Casio Fx 3650P II 3650PII CN

User Manual: Casio fx-3650PII fx-3650P II | 计算器 | 说明书 | CASIO

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Ck

٫ዓࣜ๻ಹ

fx-3650P II
ᅋ࡟ํடร

৘ྩఛഩഒीᆅཌሂ

http://edu.casio.com

RJA527886-001V02

෼೐ኼӄ
‫ݮ‬ဩఀၭ޶ӊ DBTJP դ౹ă
• ᇀෳᅋդ౹೐ഋᆪ‫ڣ‬ᅋ࡟ํடรă
• ഋटດүߘࠝLjჾӯ൓ࡍၖე෫௢޷๾෫Ըሙ ) үૠӄ
ᅋ *ă!
ᇀჾ࿒ཌሂნ৹ჾᆪ‫ڣ‬ᅋ࡟ํடรă!
iuuq;00xxx/dbtjp/dpn/do0tvqqpsu0nbovbm0

k ᇀฑ‫״‬ෳᅋӊࣜ๻ಹቐ೐ ///
ෳᅋࣜ๻ಹቐ೐Ljटү࡜৷ဂ࿒
ࡤ‫ڑ‬Ԍട࿒Ljഹࡍटү࡜৷߈‫ڊ‬
‫ࣜف‬๻ಹ‫و‬ҿஎLj൥ᅚ༐ຑ෸ă

A ࣜ๻ಹෳᅋ༾ӛࡍ ///
‫ࣜ׹‬๻ಹ‫و‬ҿஎട࿒ү࡜৷LjԌटದቺူໍᇀቁஎă

k ൥ࠨटࣜ๻ಹ‫཭ݒ‬ཛྷֽ෶യෛኴຢ
ეෳࣜ๻ಹ‫و‬හብ۵࢐ባದֽ෶യෛኴຢ෫Ljഋቖှ࿒ะ
ՃዷăഋኢᄌLj‫ױ‬Ճዷࡱटഅ‫ׅ‬،‫׈‬ಹቲ‫و‬ຑᅘ௠൛DŽ‫ڢ‬
઎،‫׈‬ಹLjӰફ،‫׈‬ಹLj‫ؖ‬Ѧ،‫׈‬ಹLj༇ࣜࣜ๻Ⴥӊืয
ࣆ֔ၠืযDž
ă!
!9(CLR)3(All)w

Ck-1

k ߔᅢӊํடร
• ӊᅋ࡟ํடรቲ‫ࡥو‬எࣆՏ༐DŽऒٌࣝࠟDž४ཛྷ෸۶ቐᅋLj
৹௢࢙ᅳದ‫ؠ‬ӹ‫و‬෯࣠࿾௅ᅘຑԥༀă
• ӊํடรቲ‫و‬௠൛൥ᅘ‫ݢޚ‬Ljูԥ૙ှ໼ቌă
• ৘ྩఛࣜ๻ࢲާ๖DŽDBTJP!Dpnqvufs!Dp/-!Mue/Dž‫ڶ‬ᅢᄜ޶
଼ࢪෳᅋӊդ౹ࣆದ‫ݛ‬औۚ‫ـ‬ቤࢪᄧಲ‫و‬ൌࠨ໎ผ‫و‬Ă
ࣺे‫و‬Ă‫ݛ‬๾‫ࢪو‬࿰ߔ‫و‬ຈࠀԥ‫ݘ‬ൌࠨᇖൌă‫ױ‬༶Lj৘
ྩఛࣜ๻ࢲާ๖DŽDBTJP!Dpnqvufs!Dp/-!Mue/Dž‫ڶ‬ᅢൌࠨٞ
ൻሣᄜෳᅋӊդ౹ࣆದ‫ݛ‬औຑᄧಲ‫و‬ൌࠨቸ੮‫و‬ຏెԥ
‫ݘ‬ᇖൌă

Ѡഩၙቌ
• ഋटդ౹ĂҪኰԮ઻үߘᇀᄬᅟۛྐۨ‫وࣆ׋‬ٜ‫۽‬ă

危险

ӹ෸൲ྐญ‫ױ‬Ӷ෰६ှྥՃዷLj৹௢‫ـ‬ቤ൉ᆗ
๘ཊࢪቺටཕ࿥‫ૅو‬॰ă

● ऄ၂٫֠ቲ૳‫و־‬ფ໛ԥී൩Ⴇ෫Ljഋ઎࣊Գടჾ
࿒ؑ෣ă
2/!ԥე൞ႧLj઎࣊ᅋഅๆ֭࿄ă
3/!઎࣊টყተલă൲‫܅‬ൌԥߘLj৹௢࢙ᇒ֑෡டă

Ck-2

警告

ӹ෸൲ྐญ‫ױ‬Ӷ෰६ှྥՃዷLj৹௢‫ـ‬ቤ൉ᆗ
๘ཊࢪ෉‫ݘ‬ቺටă

● ഋट٫֠ብᅢᄬᅟۛྐۨ‫وࣆ׋‬ٜ‫۽‬ăཆქᄬᅟۛ
ԥීྥ෭Ljഋ઎࣊টყተલă
● ٫֠ෳᅋ‫ྥؓۨ۽‬෫Lj࢙ᇒ֑٫֠૳ფ‫ـ‬ቤቾཙྍ
ຈࢪᇒ֑٫֠ಈઽ‫ـ‬ቤࢨᆼࢪᄌ༶ටࠀăᄜ‫ױ‬ഋႛ
‫ޏ‬ዱฒჾ࿒෼࿾ă
• ഋኢᄌࣁ၂ ) LJࠧlj‫و‬շဂ *Ljቁവኰ൩ă
• ഋྡྷෳᅋӊࢲಹསቚ‫وڊ‬٫֠ă
● ഋԥე‫ڶ‬٫֠६ှ֬٫Ă՚ॖჾࣆದຓ࢙‫ـ‬ቤ‫ଁڮ‬
‫و‬ൌࠨှཛྷă
● ഋྡྷटӊࢲಹࢪ٫ࣩ֠െࢪ‫ڌ‬൩ࢨቲăܱᇘ৹௢ෳ
ࢲಹಈઽ‫ـ‬ቤࢨᆼࢪᄌ༶ටࠀă

注意

ӹ෸൲ྐญ‫ױ‬Ӷ෰६ှྥՃዷLj৹௢‫ـ‬ቤ൉ᆗ
ถටࣆྡ౹ຈටă

● ߔᅢ࿤෸ಃு
• ഋྡྷᅋ઒Ѣႅࢪቺࢯფॹ࿤෸ಃăܱᇘფॹ࿤෸ಃ
‫و‬ԍઓ৹௢ಈઽLj‫ـ‬ቤᄌ༶ටࠀă
• ფॹ࿤෸ಃಈઽ෫Ljഋྡྷ‫׋‬஦࿤෸ಃ௠ᄑ‫و־‬ფ໛ă
• ԥීྥ෭ಃுᄑ‫و־‬ფ໛෫LjᄮଷණุਊԌ઎࣊ট
ყተલă
• Ⴇॸࢪ౦ܴԥීे‫ف׋‬ಃுᄑ‫و־‬ფ໛෫Ljഋ࿘ᅋ
അๆ֭࿄ባඵ 26 ‫ܖ‬ትჾණLjഹࡍ઎࣊টყተલă

Ck-3

Ճዷၙቌ
• 即使计算器运行正常,也应至少每三年 (LR44 (GPA76))
更换一次电池。
܏ছ٫֠৹௢࢙૳ფLj‫ࣜڶۚ׹‬๻ಹᇒ֑ຈࠀԌෳದդ
ූ߆ሓăഋྡྷट܏ছ٫֠ჯૠᇀࣜ๻ಹቲă٫֠༾ഩୣ
ᅘ٫෫Ljഋྡྷᆿฎ༐ෳᅋࣜ๻ಹă
• 配备的电池在运输和存放期间可能会产生轻微放电。因
此,更换时间可能会比正常电池寿命结束时间要早。
• 请勿对本产品使用镍氢电池 * 或任何其他使用镍作为材
料的电池。电池和产品规格不兼容可能会导致电池寿命
缩短并使产品发生故障。
• 电池电力不足会造成存储内容损坏或完全丢失。请务必
保留所有重要数据的书面记录。
• 请避免在超出温度极限、湿度过高和灰尘过多的区域使
用和存放计算器。
• 切勿过度撞击、挤压或弯曲计算器。
• 请勿尝试拆卸计算器。
• 请使用柔软的干布清洁计算器的外部。
• 无论何时丢弃计算器或电池,请确保遵循您所在地区的
法律和法规要求。
• 请务必将所有用户文件妥善保管以便日后需要时查阅。
+!ӊฐՋቲෳᅋ‫ާو‬๖ࠧդ౹ண֎৹௢ก‫ާޔޕ‬๖ࠧդ౹
ຑᅘሣ‫و‬ኢՋඨӶࢪඨӶă

Ck-4

௅ଆ
෼೐ኼӄ!//////////////////////////////////////////////////////////////////// 2
Ѡഩၙቌ!//////////////////////////////////////////////////////////////////// 3
Ճዷၙቌ!//////////////////////////////////////////////////////////////////// 5
ᇀ৚෶६ှࣜ๻ቐ೐ ///!///////////////////////////////////////////// 7
ࣜ๻ன෷ࠧහብ!///////////////////////////////////////////////////////// 9
๻෷ࠧื቗‫و‬พ൩!/////////////////////////////////////////////////// 22
ࢱӊࣜ๻!////////////////////////////////////////////////////////////////// 27
ࣜ๻଎ઈࣆՓᆪ!/////////////////////////////////////////////////////// 31
ࣜ๻ಹ‫و‬،‫׈‬ಹՃዷ!/////////////////////////////////////////////// 32
৶ၳࠉืࣜ๻!////////////////////////////////////////////////////////// 37
൥ࠨෳᅋ 214!‫ޠ‬ၳࣝืۨDŽFOHDž
!/////////////////////////// 4:
‫ࣜืݒ‬๻DŽDNQMYDž
!///////////////////////////////////////////////// 51
༇ࣜࣜ๻DŽTE0SFHDž
!///////////////////////////////////////////////// 55
ࢱืࣜ๻DŽCBTFDž
!//////////////////////////////////////////////////// 74
֔ၠன෷DŽQSHNDž!/////////////////////////////////////////////////// 78
‫ݛ‬ଆ!////////////////////////////////////////////////////////////////////////// 92
٫ᆚეഓ!////////////////////////////////////////////////////////////////// 99
ߢ‫!ޏ‬////////////////////////////////////////////////////////////////////////// 9:

Ck-5

ᇀ৚෶६ှࣜ๻ቐ೐ ///
k ࣜ๻ಹ‫و‬৚ࢲ
Ѣ Oăࣜ๻ಹट६൩ණ‫ࢲߔ״‬෫‫ࣜو‬๻ன෷ ) ٞ 9 ო *ă

A ࿤෸ಃ‫ڶ‬Ӕ‫ٻوڪ‬ॎ
൥߷ࡥஎණ‫و‬ዖܻௗჾ৤അLjഋ‫ٻ‬ॎ࿤෸ಃ‫ڶو‬Ӕ‫ڪ‬ă
2/!Ѣ !N)TFUVQ*db)Dpousbtu*ă
L I GHT
DARK
• ‫ױ‬෫‫ڶ‬Ӕ‫ٻڪ‬ॎࡥஎ࢙‫־‬࿦ă
CASIO
3/!ᅋ d!ࠧ e!‫ٻ‬ॎ࿤෸ಃ‫ڶو‬Ӕ‫ڪ‬ă
4/!හ‫ڊ‬༾ӛࡍLjѢ A!ࢪ !p)FYJU*ă
ኢ
‫ص‬Ѣ ,!ऒ‫־‬࿦‫ࣜو‬๻ன෷Ե‫ة‬࿤෸෫Ljఀࡱ৹ჾෳᅋ
+!ࠧ -!‫ٻ‬ॎ‫ڶ‬Ӕ‫ڪ‬ă
ቺეƽ
࣯൥‫ٻ‬ሿ࿤෸ಃ‫ڶ‬Ӕ‫ڪ‬LjԌས‫ݢ‬ජ࿤෸৹‫ڣ‬၂Ljᇘ࠶ᅘ৹
௢ก٫઒ԥ޷ăഋ‫ࡳޚ‬٫֠ă

A ࣜ๻ಹ‫ࢲߔو‬
Ѣ !A)PGG*ă
ߔӡࣜ๻ಹ‫و‬٫ᆚࡍLj࿒઼ืযԥ࢙‫ڌ‬෡ă!
• ࣜ๻ன෷ࠧහብDŽٞ 9 ოDž
• ‫ؖ‬Ѧ،‫׈‬ಹDŽٞ 32 ოDž
Ă‫ڢ‬઎،‫׈‬ಹDŽٞ 34 ოDž
Ăჾࣆ
Ӱફ،‫׈‬ಹDŽٞ 35 ოDžቲ‫ืو‬য

Ck-6

k ऒӶࣝ
M–

x!

A

M

8
LOGIC

DT CL

‫ޢ‬௢

Ⴁඇ

൥ࠨቖှ‫ޢݡ‬௢

1

M+

!

2

M–

ྲྀዖ ǖዘࡾඇ Ѣ !!ࡍѢ‫ױ‬ऒă

3

M

ྲྀዖ ǖࡆඇ

Ѣ a!ࡍѢ‫ױ‬ऒă

4

DT

ྲྀዖ ǖ੄ඇ

ᇀ TE ࢪ SFH ன෷ቲLjѢ‫ױ‬ऒă

5

CL

ྲྀዖ ǖዘࡾඇ ᇀ TE ࢪ SFH ன෷ቲLj
ਢ ǖ੄ඇ
Ѣ !!ࡍѢ‫ױ‬ऒă

6

∠

ྲྀዖ ǖዘࡾඇ ᇀ DNQMY ன෷ቲLjѢ !!
ਢ ǖዏඇ
ࡍѢ‫ױ‬ऒă

7

A

ྲྀዖ ǖࡆඇ
ਢ ǖଖඇ

8 LOGIC ྲྀዖ ǖଖඇ

Ѣ‫ױ‬ऒă

Ѣ a!ࡍѢ‫ױ‬ऒDŽӰફ BDž
ă
ᇀ CBTF ன෷ቲLjѢ‫ױ‬ऒă
ᇀ CBTF ன෷ቲLjѢ‫ױ‬ऒă

k ࿤෸ࡥஎ
A พ൩ӹؕ෷Ԍࣜ๻ॕ߷
ӊࣜ๻ಹ৹ᇀༀქ‫ࡥޔ‬எණༀ෫࿤෸ఀพ൩‫و‬ӹؕ෷ࣆࣜ
๻ॕ߷ă
!
พ൩ӹؕ෷
2× ( 5+ 4 ) – 2× - 3
!
ࣜ๻ॕ߷
24
Ck-7

A ࿤෸ܻࠟ
‫־‬࿦ᇀࣜ๻ಹ࿤෸ಃණ‫و‬࿒ะܻࠟӹ෸࿦ᇀ‫ࣜو‬๻ன෷Lj
ࣜ๻ಹ‫و‬හብࣆࣜ๻߹ٌ֔ăᇀӊํடรቲLj
Đ৚ಶđქ
‫װ‬ᅋᅢӹ෸ქ‫־ܻࠟޔ‬࿦ᇀࡥஎණLjۚĐॖ‫ׅ‬đქ‫װ‬ᇘӹ
෸ದဋ෡ă
సӫ‫و‬෸۶ࡥஎӹ෸ 7!ܻࠟă!

ࣜ๻ன෷ࠧහብ
k ࣜ๻ன෷‫و‬ၭᇗ
ӊࣜ๻ಹޮᅘ૥ቸĐࣜ๻ன෷đ
ă
2/!!Ѣ ,ă
• ࣜ๻ன෷Ե‫־ة‬࿦ă
• ࣜ๻ன෷Ե‫ة‬ᅘ઩‫ࡥޔ‬எăѢ ,!६ှၭࡳăෳᅋ
d ࠧ e ნ৹ၭࡳԵ‫ࡥة‬எă
COMP CMPLX BASE

SD

REG

1

4

5

2

3

PRGM

6

3/!!ቖှ࿒ะՃዷቐქၭᇗຑၖე‫ࣜو‬๻ன෷ă
b!)DPNQ*;!DPNQDŽᆱ๻Dž c!)DNQMY*;!DNQMYDŽ‫ืݒ‬Dž
d!)CBTF*;!CBTFDŽࢱ!ื !* e!)TE*;!TEDŽ‫ة‬Ӱફ༇ࣜDž
f!)SFH*;!SFHDŽใӰફ༇ࣜDž
g!)QSHN*;!QSHNDŽ֔ၠDž
• Ѣ‫ ׹‬b ባ g ‫ืو‬ዖऒ৹ၭᇗ࿰ᄮன෷Ljྐଥ௅೐࿤
෸‫و‬Ե‫ࡥة‬எཛྷࠨă

Ck-8

k ࣜ๻ಹහብ
ࣜ๻ಹහብ৹ᅋᅢైብพ൩ࠧพ‫־‬හ‫ڊ‬Ăࣜ๻Ըืࣆದຓ
හ‫ڊ‬ăහብ৹ෳᅋහብࡥஎ६ှైብLjѢ !,)TFUVQ*
ऒ৹‫ོ܃‬හብࡥஎăޮᅘ૥‫ޔ‬හብࡥஎLjᅋ d ࠧ e ৹
ᇀದࣺ६ှၭࡳă

A ऻ‫و཭ةڪ‬ቚ‫ڊ‬

π !࡙‫!>!ڪ‬211 ҇‫ڪܖ‬
:1˚!>!Ċ
3
ऻ‫཭ةڪ‬

ቖှ‫ױ‬ऒՃዷ ǖ

‫ڪ‬

!,!b!)Efh*

࡙‫ڪ‬

!,!c!)Sbe*

҇‫ڪܖ‬

!,!d!)Hsb*

A ࿤෸཭ื‫و‬ቚ‫ڊ‬
ቚื࿤෸

ቖှ‫ױ‬ऒՃዷ ǖ

ဏื཭ื

!,!e!b!)Gjy*a!)1* ባ!
j!):*

ᅘပ཭ื

!,!e!c!)Tdj*b!)2* ባ!
j!):*-!a!)21*

ቚื࿤෸۶ཙ

!,!e!d!)Opsn*b!)Opsn2*!ࢪ
c)!Opsn3*

࿒எढ़මࣜ๻ॕ߷ก൥ࠨ‫ޗ‬যఀቚ‫وڊ‬හ‫ڊ‬६ှ࿤෸‫و‬ă!
• ‫ޗ‬যఀቚ‫وڊ‬ဏื཭ืDŽGjyDž࿤෸૏‫ف‬গ཭ဏืăࣜ๻
ॕ߷Ӈල൩‫ف‬ቚ‫وڊ‬ဏื཭ืණă
۶ઋ ǖ
!100 ÷ 7 = 14.286 (Fix = 3)
Ck-9

• ᅋ Tdj ቚ‫ڊ‬ષᅘပ཭ืࡍLjࣜ๻ॕ߷ෳᅋᅘပ཭ืࣆ 21
཭ื‫و‬࿰ᄮ֓‫۽‬६ှ࿤෸ăࣜ๻ॕ߷Ӈල൩‫ف‬ቚ‫཭وڊ‬
ืණă
۶ઋ ǖ! 1 ÷ 7 = 1.4286 × 10–1 (Sci = 5)
• ၭᇗ Opsn2 ࢪ Opsn3 ࡍLj‫ࣜص‬๻ॕ߷ᇀ࿒෸۶ཙቐ௠෫Lj
ದटჾቚืࣝืۨ࿤෸ă
Norm1: 10–2 > 앚x앚, 앚x앚 > 1010
Norm2: 10–9 > 앚x앚, 앚x앚 > 1010
۶ઋ ǖ!1 ÷ 200 = 5. × 10–3 (Norm1)

0.005 (Norm2)

