity.

(1+tane)2+(1-tane)2

Section B

2

COS

riangle.

報日僑華

A equilateral has a perimeter of 30cm. Another triangle is form a by joining the mid joints of the endea of the given triangle another is T.bned by: joining the mid-pointe of the sides of the 2nd sriangle and so on. Find (a) the sum of periet-

ers all triangles so formed,

(b) the sum of areas of

all triangles so

formed.

10. The cost of making to

painted ball varies partly as: the square. and partly as the cube of its radius. If the cost of a painted ball of radius 12cm is $37:5 aid that of radius Scm.

is $133, find the cost

of a ball whose radius

is 4cm.

三期墨

As shown in figure 3, from a point A: on the horizontal ground due south of a tower, the angle of elevation of the top of a tower 1日: 250.

From a point B. on the same horiz- coidal ground, due eaut

of the tower, the angle of elevation of C is 0. Find e if the distance

oints of between the observation is four times as the height of

the tower

figure 3.

12. In figure 4, ABC is a

right angled triangle with right angled at CAEC, CDB and ACB are semi-circles with diameters AC, CB and AB. Find the ratio of the area of the shaded region to the area of triangleABC.

13. Plot the raph of y=1+3x-2x?(−2≤x≤4)

(i) What is the greatest,

valve

?

(ii) By arawing suitable

linear graph, solve the equation

2x-3x-3=0.

日九廿月十年〇八九一番公年九十六國民颧中育教訊航

(iii) Aalo, by drawing

another suitable.

linear graph, find

the value of √3.

14. In figure 5, AB 18

arallel to CD, AB=BE

and CD=CE.

If AB⇒p, BE-g and

BE:ED=1:2

(1 express 45 in täims of

p and 3.

(ii) express DE in terms

ofp and d

llence, or otherwise prove that AB is perpendicular to DE.

15. 200 students took

examinatione in inglish, Chinese and Mathematics.

25 passed in Chinese

and English; 15 passed in Chinese and Mathemat. ics; 10 passed in

Mathematics and English;

30 passed in English only; 40 passed in Cninese only; 20 passed

in Mathe:atics only.

Tnere are altogether

40 passed in Nathematics.

If a student is pick- ed at rundom, find the probability that he passed in

(1) all three subjects,

(11) One subject only, ((111) no subject. (b) Te a student se

picked at random from those who passed in

English, find the

provability that he

also passed; in. Mathematics.

16. A farmer has 25 acres

of land, $1000 capital wang120 man-daya of

labour to prepare for two crops A and B. The coat per acre for sowing crop A Le $20 and that for erop is $50. Crop A takes 6 mall-days per acre, while crop B takes 3. man-daya per acre. The profit on crop Ai

11 per acre and that on crop B is $18 per acre. if the farmer spent xK acres and y acres of. land for orop A and cwop B.respectively.

(a) Write down the

constraints in terme

of x and y. (b) Write down the profit

in terms of x ad y,

(c) Using the provided

graph, find the values of x und y if he wants.

to have maximum profit.

(a) what in tids maxium

profit?

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