1968-11-14 — Page 23

HM HERBAR. 日四廿月九年申代麼表

WAM KIU YAT, PO

Remainders:

$#&%$#$%$$%$#$%#*3+

£5#5%9 #3%$ #8%3 #$%$ #5%3#8%%#2%34°

10100

10.

10100

Answer: the numeral based on2 is

Remainders

1969

現代數學科

MODERN MATHEMATICS%(2)

olutions

សសសស សស ស

Answer: the numeral based on 2 18

umerali

12(18)

12 (12+6)

=37514 50, 20:

446·

Answer: the decimal

fa 446

0.5465

or

17

Answer:z the decimal numeral of 0

3x4

64+32+12+1

12 1216

12 18

Remaindera

121

Answer: the numeral based on12 de 160,

Miscellaneous Examples.

(a)

日四十月一十年八六九一层公年七十五國民高中

(第六張第二買)

一九六九年文学會考試題預習

數學科

播仲強、

B

ab SAP

ic+ca 诚去之,

ab+ca.

ab bc be+ca & AP

a(bic), ficra), c(a+b) & AP. ($9 27 (4)

(2) EE 06 a+b al brc & HP <★‚§ 144 £ a b c

(11−) A a+b ab, boc #HP.

2f(a+b) a b (bic) (a - b) (b, c) = (b−c)(

в в час в

ac=

af

#GP

G F

2b (√a+se)

2f(b+c)

au (atlec)

fac-C

Change 543, to a numeral based on 4]

sa-se

Tab (2) ** ** at 2+8

着

Fac

Answer:" the decimal numeral of

10 45

0.11011

1x2

Solution:

4 15.4.

Remainders)

20

Answer: the numeral is 3033,

Express 63 as the sum of power of 2. Solution:

63

26

AP

ab b + c d HP (ASM)\

本題宮市出比例中項 flac 以そ代入計算走し ...成某種級數時解答題目時之一般方谑 雖然計算有時繁琐但是必可得到结果 王希讀者留意.

& CHP 1

其逆定理 赤常真香

16.

Answer: the decimal numeral of 0.110172

$13 lis.

3x4

Answer the decimalInumeralfof

12. 300-125-13x52+0x5 +0x5 +1x5+2x-2

1751+10

=1955

the decimal numeral of 300.12

1660343

1440 + 12 +11

*80x12 +0x123+10x122.

1658880, 40

Answer: the decimal numeral of 80tle,

is 1660343

[1h.-65.48ppe 6x7 + 5x7 +14x7

4

=1421+ 5+ 7+191

Answer: the expression" is

In what base is 1234 is a factor of 11101:

Solution:

The base must be greater thân since the greatest digit is 4. found to be 5. Verify;

1234 = 194 10

and 11101

77610

= 4x 194

Answer: the base of the number de

is)

A number in the decimal system can e digits. If x is the number of digits it has when it is expressed in binary system, what are the limite of x.

Solution:

Let ab be the numeral. Then the smallest number represented by

is 10 and the greatest one is 99.

10101010

2 and 99101100011.

46 AP 2 2 13

其逆定理鳥

+c

:@ccc-as

R1 a b c & H.P.

-28-(a+c)

c)=acab—ya+c)]

(a+c) rac]=2adc-ac(a+c)

atcj

b(a+c) { b−(a+c)] — 2ac{ |—raxc}}==0

*BE (&-(Q+c)} { blater-zacimo

·b(a+c,-

-Rac

arc

"Answer. thedecimal numeral of

First method:

3.401- 3+0.407

10

0.401x7

0.401

2.807

.807

10 0.807

0.807x7.

7x7

9.6499

0.649

0.649x7

0-543

3.401

Answer: the septimal numeral of 3.401,0

15. 20

Ox3

1x32+0x32 +0x3

100% 1001

100

Answer; the numeral based on

14.03510

0.210

26

100.

0.035

Entegr parta

"Answers_the_numeral based on 6 is 4.011.<.

that abcd represents a number, divisible by 5.If a+b+c+d is divisible

by 5.

Proof: ab

= 216a + 36b + 60

a(215+1)+bx(35+1)+c(5+1)+d.

(215a+35b+5c) + (a+b+c+d)

a multiple of 5 + (a+b+c+d)

sbedzis divisible by 5 if a+b+c+d le divisible by 5.

Problens" for this week'

Change 2332 to a numeral based on-

Change 2331 to a numeral based on 7.

Express 31 as the sum of powers of 2 Whatswould be the sum of 1+2+22+23+2

*Tanunder in the decimal system has 3 digits. If y is the number of gigits it has when éxpressed in the binary scale, what can you say about y?

A number in the binary system has 6 digits: If is the number of digits it has when

expressed in the decimal system, what can you say about z ?

In the duodecimal system," what is the greatest decimal value of two digits? Frove that abcde, is divisible by 2711f) 6=αme=0.

Prove that abcde, represents a number divisible by 7: a+b+c+d+e is divisible. by7.

Fill the vacant places of the following

numerals so that the number they represent) are divisible by 91

(a)174_58;

(b):8.683)

Mu abc.

ezonini ifte

(1) ban arc wa

故其逆定理不常喜

()

WBABCH ☆ aina sino si C & M P TX SE

ONA, 1-OKR 1-00C T# H.P. R‡ux**** 確否?

(TL) 1

得

15-415-4) (8-465-4) ((-1)

**** un'A-(5-4) (5-6 un (0-0)(5-3),

**Fi Gat A.

英逆定理的证明,

bc

Bab A

AP

•CAB 1-004C 2 H.F. (ZES 本正逆推上去(因吁乘各數 馍术】

零)故逆定理是真確的