A ‫ืܖ‬࿤෸ြ෷‫و‬ቚ‫ڊ‬
‫ืܖ‬ြ෷

ቖှ‫ױ‬ऒՃዷ ǖ

‫ืܖ؞‬

!,!ee!b!)bc0d*

࣯‫ืܖ‬

!,!ee!c!)e0d*

A ‫ืݒ‬࿤෸ြ෷‫و‬ቚ‫ڊ‬
‫ืݒ‬ြ෷

ቖှ‫ױ‬ऒՃዷǖ

ቓऻዸӶ

!,!eee!b!)a!,b!i!*

ࣁዸӶ

!,!eee!c!)r!∠!!*

A ༇ࣜ౷ଔ‫و‬හ‫ڊ‬
౷ଔහ‫ڊ‬

ቖှ‫ױ‬ऒՃዷǖ

౷ଔ৚ಶ

!,!dd!b!)GsfrPo*

౷ଔॖ‫ׅ‬

!,!dd!c!)GsfrPgg*

Ck-10

k ࣜ๻ன෷ࠧහብ‫و‬അ‫ׅ‬
ቖှ࿒ะՃዷ৹അ‫ׅ‬௅೐‫ࣜو‬๻ன෷ࣆຑᅘහብLjԌटࣜ
๻ಹֽ෶ࡧཛྷ࿒෸ైብă!
ࣜ๻ன෷!///////////////////////////DPNQDŽᆱ๻ன෷Dž
ऻ‫!཭ةڪ‬///////////////////////////EfhDŽ‫ڪ‬Dž
ቚื࿤෸!///////////////////////////Opsn2
‫ืܖ‬ြ෷!///////////////////////////bc0d!
DŽ‫ืܖ؞‬Dž
‫ืݒ‬ြ෷!///////////////////////////a,biDŽቓऻዸӶDž
!
౷ଔහ‫!ڊ‬///////////////////////////GsfrPoDŽ౷ଔ৚ಶDž
ቖှ࿒ะऒՃዷ৹അ‫ׅࣜ‬๻ன෷ࣆහብă
!9(CLR)2(Setup)w
ԥ࿻അ‫ׅࣜ‬๻ಹ‫و‬හ‫ڊ‬෫LjഋᇀණะՃዷቲѢ A!ۚԥѢ
wă

๻෷ࠧื቗‫و‬พ൩
k ๻෷‫و‬พ൩
ӊࣜ๻ಹ৹ဃฐဢქჅพ൩๻෷LjԌѢ w ቖှăࣜ๻ಹ
ዔ‫ڑ‬ৈ‫ࣩۨڊ‬ĂऋۨĂ֓ۨĂ‫ׅۨ‬Ăࠉืࣆਸ਼ࠟ‫و‬ቁവᅍ
࿘๋ၠă
۶ઋ ǖ
!2 × (5 + 4) – 2 × (–3) =
2*(5+4)- 2 × ( 5 + 4 ) – 2 × - 3
2*-3w
24

Ck-11

A ‫؞‬ਸ਼ࠟ৶ၳࠉื‫و‬พ൩ )tjo-!dpt-!'LjٌDž
ӊࣜ๻ಹ৹พ൩࿒઼‫؞‬ਸ਼ࠟ‫و‬৶ၳࠉืăഋኢᄌLjᇀพ൩
ԸืࡍLjӤၙѢ ) ߔӡਸ਼ࠟă
sin(, cos(, tan(, sin–1(, cos–1(, tan–1(, sinh(, cosh(, tanh(,
sinh–1(, cosh–1(, tanh–1(, log(, ln(, e^(, 10^(, '(, 3'(,
Abs(, Pol(, Rec(, arg(, Conjg(, Not(, Neg(, Rnd(, ∫(,
d/dx(
۶ઋ ǖ
!sin 30 =
( )
s30)w s i n 30

05

A ֓ࠟ‫و‬ෛଞ
֓ࠟ৹ჾᇀ࿒ะഉਦ࿒ෛଞă
• ᇀ৚ਸ਼ࠟቐ೐ǖ3!ġ!)6!,!5*
• ᇀ‫؞‬ਸ਼ࠟ‫و‬৶ၳࠉืቐ೐ǖ3!ġ!tjo)41*-!3!ġ!')4*
• ᇀ೐ብܻࠟDŽҪਸ਼‫ࠟݘ‬Džቐ೐ǖ3!ġ!i234
• ᇀӰફணĂիืࢪ๾ࢲืቐ೐ǖ31!ġ!B-!3!ġ!π
ቺეƽ
൥߷ቖှҪࠆ‫ׅۨ‬ᆱ๻ࠧෛଞ֓ࠟ‫ۨ֓و‬ᆱ๻‫ࣜو‬๻Ljᇘ
࢙൥࿒எ‫و‬۶ઋຑ෸ዔ‫ڑ‬Տ൩ਸ਼ࠟă
• ෛଞ৚ਸ਼ࠟቐ೐ࢪߔਸ਼ࠟቐࡍ‫ࠟ֓و‬෫ă
6 ÷ 2 (1 + 2) p 6 ÷ (2 (1 + 2))
6 ÷ A (1 + 2) p 6 ÷ (A (1 + 2))
1 ÷ (2 + 3) sin(30) p 1 ÷ ((2 + 3) sin(30))

Ck-12

• ෛଞӰફĂիืٌቐ೐‫ࠟ֓و‬෫ă
6 ÷ 2π p 6 ÷ (2π)
2 ÷ 2'(2) p 2 ÷ (2'(2))
4π ÷ 2π p 4π ÷ (2π)
• พ൩ෳᅋ‫ืࠉوࠟڜ‬DŽઋ൥ QpmĂSfdDž෫LjഋྣӤพ൩
ӹؕ෷ຑეഓ‫ߔو‬ਸ਼ࠟă൥߷ԥพ൩ߔਸ਼ࠟLjᇘ৹௢ྐ
ۨ൥ණຑะዔ‫ڑ‬Տ൩ਸ਼ࠟă

A ዮࡍ‫ߔو‬ਸ਼ࠟ
ᇀѢ w!ऒቐ೐‫و‬๻෷ዮࡍ‫ߔو‬ਸ਼ࠟ৹ჾෛଞქ‫ޔ‬ჾණă!
۶ઋ ǖ!(2 + 3) × (4 – 1) = 15
(2+3)*
(4-1w

( 2+ 3 ) × ( 4– 1

15

A ࡥஎ‫و‬ዳᅚি‫ڑ‬
พ൩ӹؕ෷
࿤෸‫و‬ӹؕ෷

12345 + 12345 + 12345
345 + 12345 + 12345I

ߞӶ
• ‫ ص‬b!ܻࠟ‫־‬࿦ᇀࡥஎණ෫Lj৹ჾෳᅋ d!ऒဂዳჰ‫ڑ‬
ߞӶԌি‫ࡥڑ‬எă
• ဂዳি‫࢙ڑ‬ෳӹؕ෷‫و‬ქԩ‫ܖ‬ᄑ‫ࡥ־‬எ‫و‬ᅚՊLj‫ױ‬෫ \!
ܻ࢙ࠟ‫־‬࿦ᇀᅚՊă‫־ܻࠟ!\ ص‬࿦ᇀࡥஎණ෫Lj৹ჾෳ
ᅋ e!ऒဂᅚჰ‫ߞڑ‬ӶԌি‫ࡥڑ‬எă
• ఀࡱ৹ჾѢ f!໮ባӹؕ෷‫و‬৚་LjࢪѢ c!໮ባயཤă

Ck-13

A พ൩‫و‬ዖܻืDŽዖॎDž
‫ص‬ఀพ൩ืၳӹؕ෷෫Ljದटү،ᇀ֎ཛྷĐพ൩ഘđ‫و‬،
‫׈‬ഘቲLj‫ױ‬พ൩ഘ‫و‬൛ફཛྷ :: ዖॎăნটกํLjᇀქ‫ޔ‬
ืၳӹؕ෷ቲዮ‫ۂ‬௢พ൩ :: ዖॎ‫و‬ዖܻă
໼իLjӹ෸‫ص‬೐พ൩཭ብ‫ߞو‬Ӷᇀࡥஎණඝ‫ڑ‬ཛྷዝ໫DŽ|Dž
ࢪ࠻໫DŽ!*ă‫ص‬พ൩ഘ‫و‬ෝᅨ൛ફඵᅢ 21 ዖॎ෫LjߞӶ
टӰཛྷඝ‫۽وڑ‬ਙDŽk*ă
‫ױ‬ቸഉਦۢූ෫Ljഋᇀค‫཭وص‬ብ໷ቛพ൩‫ص‬೐‫و‬ӹؕ෷
Ԍࣜ๻ದॕ߷ă!

k ࣜ๻෷‫و‬Ӭࣃ
A Տ൩ன෷ࠧ‫ݥݐ‬ன෷
ӊࣜ๻ಹᅘ઩ቸพ൩ன෷ăՏ൩ன෷ᇀߞӶ཭ብՏ൩ఀพ
൩‫و‬ዖܻLjԌटߞӶᅚՊ‫و‬ຑᅘዖܻဂᅚჰ཭ჾ໐‫־‬ਅࣺă
‫ݥݐ‬ன෷टఀพ൩‫و‬ዖܻණဢᇀߞӶ཭ብ‫و‬ዖܻණă!
ᆓӹؕ෷
Տ൩ன෷

1+2|34

Ѣ+
1+2+|34

ߞӶ
‫ݥݐ‬ன෷

1+2 3 4

ߞӶ
ֽ෶യෛพ൩ன෷හ‫ڊ‬ཛྷՏ൩ன෷ă
ე‫ݢ‬Ӱཛྷ‫ݥݐ‬ன෷෫LjഋѢ 1D)JOT*ă

Ck-14

1+2 + 4!

A ‫ݳ‬พ൩‫و‬ऒՃዷ‫و‬Ӭࣃ
۶ઋ ǖ!ე‫ޚ‬ቁ!47:!ġ!24!ෳದӰཛྷ!47:!ġ!23!෫
369*13 369 × 13I
D2 369 × 12I

A ऒՃዷ‫و‬ක‫ׅ‬
۶ઋ ǖ!ე‫ޚ‬ቁ!47:!ġġ!23!ෳದӰཛྷ!47:!ġ!23!෫
Տ൩ன෷
369**12 369 ×× 12I
ddD 369 ×I12
‫ݥݐ‬ன෷
369**12 369 ×× 12
dddD 369 × 12

A ӹؕ෷ቲऒՃዷ‫و‬Ӭࣃ
ᇀՏ൩ன෷࿒Ljᅋ d!ࠧ e!टߞӶჰ‫ڑ‬ባఀეӬࣃ‫و‬
ऒՃዷ‫و‬ᅚՊLjѢ D!टದක‫ׅ‬Ljഹࡍቖှቁവ‫و‬ऒՃዷă
ᇀ‫ݥݐ‬ன෷࿒LjटߞӶჰ‫ڑ‬ባఀე‫ޚ‬ቁ‫و‬ऒՃዷ཭ብLjഹ
ࡍቖှቁവ‫و‬ऒՃዷă!

A ൥ࠨᇀӹؕ෷ቲՏ൩ऒՃዷ
ეᇀӹؕ෷ቲՏ൩ऒՃዷ෫ӤၙၭᇗՏ൩ன෷ăᅋ d!ࠧ
ഹࡍ६ှऒՃዷă!
e!टߞӶჰ‫ڑ‬ባეՏ൩ऒՃዷ‫཭و‬ብLj

Ck-15

k ؓྥ཭ብ‫و‬Փሖ
൥߷๻෷ԥቁവLj‫ص‬ఀѢ w!ቖှ๻෷෫Ljؓྥဳྲट‫־‬
࿦ᇀࡥஎණăؓྥဳྲ‫־‬࿦ࡍLjѢ d!ࢪ e!ऒ৹ෳߞ
Ӷ໮ባ๻෷ቲդූؓྥ‫཭و‬ብ‫׌‬Ljჾӯఀ‫ޚ‬ቁă!
۶ઋ ǖ
! !‫ص‬ఀეพ൩ 25!Ģ!21!ġ!3!>Ljലพ൩ષ 25!Ģ!1!ġ!
3!> ෫
DŽ࿒ઋෳᅋՏ൩ன෷ă
Dž
14/0*2w

Mat h ERROR

e!ࢪ d 14 ÷ 0I×2
ؓྥ཭ብ
÷ ×
d1w 14 10 2

28

ࢱӊࣜ๻
‫܇ׅ‬૙ှኢடLjӊॎढ़ම‫ࣜو‬๻৹ᇀࣜ๻ಹ‫و‬ൌࠨࣜ๻ன
෷ቲ६ှLj‫ د‬CBTF ன෷‫ׅ‬༶ă

k ๜ᇘᆱ๻
๜ᇘᆱ๻৹ᅋᅢ६ှࣩDŽ+*-!ऋ )-*-!֓ )**-!‫) ׅ‬/*
ࣜ๻ă
۶ઋ ǖ
!7 × 8 − 4 × 5 = 36
7*8-4*5w

Ck-16

36

k ‫ืܖ‬
‫ืܖ‬ෳᅋቚ‫ *{) ܻޒܖوڊ‬พ൩ă

A ‫ࣜืܖ‬๻۶ઋ
1
2
11
۶ઋ 2ǖ 3 4 + 1 3 = 4 1 2
3$1$4+
1$2$3w
2
1
7
۶ઋ 3ǖ 3 + 2 = 6 DŽ‫ืܖ‬࿤෸ြ෷
!
ǖe0d*
2$3+1$2w

4{11{12

7{6

ኢ
• ൥߷‫ࣜืܖ‬๻ॕ߷‫ޕ‬ԩ‫ܖ‬DŽሿื , ‫ܖ‬ዓ , ‫ܖ‬ா , ‫ܻޒܖ‬Dž
‫و‬ዜ཭ืմ߹ 21 ཭Ljࣜ๻ॕ߷टჾဏืြ෷࿤෸ă
• ൥߷พ൩‫ࣜو‬๻ཛྷ‫ืܖ‬ᅳဏื቗‫ࣜࠩࢤو‬๻Ljࣜ๻ॕ߷
टჾဏืြ෷࿤෸ă
• ‫ޕوืܖ‬ԩ‫ܖ‬ቝ௢พ൩ሿืăพ൩‫܇‬ሿืटդූဏืြ
෷‫ࣜو‬๻ॕ߷ă!

A ‫ืܖ؞‬ြ෷ᅳ࣯‫ืܖ‬ြ෷ࣺ‫و‬Ӱࡳ
ეट‫ืܖ؞‬Ӱࡳཛྷ࣯‫ืܖ‬DŽࢪट࣯‫ืܖ‬Ӱࡳཛྷ‫ืܖ؞‬Dž෫Lj
ഋѢ !$)e0d*ă

A ဏืြ෷ᅳ‫ืܖ‬ြ෷ࣺ‫و‬Ӱࡳ
Ѣ $ ৹ᇀဏื቗ᅳ‫ืܖ‬࿤෸ြ෷ቐࣺӰࡳă
ኢ
൥߷‫ޕืܖ‬ԩ‫ܖ‬DŽሿื , ‫ܖ‬ዓ , ‫ܖ‬ா , ‫ܻޒܖ‬Dž‫و‬ዜ཭ื
մ߹ 21 ཭Ljᇘࣜ๻ಹԥ௢‫׹‬ဏืြ෷Ӱࡳཛྷ‫ืܖ‬ြ෷ă
Ck-17

k ҇‫ܖ‬Ӕࣜ๻
พ൩ქ‫ืޔ‬቗ࡍพ൩҇‫ *&) ࠟܖ‬৹ෳ‫ืݡ‬቗Ӱཛྷ҇‫ืܖ‬ă

A ҇‫ܖ‬Ӕࣜ๻۶ઋ
۶ઋ 2ǖ 2 % = 0.02

2
(!100 )
2!((%)w

002

20
(150 × 100 )
150*20
!((%)w

30

۶ઋ 4ǖ 771 ก 991 ‫ܖ҇و‬ቐ࣎Ǜ
660/880
!((%)w

75

۶ઋ 5ǖ ट 3-611 ᇜࣩ 26&ă
2500+2500*
15!((%)w

2875

۶ઋ 6ǖ ट 4-611 ऋඵ 36&ă
3500-3500*
25!((%)w

2625

۶ઋ 3ǖ 150 × 20% = 30

۶ઋ 7ǖ ट 279-!:9 ࣆ 845 ‫ࠧو‬ऋඵ 31&ă
168+98+734w

1000

-G*20!((%)w

800

Ck-18

۶ઋ 8ǖ ट 411 ৻ࣩባՌฎჅӊᆓቺ‫ و‬611 ৻ණLj‫ فه‬911
৻‫و‬ዮቷՌฎჅӊă611 ৻‫ܖ҇و‬ቐ࣎ก 911 ৻Ǜ
(500+300)
160
/500!((%)w
۶ઋ 9ǖ ‫ืص‬቗‫ ׹‬51 ᇜࣩ‫ ف‬57 ෫LjӰࡧଔཛྷ‫ۂ‬ඵǛ
(46-40)/40
15
!((%)w

k ‫ܖڪ‬ஓDŽ૥෨६ቨDžࣜ๻
A ૥෨६ቨื቗‫و‬พ൩
࿒எढ़මพ൩૥෨६ቨื቗‫ࢱو‬ӊশۨă!
| ‫!~ ڪ‬$!| ‫!~ ܖ‬$!| ஓ ~!$
۶ઋ ǖ!ეพ൩ 3°41´41˝ ෫
2$30$30$w

2 ˚ 30 ˚ 30 ˚

2 ˚ 30 ˚ 30

• ഋኢᄌLj‫ܖࣆڪ‬Ӥၙพ൩ᅘื቗Lj࣊ෳದཛྷ૏ă!

A ૥෨६ቨࣜ๻۶ઋ
࿒઼੮ျ‫و‬૥෨६ቨࣜ๻टդූ૥෨६ቨ‫ࣜو‬๻ॕ߷ă
• ઩‫ޔ‬૥෨६ቨื቗‫ࢪࣩۨو‬ऋۨ
• ૥෨६ቨื቗ᅳ෨६ቨื቗‫ׅۨࢪۨ֓و‬
۶ઋ ǖ!3°31´41˝!,!4:´41˝!>!4°11´11˝
2$20$30$+
0$39$30$w
Ck-19

3 ˚ 0˚ 0

A ૥෨६ቨᅳ෨६ቨࣺ‫ࡳو‬๻
‫ࣜص‬๻ॕ߷࿤෸෫LjѢ $!৹ᇀ૥෨६ቨᅳ෨६ቨࣺࡳ๻
ื቗ă!
۶ઋ ǖ!ეट 3/366 ࡳ๻ཛྷ૥෨६ቨ෫
2.255w$

2 ˚ 15˚ 18

ࣜ๻଎ઈࣆՓᆪ
ࣜ๻଎ઈүૠᅘఀ६ှ‫ࣜޕو‬๻‫ࣝو‬ଆLjದቲҪਸ਼ఀพ
൩‫و‬ӹؕ෷ࣆࣜ๻ॕ߷ăࣜ๻଎ઈ৹ᇀ DPNQ-!DNQMY ࣆ
CBTF ன෷ቲෳᅋă!

k ࣜ๻଎ઈ‫ོ܃و‬
ࡥஎᅚණऻණ‫ܻࠟ!`!و‬ӹ෸ࣜ๻଎ઈቲү،ᅘืযăე
Փᆪࣜ๻଎ઈቲ‫ืو‬য෫Lj
ഋѢ făѢ f!टဂණ
DŽဂࡍDž
ি‫ࣜڑ‬๻Ljༀ෫࿤෸๻෷ࣆದॕ߷ă!
۶ઋ ǖ! 1+1w2+2w3+3w
3+ 3

6

f 2+2

4

f 1+1

2

ি‫ࣜڑ‬๻଎ઈࣝଆ෫Lj$!ܻࠟट‫־‬࿦ᇀࡥஎණLjದӹ෸
‫ص‬೐ࣜ๻‫و‬࿒எᅘDŽृူ‫و‬Džࣝଆă‫ܻࠟױص‬৚ಶ෫LjѢ
c!৹ဂ࿒DŽဂ೐Džি‫ࣜڑ‬๻଎ઈࣝଆă
ቺეƽ
• Ѣ p ෫Lj‫ݢ‬Ӱࣜ๻ன෷෫Ljࢪቖှൌࠨ‫཭ݒ‬Ճዷ෫Lj
ࣜ๻଎ઈࣝଆटӇഩԩഅ‫ׅ‬ă
Ck-20

• ࣜ๻଎ઈ‫و‬൛ફกᅘ࿮‫و‬ă‫ࣜص‬๻଎ઈ჻ୄ෫Lj६ှူ
‫ࣜو‬๻टෳࣜ๻଎ઈቲዮছ‫ࣝو‬ଆዔ‫ڑ‬Ӈක‫ׅ‬Ljჾཛྷူ
ࣜ๻໐‫־‬ਅࣺă

k Փᆪ‫ޢ‬௢‫و‬ෳᅋ
‫ࣜص‬๻଎ઈࣝଆ࿤෸ᇀࡥஎණ෫LjѢ d!ࢪ e!࿤෸ߞ
ӶԌ६൩Ӭࣃன෷ăѢ e!৹ෳߞӶᇀ๻෷‫و‬৚་‫־‬࿦Lj
ۚѢ d!৹ෳߞӶᇀ๻෷‫و‬யཤ‫־‬࿦ă६ှ༾ӛຑၖე‫و‬
Ӱ‫ࡍޚ‬LjѢ w!ቖှࣜ๻ă
۶ઋ ǖ!4 × 3 + 2.5 = 14.5
4 × 3 – 7.1 = 4.9
4*3+2.5w

