1975-11-12 — Page 27

真四第張士第日十初月十年卯乙展夏

0903 中學會考試題預習專欄

WAH KIU YAT PO

報日僑霋

came to rest on the ground.. (Give answer to the nearest cm.)

JLT

數學科 (一)

葉柏芳。

TRADITIONAL MATHEMATICS

(1)

"This course is intended to give

the candidates of HKCEE a general

revision on traditional mathematics. We hope the candidates will be acquainted with the Examination after doing each exercise. Exercise 1ER

Section A (Answer ALL questions in

this section. Each question. carries 5 marks. Show your work briefly; geometric theorems need not be quoted when used.)

3

Simplify 4(x-1) ► 4(x+1) + 2(x2-1) Show that x2-4px+4p2-q2-10qr-25r

=0

has rational roots, where

P, rare integers.

3. In Fig.1, 0 is

the centre of

the circle,

QABC is a

parallelogram,

and BCD is a

straight line. Find ZOAD.

4. In Fig.2, AB-AC,

and BF BG.

If

/EAB-20°, find'

ZEDG

Solve the equation

tan.0+ cot = 2

0°0360o --

Fig.

Find a relation for x and y independent of from the equat

ions

x sin y cos

X cosec

a

-y sec 0 =

b sec cosec 0.

If A sold an article to B at a profit of 5%, and afterwards B sold back the article to A at a loss of 10%. In this way, A made a net gain of $22, find the price A originally bought.

8. Aman bought a house for $100,000

and rented it out. He received $1000 each month, but he had to pay a yearly tax of 15%. Find the ratio of the annual real. income to the purchase price. Section B (Attempt any SIX questions

in this section. Each question carries 10 marks.)

9. The base of a right pyramid is square of side 5cm; each face makes an angle of 500 with the base. Find

(1) the height of the pyramid, (ii) the angle each slant side makes with the base.

10. A ball was dropped from a height

öf 100 cm., rebounded to a height of 80 cm., and continued to fall and rebound, rising after each rebound to four-fifths of the height it previously fell from. Find

(i) the height it reached at the

5th rebound..

(ii) the total distance through

which it travelled before it

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11. In Fig. 3,

AQ=BP, AY=CK,

RQ//CX and

RB PQ-RP BC.

Show that

(1) ABPQ and

ACXY are.

//gram.

12. (1) Let y = +(

P

三期星

日二十月一十年五七九一膳公年四十六國民輩中

ively.

pm. I started from rat bukit./nr.

for an hour, rested for another hour

and reached B at 4 pm.

(i) Draw the travel graph of Y.

(ii) Find from the graph the time

X and Y met. (2 solutions)

(iii) Find from the graph the places they met, measured away from A.

Fig. 3

新數學 (一)

文長波

(ii) Area of

ABPQ=Area of ACXY.

+(x2-x+10). Show that 3x2-21x+26 can be, written in the form ay+b. (ii) Solve the equation 3y2-4y-4

= 0

(iii) Hence or otherwise solve

3x2 - 21x+26=4(x2-7x+10)

13. A train travelling at 50 km./hr.

in the direction of N.45°E. overtook at noon a man walking at 6 km/hr. in the direction of N:1509. At 12.12pm. the train stopped in a station.

(1) Find how far the man was

from the station at the time the train stopped.

(ii) Find the distance the man.

would be nearest to the station, and the time when he was at that point.

14. The cost of producing an article

is made up of 65% of labour and 35% of material. It is sold at. a profit of 50%. If now labour cost increases by 20%, and the selling price is increased by 30% the profit is still 50%. Find the percentage change of material cost.

15. Fig. 4 shows an

16.

inverted conical container: a ball is put into the A container until they make close contact... The diameter of the ball and the

height of the

container are both

28 cm. Water is

Fig.

then poured into the container until it is full to the rim. It ie found that half of the sphere is now above the water surface. If the ball is then removed find the volume of water remaind- ed. (Given your answer in terms. oft and a).

3pm

A and B are two towns 120km.

rekm

apart. At noon X started from A to And his travel graph is as shown.

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MODERN MATHEMATICS (1)

This course provides the candidates of HKCEE. 1976 a general revision in Modern Mathematics. A knowledge of mathematics up to HKCEE is assumed, and the subject is developed by a con centric treatment in which each exer cise is used to illustrate ideas already treated.

Exercise 1

Attempt ALL questions in Section A and any SIX questions in Section B. Section A (Answer ALL questions in

this section. Each question carries 5 marks. Show your working briefly: geometric theorem need not be quoteć when used.)

find the value of

1. Given an acute angle X with

11 tan e = (sin + cos e) without using tables

a3 2. Factorise a' (a-2b) - b3 (b- 2a) 3. Find the value of x if

210g 2+ log 2-log 8, the base of logarithm being 10.

4. In figure 1, what is the value of

X?

.(Figure 1)

Rewrite the inequalities

in the form a 12x-5111

Find the

6. If p and q are the roots of the

equation 2x2 - 3x − 1 = 0. value of p2 + q2 and 2+

If xoc, fill up the gaps in the following table:

X

Y

6

1.2

8

1.5

0.8

8. A is 20% more than B and B is 20%

more than C. What is the percent- age of A more than C?

Section B (Attempt any six questions

Each question carries 10. marks).

9. Prove by Mathematical Induction

tha222

10.

n(n+1)(2n+1}

for any natural numbers of n. Hence or otherwise, find the value of

212 +22

222+

50?

(Figure 2)

In figure 2, the co-ordinates. of A, B and C are

(4.1),(6,2) and (5,3) respect

Find

育教僕康

a) Express A and AC in 1,3 form.

AB. ·AČ ||AB||AC]

b) Evaluate

where [AB] and

AC are the magnitudes of AB and AC respectively.

c) Hence or otherwise, calculate.

CAB.

11. In figure 3,

ABC is in a horizontal plane

and IC is vertical. The

angles of ele- vation of A and B to D are 450 and 30

respect

ively. If AB-100m. and CD - hm, Find a) the length of AC and BC

in terms of h.

b) the height of CD.

12. A manufacturer produces two

different models. A and B of a product. Each model must be pro- cessed by two machines M1 and M2. To complete one unit of each model, the two machines must work the number of hours indicated in the following table.

A B

M1

3

1

M2

.1 3

No machine may operate more than 12 hours. per day. The profit is $3 on each unit of model of A and

How $6 on each unit of model B." many of each should be produced. daily in order to maximize his profit?

13. The equation of lines and

are x+3y=7 and 3x-y-1 respectively. Find.

a) the equation represented a famil

of straight lines passing through the intersection of l1 and (21- b) the equation of the line which

passes through the origin and the intersection of 1 and 12.

O

c) Find the co-ordinates of the

intersection of l1 and l2.. 14. If 8 cpins tossed upon a table,

find the probability that exactly 6 will come up heads: exactly 3 will come up heads:. at least 5 will come up heads and d) at least 3 will come up heads. 15., An open box is to be formed by cutting out equal squares from the corners of a square sheet tin and folding up the sides. The box is to be 10 cm.deep and is to contain 2250.eu.cm. Find the length of a side of the. aquare sheet of tin. Three squares are arranged in a row along a straight line AB as shown in Fig.4. If the marked angle in the figure are equal and the length of the side of the smallest square is X am.

a) Find the lengths of the sides of the other two squares in terms ₫ X and 0.

b) Prove that the lengths of the

sides of the three squares are

in geometric progression.

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