1976-11-10 — Page 20

真四第張五第 日九十月九年度丙座赟

WAH KIU YAT PO

報日僑業

Find the length of the journey and the original speed.

1977中學會考試題預習專欄

明德社主編

數

(-)

Mathematics (1)

文長波

This course provides the candidates of HKCEE 1977 a

general revision in Mathematics (Alternate Syllabus B). A Know- ledge of mathematics up to HKCEE is assumed, and the subject is developed by a concentric treat ment in which each exercise 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. Each question carries 5 márks.)

1. Given an acute angle xo with

11 tan x°=

find the value

of (sin x2 + cos x°) wi using tables.

2

2. If 8 sin2- 9 cos2 e

= 6 sin e cose, find

out

(a) the values of tan e (b) all values of 9 (0° LØS

360°) that

equation.

Patisfy the

3. Form a quadratic equation.

whose roots are the square of the roots of x-x-12=0

Express your equation in the form ax bx + c = 0 where

4. SOL

b

are integers

the in equality (x+4)> 18.

5. In figure, Z BAC = 90°, AC 3cm; AB = 4 cm. AE is the angle bisector of BAC.AD is perpendicular to BC. Calculate the length of ED. (Geometry: theorems need not be quoted when used.)

E D

6. In figure, XZ and TY are tan- gents of the circle, and LYXZ = 50°. Find ZXYT, (Geometry theorems need not be queted when used.):

'. A can do a piece of work in

20 days, B an 12 days; A and B work at it together for 6 days, and then C finishes it in 2 days; in how many days could C have done it alone? 8. Two persons, A and B,,hold a

field in common at a rental of $14400/A puts in 23 horses for 27 days, and B 21 horses for 39 days: how much of the rent should be paid by each?

Section B (Attempt any six questions. Each question carries 10 marks.)

9. The perimeter of a triangle

is p an. A second triangle is formed by joining the mid- points of the three sides. A third, fourth and fifth tria triangles are formed in the same manner (i.e. by joining the min-points of the three sides of the preceding triangle.) If the perimeter of the fifth triangle is 1.5

find

-

(a) the ratio of 1the perimeter

of the first and second tri- angles,

(b) the value of p.

(c) the sum of the perimeters of

the five triangles.

10. The time for a journey is

reduced by 25 min. by increas- ing the average speed by 5 km

per hour; a further increase of 5 km per hour causes a further reduction of 20 min.

}

11. In figure, A ABC is in a

horizontal plane and DC is -vertical. The angle of

elevation of A and B to D are 45° and 30° respectively. If AB 100m, ACB = 90° and CD hm, Find

(a) the length of AC and BC în

terms of h.

(b) the height of CD.

A

12. The figure is an ellipse and

S is one of the foci. IË P is a variable point on the curve, the length of SP units, is given by re

12 where XSP = 3° 2-cose

Y is a point on the curve such that SY = · xx. Calcu late the lengths of 5X, SX! and Z XSY.

13. The graph of y =

2. \\(x + b} Passes through the points (0,-3), (1,0) and (C,0) as shown in figure.

Find a, b and c. (b) What is the greatest

value of y?``

14. A svimming pool at Victoria

Park is 50 meters long and 20 meters vide and its sides are vertical. The floor of the swimming Pool slopes uniformly from c depth of 1 meter at the shallow end to 5 meters at the deep end. (a) Find the time it takes

to fill the pool if/ water is pumped in at a uniform rate of 18000 litres per minute.

(b) Find the depth of water at the shallow end when the pool contain 2250 cu.m. of vater.

15. In figure, D, E and F are

the mid-points of the sides of A ABC and AG is per- pendicular to BC. Prove that

<AEF= FEG (b) D, G, E and Fare

concyclic.

DG

16. In figure, ABC is a triangle

right-angled at B. AF bi- sects A; BELLAC, AB=AG. Prove FG // BC.

新數學 (一

姜榮家

MODERN MATHEMATICS (1)

This course provides the candi-

· dates' of HKCEE 1977 a general revi- #ion in Modern Mathematics. A know- ledge of mathematics up to HKCEE is asgusted and a series of conventionai test papers are set up for rehearsal purpose, with answers given in the following weeks.

三期星 日十月一十年六七九一磨公年五十六國民華中育教僑

This course is not intended to be an instant miraculous help for la ay studenta, it aims to encourage the candidates in their over-all revision and to develop the ability of solving various type of problems.

Exercia

Attempt ALI, questions in section A and any SIA în section B. All work- ing must be clearly shown, Section A (40 marks)

1. Solve the equation

2

8 X.

x 10.