4×3+ 2 . 5

145

d 4 × 3 + 2 . 5I
DDDD-7.1w

4×3 –7 . 1

49

ࣜ๻ಹ‫و‬،‫׈‬ಹՃዷ
k ‫ؖ‬Ѧ،‫׈‬ಹDŽBotDž‫و‬ෳᅋ
ఀᇀࣜ๻ಹණ६ှ‫وူو‬ქ‫ࣜ״‬๻‫و‬ॕ߷टዔ‫ڑ‬Ӈү،ᇀ
‫ؖ‬Ѧ،‫׈‬ಹDŽBotDžቲă

ABot ‫ࠧူޚ‬ක‫وׅ‬෫ࢲ
ᇀࣜ๻ቲෳᅋ Bot ෫Ljࣝኡದ௠൛กࠨ෫ჾࣆ൥ࠨ‫ݢ‬Ӱ‫و‬
࠶ቺეăഋኢᄌ࿒઼࣎٧ă!
Ck-21

• ‫ص‬ఀ६ှ࿒ะൌࠨՃዷ෫LjBot ቲ‫و‬௠൛࢙Ӈ‫ူޚ‬ǖෳᅋ
ࣜ๻ॕ߷६ှࣜ๻Ljᇀ‫ڢ‬઎،‫׈‬ಹቲࣩ൩ื቗ࢪ‫׹‬ದቲ
ऋണื቗LjཛྷӰફ‫ݑ‬቗ࢪ‫׹‬Ӱફቲ‫ื־ٻ‬቗Ljᇀ TE ன෷
ࢪ SFH ன෷ቲพ൩༇ࣜืযă
• ᇀ࢙դූქ‫ޔ‬ჾණࣜ๻ॕ߷‫ࣜو‬๻ቲDŽ൥ዸӶࣜ๻ٌDž
Lj
ฑ࿘‫־‬࿦ᇀࡥஎණ‫و‬ॕ߷࢙Ӈү،ᇀ Bot ቲă
• ൥߷‫ص‬೐‫ࣜو‬๻‫־‬࿦ષؓྥLjᇘ Bot ‫و‬௠൛ԥ࢙‫ݢ‬Ӱă
• ᇀ DNQMY ன෷ቲ६ှ‫ࣜืݒ‬๻෫Ljॕ߷‫و‬෯ืԩࠧၗื
ԩ‫ڞ‬टӇү،ᇀ Bot ቲă‫د‬ഋኢᄌLj൥߷ఀ‫ݢ‬Ӱባದຓ
ࣜ๻ன෷Ljᇘื቗‫و‬ၗืԩटӇഅ‫ׅ‬ă!

A ൥ࠨᇀઘၦࣜ๻ቲዔ‫ڑ‬Տ൩ Bot
۶ઋ ǖ!ეट 4!ġ!5 ‫ࣜو‬๻ॕ߷‫ׅ‬ჾ 41 ෫
3*4w
DŽഹࡍDž/30w

12
Ans ÷ 30

04

Ѣ /!৹ዔ‫ڑ‬พ൩ Botă
ኢ
‫ڶ‬ᅢ‫؞‬ᅘਸ਼ࠟԸื‫ืࠉو‬DŽٞ 23 ოDž
Lj‫ص‬ఀቝพ൩ࠉืࡍ
Ѣ w ෫LjBot ԯዔ‫ڑ‬ӰཛྷԸืă

Ck-22

A ൥ࠨᇀࣜ๻ቲฐ‫ڑ‬Տ൩ Bot
۶ઋ ǖ!ეᇀದຓࣜ๻ቲෳᅋ 234!,!567 ‫ࣜو‬๻ॕ߷෫Lj६
ှ൥࿒ຑ෸Ճዷ!
123 + 456 = 579
789 – 579 = 210
123+456w

579

789-Kw

210

k ‫ڢ‬઎،‫׈‬ಹ‫و‬ෳᅋ
‫ڢ‬઎،‫׈‬ಹ )N* ኙეᅋᅢࣜ๻੩ࢵዜࠧă
ࡥஎණ‫־‬࿦ N ܻࠟ෫Ljӹ෸‫ڢ‬઎،‫׈‬ಹቲ،ᅘ‫܇‬૏‫ืو‬቗ă
‫ڢ‬઎،‫׈‬ಹ৹ᇀ‫ ׅ‬TE ன෷ࠧ SFH ன෷ቐ༶‫و‬ຑᅘࣜ๻ன
෷ቲෳᅋă
N ܻࠟ

10M+

A ൥ࠨᇀ‫ڢ‬઎،‫׈‬ಹቲࣩ൩ื቗
‫ص‬ఀพ൩‫ืو‬቗ࢪࣜ๻ॕ߷࿤෸ᇀࡥஎණ෫LjѢ m!৹ट
‫ืݡ‬቗ࣩ൩‫ڢ‬઎،‫׈‬ಹ )N* ቲă!
۶ઋ ǖ!ეट 216!Ģ!4 ‫ࣜو‬๻ॕ߷ࣩ൩‫ڢ‬઎،‫׈‬ಹ )N* ቲ෫
105/3m

Ck-23

35

A ൥ࠨ‫ڢ׹‬઎،‫׈‬ಹऋണื቗
‫ص‬ఀพ൩‫ืو‬቗ࢪࣜ๻ॕ߷࿤෸ᇀࡥஎණ෫LjѢ
1m)Nlj* ৹‫ڢ׹‬઎،‫׈‬ಹ )N* ऋണ‫ืݡ‬቗ă
۶ઋ ǖ!ე‫ڢ׹‬઎،‫׈‬ಹ )N* ऋണ 4!ġ!3!‫ࣜو‬๻ॕ߷෫
3*21m(M–)

6

ኢ
‫ࣜص‬๻ॕ߷࿤෸ᇀࡥஎණ෫LjѢ m!ࢪ 1m)Nlj* ৹
ट‫ืݡ‬቗ࣩ൩‫ڢ‬઎،‫׈‬ಹቲࢪ‫ڢ׹‬઎،‫׈‬ಹऋണ‫ืݡ‬቗ă
ቺეƽ
ᇀࣜ๻ॕา෫Ѣ m!ࢪ 1m)Nlj*!
DŽۚԥѢ wDž෫‫־‬
࿦ᇀࡥஎණ‫ืو‬቗ཛྷࣜ๻ॕ߷DŽ‫ݡ‬ॕ߷टӇࣩ൩‫ڢ‬઎،‫׈‬
ಹLjࢪ‫ڢ׹‬઎،‫׈‬ಹऋണ‫ݡ‬ॕ߷Dž
ăದԥก‫ڢ‬઎،‫׈‬ಹቲ
࿦ᇀү،‫ืو‬যă

A ‫ڢ‬઎،‫׈‬ಹ௠൛‫و‬Փᆪ
Ѣ tm)N*ă

A ൥ࠨഅ‫ڢׅ‬઎،‫׈‬ಹቲ‫ืو‬যDŽባ 1Dž
01t)TUP*m)N*
അ‫ڢׅ‬઎،‫׈‬ಹटෳ N ܻࠟဋ෡ă!

k Ӱફ‫و‬ෳᅋ
ӊࣜ๻ಹӄᅘணཛྷ BĂCĂDĂEĂY ࣆ Z ‫و‬૥‫ޔ‬ӰફLj৹
ᇀၖე෫ᅋᅢү،ื቗ăӰફ৹ᇀຑᅘࣜ๻ன෷ቲෳᅋă

Ck-24

A ൥ࠨटื቗ࢪࣜ๻ॕ߷‫ޖݑ‬Ӱફ
ഋෳᅋ࿒ะՃዷटื቗ࢪࣜ๻෷‫ޖݑ‬Ӱફă
۶ઋ ǖ!ეट 4!,!6 ‫ޖݑ‬Ӱફ B ෫
3+51t)TUP*-)B*

A ൥ࠨՓ৤‫ޖݑ‬Ӱફ‫ืو‬቗
ეՓ৤‫ޖݑ‬Ӱફ‫ืو‬቗෫LjഋѢ t!ࡍቚ‫ڊ‬Ӱફணă
۶ઋ ǖ! ეՓ৤‫ޖݑ‬Ӱફ B ‫ืو‬቗෫!!!!!!!!!!t-)B*

A ൥ࠨᇀࣜ๻ቲෳᅋӰફ
ఀ৹ჾဃෳᅋื቗ქჅᇀࣜ๻ቲෳᅋӰફă
۶ઋ ǖ! ეࣜ๻ 6!,!B ෫!!!!!!!!!!5+a-)B*w

A ൥ࠨഅ‫ׅ‬Ӱફቲ‫ืو‬቗DŽባ 1Dž
۶ઋ ǖ! ეഅ‫ׅ‬Ӱફ B ෫!!!!!!!!!!01t)TUP*-)B*

k ൥ࠨഅ‫ׅ‬ຑᅘ،‫׈‬ಹቲ‫و‬௠൛
ეഅ‫ڢׅ‬઎،‫׈‬ಹĂӰફ،‫׈‬ಹჾࣆ‫ؖ‬Ѧ،‫׈‬ಹቲ‫و‬௠൛
෫Ljഋቖှ࿒ะऒՃዷă!
19(CLR)1(Mem)w
• ԥ࿻അ‫ׅࣜ‬๻ಹ‫و‬හ‫ڊ‬෫LjഋᇀණะՃዷቲѢ A!ۚԥ
Ѣ wă

Ck-25

৶ၳࠉืࣜ๻
‫܇ׅ‬૙ှኢடLjӊॎቲढ़ම‫ืࠉو‬৹ᇀࣜ๻ಹ‫و‬ൌࠨࣜ๻
ன෷ቲෳᅋLj‫ د‬CBTF ன෷‫ׅ‬༶ă!

৶ၳࠉืࣜ๻ၙቌ
• ६ှࠆᅘ௠Ղ৶ၳࠉื‫ࣜو‬๻෫Ljࣜ๻ॕ߷৹௢࢙ၖე
ქဗ෫ࣺԯ࢙‫־‬࿦ăቓ‫ࣜف‬๻ॕ߷‫־‬࿦ཛྷቛLjഋԥე६
ှൌࠨऒՃዷă
• ეቲ‫ڱ‬ቁᇀ६ှ‫ࣜو‬๻෫LjഋѢ Aă

ߔᅢ৶ၳࠉื‫و‬শۨ
• ‫ؠ‬ӹࠉืԸื‫ྲྀو‬ዖਸ਼ᇀ‫ؙ‬ਸ਼ࠟ )|!~* ቲăԸื໼իཛྷ | ื
቗ ~ ࢪ | ӹؕ෷ ~ă
• ‫ؙص‬ਸ਼ࠟ )|!~* ‫و‬༶எᅞਸ਼ᅘᆘਸ਼ࠟ෫Ljದӹ෸ᇀᆘਸ਼ࠟ
௠พ൩‫و‬ຑᅘ࿾௅োཛྷத૚ă

k ᆘቾଔ )π* ࠧዔഹ‫وืڶ‬ٛ e
ӊࣜ๻ಹ৹ჾᇀࣜ๻ቲพ൩ᆘቾଔ )π* ࠧዔഹ‫وืڶ‬ٛ eă
π!ࠧ e!৹ჾᇀຑᅘன෷ቲෳᅋLj‫ د‬CBTF ன෷‫ׅ‬༶ă࿒෸
ཛྷӊࣜ๻ಹ‫ޕ‬௠Ղիื‫و‬቗ă
π = 3.14159265358980 (1e(π))
e = 2.71828182845904 (Si(e))

Ck-26

k ൻऻࠧ۴ൻऻࠉื
A শۨࠧพ൩
sin({n}), cos({n}), tan({n}), sin–1({n}), cos–1({n}),
tan–1({n})
۶ઋ ǖ!sin 30 = 0.5, sin–10.5 = 30DŽऻ‫཭ةڪ‬ǖEfh*
s30)w

05

–1
1s(sin )0.5)w

30

Aኢ
• ቝეԸืསෳᅋ‫ืݒ‬Ljሦဗࠉื‫ڞ‬৹ᇀ DNQMY ன෷ቲෳ
ᅋăઋ൥Lj৹ჾ६ှሦჅ‫ࣜو‬๻ ǖ
i!ġ!tjo)41*-!‫د‬ԥ৹६ှሦჅ‫ࣜو‬๻ ǖtjo)2!,!iDžă
• ᇀࣜ๻ቲၖეෳᅋ‫཭ةڪऻو‬ก௅೐ၭᇗཛྷയෛ‫ڪऻو‬
‫཭ة‬ă!

k ऻ‫཭ةڪ‬Ӱࡳ
ఀ৹ჾटᅋქቸऻ‫཭ةڪ‬พ൩‫ืو‬቗Ӱࡳཛྷ૙ქቸऻ‫ةڪ‬
཭ăพ൩ื቗ࡍLjѢ 1G)ESH'* ࿤෸࿒෸Ե‫ࡥة‬எă
! D
! 1
!

R

G

2 3

1(D):!‫ڪ‬
2(R):!࡙‫ڪ‬
3(G):!҇‫ڪܖ‬

Ck-27

π
۶ઋ ǖ!ეट!! !࡙‫ڪ‬Ӱࡳཛྷ‫ڪ‬෫DŽऻ‫ ཭ةڪ‬ǖEfh*
3
(1e(π)/2)
1G(DRG')2(R)E

( π ÷2 ) r

90

k ใച࿯ࠧ۴ใച࿯ࠉื
A শۨࠧพ൩
sinh({n}), cosh({n}), tanh({n}), sinh–1({n}), cosh–1({n}),
tanh–1({n})
۶ઋ ǖ!sinh 1 = 1.175201194
ws(sinh)1)E

1175201194

Aኢ
• Ѣ w!ቚ‫ڊ‬ใച࿯ࠉืࢪѢ 1w!ቚ‫ڊ‬۴ใച࿯ࠉื
ࡍLjѢ s-!c ࢪ tă
• ሦဗࠉื৹ჾᇀ DNQMY ன෷ቲෳᅋLj‫د‬Ըืԥ௢ෳᅋ‫ݒ‬
ืă

Ck-28

k ቚืࠧ‫ืࠉืڶ‬
A শۨࠧพ൩
10^({n}) ........... 10{n}

e^({n}) ............. e{n}
log({n}) ............ log10{n} DŽիᅋ‫ืڶ‬Dž
log({m},{n}) ...... log{m}{n} ) ჾ {m} ཛྷٛ‫* ืڶو‬
ln({n}) .............. loge{n} DŽዔഹ‫ืڶ‬Dž
۶ઋ 2ǖ
! log216 = 4, log16 = 1.204119983
l2,16)E

4

g( )
l16)E l o 16

1204119983

སቚ‫ڊ‬ٛ෫ӹ෸ჾ 21 ཛྷٛDŽիᅋ‫ืڶ‬Dž
ă!
۶ઋ 3ǖ ln 90 (loge 90) = 4.49980967
I90)E

Ck-29

449980967

k ֓‫ืࠉޗ۽֓ࠧืࠉ۽‬
A শۨࠧพ൩
{n} x2 ............... {n}2

) ౿‫* ۽‬

{n} x3 ............... {n}3

) ઎‫* ۽‬

{n} x–1 .............. {n}–1

) ‫* ืؽ‬

{(m)}^({n}) ....... {m}{n}

) ֓‫* ۽‬

'({n}) ........... {n}
3
3
'({n}) .......... {n}

) ౿‫* ޗ۽‬

({m})x'({n}) ... {m} {n}

) ઎‫* ޗ۽‬
DŽ֓‫ޗ۽‬Dž

2 + 1) ('
2 – 1) = 1
۶ઋ 2ǖ ('
(92)+1) ('( 2 ) + 1 ) ('( 2 ) – 1 )
(92)-1)E
1
2
3

۶ઋ 3ǖ –2 = –1.587401052
-2M2$3)E

– 2 ˆ ( 2{3 )

-1587401052

Aኢ
• ࠉื x3-!x4 ࣆ x−2!৹ᅋᅢ DNQMY ன෷ቲ‫ࣜืݒو‬๻ă‫ݒ‬
ื‫ऻܸو‬ნ৹ჾෳᅋሦဗࠉืă
x
• _)-!')-!4')-! ') ნ৹ჾᇀ DNQMY ன෷ቲෳᅋLj‫ݒد‬
ื‫ऻܸو‬ԥ௢ෳᅋሦဗࠉืă

Ck-30

k ዸӶӰࡳDŽቓऻዸӶ ↔ ࣁዸӶDž
ӊࣜ๻ಹ৹ჾᇀቓऻዸӶࠧࣁዸӶቐࣺ६ှӰࡳă

o

o

!

ቓऻዸӶ )Sfd*!

ࣁዸӶ )Qpm*

A শۨࠧพ൩
ቓऻዸӶӰࡳཛྷࣁዸӶ )Qpm*
Pol(x, y)
x ǖቓऻዸӶ x ቗
y ǖቓऻዸӶ y ቗
ࣁዸӶӰࡳཛྷቓऻዸӶ )Sfd*
Rec(r, )
r ǖࣁዸӶ r ቗
 ǖࣁዸӶ  ቗
۶ઋ 2ǖ
! ეटቓऻዸӶ )'
3-!'
3!* ӰࡳཛྷࣁዸӶ෫!
DŽऻ‫ةڪ‬
཭ ǖEfh*
1+(Pol)92)
2
,92))E
DŽՓ৤  ‫و‬቗ *
t,(Y)

Ck-31

45

۶ઋ 3ǖ
! ეटࣁዸӶ )3-!41˚* ӰࡳཛྷቓऻዸӶ෫
DŽऻ‫཭ةڪ‬ǖ
Efh*
1-(Rec)2,
30)E 1732050808
DŽՓ৤ y ‫و‬቗ *
t,(Y)

1

Aኢ
• ሦဗࠉื৹ჾᇀ DPNQLjTE ࣆ SFH ன෷ቲෳᅋă
• ࣜ๻ॕ߷ቝӹ෸ٞქ‫ ޔ‬r!቗ࢪ x!቗ă
• ࣜ๻ॕ߷‫!و‬r ቗DŽࢪ x ቗DžӇ‫ޖݑ‬Ӱફ YLjۚ  ቗DŽࢪ
y ቗DžӇ‫ޖݑ‬Ӱફ ZDŽٞ 36 ოDžăეՓ৤  ቗DŽࢪ y ቗Dž෫Lj
ഋ࿤෸‫ޖݑ‬Ӱફ Z ‫ืو‬቗Lj൥۶ઋຑ෸ă
• ‫׹‬ቓऻዸӶӰࡳཛྷࣁዸӶ෫Lj!቗‫و‬۶ཙཛྷ –291°<  <
291°ă
• ᇀࣜ๻෷௠६ှዸӶӰࡳ෫Ljࣜ๻ಹෳᅋዸӶӰࡳդූ
‫و‬ٞქ‫ืޔ‬቗ )r ቗ࢪ x ቗Dž
ă
۶ઋ ǖ!Qpm!)'
3-!'
3!*!,!6!>!3!,!6!>!8

Ck-32

k ࢵ‫ࣜܖ‬๻ࠧཔ‫ࣜܖ‬๻
A ࢵ‫ࣜܖ‬๻
ӊࣜ๻ಹԳᅋ‫ݽ‬๑-৻੘ନ‫ۨن‬६ှࢵ‫ܖ‬ᆱ๻ă

শۨࠧพ൩
∫ ( f (x), a, b, tol)
!f (x);!Y ‫ืࠉو‬DŽพ൩Ӱફ Y ຑෳᅋ‫ืࠉو‬ă
Dž
! a;!ࢵ‫ܖ‬ഘᅺ‫و‬࿒࿮
! b;!ࢵ‫ܖ‬ഘᅺ‫و‬ණ࿮
! tol;!ާ՘۶ཙ
•!‫ݡ‬Ըื৹ჾෛଞăᇀሦቸഉਦ࿒Ljटෳᅋ!
2!×!21−6!‫ާو‬՘ă
e

