1978-03-28 — Page 26

育收僑華

R=BLB B+=A=#FREI WAH KIU YAT A

ABC is a triangle right angled-at A.ADLDCA

報日僑

D. decreased by 1504

If

B. degreased by 100g Answers:.

BD-4cm and DC÷12cm; then. AB is

1. E 2. E

1978

A. 8cm

B. 8√3cm

5. A 6. B 9. C 10. A 15. H 14. B

【中視會考試題預習專F

C. 12cm

3. C 7. A 8. B 11. E 12. C 15. D 17. D 18, E 19. D

4. B

16. D

40. C

D. 12/5cm

E. 43cm

MIN& © Peris

二期

greater than 1100,

日八廿月三年八七九一曆公年七十六國民華中 育教

(i) Fill in table 2 below

̇新數學 廿六

香榮家

Table 2

Range of

Number of candi

marks dates falling in

this range

0-4

59

數學 十六女長波

Mathematics 26

Exercise 12

Multiple choice questions.

1. Find

B. 1

C-1

D. 11

E. no real value possible: If k+1 represents a given odd integer, which of the following must also be an odd number?

A. 2(k+1)

B.

(k+1)

C. (k+1)(k+2)

Do (k+1)(k-1)

E. (k+1)=-1

The graph of one cycle y-3sing is given as shown. What is the x-coordinate

of pg

C. 21

64

If loga-loge Logb A. a-cab

B. a=be

D.

b

loga

Toge.. log-b

E I

If a and x are any positive

integers, which of the following is always an

E. (xa

Which of the following. indicates the range of f(x)=-4sin4x?

B. -7(xki

D. -14 f(x)<t

E

f(x)<

N

ABGH, BCFG and CDEF are three consecutive squares,

which of the following is not true?

A. MN=AH

BGM=MN=NB

C. F4-HD

D Area of AMON: Area of

-4A0-1:9-

E. AQ=UC

12. If sinx20 and CоXX:

tane is equal

then

B

Di

E. cannot be determined.

13. The value of the expression

350/0.0007203

65.5x0.7489

A. is less than 0.1

B. lies between 0.1 and 0.3 Calies between 0.5 and 1

D. lies between 1 and 3

E. is greater than 3 14.The arithmatic mean between

the roots of the equation. 3x+8x=6=0 is

A.

B.

E.

Which of the following is

the most possible value of

x in the figure?

4. 1.

B2

C. .3

D.

E no value possible 16.How many angles of a

quadrilateral may have negative cosines?

B. 1

C. 2

D...

E

17.

If M is the mid-point of CD of parallelogram ABCD. What is the ratio of area

of AAMD and ABCM?

AD is the diameter of the semi-circle ABCD and

ZCAD-20° Find LABC

A. T

B. 1:2

A. 90° H. hoa

MODERN MATHEMATICS (26)

Revision Exercise.

Paper I

Anawer ALL questions in Sect- ion A and any SIX in Section

B All necessary working must be shown clearly.

SECTION A

1. In figure 1; AB is a chord of a circle centred at 0, If

the radius of the circle is

8cm und AOB 60o, find (a) the perimeter.

(b) the area

of the shaded region (Take 3.14):

Figure

A(x − 1)2+ B(×

is an identity in x, find the values of A, B and C.

5. a man puta. $190000 into. Bank & and he also puts $10000 into Bank B. Bank pays 47 compounded and Bank B pays 5% simple - terest a year, after 41 years, which bank wild pay.

more? How much more 4. If

25

where

Find A and B.

77

5. Find the set of real num-

bera satisfying the in-

equality

2

6. If the straight line

ym mhx ak touches the

curve y 2x

12x+ 20,

find the value of k

2

7. If a

21 + 33. i 12 and a

- 25

find the scatura m and n

Figure 2

In figure 2, ABCD is a rectangle EF are points

on CD and BC such that

DE!