+8

x + 2

2. Find the equation of the straight

line which passes through (3,4) and perpendicular to 2x - 3y+4=0) 3. If tan ə

find the value of

Jsinė +

·4cose 5sine "bé os ◊

4. Find the set of values of

such that

1

☎ * (x − 2) á

5. Find the value of

(a) Find the mean circumference of the

sample of trees.

(b) Draw the histogram of the above

frequency distribution,

fe). T is intended to cut down the

largest 25% of trees. From your histogram, determine the smallest circumference of the trees that should be cut down.

1977中學入學試試題預習專欄

智慧社主編

英文(一)

ENGLISH (1)

Choose the best answer.

the brackets.

Write the LETTER in

g. Is this villa

hire?

(A. to B. at G. D. for E. from)

», Find the value of a

ai

3+41

2 i +

and b if

where i

I often meat Tom

(A. at. B. for. C. on

E. into)

Monday morning.

D. in

x). 4 x 2 m(AC) * 10cm.

10

(A. from

2. We had a good time

B. on

C. in

Christmas.

at

E. over)

find the radius

7. Find the values of p and q

p(x2 + x) – b(x2.

3. In fig. 1, m(AB).

m(BC) = 16cm.

of the circle.

fig-1

Section B (60 marks)

16cm

10c

9. Prove by mathematical induction

32

+

(2n

(2n + 1)(2n

-

1)

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

of 512 + 522532.

1112

10. If the sum of the first a terms of

, nín + 6}, find

a series is S(n) the first term and the rth term.

11(a) Solve for x

2

4a

48x +

9.

2

(b) In the equation 15x + a2 - 8=0

the product of the roots exceeds the sum of the roots by 2/5. Find the value of m, hence solve the

12. A manation.

$8000 to be repaid with interest at 8% p.a. in 2 equal annual instalments, the first payment being due at the end of the first year. Find the annual payment, 13. A right circular cone is divided

into 3 portions A, B and C by planes parallel to the base as shown in fig.2

The heights ofthe portions are 1, 2 and 3 units repectively. Galculate (a) the ratio of the volume of A to

the volume of i.

(b) the ratio of the volume of B to

that of c, and

(c) the ratio of the area ofthe curved

surface ofB to that of C.

B

C

fig.z

3. How much did you pay

dress?

your new

(A. for B. at C. with

B. against)

D. under

our captai

4. We don't agree

(A. at B. to C. with D. in

E. against)

5. My

unger brother is twelve years

age.

at B. on C. within' D. of E. from)

6. They are angry

(P. for Qat

what he says.

R. against

S. before Ton)

6.()

the sea to

7.6

7. The swimmer jumped

catch a fish.

(F. to Q. into R. on S. under

Tat)

8. Mary met me

my way home.

(P. along Q. on B. in S. through

Tunder)

9. I'll ring you

if I have time (P. on Q. except R. in

T. up):

10. There is no difference

two bats.

(F. between -Q. among

Son T. to)

S. out

9.0

the se

R. across

10.(

11. Mr. Kan marked our papara

the test.

(A. within Bater C. before -D. at

E. in)

12. Please switch very hot now.

קט.

11.(

the fan.

It's

(A. on B. off C. u

E. by)

D.

down

12.(

13()

D. in E. to)

the harbour in half

13. Mr. Long Legs saved his brother

drowning.

(A. from B. for C. at

14. Can you swim an hour?

(A. from B. for C. Baross D. to

E. through)

15. We are really sorry

(A. with B. from C. at D. for

E. to)

16. They sat

his death.

15.()

early to climb the

(P. for Q. to

T. off)

R. over S. in

16.(

17. The story is

a wicked

superor.

17.()

mountain.

R. on

1

business.

14. A boy wishes to ride up a slope of

inclination, where sinė - ‡, but can do so only by zigzagging up. a. track whose inclination is, where sing- 1/5. rind the angle between the track and a line of the greatest alope.

15. The circumferences of a random sample of100 tress from a small forest are measured and the frequency dia- tribution is as follows :

circumference (in m) frequency

(P. by Q to R. about S. at T. on)

18. Tom visited his aunt

in Hong Kong.

(P. in Q. during R. at

19. Ky father went to Japan

(F. with Q. in

20. I studied the poem.

(P. with Q- by

his stay

18.()

S. of T.on)

S. at

T. for

19. [or

heart. 20.() 5. to E.in)

R. at

ANSWERS

0.4 - 0.5

A

0.5 0.6

8

0,6 – 0,7

20

1. C

0.7

0.8

28

0.8 - 0.9 0.9 - 1.0 1.01.1

20

6. Q

2. D.

7. Q

10

11. B

1.1

-

1.2

12. A 13. A

16. T17. R 18. Q

3. A

8. Q 9.

14.0

19.B

4.C

5. D

10. P

15. D

20. Q

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