۶ઋ ǖ!∫1 In( x ) = 1
fIa0(X))
,1,aI(e))E

Ck-33

∫ ( I n ( X ) , 1, e )

1

A པ‫ࣜܖ‬๻
ӊࣜ๻ಹ‫ޗ‬যቲဲ՘‫ࣜۨܖ‬๻॰๞‫ืـ‬ă

শۨࠧพ൩
d/dx( f (x), a, tol)
f! )x*;!Y ‫ืࠉو‬DŽพ൩Ӱફ Y ຑෳᅋ‫ืࠉو‬ăDž
! a;!พ൩ຑၖཔ‫ܖ‬࿅ื‫و‬٧DŽཔ‫ܖ‬٧Dž‫و‬቗
! tol;!ާ՘۶ཙ
• ‫ݡ‬Ըื৹ჾෛଞăᇀሦቸഉਦ࿒Ljटෳᅋ
2!×!21−21 ‫ާو‬՘ă
۶ઋ ǖ
!ეࢩ‫!ืࠉه‬y!>!tjo)x* ᇀ٧ x >! π !‫ืـو‬
2
DŽऻ‫ ཭ةڪ‬ǖSbeDž
1f(d/dx)sa0(X)), d/ dx ( s i n ( X ) , π ÷2 )
1e(π)/2)E
0

A ࢵ‫ࣜܖ‬๻ࠧཔ‫ࣜܖ‬๻‫و‬ኢᄌ෼࿾
• ४৹ᇀ!DPNQ!ன෷ࠧ QSHN ன෷DŽᆱှன෷ ǖDPNQDžቲ
ቖှࢵ‫ࣜܖ‬๻ࠧཔ‫ࣜܖ‬๻ă!
• ᇀ!f)x* ቲԥ৹ෳᅋჾ࿒ܻࠟ ǖ
!QpmĂSfdăᇀ!f)x*ĂaĂb!
ࢪ!tol!ቲԥ৹ෳᅋჾ࿒ܻࠟ ǖ
!∫Ăd0dxă
• ᇀ!f)x*!ቲෳᅋൻऻࠉื෫Ljഋट!Sbe!ቚ‫ڊ‬ཛྷऻ‫཭ةڪ‬ă
• tol!቗ᆣဏLjॽവ‫ڪ‬ट࢙ᆣ‫ݽ‬Lj‫د‬ሦༀ෫ნ࢙႟լࣜ๻෫
ࣺăቚ‫!ڊ‬tol!෫Ljഋቚ‫ؙڊ‬ᅢࢪٌᅢ!2!×!21−25!‫و‬቗ă

Ck-34

४คᅋᅢࢵ‫ࣜܖ‬๻‫و‬ኢᄌ෼࿾
• ໼իLjࢵ‫ࣜܖ‬๻ၖე࿰‫ص‬լ‫و‬෫ࣺԯ௢༾֑ă
1
• ‫ڶ‬ᅢ!f)x*! 1Ljದቲ!a  x b ) ઋ൥Lj∫0!4x3 – 3 Ǚ –2*Lj
ࣜ๻ॕ߷टཛྷ‫ݘ‬቗ă
• ‫ޗ‬য!f)x*!‫و‬௠൛ࠧࢵ‫ܖ‬ഘᅺLjᅘ৹௢࢙ූ֑մ‫ާ־‬՘‫و‬
ࣜ๻ؓྥLj‫ـ‬ቤࣜ๻ಹ࿤෸ؓྥဋྲă

४คᅋᅢཔ‫ࣜܖ‬๻‫و‬ኢᄌ෼࿾
• ൥߷སพ൩!tol!টሖԥ‫ڶف‬ქ‫ޔ‬ॖ‫و‬ฏઞLjtol!቗टዔ‫ڑ‬
‫ٻ‬ሿLjჾവ‫־ڊ‬ॖă
• ‫܇‬ઘၦ٧Ă༏ӰԒ‫ڑ‬Ăࣁ‫ࣁࢪؙ‬ဏ٧Ăߑ٧ჾࣆԥ௢པ
‫وܖ‬௠٧Ljࢪሣഗ॰!1!‫و‬པ‫ܖ‬٧ࢪཔ‫ࣜܖ‬๻ॕ߷৹௢࢙
‫ـ‬ቤࣜ๻ॽവ‫࠶ڪ‬՘ࢪ‫ؓ־‬ă

A ֑‫ࣜܖࢵޢ‬๻࣒೩
൥߷ቾಜࠉืࢪࢵ‫ܖ‬ഘࣺդූቁ‫!ݘ‬f )x*!ࠉื቗
ഋ‫ܖ‬Ӽཛྷ୧‫ޔ‬ቾಜ‫ܖࢵڢة‬Ljࢪሣ‫ܖ‬Ӽཛྷቁืԩ‫ืݘࠧܖ‬
ԩ‫ܖࢵڢةܖ‬LjഹࡍࠩԌॕ߷ă

∫
S 正数

c
a

f(x)dx +

∫

b

c

f(x)dx

正数部分 负数部分
(S 正数) (S 负数)

S 负数

Ck-35

൥߷ᅑᅢࢵ‫ܖ‬ഘࣺ౷۱Ӱ‫ـۚڑ‬ቤࢵ‫ܖ‬቗Ԓ‫ڑ‬
࠶‫ؙ‬
टࢵ‫ܖ‬ഘࣺ‫ܖ‬ཛྷ‫ޔۂ‬ԩ‫ ) ܖ‬टԒ‫وؙ࠶ڑ‬ഘᅺ‫ܖ‬ཛྷ൲‫ݧ‬ဏ
ԩ‫* ܖ‬Lj‫ڶ‬୧‫ޔ‬ԩ‫ܖ‬ቖှࢵ‫ܖ‬LjഹࡍࠩԌॕ߷ă

∫

b

f(x)dx =

a

+

∫

b

x4

∫

x1
a

f(x)dx +

∫

x2

x1

f(x)dx + .....

f(x)dx

k ದຓࠉื
x!, Abs(, Ran#, nPr, nCr, Rnd(
x"-!nQr ࣆ nDr!ࠉื৹ჾᇀ DNQMY ன෷ቲෳᅋLj‫د‬Ըืԥ
௢ෳᅋ‫ืݒ‬ă!

A ो֓ )"*
শۨ ǖ{n}!!){n} Ӥၙกქ‫ޔ‬ዔഹืࢪ 1ă*
۶ઋ ǖ! (5 + 3)!
(5+3)
1X(x!)E

Ck-36

40320

A ৊‫ڶ‬቗ )Bct*
६ှ෯ืࣜ๻෫Ljᅋ Bct) ৹‫فه‬ქґ‫و‬৊‫ڶ‬቗ă‫ืࠉױ‬
৹ᇀ DNQMY ன෷ቲෳᅋLjࣜ๻‫وืݒ‬৊‫ڶ‬቗DŽ‫ؙ‬ဏDž
ăᅘ
ߔ࿺ഉഋԸᆪٞ 51 ოණ‫و‬Đ‫ࣜืݒ‬๻đქॎă
শۨ ǖAbs({n})
۶ઋ ǖ! Abs (2 – 7) = 5
1)(Abs)2-7)E

5

A ๾ࢲื )Sbo$*
‫ืࠉױ‬դූൻ཭ဏื )1/111 ባ 1/:::* ‫و‬ལ๾ࢲืăᅑᅢದ
ԥၖეԸืLjຑჾ৹ჾဃӰફქჅෳᅋă
শۨ ǖRan#
۶ઋ ǖ!ეෳᅋ 2111Sbo$ ട‫ه‬ൻ‫ ޔ‬4 ཭ื‫و‬๾ࢲื෫ă
10001.(Ran#)E

287

E

613

E

118

• ණ෸ื቗४ཛྷ෸۶ቐᅋă‫ืࠉױ‬෯࣠դූ‫ืو‬቗࢙ԥༀă

Ck-37

A ఩઼ )nQr*!0 ዩࠩ )nDr*
শۨ ǖ{n}P{m}, {n}C{m}
۶ઋ ǖ!‫ڶ‬ᅢქ‫ ޔ‬21 ൉‫و‬ዩLj5 ‫ޔ‬൉‫و‬఩઼ࠧዩࠩ‫ޕ‬ᅘ‫ۂ‬
ඵቸǛ
101*(nPr)4E

5040

101/(nCr)4E

210

A ල൩ࠉื )Soe*
໼߹टื቗Ljӹؕ෷ࢪࣜ๻ॕ߷ቚ‫ڊ‬ཛྷԸืLjఀ৹ჾෳᅋ
ල൩ࠉื )Soe* ‫ڶ‬ದ६ှල൩ăල൩ࠉื‫ޗ‬য࿤෸཭ืහ
‫ڊ‬टื቗ල൩ባᅘပ཭ืă

Opsn2 ࢪ Opsn3 ‫و‬ල൩
ཤืӇල൩ባ 21 ཭ืă

Gjy ࢪ Tdj ‫و‬ල൩
ื቗Ӈල൩ባቚ‫ื཭وڊ‬ă
۶ઋ ǖ!200 ÷ 7 × 14 = 400
DŽ4 ཭ဏืDž
1Ne1(Fix)3
DŽ௠ԩࣜ๻ෳᅋ
200/7E
26 ཭ืăDž
*14E

Ck-38

28571
400000

࿦ᇀෳᅋල൩ࠉื )Soe* ६ှ࿰ༀ‫ࣜو‬๻ă
200/7E
10(Rnd)E
DŽࣜ๻ෳᅋॿල൩
‫ืو‬቗ăDž
DŽල൩ॕ߷Dž
*14E

28571
399994

4

൥ࠨෳᅋ 21 !‫ޠ‬ၳࣝืۨDŽFOHDž
‫ޠ‬ၳࣝืۨ )FOH* ჾქ‫ ޔ‬2 ባ 21 ቐࣺ‫و‬ቁืᅳქ‫ ޔ‬21 ‫و‬
4 ‫ࢵ֓و۽״‬ӹ෸ื቗ăޮᅘ઩ቸ‫ޠ‬ၳࣝืۨLjFOH/!ࠧ
FOH,ă
DNQMY ன෷ԥ቉֞‫ޠ‬ၳࣝืۨ‫و‬ෳᅋă

kFOH ࣜ๻۶ઋ
۶ઋ 2ǖ
! ეෳᅋ FOH/ ჾ‫ޠ‬ၳࣝืۨӹ෸ 2345 ෫
1234E

1234

W

1234 03

W

1234 00

۶ઋ 3ǖ ეෳᅋ FOH, ჾ‫ޠ‬ၳࣝืۨӹ෸ 234 ෫
123E
1W(,)
1W(,)
Ck-39

123
0123

03

0000123

06

‫ࣜืݒ‬๻DŽDNQMYDž
ე६ှᇀӊॎቲढ़ම‫و‬෸۶Ճዷ෫Ljฑ࿘ၭᇗ DNQMY ዷ
ཛྷࣜ๻ன෷ă

k ‫وืݒ‬พ൩
A ൥ࠨพ൩ၗื )i*
۶ઋ ǖ!ეพ൩ 3!,!4i ෫
2+3W(i) 2 + 3 iI

A ൥ࠨෳᅋࣁዸӶြ෷พ൩‫ืݒ‬቗
۶ઋ ǖ!ეพ൩ 6!∠!41 ෫
51-(∠)30 5 30I
ቺეƽ!
พ൩ܸऻ  ෫Ljഋ‫ޗ‬যࣜ๻ಹ‫ص‬೐‫و‬യෛऻ‫཭ةڪ‬හ‫ڊ‬พ
൩ӹ෸ऻ‫ืوڪ‬቗ă

k ‫ࣜืݒ‬๻ॕ߷‫و‬࿤෸
‫ࣜص‬๻դූ‫ืݒ‬ॕ߷෫LjS⇔I!ܻࠟ࿤෸ᇀࡥஎ‫و‬ᅚණऻLj
Ԍೲ෯ืԩฑ࿘‫־‬࿦ăეयໜ࿤෸෯ืԩࣆၗืԩ෫Ljഋ
Ѣ 1E)Sf⇔Jn*ă

Ck-40

۶ઋ ǖ!ეพ൩ 3!,!2i!Ԍ࿤෸ದࣜ๻ॕ߷෫
1,(SETUP)eee1(a+bi) 2 + i
2+W(i)E

2
࿤෸෯ืԩă

1E(Re⇔Im)

1

࿤෸ၗืԩă
)i!ܻࠟᇀၗืԩ࿤෸߹֔ቲ‫־‬࿦ă*

A ‫ࣜืݒ‬๻ॕ߷‫و‬യෛ࿤෸ြ෷
ఀ৹ჾၭᇗቓऻዸӶြ෷ࢪࣁዸӶြ෷࿤෸‫ࣜืݒ‬๻ॕ
߷ă
ၗืኃ

ၗืኃ

o

r ⬔

a + bi

b

a

෯ืኃ

෯ืኃ

o

ቓऻዸӶ

ࣁዸӶ

ഋᅋහብࡥஎቚ‫ڊ‬ຑၖე‫و‬യෛ࿤෸ြ෷ăᅘߔ࿺ഉLjഋ
ԸᆪĐ‫ืݒ‬࿤෸ြ෷‫و‬ቚ‫ڊ‬đქॎDŽٞ 21 ოDž
ă

Ck-41

k ࣜ๻ॕ߷࿤෸۶ઋ
A ቓऻዸӶြ෷DŽa,bi*
1,(SETUP)eee1(a+bi)
3 + i) = 2'
3 + 2i = 3.464101615 + 2i
۶ઋ 2ǖ 2 × ('
2*(93)+W(i))E

3464101615

1E(Re⇔Im)

2

2 į 45 = 1 + 1iDŽऻ‫ ཭ةڪ‬ǖEfh*
۶ઋ 3ǖ '
92)1-( į )
45E
1E(Re⇔Im)

1

1

A ࣁዸӶြ෷DŽr∠*
1,(SETUP)eee2(r į )
3 + i) = 2'
3 + 2i = 4 į 30
۶ઋ 2ǖ 2 × ('
2*(93)+W(i))E

4

1E(Re⇔Im)

30

∠!ܻࠟᇀ࿤෸  ቗෫‫־‬࿦ă
۶ઋ 3ǖ 1 + 1i = 1.414213562 į 45DŽऻ‫ ཭ةڪ‬ǖEfh*
1+1W(i)E

1414213562

1E(Re⇔Im)

45

Ck-42

k ޮᦊ‫) ืݒ‬Dpokh*
۶ઋ ǖ!ഓ 3!,!4i ‫ืݒᦊޮو‬
1,(Conjg)2+3W(i))E

2

1E(Re⇔Im)

-3

k ৊‫ڶ‬቗ܸࠧऻ )Bct-!bsh*
ၗืኃ
۶ઋ ǖ!
൥ࠨഓ‫ ه‬3!,!3i ‫و‬৊‫ڶ‬቗ܸࠧ b = 2
ऻDŽऻ‫ ཭ةڪ‬ǖEfh*

o

a=2

෯ืኃ

৊‫ڶ‬቗ǖ
1)(Abs)2+2W(i))E

2828427125

ܸऻǖ
1((arg)2+2W(i))E

45

Ck-43

k യෛ‫ืݒ‬࿤෸ြ෷‫و‬Ӱ‫ޚ‬
A ൥ࠨཛྷࣜ๻ቚ‫ڊ‬ቓऻዸӶြ෷
ᇀࣜ๻‫و‬யཤพ൩ 1-)'a,biDž
ă
2 į 45 = 2 + 2iDŽऻ‫཭ةڪ‬
۶ઋ ǖ!2'
!
ǖEfh*
292)1-( į )45
1-('a,bi)E
1E(Re⇔Im)

2

2

A ൥ࠨཛྷࣜ๻ቚ‫ࣁڊ‬ዸӶြ෷
ᇀࣜ๻‫و‬யཤพ൩ 1+)'r∠Dž
ă
2 į 45 = 2.828427125 į 45
۶ઋ ǖ
!2 + 2i = 2'
DŽऻ‫ ཭ةڪ‬ǖEfh*
2+2W(i)
1+('r į )E 2828427125
1E(Re⇔Im)

45

༇ࣜࣜ๻DŽTE0SFHDž
k ༇ࣜࣜ๻Ⴥӊืয
A Ⴥӊืয‫و‬พ൩
ྐଥ༇ࣜ౷ଔก৚ಶ )GsfrPo* ࡱกॖ‫) ׅ‬GsfrPgg*Ljఀ‫ڞ‬৹
ჾพ൩Ⴥӊืযăӊࣜ๻ಹ‫ֽو‬෶യෛහ‫ڊ‬ཛྷ GsfrPoăఀ
Ck-44

৹ჾෳᅋහብࡥஎණ‫و‬༇ࣜ౷ଔහ‫ڊ‬DŽٞ 21 ოDžੂၭᇗ
ຑၖე‫و‬พ൩‫ۨ۽‬ă

A ืয࿾‫و‬พ൩ื௅࿮‫ڪ‬
௢޷พ൩‫ืو‬য࿾‫و‬ዮ‫ืؙ‬௅ც౷ଔก৚ಶ )GsfrPo* ࡱก
ॖ‫) ׅ‬GsfrPgg* ۚԥༀă!
TE!ன෷!////////// 51!࿾!)GsfrPo*-!91!࿾!)GsfrPgg*
SFH!ன෷!//////// 37!࿾!)GsfrPo*-!51!࿾!)GsfrPgg*

A Ⴥӊืয‫و‬അ‫ׅ‬
‫ݢ‬Ӱባದຓࣜ๻ன෷ࢪ‫ݢ‬Ӱ༇ࣜ౷ଔහ‫ڊ‬෫Lj،‫׈‬ಹቲ‫و‬
ຑᅘჅӊืযোटӇഅ‫ׅ‬ă

k ൥ࠨ६ှ‫ة‬Ӱફ༇ࣜࣜ๻
ე६ှᇀӊॎቲढ़ම‫و‬෸۶Ճዷ෫Ljฑ࿘ၭᇗ TE ዷཛྷࣜ
๻ன෷ă!

A Ⴥӊืয‫و‬พ൩
౷ଔ৚ಶDŽGsfrPoDž
࿒எढ़මพ൩ዩื቗ x1-!x2-!///!xnLjࣆ౷ଔ Gsfr2-!Gsfr3-!///!
Gsfrn ෫ຑၖე‫و‬ऒՃዷă
{x1}1,(;) {Freq1}m(DT)
{x2}1,(;) {Freq2}m(DT)
{xn}1,(;) {Freqn}m(DT)
ኢ
൥߷ዩื቗‫و‬౷ଔቝᅘქ‫ޔ‬LjᇘቝეѢ |xn~m)EU* พ൩
ӯ৹DŽԥၖეቚ‫ڊ‬౷ଔDž
ă
Ck-45

۶ઋ ǖ!൥ࠨพ൩ᅚӫ‫ืو‬য ;!)x-!Gsfr*!>!)35/6-!5*-!)36/6-!7*-!
)37/6-!3*
24.51,(;)4 24 .5 ; 4I
L i ne =
(DT)
m

0
1

m)EU* ໼ቌࣜ๻ಹ‫ױ‬ཛྷٞქ‫ืޔ‬য࿾‫و‬யཤă
25.51,(;)6m(DT) L i ne =
26.51,(;)2m(DT)

3

౷ଔॖ‫) ׅ‬GsfrPgg*
ᇀሦቸഉਦ࿒Ljഋ൥࿒ຑ෸‫ܖ‬Ӽพ൩‫ืޕ‬য࿾ă
{x1}m(DT) {x2}m(DT) ... {xn}m(DT)

A ൥ࠨՓᆪ࿦ᇀ‫و‬Ⴥӊืয
Ⴥӊืযพ൩༾ӛࡍLjѢ c!৹ცఀพ൩‫๋و‬ၠၭࡳืযă
$!ܻࠟӹ෸ࡥஎණ࿦ᇀ࿤෸‫و‬Ⴥӊ‫و‬࿒எࡱᅘืযăۚ!
`!ܻࠟӹ෸ණஎࡱᅘืযă!
۶ઋ ǖ!൥ࠨՓ৤ᇀٞ 56 ოණĐჅӊืয‫و‬พ൩đქॎቲ
พ൩‫ืو‬যDŽ౷ଔහ‫ ڊ‬ǖGsfrPo*
=
Ac x 1
q =
c Fre 1

Ck-46

245
4

‫ص‬༇ࣜ౷ଔහ‫ڊ‬ཛྷ GsfrPo ෫Ljืযც࿒෸๋ၠ࿤෸ ǖx1-!
Gsfr2-!x2-!Gsfr3- ც‫ױ‬੮༚ă‫ص‬༇ࣜ౷ଔහ‫ڊ‬ཛྷ GsfrPgg ෫Lj
ืযც x1-!x2-!x3- ‫๋و‬ၠ࿤෸ăఀࡱ৹ჾෳᅋ f!۴‫۽‬ဂ
ၭࡳืযă!