: EC- 1 : 3 and

BF FC -1

: 2. If AB...ii, and AD 63 where 13 are two perpendicular unit

vectors

(a) Express AF and AS in

terms of and J.

(b) Express AC in terms of

AF and A.

(c) If K is a point on PC

such that AKI EF

(1) express EF in terms of

I and J

(11) Let |DK| » k, express

AK in terms of k, Î and j (iii) find

BKKC

In a lucky draw, there are 100

tickets of which

10 are euch marked for a

prize of one gold coin, 20

tickets are marked for a

prize of one silver coin,

5 ticketa are each marked

for a prize of one gold coin and one silver coin,

and the remainder are not

marked for any prizes.

ticket is drawn

what is the probability of getting

(i) and gold coin only

(ii) at les?" "he gold coin'

(b) If now two tickets are

drawn one after the other

and the first ticket drawn is replaced immediately be- fore the second drawingə then what is the probability of getting

(i) two gold coins and one

silver coin

(11) exactly one gold coin and one silver coin,

13 Table 1 shows the dia-

tribution of 50 candidates

in a mathematics test and

its data is plotted in the accompanying graph,

Table 1.

Number of candi Marka dates who score above thin murk

a

8. If a band are three

positive numbers such that

b. : 2

6

2

2

and a 36

2¢

* 376,

5

44

b.and

10

35

is equivalent to

15

1.5

20

9% (a)

25

10 14

20

15 19

24

(ii) Hence, find the mean score in the test (111) If 46% of the candi- da te failed in the test, estimate the pass mar

mark

the test.

14. A balloon rise from

point on the horizontal ground with speed v

of

મેં

SJE

wintes later, com a point A on the same hori- zontal ground due south

the angle of elevat- ion of the ballosu is 30o. At the same time, the angle of elevation of a point B, which is on the same hori, zontal ground and is due

rant of 0 is too to he $50

find the value of if the distance between

and B is 20 km (See. figure 3)

15

Fi

20 km

Consider the equation x2. (k + 2)x

2k8

(a) If one of the roots of

this equation is 2 (1) what is the value of k (ii) what is the other root (b) If m,u are the roots of

the equating and m (1) what is the value of k (ii)hence, form a quadratic equation whose roots are

and

(Express your equation in the form

2

2

n

+ bx + c = 0, where. b and c are integers)

(0.5)

(1,0)

D. 1:3

E. 3:1

8. If A, B, C are the angles'

[of AABC, which of the

following is not true?

A sin(A+B)=sinC

B. co=2(A+B) --suc

C. sing-cos+C

D. A+B+C= T

E. none of these

9%. If √x2+4x+\=x+2, x=

10,

Aany real numbers

B. any real numbers except

-2.

C. x>-2

D. x4-2

Ex>=2

C. 105°

D. 110

E. 120"

18.

x+1

A. x7-2

19.

B. x20

D. -24x4-1

C. x$-2 or: x2

E. x4-2 or 3-1

Piss point inside the equilateral ANC, PXLBC, PYLAC PZLAB, PX+PY+PZ is equal to A. Be

D. 28C.

C. (AB+BC+CA).

D. BC

EBC

20.If the base, radius of a cylinder is doubled and its height is halved, then its volume is

1. unaltered

B. increased by 50%.

C. increased by 100%

find the values of

SECTION B3

that for all eN,

ind mathematical

13. 23+33 +0

· |-(n + 1)2

(1) Hence find the smallest

value of a such that

+

03 2025

10. The sum of first three

terms of a geometric pro-

gression is 39 and the

product of the three terms

is 729

(a) *ind the first term

and the common ratio of the progression. (b) How many, terms of the progression must be

taken

an that the sum

10:

S

10

Marks

20

The graphs of y ~(x+4)2+ b passes through the points

= (0,5), (1,0) and (c ̧0) shown in the figures (a) Find

b and c

(b) What is the least value

of y

(e) What additional linear

graph would be necessary to solve graphically the

equations (1)2

- 4x - 5 - 0

(11) 3x2- x * 3. 0