1979-12-31 — Page 22

頁二第張六第日三十月一十年未己WAH KIU YAT PO

1980

中學會考試題預習專欄

新數學(十三) 明德出版社魯榮家提供資料

Modern Mathematics (13)

V. K. Lo

(Mill & Dale Press Ltd)

Test 5

Attempt ALL questions in Section A and SIX in Section B.

Section A (40%)

1. If one of the roots of

the quadratic equation

2

6x=413x+k - 0 i

(i) the value of k

(ii) the other root.

find

Find the values of á and b

4. The equation

2x-3y+4+k(2x-y) - U represents a family of straight lines passing through a fixed point P. (i) Find the value of k

such that the equation represents a straight line in the family

perpendicular to 3x-y = 0. (ii) Find the coordinates

of P.

2

5. If sine+cose = 425 find the

value of (sin@-cose)". 6,-In-figure-2,¬AF»¤¬8¢m ̧

FD = 4cm, AB 4cm and CD = 6cm.

A

B

figure 2

Find the length of EF.

7. Sum the series

if 2+1 =

3+41 a+bi

where i

/-1.

8.

3. As shown in figure 1, ABF and

BCE are straight lines,

LAEB - 40°, LAFU = 36°,

find

BCF.

figure 1

報日僑華

P

10.

一期星 ·日一卅月二十年九七九一服公年八十六國民雄中有教僑言:

WAS of the bowl's capacity,

{

express

(i) the volume of water in

terms of p, q and r, (ii) d in terms of p, q, r

and .

A man prepares two types of fertilizer X and Y. Each bag of X contains 2kg of chemical A, 4kg of chemical B and Okg of chemical. C. Each bag of Y contains 4kg of chemical A, 2kg of chemical R and 5kg of chenical G. Each bag of X yields a profit of 850 and each bag of Y yields 8 profit of $30. The amount of chemicals available is 50kg of A, 40kg of B and 75kg of C.

(i) How many bags of each

should be prepare, and (ii) what is the greatest

profit?

3(2x+3y)+3(3x+2y)+3(4x+y) + • - 11. A hill slopes up at an

to 20 terms.

A new car costs $10,000, If its value at the end of each year is 15% less than its value at the beginning of the year, find, in which year its value first falls. below $6,000,

Section B (60%)

9. A hemisperical bowl, of

radius r cm, is partially-

filled with water, a marbles 12. each of diameter d cm, are added until the bowl is just ful 1. If the volume of water

angle of 30" with the horizontalc mạn without load on his hack cần climb at an angle of 20° with the horizontal and the other man with load on his back can climb at an angle of 10° with the horizontal, What is the angle between their tracks on the hill?

As shown in figure, three circles with centres A, B and C touch each other,

3.9). W. DIR

J

B

4cm C

If the radii of the circles are respectively 5cm, 4cm and 4cm, calculate (i) the perimeter of the

shaded region,"

(ii) the area of the shaded

Tegion.

13. As shown in figure,

[BAC = 90°, AD AÐ

-BD.DC.

(1) Express AD in terms of

(a) AD and BD,

S

(b) AC and CD. (TT) Show that ACUEBD) (111) "Hence, deduce tha

ADL BC.

14. In an arithme

all terms progression positives the sun-of first 3 terus ta 15 and -

their product 45

(1) Find the first term and

the common difference

rogression.

(ii) Write down the sun o first terms of the

* FEEL On · in terms

Izard tires zumber so f PETUTIBUSt be taken such that, the sum greater than 100, 15. As shown in figure, P(5,6) is a point in the circle tf whose centre A(1

.A

(1,3)

ion.

(i) write down the equ

of the ciretez C. (1), Khatris The Tipperat

the life joining a and (ifi) I is a tangent Vurch

touches-Gattering

Wha

of t

12

(b) find the equat

of L..

16, Consider the expression

7-5x-2x

2

( 13-Frite down the

expression in

<form a{X+b)=+c

(44) Find the values a hand e

(iii) What is the maxi

value of the

texpression?

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