A Ⴥӊืয‫و‬Ӭࣃ
ეӬࣃჅӊืয෫Ljഋटದ‫־ٻ‬Ljพ൩ူื቗LjഹࡍѢ Eă
۶ઋ ǖ!൥ࠨӬࣃᇀٞ 56 ოණĐჅӊืয‫و‬พ൩đქॎቲ
พ൩‫و‬ჅӊืযĐGsfr4đ
q =
Af F r e 3

q =
3E F r e 3

2
3

A Ⴥӊืয‫و‬ක‫ׅ‬
ეක‫ׅ‬Ⴥӊืয෫Ljഋटದ‫־ٻ‬LjഹࡍѢ 1m)DM*ă
۶ઋ ǖ
!൥ࠨක‫ׅ‬ᇀٞ 56 ოණĐჅӊืয‫و‬พ൩đქॎቲ
พ൩‫و‬Đx2đืয
=
Accc x 2
=
1m(CL) L i ne

Ck-47

255
2

ኢ
• ࿒எढ़මක‫ׅ‬Ճዷ೐ࡍࡥஎ࿤෸‫ืو‬য௠൛ă
ቐ೐
ቐࡍ
x1! !;!35/6
x1! !;!35/6
Gsfr2;!5
Gsfr2;!5
!
x2! !;!36/6
x2! !;!37/6
Gsfr3;!7
Gsfr3;!3
x3! !;!37/6
Gsfr4;!3
ဂණჰ཭ă
!
• ‫ص‬༇ࣜ౷ଔහ‫ڊ‬ཛྷ৚ಶ )GsfrPo* ෫Lj࿰ᄮ‫ و‬x ืযࠧ౷
ଔืয‫ڶ‬टӇක‫ׅ‬ă

A ൥ࠨක‫ׅ‬ຑᅘჅӊืয
ቖှ࿒ะऒՃዷ৹ක‫ׅ‬ຑᅘჅӊืযă
19(CLR)1(Stat)E
ԥ࿻ක‫ׅ‬ຑᅘჅӊืয෫Ljഋᇀණ෸ՃዷቲѢ ALjۚ‫܇‬
Eă

A ෳᅋพ൩‫و‬Ⴥӊืয‫و‬༇ࣜࣜ๻
ე६ှ༇ࣜࣜ๻෫Ljഋพ൩࿰ᄮ‫و‬த૚ԌѢ Eă

ATE ன෷༇ࣜத૚Ը৬
11)T.TVN*1

x2!
ഓჅӊืয‫و‬౿‫ࠧ۽‬ă

Σ x2 = Σ xi2
11)T.TVN*2

x!
ഓჅӊืয‫و‬ዜࠧă

Σ x = Σ xi
Ck-48

11)T.TVN*3

n!
ഓჅӊืă

12)T.WBS*1

x̄!
ഓ౿ো቗ă

Σ xi
o= n
σx!

12)T.WBS*2

ഓዜ໛Ӷኼ౭՘ă

σx =

Σ(xi – o)2
n
12)T.WBS*3

sx!
ഓჅӊӶኼ౭՘ă

sx =

Σ(xi – o)2
n–1
12)T.WBS*e1

minX!
ഓჅӊ‫و‬ዮဏ቗ă

12)T.WBS*e2

maxX!
ഓჅӊ‫و‬ዮ‫ؙ‬቗ă

Ck-49

k ൥ࠨ६ှใӰફ༇ࣜࣜ๻
ე६ှᇀӊॎቲढ़ම‫و‬෸۶Ճዷ෫Ljฑ࿘ၭᇗ SFH ዷཛྷࣜ
๻ன෷ă

A ࢐ߥࣜ๻‫و‬ቸ੮
୧‫״‬६൩ SFH ன෷ࡍLjఀӤၙၭᇗეෳᅋ‫ࣜߥ࢐و‬๻‫و‬ቸ
੮ă!

࢐ߥࣜ๻ቸ੮‫و‬ၭᇗ
2/!६൩ SFH ன෷ă
• ‫ױ‬෫ࡥஎ࿤෸࢐ߥࣜ๻‫ֽو‬෶ၭᇗԵ‫ة‬ăԵ‫ޮة‬ᅘ઩
‫ࡥޔ‬எLjᅋ d!ࠧ e!৹ᇀದࣺ६ှၭࡳă
3/!ቖှ࿒ะՃዷቐქၭᇗຑၖე‫ࣜߥ࢐و‬๻ă
ეၭᇗ‫ߥ࢐ױ‬੮ျ෫ǖ
Ѣ‫ױ‬ऒǖ
࿯၂࢐ߥ!( y = a + bx)
1!)Mjo*
‫ (!ߥ࢐ืڶ‬y = a + b Inx)
2!)Mph*
e!ቚื࢐ߥ!(y = aebx)
3!)Fyq*
֓‫(!ߥ࢐۽‬y = axb)
4!)Qxs*
௬࢐ߥ!( y = a + b/x)
e!1!)Jow*
۠‫ (!ߥ࢐״‬y = a + bx + cx 2) e!2!)Rvbe*
ab!ቚื࢐ߥ!( y = abx)
e!3!)BC.Fyq*
ኢ
ၖე෫Ljఀ৹ჾᇀ SFH ன෷ቲ೰ࡳཛྷದຓ࢐ߥࣜ๻੮ျă
Ѣ 12)T.WBS*3)UZQF* ৹࿤෸ᇀණะٞ 2 ԧቲढ़ම
‫و‬Ե‫ࡥة‬எăഋቖှණะՃዷԧኊၭᇗຑၖე‫ࣜߥ࢐و‬๻
ቸ੮ă
Ck-50

A Ⴥӊืয‫و‬พ൩
౷ଔ৚ಶDŽGsfrPoDž
࿒எढ़මพ൩ዩื቗ )x1-!y1*Lj)x2-!y2*Lj///!)xn-!yn*Ljࣆ౷
ଔ Gsfr2-!!Gsfr3-!///!Gsfrn ෫ຑၖე‫و‬ऒՃዷă
{x1},{y1}1,(;) {Freq1} m(DT)
{x2},{y2}1,(;) {Freq2} m(DT)
{xn},{yn}1,(;) {Freq n} m(DT)
ኢ
൥߷ዩื቗‫و‬౷ଔቝᅘქ‫ޔ‬LjᇘቝეѢ |xn~,|yn~
ă!
m)EU*!พ൩ӯ৹DŽԥၖეቚ‫ڊ‬౷ଔDž

౷ଔॖ‫) ׅ‬GsfrPgg*
ᇀሦቸഉਦ࿒Ljഋ൥࿒ຑ෸‫ܖ‬Ӽพ൩‫ืޕ‬য࿾ă
{x1},{y1} m(DT)
{x2},{y2} m(DT)
{xn},{yn} m(DT)

A ൥ࠨՓᆪ࿦ᇀ‫و‬Ⴥӊืয
Ⴥӊืযพ൩༾ӛࡍLjѢ c!৹ცఀพ൩‫๋و‬ၠၭࡳืযă
$!ܻࠟӹ෸ࡥஎණ࿦ᇀ࿤෸‫و‬Ⴥӊ‫و‬࿒எࡱᅘืযăۚ
`!ܻࠟӹ෸ණஎࡱᅘืযă
‫ص‬༇ࣜ౷ଔහ‫ڊ‬ཛྷ GsfrPo ෫Ljืযც࿒෸๋ၠ࿤෸ ǖx1Lj
y1LjGsfr2Ljx2Ljy2LjGsfr3Ljც‫ױ‬੮༚ă‫ص‬༇ࣜ౷ଔහ‫ڊ‬ཛྷ
GsfrPgg ෫Ljืযც x1Ljy1Ljx2Ljy2Ljx3Ljy3Lj‫๋و‬ၠ࿤෸ă
ఀࡱ৹ჾෳᅋ f!۴‫۽‬ဂၭࡳืযă

Ck-51

A Ⴥӊืয‫و‬Ӭࣃ
ეӬࣃჅӊืয෫Ljഋटದ‫־ٻ‬Ljพ൩ူื቗LjഹࡍѢ Eă

A Ⴥӊืয‫و‬ක‫ׅ‬
ეක‫ׅ‬Ⴥӊืয෫Ljഋटದ‫־ٻ‬LjഹࡍѢ 1m)DM*ă

A ൥ࠨක‫ׅ‬ຑᅘჅӊืয
ഋԸᆪĐ൥ࠨක‫ׅ‬ຑᅘჅӊืযđ
DŽٞ 59 ოDž
ă

A ෳᅋพ൩‫و‬Ⴥӊืয‫و‬༇ࣜࣜ๻
ე६ှ༇ࣜࣜ๻෫Ljഋพ൩࿰ᄮ‫و‬த૚ԌѢ Eă

ASFH ன෷༇ࣜத૚Ը৬
ዜࠧࣆჅӊืத૚ )T.TVN Ե‫* ة‬
11)T.TVN*1

x2!
ഓჅӊืয x ‫و‬౿‫ࠧ۽‬ă

Σ x2 = Σ xi2
11)T.TVN*2

x!
ഓჅӊืয x ‫و‬ዜࠧă

Σ x = Σ xi
11)T.TVN*3

n!
ഓჅӊืă

11)T.TVN*e1

y2!
ഓჅӊืয y ‫و‬ዜࠧă

Σ y2 = Σ yi2
Ck-52

11)T.TVN*e2

y!
ഓჅӊืয y ‫و‬ዜࠧă

Σ y = Σ yi
11)T.TVN*e3

xy!

ഓჅӊืয x ࠧ y ‫ࠧࢵ֓و‬ă
Σ xy = Σ xiyi
11)T.TVN*d1

x2y!

ഓჅӊืয x ‫و‬౿‫۽‬ᅳ y ‫وࢵ֓و‬ዜࠧă

Σ x2y = Σ xi2yi
11)T.TVN*d2

x3!
ഓჅӊืয x ‫و‬઎‫ࠧ۽‬ă

Σ x3 = Σ xi3
11)T.TVN*d3

x4!
ഓჅӊืয x ‫و‬๜‫ࠧ۽״‬ă

Σ x4 = Σ xi4

౿ো቗ࠧӶኼ౭՘த૚DŽWBS Ե‫ة‬Dž
12)T.WBS*1)WBS*1

x̄!
ഓჅӊืয x ‫و‬౿ো቗ă

Σ xi
=
o
n
Ck-53

σx!

12)T.WBS*1)WBS*2

ഓჅӊืয x ‫و‬ዜ໛Ӷኼ౭՘ă

σx =

Σ(xi – o)2
n
12)T.WBS*1)WBS*3

sx!

ഓჅӊืয x ‫و‬ჅӊӶኼ౭՘ă

Σ(xi – o)2
n–1

sx =

12)T.WBS*1)WBS*e1

ȳ!

ഓჅӊืয y ‫و‬౿ো቗ă

Σyi
p= n
σy!

12)T.WBS*1)WBS*e2

ഓჅӊืয y ‫و‬ዜ໛Ӷኼ౭՘ă

σy =

Σ (yi – y)2
n
12)T.WBS*1)WBS*e3

sy!

ഓჅӊืয y ‫و‬ჅӊӶኼ౭՘ă

sy =

Σ (yi – y)2
n–1
Ck-54

‫ߥ࢐وߥ࢐״۠܇‬࿅ืࠧ޼ࣜ቗த૚DŽWBS Ե‫ة‬Dž
a!

12)T.WBS*1)WBS*ee1

ഓ࢐ߥާ෷‫و‬իื࿾ bă

b!

12)T.WBS*1)WBS*ee2

ഓ࢐ߥާ෷‫و‬࿅ื că

r!

12)T.WBS*1)WBS*ee3

ഓ࿰ߔ࿅ื să
12)T.WBS*1)WBS*d1

x̂!

‫ޗ‬য࿦ᇀၭᇗ‫ࣜߥ࢐و‬๻‫ާߥ࢐و‬෷Ljჾᇀ‫ױ‬த૚೐எพ
൩‫ืو‬቗ዷཛྷ y ቗Ljഓ x!‫ࣜ޼و‬቗ă
12)T.WBS*1)WBS*d2

ŷ!

‫ޗ‬য࿦ᇀၭᇗ‫ࣜߥ࢐و‬๻‫ާߥ࢐و‬෷Ljჾᇀ‫ױ‬த૚೐எพ
൩‫ืو‬቗ዷཛྷ x ቗Ljഓ y!‫ࣜ޼و‬቗ă

۠‫ߥ࢐وߥ࢐״‬࿅ืࠧ޼ࣜ቗த૚DŽWBS Ե‫ة‬Dž
a!

12)T.WBS*1)WBS*ee1

ഓ࢐ߥާ෷‫و‬իื࿾ bă

b!

12)T.WBS*1)WBS*ee2

ഓ࢐ߥާ෷‫و‬࿅ื că!

Ck-55

c!

12)T.WBS*1)WBS*ee3

ഓ࢐ߥާ෷‫و‬࿅ื dă

x̂ 1!

12)T.WBS*1)WBS*d1

ჾᇀ‫ױ‬த૚೐எพ൩‫ืو‬቗ዷཛྷ y ቗Ljෳᅋٞ 69 ოණ‫و‬
ާ෷ഓ x ‫و‬૙ქ‫ࣜ޼ޔ‬቗ă

x̂ 2!

12)T.WBS*1)WBS*d2

ჾᇀ‫ױ‬த૚೐எพ൩‫ืو‬቗ዷཛྷ y ቗Ljෳᅋٞ 69 ოණ‫و‬
ާ෷ഓ x ‫و‬૙ქ‫ࣜ޼ޔ‬቗ă

ŷ!

12)T.WBS*1)WBS*d3

ჾᇀ‫ױ‬த૚೐எพ൩‫ืو‬቗ዷཛྷ x ቗Ljෳᅋٞ 69 ოණ‫و‬
ާ෷ഓ y ‫ࣜ޼و‬቗ă

ዮဏ቗ࠧዮ‫ؙ‬቗த૚ )NJONBY Ե‫* ة‬
minX!

12)T.WBS*2)NJONBY*1

ഓჅӊืয x ‫و‬ዮဏ቗ă

maxX!

12)T.WBS*2)NJONBY*2

ഓჅӊืয x ‫و‬ዮ‫ؙ‬቗ă

minY!

12)T.WBS*2)NJONBY*e1

ഓჅӊืয y ‫و‬ዮဏ቗ă

maxY!

12)T.WBS*2)NJONBY*e2

ഓჅӊืয y ‫و‬ዮ‫ؙ‬቗ă
Ck-56

A ࢐ߥ࿅ืࠧ޼ࣜ቗ࣜ๻ާ෷ӹ
࿯၂࢐ߥ!
த૚
࢐ߥާ෷‫و‬իื࿾ b
࢐ߥ࿅ื c
࿰ߔ࿅ื s
޼ࣜ቗ m
޼ࣜ቗ n

ࣜ๻ާ෷
Σyi – b.Σxi
a=
n
n.Σxiyi – Σxi.Σyi
b= . 2
n Σxi – (Σxi)2
n.Σxiyi – Σxi.Σyi
r=
{n.Σxi2 – (Σxi)2}{n.Σyi2 – (Σyi)2}
y–a
m=
b
n = a + bx

۠‫ߥ࢐״‬
த૚
࢐ߥާ෷‫و‬իื࿾ b
࢐ߥ࿅ื c
࢐ߥ࿅ื d

ࣜ๻ާ෷
Σyi
Σxi
Σxi2
a=
–b
–c
n
n
n
Sxy.Sx 2x 2 – Sx 2y.Sxx 2
b=
Sxx.Sx2x2 – (Sxx2)2
Sx 2y.Sxx – Sxy.Sxx2
c=
Sxx.Sx2x2 – (Sxx2)2

‫د‬กLj

( ) ( )

.Σxi 2)
(
Σx
i
Sxx = Σxi –
2

Sxx = Σxi –
2

(Σxi )2

n
(Σxi .Σyi )
Sxy = Σxi yi –
n

3

n

2 2
(
Σx
)
i
Sx x = Σxi –
2

2

4

n
2.
2
2
Σyi )
(
Σx
i
Sx y = Σxi yi –
n
Ck-57

த૚

ࣜ๻ާ෷

– b + b2 – 4c(a – y)
m1 =
2c

޼ࣜ቗ m1

– b – b2 – 4c(a – y)
m2 =
2c
n = a + bx + cx 2

޼ࣜ቗ m2
޼ࣜ቗ n

‫ߥ࢐ืڶ‬
த૚
࢐ߥާ෷‫و‬ի
ื࿾ b
࢐ߥ࿅ื c
࿰ߔ࿅ื s
޼ࣜ቗ m
޼ࣜ቗ n

ࣜ๻ާ෷
Σyi – b.Σlnxi
a=
n
n.Σ(lnxi)yi – Σlnxi .Σyi
b=
n.Σ(lnxi)2 – (Σlnxi)2
n.Σ(lnxi)yi – Σlnxi.Σyi
r=
{n.Σ(lnxi)2 – (Σlnxi)2}{n.Σyi2 – (Σyi)2}
y–a
b

m=e
n = a + blnx

e!ቚื࢐ߥ
த૚
ࣜ๻ާ෷
.Σxi
࢐ߥާ෷‫و‬
Σ
ln
y
–
b
i
a = exp
n
իื࿾ b

(

࢐ߥ࿅ื c

)

n.Σxilnyi – Σxi.Σlnyi
b=
n.Σxi2 – (Σxi)2
Ck-58

n.Σxilnyi – Σxi.Σlnyi
r=
{n.Σxi2 – (Σxi)2}{n.Σ(lnyi)2 – (Σlnyi)2}

࿰ߔ࿅ื s

lny – lna

޼ࣜ቗ m

m=

޼ࣜ቗ n

n = aebx

b

ab!ቚื࢐ߥ
த૚
ࣜ๻ާ෷
.Σxi
࢐ߥާ෷‫و‬
Σ
ln
y
–
ln
b
i
a = exp
իื࿾ b
n

(
)
n.Σx y – Σx .Σ y
( n.Σx – Σx )
iln i

ln i

i

࢐ߥ࿅ื c

b = exp

࿰ߔ࿅ื s

n.Σxilnyi – Σxi.Σlnyi
r=
{n.Σxi2 – (Σxi)2}{n.Σ(lnyi)2 – (Σlnyi)2}

޼ࣜ቗ m
޼ࣜ቗ n

2

i

(

2
)
i

lny – lna
m=
lnb
n = abx

֓‫ߥ࢐۽‬
த૚

ࣜ๻ާ෷

.Σlnxi
࢐ߥާ෷
Σ
ln
y
–
b
i
a = exp
‫و‬իื࿾ b
n

(

)

n.Σlnxilnyi – Σlnxi.Σlnyi
࢐ߥ࿅ื c b =
n.Σ(ln xi)2 – (Σln xi)2
Ck-59

n.Σlnxilnyi – Σlnxi.Σlnyi
࿰ߔ࿅ื s r =
{n.Σ(lnxi)2 – (Σlnxi)2}{n.Σ(lnyi)2 – (Σlnyi)2}
޼ࣜ቗ m
޼ࣜ቗ n

ln y – ln a
b

m=e
n = a xb

௬࢐ߥ
த૚

ࣜ๻ާ෷

࢐ߥާ෷‫و‬իื࿾ b
࢐ߥ࿅ื c
࿰ߔ࿅ื s
‫د‬กLj

Sxx = Σ(xi ) –

Σyi – b.Σxi–1
a=
n
Sxy
b=
Sxx
Sxy
r=
Sxx.Syy
(Σxi–1)2

(Σyi)2

Syy = Σyi –
n
n
Σxi–1.Σyi
–1
Sxy = Σ(xi )yi –
n
–1 2

2

த૚

ࣜ๻ާ෷
b

޼ࣜ቗ m

m=

޼ࣜ቗ m

n=a+

y–a
b

x

Ck-60

k ༇ࣜࣜ๻۶ઋ
ᅚӹ઼‫־‬ષူූۛᇀ‫ࡍූ־‬໛ቺ‫و‬
Ӱࡧă
1!ഓሦဗืয‫و‬࿯၂࢐ߥ‫ާߥ࢐و‬
෷ࠧ࿰ߔ࿅ืă
2!ഓሦဗืয‫ާߥ࢐وߥ࢐ืڶو‬
෷ࠧ࿰ߔ࿅ืă
3!‫ޗ‬য࢐ߥࣜ๻ॕ߷ሖ‫־‬ዮคࠩሦ
ဗืযഗ฀‫ާߥ࢐و‬෷LjᆿѢሙ
‫ާߥ࢐ױ‬෷ᆊՌူූۛ‫ ූ־‬461
໢ࡍ‫و‬໛ቺă

൓ื
20
50
80
110
140
170
200
230
260
290
320

Ճዷԧኊ
६൩ SFH ன෷Ԍၭᇗ࿯၂࢐ߥ ǖ
N5(REG)1(Lin)
ट༇ࣜ౷ଔහ‫ڊ‬ၭᇗཛྷ GsfrPgg;
1N(SETUP)dd2(FreqOff)
พ൩Ⴥӊืয ;
20,3150m(DT)
50,4800m(DT)
80,6420m(DT)
110,7310m(DT)
140,7940m(DT)
170,8690m(DT)
200,8800m(DT)
230,9130m(DT)
Ck-61

໛ቺDŽ৻Dž
3150
4800
6420
7310
7940
8690
8800
9130
9270
9310
9390

260,9270m(DT)
290,9310m(DT)
320,9390m(DT)

1!࿯၂࢐ߥ!
࢐ߥާ෷‫و‬իื࿾ bǖ
!
12(S-VAR)1(VAR)
ee1(a)E

4446575758

࢐ߥ࿅ื cǖ
!
12(S-VAR)1(VAR)
ee2(b)E

1887575758

12(S-VAR)1(VAR)
ee3(r)E

0904793561

࿰ߔ࿅ืǖ!

2!‫ߥ࢐ืڶ‬
ၭᇗ‫ߥ࢐ืڶ‬ǖ
12(S-VAR)3(TYPE)2(Log) x 1 =
࢐ߥާ෷‫و‬իื࿾ bǖ
!
A12(S-VAR)1(VAR)
ee1(a)E

20

–4209356544

࢐ߥ࿅ื cǖ
!
12(S-VAR)1(VAR)
ee2(b)E
Ck-62

2425756228

࿰ߔ࿅ืǖ!
12(S-VAR)1(VAR)
ee3(r)E

0991493123

3!ᆊՌ໛ቺ
ᄜཛྷ‫وߥ࢐ืڶ‬࿰ߔ࿅ื‫و‬৊‫ڶ‬቗े॰ᅢ 2Ljຑჾෳᅋ‫ڶ‬
ื࢐ߥ६ှ໛ቺᆊՌࣜ๻ă
‫ ص‬x!>!461 ෫ഓ !ǖ
350
y
12(S-VAR) 350
1(VAR)d2(n)E 1000056129

ࢱืࣜ๻DŽCBTFDž
ე६ှᇀӊॎቲढ़ම‫و‬෸۶Ճዷ෫Ljฑ࿘ၭᇗ CBTF ዷཛྷ
ࣜ๻ன෷ă

k ൥ࠨ६ှࢱืࣜ๻
A ൥ࠨቚ‫ڊ‬യෛื࿅
ෳᅋᅚӫ઼ফ‫و‬ऒၭᇗയෛื࿅ ǖx)EFD* ᅋᅢ෨६
ቨLjM)IFY* ᅋᅢ෨૥६ቨLjl)CJO* ᅋᅢ۠६ቨLjࢪ
i)PDU* ᅋᅢѹ६ቨă

A ࢱืࣜ๻۶ઋ
۶ઋ ǖ! ൥ࠨၭᇗ۠६ቨዷཛྷื࿅Ԍࣜ๻ 23!,!23

Ck-63

Al(BIN)1+1E

1+ 1

10

b

ื࿅ቚ෸ܻ
DŽe ǖ෨६ቨLjI ǖ෨૥६ቨLjc ǖ۠६ቨLjp ǖѹ६ቨDž
• พ൩ྐပ‫ืو‬቗࢙դූশۨؓྥ )Tzouby!FSSPS*ă
• ᇀ CBTF ன෷ቲԥ௢พ൩‫ืܖ‬DŽဏืDž቗ࠧቚื቗ăࣜ
๻ॕ߷‫و‬ဏืԩ‫ܖ‬टӇලണă

A ෨૥६ቨื቗‫و‬พ൩ࣆࣜ๻۶ઋ
ഋෳᅋᅚӫ઼ফ‫و‬ऒพ൩෨૥६ቨื቗ຑၖე‫و‬ዖாǖ
-)B*-!$)C*-!w)D*-!s)E*-!c)F*-!t)G*/
۶ઋ ǖ!൥ࠨၭᇗ෨૥६ቨዷཛྷื࿅Ԍࣜ๻ 2G27!,!227
AM(HEX)1t(F)+1E

20

H

A ᅘပࣜ๻۶ཙ
ื࿅
۠६ቨ
ѹ६ቨ
෨६ቨ
෨૥६ቨ

ᅘပ۶ཙ
ቁื ǖ0 < x < 111111111
‫ ืݘ‬ǖ1000000000 < x < 1111111111
ቁื ǖ0 < x < 3777777777
‫ ืݘ‬ǖ4000000000 < x < 7777777777
–2147483648 < x < 2147483647
ቁื ǖ0 < x < 7FFFFFFF
‫ ืݘ‬ǖ80000000 < x < FFFFFFFF

‫ࣜص‬๻ॕ߷մ‫ص־‬೐യෛื࿅‫و‬ᅘပ۶ཙ෫࢙ۢූࣜ๻ؓ
ྥDŽNbui!FSSPSDž
ă
Ck-64

k ൥ࠨट࿤෸‫ࣜو‬๻ॕ߷Ӱࡳཛྷದຓื࿅
‫ص‬ᅘࣜ๻ॕ߷࿤෸෫Ѣ x)EFD*LjM)IFY*Ljl)CJO* ࢪ
i)PDU*Lj‫ݡ‬ॕ߷टӇӰࡳཛྷ࿰ᄮ‫ืو‬࿅ă!
۶ઋ ǖ!൥ࠨट෨६ቨื቗ 4121!Ӱࡳཛྷ۠६ቨĂѹ६ቨࣆ
෨૥६ቨြ෷
Ax(DEC)30E

30

d

l(BIN)

11110

b

i(OCT)

36

o

M(HEX)

1E

H

k!MPHJD Ե‫وة‬ෳᅋ
ᇀ CBTF ன෷ቲLjX!ऒ‫ޢو‬௢Ӱཛྷ MPHJD Ե‫وة‬࿤෸ऒă
MPHJD Ե‫ޮة‬ᅘൻ‫ࡥޔ‬எLjᅋ d!ࠧ e!৹ᇀದࣺ६ှၭ
ࡳă!

k ൥ࠨཛྷ໎‫ืڊ‬቗ቚ‫ืڊ‬࿅
พ൩ื቗෫Lj
ఀ৹ჾቚ‫ڊ‬ქ‫ޔ‬ᅳ‫ص‬೐യෛื࿅ԥༀ‫ืو‬࿅ă!

A ෳᅋࢱืቚ‫ࣜوڊ‬๻۶ઋ
۶ઋ ǖ!൥ࠨ६ှ 621!,!627 ‫ࣜو‬๻LjԌჾ۠६ቨ࿤෸ࣜ๻ॕ
߷
Al(BIN)X(LOGIC)d1(d) d5 + h5
5+X(LOGIC)d2(h)5E
1010 b
Ck-65

k ൥ࠨෳᅋ଩ࣃᆱ๻ࠧ۠६ቨ‫ݘ‬቗६ှࣜ๻
ӊࣜ๻ಹ௢६ှ 21 ཭DŽ21 Ӕ໎Dž‫۠و‬६ቨ଩ࣃᆱ๻ࠧ‫ݘ‬
ืࣜ๻ăຑᅘ࿒෸۶ઋোჾ CJODŽ۠६ቨDžዷཛྷയෛื࿅
६ှࣜ๻ă

A ଩ࣃࢵDŽboeDž
۵࢐཭ࢵ‫ࣜو‬๻ॕ߷ă!
۶ઋ ǖ!10102 and 11002 = 10002
1010X(LOGIC)
1(and)1100E

1000

b

11011

b

110

b

A ଩ࣃࠧDŽpsDž
۵࢐཭ࠧ‫ࣜو‬๻ॕ߷ă
۶ઋ ǖ!10112 or 110102 = 110112
1011X(LOGIC)
2(or)11010E

A ᄖ଩ࣃࠧDŽypsDž
۵࢐཭ᄖ଩ࣃࠧ‫ࣜو‬๻ॕ߷ă
۶ઋ ǖ!10102 xor 11002 = 1102
1010X(LOGIC)e
1(xor)1100E

Ck-66

A ᄖ‫܇‬଩ࣃࠧDŽyopsDž
۵࢐཭ᄖ଩ࣃܱࠧ‫ࣜو‬๻ॕ߷ă
۶ઋ ǖ!11112 xnor 1012 = 11111101012
1111X(LOGIC)
3(xnor)101E

1111110101

b

1111110101

b

1111010011

b

A ԣ 0 ௬DŽOpuDž
۵࢐ื቗‫و‬ԣDŽ཭௬Dž
ă
۶ઋ ǖ!Not(10102) = 11111101012
X(LOGIC)e2(Not)
1010)E

A ܱDŽOfhDž
۵࢐ื቗‫ و‬3 ‫و‬ԣă
۶ઋ ǖ!Neg(1011012) = 11110100112
X(LOGIC)e3(Neg)
101101)E

֔ၠன෷DŽQSHNDž
ఀ৹ჾᅋ QSHN ன෷टე६ှ‫ࣜو‬๻ዷ֑֔ၠԌү،ಲੂă
֔ၠቲ৹ჾҪࠆൌࠨ௢޷ᇀ DPNQĂDNQMYĂCBTFĂTE ࢪ
SFH ன෷ቲ६ှ‫ࣜو‬๻ă

Ck-67

k ֔ၠன෷‫ݣ‬ე
A ֔ၠᆱှன෷‫و‬ቚ‫ڊ‬
๼ഹ֔ၠᇀ QSHN ன෷ቲ‫ך‬जࠧᆱှLj‫֔ޕد‬ၠ‫ڞ‬ᅘქ
‫ޔ‬Đᆱှன෷đ
Lj֔ၠᇀ‫ױ‬ன෷ቲᆱှăDPNQĂDNQMYĂ
CBTFĂTE ࢪ SFH ன෷৹ჾቚ‫ڊ‬ཛྷ֔ၠ‫و‬ᆱှன෷ăნট
กํLj
ఀၖე৬଑֔ၠຑዶ‫ࣜو‬๻Ԍၭᇗ࿰ᄮ‫و‬ᆱှன෷ă!

A ֔ၠ،‫׈‬ಹ
֔ၠ،‫׈‬ಹޮᅘ 4:1 ዖॎ‫و‬൛ફLj৹‫ޥ‬๜‫֔ޔ‬ၠޮ࿽ă֔
ၠ،‫׈‬ಹ،ୄࡍӯྐۨᆿү،ದຓ֔ၠă

k ֔ၠ‫ךو‬ज
A ူ֔ၠ‫ךو‬ज
۶ઋ ǖ!൥ࠨ‫ך‬जქ‫ޔ‬टᄪ‫؍‬Ӱࡳཛྷੳ୿‫֔و‬ၠDŽ2 ᄪ‫!>!؍‬
3/65 ੳ୿Dž
? → A : A × 2.54
2/!Ѣ ,g)QSHN* ६൩ QSHN ன෷ă!
ED I T RUN DEL

1

3/!Ѣ b)FEJU*ă

2

3

჻ࠆᅘ֔ၠืয‫֔و‬ၠഘDŽQ2 ባ Q5Dž
EDI T Pr o g r am

P-1234 380

ෝᅨ֔ၠ،‫׈‬ಹ൛ફ

Ck-68

4/!Ѣ‫ڶ‬ᄮᅢསෳᅋ‫֔و‬ၠഘӬࠟ‫ืو‬ዖऒă
• ࡥஎණ‫־‬࿦ᆱှன෷ၭᇗԵ‫ة‬ăᅋ e!ࠧ!d!ၭࡳԵ
‫ࡥة‬எ 2 ࠧࡥஎ 3ă
MODE : COMP CMPLX

1

MODE : BASE SD REG

2

3 45

ࡥஎ 2

ࡥஎ 3

5/!Ѣ‫ڶ‬ᄮᅢეၭዷ֔ၠᆱှன෷‫ืو‬ዖ I
ऒă!
000
• ᇀ‫ױ‬ઋቲLjᇀࡥஎ 2 ණၭᇗ
b)DPNQ*ă‫ױ‬෫ DPNQ Ӈၭᇗዷཛྷᆱှன෷Ljࣜ๻ಹ
ट࿤෸֔ၠӬࣃࡥஎă!
ቺეƽ!
֔ၠ‫و‬ᆱှன෷ქ‫ح‬Ӈቚ‫ڊ‬Ljӯྐۨ‫ݢ‬Ӱăቝᅘᇀ‫ך‬जူ
‫֔و‬ၠ෫ԯ௢ቚ‫ڊ‬ᆱှன෷ă
6/!พ൩֔ၠă

? →A : A × 2. 54

010

• ࿒எढ़ම൥ࠨพ൩֔ၠă
֔ၠ

? → A : A × 2.54

ऒՃዷ

!d(P-CMD)b(?)
!~(→)-(A)w
a-(A)*c.fe

• !d)Q.DNE* ࿤෸ქ‫ޔ‬ቚ‫֔ڊ‬ၠத૚‫و‬พ൩ࡥஎă
ᅘߔ࿺ഉഋԸᆪٞ 82 ოණ‫و‬Đத૚‫و‬พ൩đქॎă

Ck-69

7/!พ൩֔ၠࡍLjѢ A!ࢪ !5)FYJU*ă
• ეᆱှ‫ךݳݳ‬ज‫֔و‬ၠ෫Ljഋᇀ‫ױ‬෫Ѣ w!࿤෸֔ၠ
ᆱှDŽSVO!QsphsbnDžࡥஎăᅘߔ࿺ഉLjഋԸᆪĐ֔ၠ
‫و‬ᆱှđქॎDŽ࿒ะDž
ă
• ე۵࢐໼ի‫ࣜو‬๻ࡥஎ෫LjഋѢ ,b!६൩ DPNQ
ன෷ă!

A ࿦ᅘ֔ၠ‫و‬Ӭࣃ
2/!Ѣ ,g)QSHN*b)FEJU* ࿤෸֔ၠӬࣃ )FEJU!
Qsphsbn* ࡥஎă
3/!ᅋืዖऒ b!ባ e ၭᇗࠆᅘეӬࣃ‫֔و‬ၠ‫֔و‬ၠഘă!
4/!ᅋ e!ࠧ!d!ᇀ֔ၠቲჰ‫ߞڑ‬ӶLjԌቖှຑၖე‫و‬Ճ
ዷӬࣃ֔ၠ‫و‬௠൛ࢪ኷ࣩူ௠൛ă!
• Ѣ f!৹໮ባ֔ၠ‫و‬৚་LjۚѢ c!৹໮ባயཤă
5/!֔ၠӬࣃ༾ӛࡍLjѢ A!ࢪ !5)FYJU*ă

k ֔ၠ‫و‬ᆱှ
֔ၠ৹ჾᇀ QSHN ன෷ࢪದຓன෷ቲᆱှă!

A ൥ࠨᇀ QSHN ன෷ჾ༶‫و‬ன෷ቲᆱှ֔ၠ
2/!Ѣ 5ă
3/!ᅋืዖऒ b!ባ e ၭᇗ֔ၠഘԌቖှದ֔ၠă

A ൥ࠨᇀ QSHN ன෷ቲᆱှ֔ၠ
2/!Ѣ ,g)QSHN* ࿤෸ QSHN ன෷‫ֽو‬෶ࡥஎă
3/!Ѣ c)SVO*ă
• ࣜ๻ಹ࿤෸֔ၠᆱှDŽSVO!QsphsbnDžࡥஎă
჻ࠆᅘ֔ၠืয‫֔و‬ၠഘDŽQ2 ባ Q5Dž
RUN Pr o g r am

P-1234 380

ෝᅨ֔ၠ،‫׈‬ಹ൛ફ
Ck-70

4/!ᅋืዖऒ b!ባ e ၭᇗࠆᅘეᆱှ‫֔و‬ၠ‫֔و‬ၠഘă
• ఀၭᇗ‫֔و‬ၠഘቲ‫֔و‬ၠӯӇቖှă!

A!ؓྥဳྲ‫־‬࿦෫ᄮԳട‫ؑو‬෣
Ѣ d ࢪ eă‫ױ‬෫֔ၠ‫و‬Ӭࣃࡥஎट‫־‬࿦LjۚߞӶ཭ᅢ
ؓྥդූ‫཭و‬ብLjჾӯുఀ६ှ၌‫ݢ‬ă

k ֔ၠ‫و‬ක‫ׅ‬
໼߹ቚ‫֔ڊ‬ၠഘӬࠟ৹ჾක‫ׅ‬࿦ᅘ‫֔و‬ၠă

A ൥ࠨක‫ׅ‬ቚ‫֔ڊ‬ၠഘቲ‫֔و‬ၠ
2/!Ѣ ,g)QSHN* ࿤෸ QSHN ன෷‫ֽو‬෶ࡥஎă
3/!Ѣ d)EFM*ă
჻ࠆᅘ֔ၠืয‫֔و‬ၠഘDŽQ2 ባ Q5Dž
DELETE Pr o g r am

P-1234 380

ෝᅨ֔ၠ،‫׈‬ಹ൛ફ

4/!ᅋืዖऒ b!ባ e ၭᇗეක‫ׅ‬ದ֔ၠ‫֔و‬ၠഘă
• ࠆᅘఀ‫ݳݳ‬ක‫֔وׅ‬ၠ‫֔و‬ၠഘӬ
DELETE Pr o g r am
ࠟసӫ‫ܻࠟو‬टဋ෡Ljༀ෫֔ၠ،
P-1234 390
‫׈‬ಹ‫و‬ෝᅨ൛ફटᇜࣩă

k த૚‫و‬พ൩
A ൥ࠨพ൩ቚ‫֔ڊ‬ၠத૚
2/!‫֔ص‬ၠӬࣃࡥஎ࿤෸෫LjѢ !d)Q.DNE*ă
• ‫ױ‬෫ࡥஎ࿤෸த૚Ե‫وة‬ٞ 2 ოă
3/!ᅋ e!ࠧ!d!ၭࡳԵ‫ة‬Ԍ࿤෸ࠆᅘຑၖத૚‫ࡥو‬எă
4/!ᅋืዖऒ b!ባ e!ၭᇗԌพ൩ຑၖე‫و‬த૚ă
Ck-71

ኢ
ეพ൩‫ *;) ࠟܖ‬෫LjഋѢ wă

A ৹ዷཛྷ֔ၠத૚พ൩‫ޢو‬௢
ᇀ໼ի‫ࣜو‬๻෫௢޷พ൩‫و‬හ‫ࠧڊ‬ቖှ‫و‬ದຓՃዷ‫ڞ‬৹ᅋ
ዷ֔ၠத૚ăᅘߔ࿺ഉLjഋԸᆪ࿒ะĐத૚Ը৬đ
ă

k த૚Ը৬
ӊॎ࿺࿈ढ़ම৹ჾᇀ֔ၠቲෳᅋ‫ޕو‬ቸத૚ă
Ӷ໘ቲࠆᅘ g!‫و‬த૚৹ჾᇀѢ !d)Q.DNE* ࢪ
5 ࡍ‫־‬࿦‫ࡥو‬எණพ൩ă

A ࢱӊࣜ๻த૚ g
?!DŽพ൩໗෸ܻDž
?!→!| Ӱફ ~
শۨ!
‫ޢ‬௢!
࿤෸พ൩໗෸ܻĐ| Ӱફ ~?đԌटพ൩‫ืو‬቗‫ݑ‬
‫ޖ‬ქ‫ޔ‬Ӱફă
?!→!A
۶ઋ!
→!DŽӰફ‫ݑ‬቗Dž
শۨ!
| ӹؕ෷ ; ?~!→!| Ӱફ ~
‫ޢ‬௢!
टᅑዳՊᆐ๰ഓ‫ืوه‬቗‫ޖݑ‬ᅚՊ‫و‬Ӱફă
A+5 → A
۶ઋ!
:!
DŽ‫ތܖ‬ଵDž
শۨ!
| ᅷশ ~ : | ᅷশ ~ : ... : | ᅷশ ~
‫ޢ‬௢!
‫ތܖ‬ᅷশăԥ໷ቛ֔ၠ‫و‬ቖှă
? → A : A2 : Ans2
۶ઋ!
Ck-72

^!) พ‫־‬த૚ *
শۨ!
| ᅷশ ~^!| ᅷশ ~
‫ޢ‬௢!
ᇃ໷֔ၠ‫و‬ቖှԌ࿤෸࿦ᇀ‫و‬ቖှॕ߷ă֔ၠ
‫و‬ቖှᄜ‫ױ‬த૚ۚᇃ໷෫LjQ!ܻ࢙ࠟ‫־‬࿦ă
?!→!A : A2!^!Ans2
۶ઋ!

A ‫܇‬໫औኪჰத૚ g
Goto ~ Lbl
শۨ!
‫ޢ‬௢!
۶ઋ!

Goto n : .... : Lbl n ࢪ Lbl n : .... : Goto n!)n!>!1
ባ : ‫و‬ሿื *
ቖှ Hpup nLj໮ባ࿰ᄮ‫ و‬Mcm n ‫׌‬ă
? → A : Lbl 1 : ? → B : A × B ÷ 2 ^ Goto 1

ቺეƽ
൥߷ᇀ Hpup!n ຑᇀ‫و‬ༀქ֔ၠቲୣᅘ࿰ᄮ‫ و‬Mcm!nLjশۨ
ؓྥ )Tzouby!FSSPS* ӯ࢙ۢූă

A!໫औኪჰத૚ࠧ໫औӹؕ෷ g
S
শۨ!
!
‫ޢ‬௢!
!

1!!| ӹؕ෷ ~!| ߔ࿅ᆱ๻ܻ ~!| ӹؕ෷ ~!S!| ᅷশ 2~
: | ᅷশ 3~ : ////
2!!| ӹؕ෷ ~!S!| ᅷশ 2~!;!| ᅷশ 3~!;!////
ᅳߔ࿅ᆱ๻ܻქಲෳᅋ‫و‬໫औ‫ܖ‬ቈத૚DŽ=, ≠, >,
>, <, <*ă
শۨ 1ǖ
൥߷ S!த૚ዳӫ‫و‬໫औཛྷሪᇘቖှ | ᅷ
শ 2~!- ഹࡍก | ᅷশ 3~Ljቐࡍ‫و‬ᅷশᇘც‫״‬ቖှă
൥߷ S!த૚ዳӫ‫و‬໫औཛྷ࣯ᇘ໮߹ | ᅷশ 2~!ഹࡍቖှ | ᅷশ 3~ ࣆದ๾ࡍ‫و‬ᅷশă
Ck-73

!

۶ઋ!

শۨ 2ǖS!த૚ዳՊ‫و‬໫औ‫و‬ಂࣱॕ߷ԥก૏
෫ದटӇॖงཛྷĐሪđ
Ljᄜ‫ױ‬ቖှ | ᅷশ 2~Ljഹ
ࡍก | ᅷশ 3~ ࣆದຓ๾ࡍ‫و‬ᅷশăS!த૚ዳՊ
‫و‬໫औ‫و‬ಂࣱॕ߷ก૏෫ದटӇॖงཛྷĐ࣯đ
Lj
ᄜ‫ױ‬໮߹ | ᅷশ 2~Ljഹࡍቖှ | ᅷশ 3~ ࣆದຓ๾
ࡍ‫و‬ᅷশă
Lbl 1 : ? → A : A > 0 S!'(A)!^ Goto 1

=, ≠, >, >, <, <DŽߔ࿅ᆱ๻ܻDž
!
শۨ!
| ӹؕ෷ ~!| ߔ࿅ᆱ๻ܻ ~!| ӹؕ෷ ~!
‫ޢ‬௢!
ሦဗத૚ಂࣱ઩ӫ‫و‬ӹؕ෷LjԌ۵࢐ქ‫ޔ‬ሪDŽ2Dž
ࢪ࣯DŽ1Dž‫و‬቗ăᇀ޵ࣲ Jg ᅷশࢪ Xijmf ᅷশ‫و‬ȗ໫
औӹؕ෷ș
෫Lj
ሦဗத૚ࠧ‫ܖ‬ቈத૚ S ქಲෳᅋă
۶ઋ!
ഋԸᆪ SDŽණะDž
!
Lj
Jg ᅷশ
DŽ࿒ะDž
ࣆ Xijmf ᅷশ
DŽٞ
87 ოDž‫ํو‬டă
ኢ
ሦဗத૚ಂࣱ઩ӫ‫و‬ӹؕ෷LjԌ۵࢐ქ‫ޔ‬ሪDŽ2Džࢪ࣯DŽ1Dž
‫و‬቗Ljഹࡍटॕ߷ү،ᇀ Bot ቲă

A ॕ޵ਈቨத૚ 0!Jg ᅷশ g
Jg ᅷশᅋᅢ‫ޗ‬য Jg ቐࡍ‫و‬ӹؕ෷DŽ‫ܖ‬ቈ໫औDžกሪࡱก࣯
ੂਈቨ֔ၠቖှ‫ܖو‬ቈă

Jg ᅷশၙቌ
• Jg Ӥၙᅳ Uifo ై‫ڶ‬ෳᅋăෳᅋ Jg ‫د‬ୣᅘ࿰ᄮ‫ و‬Uifo ෫
टդූশۨؓྥ )Tzouby!FSSPS*ă
• ӹؕ෷LjHpup த૚ࢪ Csfbl த૚৹ᇀ Uifo ࠧ Fmtf ࡍஎ‫ | و‬ӹ
ؕ෷ +~ ቲෳᅋă
Ck-74

If~Then (~Else) ~IfEnd
If!| ໫औӹؕ෷ ~!:!Then!| ӹؕ෷ +~!: Else!| ӹؕ
শۨ!
෷ +~!: IfEnd!: | ᅷশ ~!: ...
•!‫ ص‬Jg ࡍஎ‫و‬໫औᅷশཛྷሪ෫Lj֔ၠቖှ‫׹‬
‫ޢ‬௢!
Uifo ‫ ف‬Fmtf ቐࣺ‫و‬ᅷশLjഹࡍቖှ JgFoe ࡍஎ
‫و‬ᅷশă‫ ص‬Jg ࡍஎ‫و‬໫औᅷশཛྷ࣯෫Lj֔ၠ
ቖှ Fmtf ࡍஎ‫و‬ᅷশࡍቖှ JgFoe ࡍஎ‫و‬ᅷশă
• !Fmtfȗӹؕ෷ș৹ჾෛଞă
• !Ӥၙࠆᅘ JgFoe ǖ
ȗᅷশș
ăटದෛଞԥ࢙դූ
ؓྥLj‫ د‬Jg ᅷশࡍஎ‫֔و‬ၠ৹௢࢙դූᄌ࿻
ԥ‫وف‬ॕ߷ă
۶ઋ 2! ? → A : If A < 10 : Then 10A ^ Else 9A ^
IfEnd : Ans×1.05
۶ઋ 3! ? → A : If A > 0 : Then A × 10 → A : IfEnd :
Ans×1.05

A ॕ޵ਈቨத૚ 0!Gps ᅷশ g
ቝეਈቨӰફቲ‫و‬቗ᇀቚ‫ڊ‬۶ཙቐ௠LjGps ᅷশӯ࢙۴‫ݒ‬
ቖှ Gps ᅳ Ofyu ቐࣺ‫و‬ᅷশă!

Gps ᅷশၙቌ
Gps ᅷশӤၙዜกҗᅘ Ofyu ᅷশăෳᅋ Gps ‫د‬ୣᅘ࿰ᄮ‫و‬
Ofyu ෫टդූশۨؓྥ )Tzouby!FSSPS*ă
For~To~Next
For!| ӹؕ෷ ) ৚෶቗ *~!→!| Ӱફ ) ਈቨӰફ *~!
শۨ!
To!| ӹؕ෷ ) ॕา቗ *~!;!| ᅷশ ~!; ...!| ᅷশ ~!;!
Next!; ....
Ck-75

‫ޢ‬௢!

۶ઋ!

۴‫ݒ‬ቖှ‫ ׹‬Gps ‫ ف‬Ofyu ቐࣺ‫و‬ᅷশ෫LjਈቨӰ
ફट‫׹‬৚෶቗৚෶Lj୧ቖှ 2 ‫״‬ӯࣩ 2ă‫ص‬ਈቨ
቗‫ؕف‬ॕา቗෫Lj֔ၠ໮ባ Ofyu ࡍஎ‫و‬ᅷশቖ
ှă൥߷ Ofyu ࡍஎୣᅘᅷশLj֔ၠӯ໷ቛቖှă
For 1 → A To 10 : A2 → B : B ^ Next

For~To~Step~Next
For!| ӹؕ෷ ) ৚෶቗ *~!→!| Ӱફ ) ਈቨӰફ *~!
শۨ!
To!| ӹؕ෷ ) ॕา቗ *~!Step!| ӹؕ෷ ) ԧ *~!;!| ᅷ
শ ~!; ...!| ᅷশ ~!;!Next : ....
‫ޢ‬௢!
۴‫ݒ‬ቖှ‫ ׹‬Gps ‫ ف‬Ofyu ቐࣺ‫و‬ᅷশ෫LjਈቨӰ
ફट‫׹‬৚෶቗৚෶Lj୧ቖှ 2 ‫״‬ӯࣩԧืă‫ׅ‬
‫ױ‬٧ቐ༶Lj‫ױ‬த૚ᅳ For~To~Next ࿰ༀă
For 1 → A To 10 Step 0.5 : A2!→ B : B ^ Next
۶ઋ!

A ॕ޵ਈቨத૚ 0!Xijmf ᅷশ g
While~WhileEnd
While!| ໫औӹؕ෷ ~!;!| ᅷশ ~!;!///!| ᅷশ ~!;!
শۨ!
WhileEnd :!////
‫ޢ‬௢!
‫ ص‬Xijmf ࡍஎ‫و‬໫औӹؕ෷ཛྷሪDŽ‫܇‬૏Dž෫Lj֔
ၠ۴‫ݒ‬ቖှ Xijmf ባ XijmfFoe ቐࣺ‫و‬ᅷশă‫ص‬
Xijmf ࡍஎ‫و‬໫औӹؕ෷Ӱཛྷ࣯DŽ1Dž෫Lj֔ၠ
ቖှ XijmfFoe ࡍஎ‫و‬ᅷশă
? → A : While A < 10 : A2!^ A+1 → A :
۶ઋ!
WhileEnd : A÷2
ኢ
‫ױص‬த૚ฑ‫״‬Ӈቖှ෫Lj൥߷ Xijmf ᅷশ‫و‬໫औཛྷ࣯Ljቖ
ှቓे໮ባ XijmfFoe ࡍஎ‫و‬ᅷশLjۚ Xijmf ባ XijmfFoe ቐ
ࣺ‫و‬ᅷশქ‫״‬ნԥӇቖှă
Ck-76

A ֔ၠਈቨத૚ g
Break
.. : {Then ; Else ; S } Break : ..
শۨ!
‫ޢ‬௢!
‫ױ‬த૚೟ቨቲ‫ ڱ‬Gps ࢪ Xijmf ၹ࡯LjԌ໮ባ࿒ქ
‫ޔ‬த૚ă໼իLj‫ױ‬த૚ᅋᇀ Uifo ᅷশቲLj໗‫ޥ‬
Csfbl ‫و‬໫औă
?!→ A : While A > 0 : If A > 2 : Then Break :
۶ઋ!
IfEnd : WhileEnd : A ^

A හብத૚
ሦဗத૚‫ޢو‬௢ᅳࣜ๻ಹ‫ޕو‬ቸහብ࿰ༀăᅘߔ࿺ഉLjഋ
Ըᆪٞ : ოණ‫و‬Đࣜ๻ಹහብđ
ă
ቺეƽ!
‫ڶ‬ᅢᅘဗහብத૚Lj࣊ෳ֔ၠᆱှॕาષLj‫ݡ‬த૚ຑዶ‫و‬
හብ൒ट࣢ၦᅘပă

ऻ‫཭ةڪ‬த૚
Deg, Rad, Gra!
(COMP, CMPLX, SD, REG)!
.. : Deg : ..
শۨ!
.. : Rad : ..
.. : Gra : ..
Ճዷ!
!,(SETUP)b(Deg)
!
!,(SETUP)c(Rad)
!
!,(SETUP)d(Gra)
‫ޢ‬௢!
ሦဗத૚ቚ‫཭ةڪऻڊ‬ă

Ck-77

࿤෸ြ෷த૚
Fix!

(COMP, CMPLX, SD, REG)!

শۨ!
Ճዷ!
‫ޢ‬௢!

.. : Fix {n} : .. )n!>!1 ባ : ‫و‬ሿื *
!,(SETUP)eb(Fix)a ባ j
‫ױ‬த૚߈‫ڊ‬พ‫ࣜو־‬๻ॕ߷‫و‬ဏื཭ื
DŽ1 ባ :Dž
ă!

Sci!

(COMP, CMPLX, SD, REG)!

শۨ!
Ճዷ!
‫ޢ‬௢!

.. : Sci {n} : .. )n!>!1 ባ : ‫و‬ሿื *
!,(SETUP)ec(Sci)a ባ j
‫ױ‬த૚߈‫ڊ‬พ‫ࣜو־‬๻ॕ߷‫و‬ᅘပ཭ืDŽ2 ባ
21Dž
ă
Ѣ !,)TFUVQ*ec)Tdj* ࡍѢ a!ቚ‫ ڊ‬21
཭ᅘပืዖă

!

Norm!
(COMP, CMPLX, SD, REG)!
.. : Norm {1 ; 2} : ..
শۨ!
Ճዷ!
!,(SETUP)ed(Norm)b ࢪ c
‫ޢ‬௢!
‫ױ‬த૚ቚ‫ࣜڊ‬๻ॕ߷‫و‬พ‫־‬กෳᅋ Opsn2 ࡱก
ෳᅋ Opsn3ă

༇ࣜ౷ଔத૚
FreqOn, FreqOff!
(SD, REG)
.. : FreqOn : ..
শۨ!
.. : FreqOff : ..
!
Ճዷ!
!,(SETUP)db(FreqOn)!
!
!,(SETUP)dc(FreqOff)
‫ޢ‬௢!
‫ױ‬த૚‫ؘ‬৚ )GsfrPo* ࢪߔӡ )GsfrPgg* ༇ࣜ౷ଔă!
Ck-78

A അ‫ׅ‬த૚
ClrMemory!
(COMP, CMPLX, BASE)
.. : ClrMemory : ..
শۨ!
Ճዷ!
!j(CLR)b(Mem)
‫ޢ‬௢!
‫ױ‬த૚टຑᅘӰફഅ‫ׅ‬ཛྷ૏ă
ኢ
ეഅ‫ׅ‬ქ‫ޔ‬ቚ‫ڊ‬Ӱફ෫Ljᅋ 1!→!| Ӱફ ~ă
ClrStat!
(SD, REG)!
.. : ClrStat : ..
শۨ!
Ճዷ!
!j(CLR)b(Stat)
‫ޢ‬௢!
‫ױ‬த૚അ‫ׅ‬ү،ᇀ،‫׈‬ಹቲ‫و‬ຑᅘ༇ࣜჅӊื
যă!

A ‫ڢ‬઎،‫׈‬ಹத૚
M+, M–!
(COMP, CMPLX, BASE)
.. : | ӹؕ෷ ~ M+ : ..!0!.. :!| ӹؕ෷ ~!M– : ..
শۨ!
Ճዷ!
l / !l(M–)
M+ टӹؕ෷‫و‬቗ࣩ‫ڢف‬઎،‫׈‬ಹቲLjۚ M– ‫׹‬
‫ޢ‬௢!
‫ڢ‬઎،‫׈‬ಹऋണӹؕ෷‫و‬቗ă

A ල൩த૚ )Soe*
Rnd(!
শۨ!
Ճዷ!
‫ޢ‬௢!

(COMP, CMPLX, SD, REG)!
.. :!| ӹؕ෷ ~!: Rnd(Ans : ..
!a(Rnd)
‫ױ‬த૚‫ޗ‬যᅑ࿤෸ြ෷ቚ‫ื཭وڊ‬ල൩ࣜ๻ॕ
߷ă
Ck-79

A ื࿅த૚
Dec, Hex, Bin, Oct!
(BASE)
.. : Dec : .. / .. : Hex : .. / .. : Bixn : .. / .. : Oct : ..
শۨ!
Ճዷ!
x(DEC) / M(HEX) / l(BIN) / I(OCT)
‫ޢ‬௢!
ሦဗத૚ቚ‫ࣜืࢱڊ‬๻‫ืو‬࿅ă

A ༇ࣜืযพ൩த૚
DT!

(SD, REG)!

শۨ!

.. : | ӹؕ෷DŽx ቗Dž~ ; | ӹؕ෷DŽGsfr ቗Dž~!EU : ..
!
///////TE ன෷LjGsfrPo
.. : | ӹؕ෷DŽx ቗Dž~!EU : ..!//////TE ன෷LjGsfrPgg
.. : | ӹؕ෷DŽx ቗Dž~ , | ӹؕ෷DŽy ቗Dž~ ;
| ӹؕ෷DŽGsfr ቗Dž~!EU : ..! /////SFH ன෷ -!GsfrPo
.. : | ӹؕ෷DŽx ቗Dž~ , | ӹؕ෷DŽy ቗Dž~!EU : ..
!
/////SFH ன෷ -!GsfrPgg

!
!
!

ቺეƽ!
ეᇀණ෸শۨቲพ൩‫ *<) ࠟܖ‬෫LjഋѢ !,)<*ăეพ൩
‫) ࠟڜ‬-* ෫LjഋѢ ,ă
Ճዷ!
‫ޢ‬௢!

l) พ൩ EUă*
‫ױ‬த૚ᅋᅢพ൩Ⴥӊืযዩăᇀ TE ன෷ࠧ SFH
ன෷ቲLjEU த૚‫ޢو‬௢ᅳ l!ऒDŽEU ऒDž࿰ༀă

A ԥ௢ᇀ֔ၠቲෳᅋ‫ޢو‬௢
࿒઼‫ޢ‬௢ԥ௢ᇀ֔ၠቲෳᅋă
• ࣜ๻ॕ߷ӰࡳࠉืDŽFOH!/-!FOH!,-!૥෨६ቨ ↔ ෨६ቨ
ӰࡳLj‫ ↔ ืܖ‬ဏืӰࡳDž
• ‫ࣜืݒ‬๻ॕ߷࿤෸෫‫و‬࿤෸೰ࡳDŽ!w)Sf⇔Jn*Dž
ă
Ck-80

• ‫཭ݒ‬DŽ!j)DMS*d)Bmm*wDž
• හብဳྲഅ‫ׅ‬DŽ!j)DMS*c)Tfuvq*wDž

‫ݛ‬ଆ
k ࣜ๻‫و‬ᅍ࿘๋ၠ
ࣜ๻ಹ‫ޗ‬য࿒෸ᅍ࿘๋ၠ६ှఀพ൩‫ࣜو‬๻ă
• ࢱӊණLjࣜ๻กѢሙ‫׹‬ዳባᅚ‫๋و‬ၠ६ှă
• ਸ਼ᅘਸ਼ࠟ‫ࣜو‬๻ᅍ࿘ă!
๋ၠ
ࣜ๻੮ျ
ํட
2
‫؞‬ਸ਼ࠟ‫ืࠉو‬
Pol(, Rec(, ∫(, d/dx(, sin(,
cos(, tan(, sin–1(, cos–1(,
tan–1(, sinh(, cosh(, tanh(,
sinh–1(, cosh–1(, tanh–1(, log(,
ln(, e^(, 10^(, '(, 3'(,
arg(, Abs(, Conjg(, Not(,
Neg(, Rnd(
3
೐எᅘื቗‫ ืࠉو‬x2, x3, x–1, x!, ° ´ ˝, °, r, g
x
֓‫۽‬Lj֓‫ޗ۽‬
^(, '(
%
҇‫ܖ‬Ӕ
4
‫ืܖ‬
a b/c
(–) ) ‫* ࠟݘ‬
5
೐ብܻࠟ
d, h, b, o!) ื࿅ܻࠟ *
6
༇ࣜ޼ࣜ቗ࣜ๻
m, n, m1, m2

Ck-81

๋ၠ
ࣜ๻੮ျ
7
ෛଞ‫ࠟ֓و‬

8
9
:
21
22
23

ํட
ᇀ࿒઼࿾௅ቐ೐‫ࠟ֓و‬৹ჾ
ෛଞ ǖ
π-!eLjӰફDŽ2π, 5A, πA, 2i,
ٌDž
Lj‫؞‬ਸ਼ࠟ‫ืࠉو‬DŽ2'(3),
Asin(30), ٌ * ჾࣆ೐ብܻࠟ
DŽ‫ׅࠟݘ‬༶Dž
఩઼Ljዩࠩ!
nPr, nCr
‫ܻࠟืݒ‬
∠
×, ÷
֓ۨLj‫!ׅۨ‬
+, −
ࣩۨLjऋۨ
=, ≠, >, <, >, <
ߔ࿅ᆱ๻ܻ
and
଩ࣃࢵ
଩ࣃࠧLjᄖ଩ࣃࠧLj or, xor, xnor
ᄖ‫܇‬଩ࣃࠧ

ኢ
• ൥߷ࣜ๻ቲࠆᅘ‫ݘ‬቗Ljᇘ‫ݘ‬቗৹௢ၖეਸ਼ᇀਸ਼ࠟቲăઋ
൥Lj൥߷ეࣜ๻lj3 ‫و‬౿‫۽‬Ljᇘၖეพ൩ ǖ)lj3*3ă!ᄜཛྷ
x3!กქ‫ޔ‬ᅘ೐ብื቗‫ืࠉو‬DŽණ෸ᅍ࿘‫ ڪ‬3DžLj‫وืࠉױ‬
ᅍ࿘‫ݽڪ‬ᅢ‫ࠟݘ‬Lj‫ࠟݘ‬ཛྷ೐ብܻࠟDŽᅍ࿘‫ ڪ‬5Dž
ă
–22 = –4
!
-cxw!
(–2)2 = 4
(-c)xw!
• ൥࿒எ‫و‬ઋዓຑ෸Ljෛଞܻࠟ‫وۨ֓و‬ᅍ࿘๋ၠ‫ݽ‬ᅢ‫؞‬
ܻࠟ‫ׅۨࠧۨ֓و‬ă
1 ÷ 2π = 1 = 0.159154943
2P
1 ÷ 2 × π = 1 π = 1.570796327
2
Ck-82

k ࣜ๻۶ཙĂ཭ืࣆॽ‫ڪ‬
࿒ӹ઼‫־‬ષࣜ๻۶ཙDŽื቗พ൩ࠧพ‫־‬۶ཙDž
Ă௠ԩࣜ๻
ෳᅋ‫ื཭و‬Ljჾࣆࣜ๻ॽ‫ڪ‬ă
ࣜ๻۶ཙ
Ġ2ġ21 ::!ባ Ġ:/:::::::::ġ21::!ࢪ 1
௠ԩࣜ๻
26 ཭
ქґੂํLjᇀქ‫ࣜ״‬๻ቲLjٞ 21 ཭‫ॽو‬
‫ڪ‬ཛྷ Ġ2ăቚืြ෷ࣜ๻ॕ߷‫ྥو‬՘ཛྷᇀ
ॽ‫ڪ‬
ཤื‫و‬ዮࡍᅘပ཭ืණ Ġ2ăᇀઘၦࣜ๻
߹֔ቲྥ՘࢙ࢵ੩ă
—

A ࠉืࣜ๻พ൩۶ཙࠧॽ‫ڪ‬
ࠉื
sinx
cosx

พ൩۶ཙ
9
DEG 0 < | x | < 9×10
RAD 0 < | x | < 157079632.7
10
GRA 0 < | x | < 1×10
‫ | صׅ‬x | = (2n–1)×90 ෫ቐ༶Ljᅳ sinx
࿰ༀă
‫ | صׅ‬x | = (2n–1)×π/2 ෫ቐ༶Ljᅳ sinx
RAD
࿰ༀă
‫ | صׅ‬x | = (2n–1)×100 ෫ቐ༶Ljᅳ sinx
GRA
࿰ༀă
DEG

tanx

sin–1x
cos–1x
tan–1x
sinhx
coshx

0<|x|<1
0 < | x | < 9.999999999×1099
0 < | x | < 230.2585092
Ck-83

ࠉื
พ൩۶ཙ
sinh–1x 0 < | x | < 4.999999999×1099
cosh–1x 1 < x < 4.999999999×1099
tanhx 0 < | x | < 9.999999999×1099
tanh–1x 0 < | x | < 9.999999999×10–1
logx/lnx 0 < x < 9.999999999×1099
10x
–9.999999999×1099 < x < 99.99999999
ex
–9.999999999×1099 < x < 230.2585092
'
x
0 < x < 1×10100
50
x2
| x | < 1×10
100
1/x
| x | < 1×10 ; x ≠ 0
3
100
'
x
| x | < 1×10

x!
nPr
nCr
Pol(x, y)

0 < x < 69 (x กሿื )
0 < n < 1×1010, 0 < r < n (n, r กሿื )
1 < {n!/(n–r)!} < 1×10100
0 < n < 1×1010, 0 < r < n (n, r กሿื )
1 < n!/r! < 1×10100 ࢪ 1 < n!/(n–r)! < 1×10100
99
| x |, | y | < 9.999999999×10

x2+y2 < 9.999999999×1099
0 < r < 9.999999999×1099
Rec(r, )
: ᅳ sinx ࿰ༀ
100
| a |, b, c < 1×10
°’ ”
0 < b, c
100
| x | < 1×10

෨६ቨ ↔ ૥෨६ቨӰࡳ
0°0´0˝ < | x | < 9999999°59´59˝
Ck-84

ࠉื

^(xy)

พ൩۶ཙ
x > 0: –1×10100 < ylog x < 100
x = 0: y > 0
x < 0: y = n, m (m, n กሿื )
2n+1
‫د‬ก : –1×10100 < ylog | x | < 100

x'
y

y > 0: x ≠ 0, –1×10100 < 1/xlogy < 100
y = 0: x > 0
y < 0: x = 2n+1, 2n+1 (m ≠ 0; m, n กሿื )
m
‫د‬ก : –1×10100 < x log | y | < 100

a b/c

ሿืLj‫ܖ‬ዓࣆ‫ܖ‬ா‫ࣜࠩื཭و‬Ӥၙᇀ 10 ཭ჾ
௠DŽದቲҪਸ਼‫ܻޒܖ‬Dž
ă

y, 3', x!, nPr, nCr!ျࠉืၖეઘၦ௠ԩࣜ๻Lj
• ^(xy), x'
ᄜ‫ױ‬ᇀ‫ࣜޕ‬๻ቲۢූ‫ྥو‬՘࢙੩ࢵă
• ᇀࠉื‫و‬ನ٧ࠧߑ٧‫ݛ‬॰ྥ՘ᅘࢵ੩ࠧӰ‫وؙ‬ഃဂă

k ؓྥဳྲ
൥߷ࣜ๻մ‫־‬ષࣜ๻ಹ‫و‬࿮‫ڪ‬Ljࢪ൥
߷६ှષԥᆰၛ‫و‬ՃዷLjࡥஎණट‫־‬
࿦ؓྥဳྲă

Mat h ERROR

ؓྥဳྲ۶ઋ

A ؓྥဳྲ‫و‬അ‫ׅ‬
ྐଥؓྥ੮ျཛྷࠨLjቖှ࿒ะऒՃዷ৹അ‫ྲဳྥׅؓ‬ă
• Ѣ d!ࢪ e!࿤෸ؓྥۢූ೐ఀพ൩‫ࣜو‬๻ӹؕ෷‫و‬Ӭ
ࣃࡥஎLj‫ױ‬෫ߞӶट཭ᅢؓྥۢූ‫཭و‬ብăᅘߔ࿺ഉഋ
Ըᆪٞ 27 ოණ‫و‬Đؓྥ཭ብ‫و‬Փሖđქॎă
Ck-85

• Ѣ A!৹അ‫ූۢྥׅؓ‬೐ఀพ൩‫ࣜو‬๻ӹؕ෷ăഋኢᄌLj
դූؓྥ‫ࣜو‬๻ӹؕ෷ԥ࢙ࠆᇀࣜ๻଎ઈቲă!

A ؓྥဳྲԸ৬
ӊॎ઼‫־‬ષࣜ๻ಹຑ࿤෸‫و‬ຑᅘؓྥဳྲLjದᆓᄜࣆӨஊ
ؑ෣ă

Math ERRORDŽࣜ๻ؓྥDž
ᆓᄜ

• ቲࣺࣜ๻ॕ߷ࢪዮቷࣜ๻ॕ߷մ‫־‬ષ൛ၛ
‫ࣜو‬๻۶ཙă
• พ൩‫ืو‬቗մ‫־‬ષ൛ၛ‫و‬พ൩۶ཙă
• ‫وۨ܇‬๻ืᆱ๻DŽ‫ׅ‬ჾ૏ٌDž
ă!
• ൥߷ၖეLjഋंՓพ൩‫ืو‬቗Ԍऋඵ཭ืă
‫ڶ‬Չ
• ෳᅋ‫ڢ‬઎،‫׈‬ಹࢪӰફዷཛྷࠉื‫و‬Ըื෫Lj
Ӥၙവ്،‫׈‬ಹࢪӰફ቗ᇀ‫وืࠉݡ‬൛ၛ
۶ཙቐ௠ă
ᅘߔืয‫و‬൛ၛพ൩۶ཙ‫ํو‬டLjഋԸᆪٞ 94 ოණ‫و‬Đࣜ
๻۶ཙĂ཭ืࣆॽ‫ڪ‬đქॎă!

Stack ERRORDŽ‫ڳ‬ᇿؓྥDž
ᆓᄜ
‫ڶ‬Չ

ࣜ๻ෳืዖ‫ڳ‬ᇿࢪத૚‫ڳ‬ᇿմ‫־‬ષ࿮‫ڪ‬ă
• ईࡧࣜ๻ӹؕ෷Ljෳದԥմ‫ڳ־‬ᇿ‫و‬൛ફă
• ฎटࣜ๻‫ތܖ‬ཛྷ઩‫ࢪޔ‬઩‫ޔ‬ჾණ‫و‬ԩ‫ܖ‬ă

Syntax ERRORDŽশۨؓྥDž
ᆓᄜ
‫ڶ‬Չ

ࣜ๻‫ޏ‬෷ᅘོ໘ă
ंՓশۨԌ६ှຑၖე‫ޚو‬ቁă

Ck-86

Argument ERRORDŽԸืؓྥDž
ᆓᄜ
‫ڶ‬Չ

ࣜ๻ᇀԸื‫و‬ෳᅋණᅘོ໘ă
ंՓԸื‫و‬ෳᅋഉਦԌ६ှຑၖე‫ޚو‬ቁă

Time OutDŽմ෫Džؓྥ
ᆓᄜ
‫ڶ‬Չ

‫ص‬೐‫و‬པ‫ࣜܖࢵࢪܖ‬๻ॕาLj‫د‬སୄዣॕา
໫औă
པ‫ࣜܖࢵࢪܖ‬๻ ǖժฎᇜࣩ!tol!቗ăഋኢᄌ ǖ
‫ױ‬Ճዷࡱ࢙ऩّॖ‫ॽو‬വ‫ڪ‬ă

Data FullDŽืয჻ୄDž
ᆓᄜ

‫ڶ‬Չ

ᇀ TE ன෷ࢪ SFH ன෷ቲLj‫ص‬،‫׈‬ಹቲ჻ү
،ᅘຑ‫ืڊ‬ફණ࿮‫و‬Ⴥӊืয෫Ljฎ༐࣢ၦ
ү،Ⴥӊืযă
ഋटჅӊืয‫ืو‬ફ࿮ቨᇀ൛ၛ࿮‫ڪ‬ቐ௠ă
ᅘߔ࿺ഉLjഋԸᆪٞ 56 ოණ‫و‬Đืয࿾‫و‬
พ൩ื௅࿮‫ڪ‬đ
ă

Go ERRORDŽኪჰؓྥDž
ᆓᄜ
‫ڶ‬Չ

֔ၠDŽᇀ QSHN ன෷ቲज઎‫و‬DžቲᅘĐHpup!nđ
த૚Lj‫د‬ୣᅘ࿰ᄮ‫و‬ĐMcm!nđӶ೉ă
኷ࣩქ‫ޔ‬ĐMcm!nđӶ೉ੂైࠩĐHpup!nđத૚Lj
ࢪක‫ׅ‬࿰ᄮ‫و‬ĐHpup!nđத૚ă

Ck-87

k! ᇀ࡫ჳกࣜ๻ಹۢූષ߆ሓቐ೐ ///
ᇀࣜ๻߹֔ቲۢූષؓྥLjࢪࣜ๻ॕ߷մ‫־‬ᄌ༶෫Ljഋቖ
ှ࿒ะՃዷă൥߷ქԧས௢ॖৈོ໘Ljᇘჰባ࿒ქԧăഋ
ኢᄌLjᇀ६ှሦဗՃዷቐ೐Ljഋ‫ڶ‬ቺეืয६ှӄ‫ܝ‬ă!
1!ंՓࣜ๻ӹؕ෷Ljവ്ದกܱࠆᅘൌࠨؓྥă
2!വ്ఀე६ှ‫ࣜو‬๻กᇀቁവ‫و‬ன෷ቲ६ှ‫و‬ă
3!൥߷ණะՃዷས௢ෳࣜ๻ࢎ‫ݒ‬ቁիLjᇘഋѢ p ऒă
ࣜ๻ಹ࢙ᇀಲ‫ڑ‬෫‫ڶ‬ದዔ෉ኴຢ६ှዔंă൥߷ࣜ๻
ಹۢ࿦ષོ໘Ljದट۵࢐ࣜ๻ன෷Ԍ‫ݒ‬ᆓֽ෶യෛై
ብLjԌೲഅ‫ׅ‬،‫׈‬ಹቲ‫و‬ຑᅘืযă
4!൥߷ٞ 3 ԧས௢ෳՃዷࢎ‫ݒ‬ቁիLjഋ६ှ࿒઼ѢऒՃ
ዷֽ෶ࡧຑᅘன෷ࠧහ‫ ڊ‬ǖ
!j(CLR)c(Setup)wă

٫ᆚეഓ
A ٫֠‫ࡳޚو‬
ࣜ๻ಹ࿤෸ืዖӰѣӹ෸٫֠٫઒ԥዣăᇀ٫֠٫઒ԥዣ
෫࣢ၦෳᅋࣜ๻ಹ࢙‫ـ‬ቤᆱှᄖիă‫ص‬࿤෸ืዖӰѣ෫Lj
ᄮॳਜ‫ࡳޚ‬٫֠ă࣊ෳࣜ๻ಹᆱှቁիLjნᄮ‫ݡ‬୧ൻ௰ባ
ඵ‫ࡳޚ‬ქ‫״‬٫֠ă
ቺეƽ!
ဤ࿒٫֠Lj࢙ෳࣜ๻ಹ‫و‬ຑᅘ،‫׈‬ಹ௠൛ഩԩӇක‫ׅ‬ă

Ck-88

2/!Ѣ!1A)PGG*!‫ڱ‬৚ࣜ๻ಹ٫ᆚă
• ეവүఀᇀ‫ࡳޚ‬٫֠෫ԥ࢙ྐᄌቲे໼
٫ᆚLjഋटү࡜৷ࡤ‫ࣜف‬๻ಹ‫و‬೐‫ڭ‬ă
3/!Ѣ༐ቲຑ෸ဤ࿒٫֠ࠪ‫ݥ‬Ԍ‫ࡳޚ‬٫֠Ljഋ
෶ቷവүቁവ‫܅‬ብ٫֠ቁࣁ!),*!ࠧ‫!ࣁݘ‬
) . *ă
4/!‫ࡳޚ‬٫֠ࠪ‫ݥ‬ă
5/!ֽ෶ࡧࣜ๻ಹ ǖ
!
O19)DMS*3)Bmm*w)Zft*
• ೰ྡྷ໮߹ණქԧƽ

螺丝

A ዔ‫ࢲߔڑ‬
൥߷ᇀᆢ 21 ‫ܖ‬ት௠ས६ှൌࠨՃዷLjࣜ๻ಹटዔ‫ࢲߔڑ‬ă
‫ױ‬ቸഉਦۢූ෫LjѢ p!ऒ৹ቺူ৚ࢲă!

ߢ‫ޏ‬
٫ᆚეഓǖ!ມჀ௢٫֠ǖ௠Ղᇀࣜ๻ಹ‫و‬ቁஎDŽ߈‫ڊ‬Dž
!
ఉ਋٫֠ǖMS55!)HQB87*!ġ!2
‫ؙ‬ᆢ٫֠ณதǖ
!4 ௰DŽ୧໢ෳᅋ 2 ဏ෫Dž
ዷჟུ‫ڪ‬ǖ
!1ņባ 51ņ
༶ြ֧‫؍‬ǖ
!22/2!) ‫!* ݽ‬ġ!91!) ਝ *!ġ!273!) լ *!ࠛ୿
‫ؙ‬ᆢቺફǖ
!:6h!) Ҫਸ਼٫֠ *
‫ݛ‬औǖү࡜৷

Ck-89

ᅘ‫ڠ‬ᅘࠀྡቬࢪᆐ๰ண֎ࣆࠆફ
࡯ү
ෳᅋ
ಜ࿮

ᅘ‫ڠ‬ᅘࠀྡቬࢪᆐ๰
ԩऔண֎

‫ۂ‬ឫ ‫ۂ‬ឫ۠
ೆ ޫ ᮣ ૥ࣱ‫ޓ‬
ખӉ Ӊ୹
)Qc* )Ih* )De* )Ds)WJ**
)QCC* )QCEF*

෯໛
ਠ໛

Ő Ő Ő

Ő

Ő

Ő

෯ኰࢱғĄ
ġ Ő Ő
ӹ෸

Ő

Ő

Ő

ӹ෸

Ő ġ Ő

Ő

Ő

Ő

ഩ।ฮ

ġ Ő Ő

Ő

Ő

Ő

Ő Ő Ő

Ő

Ő

Ő

DE.S

備৬ ǖ
Őǖ
!ӹ෸‫ݡ‬ᅘ‫ڠ‬ᅘࠀྡቬᇀ‫ݡ‬ԩऔຑᅘোቬԮ઻
ቲ‫ࠆو‬ફোᇀ HC0U37683.3122 Ӷኼߢ‫وڊ‬࿮
ફეഓჾ࿒ă
ġǖ
!ӹ෸‫ݡ‬ᅘ‫ڠ‬ᅘࠀྡቬባඵᇀ‫ݡ‬ԩऔ‫و‬ஹქো
ቬԮ઻ቲ‫ࠆو‬ફմ‫ ־‬HC0U37683.3122 Ӷኼߢ
‫وڊ‬࿮ફეഓă
DŽᅑᅢᇀ࣒ฯණᅘਵௗDž
࡯үෳᅋಜ࿮ ǖ
‫ࠟࣝױ‬ཛྷ‫ޗ‬যቲࡢ൉ஙޮࠧ߶٫ዓဳྲդ౹ྍ഼ਈቨߘ
੻Қۨࣆ٫ዓဳྲդ౹࡯үෳᅋಜ࿮໼ᇘLjညต‫و‬٫ዓ
ဳྲդ౹‫࡯و‬үෳᅋಜ࿮ă

Ck-90

ቨᇒާ๖ ǖ৘ྩఛ٫ዓ৶࣒DŽቲ඙Džᅘ࿮ާ๖
ٜāā቙ ǖߟ‫ڍ‬ෛቲ඙ชࢨস৚ۢഘ৶࣒‫ྩلؙ‬
ާ๖ண֎ ǖ৘ྩఛDŽቲ߶Dž୛ᄁᅘ࿮ާ๖
ኢՋٜ቙ ǖቲ߶DŽණ߽Džዔᅑ୛ᄁฎႵഘ‫ݙ‬໎ҽଁ 497 ࠟ
ٞქՍ  ԩ཭
Ck-91

Manufacturer:
CASIO COMPUTER CO., LTD.
6-2, Hon-machi 1-chome
Shibuya-ku, Tokyo 151-8543, Japan

Responsible within the European Union:
CASIO EUROPE GmbH
Casio-Platz 1
22848 Norderstedt, Germany

‫ױ‬Ӷበቝคᅋᅢ FV ߶ࣨă

CASIO COMPUTER CO., LTD.
6-2, Hon-machi 1-chome
Shibuya-ku, Tokyo 151-8543, Japan

SA1404-A

Printed in China

դ౹Ӷኼࠟ ǖHC0U5:78.2::6
Ҕ‫ ״‬ǖ3125 ௰ 5 ᆨ!!!!!ቲ߶ᄩฺ
© 2014 CASIO COMPUTER CO., LTD.



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