امتحانات الشهادة الثانوية العامة فرع: العلوم العامة
|
|
- Erick Lang
- 5 years ago
- Views:
Transcription
1 وزارة التربية والتعليم العالي المديرية العامة للتربية دائرة االمتحانات امتحانات الشهادة الثانوية العامة فرع: العلوم العامة االسم: الرقم: مسابقة في مادة الرياضيات المدة أربع ساعات عدد المسائل: ست مالحظة: - يسمح باستعمال آلة حاسبة غير قابلة للبرمجة او اختزان المعلومات او رسم البيانات. - يستطيع المرش ح اإلجابة بالترتيب الذي يناسبه ( دون االلتزام بترتيب المسائل الواردة في المسابقة(. دورة العام االستثنائي ة الثالثاء آب I- ( poits) I th tabl blow, oly o of th proposd aswrs to ach qustio is corrct. Writ dow th umbr of ach qustio ad giv, with justificatio, th aswr corrspodig to it. Qustios Aswrs a b c d Th particular solutio f() of th diffrtial quatio y '' + y = such that f () = ad f ' (π) = is si si cos si cos For all >, t dt lim = If f is a odd fuctio,cotiuous ovr IR ad such that f ()d, th f ()d Lt M with affi z (z ) b a variabl poit i th compl pla rfrrd to a dirct orthoormal systm. If z z is ral, th M movs o: th circl with ctr O ad radius cpt th poit with affi th -ais cpt th poit with affi th li with quatio y = th y-ais (;)
2 II- ( poits) I th spac rfrrd to a dirct orthoormal systm O; i, j,k, cosidr th poits E ( ; ; ), F( ; ; ), ad th li (d) with paramtric quatios = t, y = t +, z = t whr t is a ral paramtr. Dot by (P) th pla dtrmid by th poit F ad th li (d). ) Vrify that E is o (d). ) Show that y + = is a quatio of (P). ) Cosidr i th pla (P) th circl (C) with ctr F ad radius FE. a- Dtrmi th coordiats of H, th orthogoal projctio of F o (d). b- Dtrmi th coordiats of L, th scod poit of itrsctio of (d) ad (C). c- Writ a systm of paramtric quatios of th bisctor of th agl EFL. ) Lt (Q) b th pla cotaiig (d) ad prpdicular to (P). Dot by ( ) th prpdicular bisctor of th sgmt [EL] i th pla (Q). Writ a systm of paramtric quatios of ( ). III- ( poits) A ur cotais whit balls ad black balls. A gam cosists of two coscutiv drawigs as follows: A ball is slctd radomly i th first drawig. If th ball slctd is whit, it is put back i th ur; othrwis, it is kpt outsid th ur. Two balls ar slctd simultaously ad radomly i th scod drawig. Cosidr th followig vts: W: «Th ball slctd i th first drawig is whit» E: «Th balls slctd i th scod drawig ar whit» F: «Th balls slctd i th scod drawig ar black» G: «Th balls slctd i th scod drawig ar of diffrt colors». ) Calculat P(E/W) ad P(E / W). Dduc that P(E) = 6 9. ) Calculat P(F) ad P(G). ) Kowig that th balls slctd i th scod drawig hav th sam color, calculat th probability that th ball slctd i th first drawig is black. ) I this part, w mark - poits for ach black ball slctd, ad + poits for ach whit ball slctd. Dot by S th sum of poits markd for th two balls slctd i th scod drawig. Calculat th probability that S is positiv.
3 IV- ( poits) Th pla is rfrrd to a dirct orthoormal systm (O ; i, j). Dot by (C) th circl with ctr I(; ) ad radius, ad by (d) th li with quatio y =. Lt L( ; ) b a variabl poit o (C). Dot by N th orthogoal projctio of L o (d) ad by M th midpoit of sgmt [LN]. ) Writ a quatio of (C). ) a- Dtrmi th coordiats of M i trms of α ad β. b- As L movs o (C), prov that M movs o th llips (E) with quatio c- Draw (E). ) Lt (P) b th parabola with vrt V (; ) ad focus F;. a- Show that y is a quatio of (P). b- Draw (P) i th sam systm as (E). ) a- Calculat d. y. b- Dduc th ara of th rgio that is abov th -ais ad boudd by (E) ad (P). ) Lt G ( ; ) b a poit o (P) ad ( ) th tagt at G to (P). Dot by H th poit of (P) whr th tagt to (P) is prpdicular to ( ). Prov that G, H ad F ar colliar. V- ( poits) Cosidr a dirct quilatral triagl ODA with sid qual to. Lt R b th rotatio with ctr O ad agl. Dot by B = R (A), D'= R (D). Lt C b th poit so that D = R(C). (C is th pr-imag of D) ) a- Mak a figur. b- Show that O is th midpoit of [CD'] ad that BC=. ) a- Justify that (AC) is prpdicular to (BD) ad that AC = BD. b- Show that (AD) is paralll to (BC). ) Dot by E th poit of itrsctio of lis (AC) ad (BD). Lt h b th dilatio with ctr E that trasforms A oto C. a- Dtrmi h (D). b- Calculat th ratio of h. ) Lt L b th midpoit of [AD] ad F = h (L). Show that O, E, F ad L ar colliar. ) Lt R b th rotatio with ctr E ad agl. Cosidr S = h R. a- Dtrmi th atur of S ad so its lmts. b- Prov that S (A) = B.
4 VI- (7 poits) A- Lt h b th fuctio dfid o IR as h(). Dot by (C) its rprstativ curv i a orthoormal systm. ) a- Dtrmi lim h(). b- Dtrmi lim h() ad show that th li (d) with quatio y = is a asymptot to (C). ) a- Calculat h () ad st up th tabl of variatios of h. b- Draw (C) ad (d). c- Dduc that for all. B- Lt f b th fuctio dfid as f (). Dot by C its rprstativ curv i aothr orthoormal systm. ) Show that f is dfid ovr IR. ) Dtrmi th asymptots to C. ) Vrify that f () ad st up th tabl of variatios of f. ) a- Writ a quatio of (T), th tagt toc at th poit E with abscissa. b- Vrify that ( ) f. c- Study, accordig to th valus of, th rlativ positios of C with rspct to (T). d- Draw C ad (T). C- For all atural umbrs, dfi th squc ) Show that th squc (u ) is icrasig. ) a- For, vrify that f (). b- Is th squc (u ) covrgt? Justify. (u ) as u f d.
5 Aswr Ky- Math SG Scod Sssio - QI Aswrs N y= Acos+Bsi. f () = A=. f ()= Asi+Bcos. f '(π)= B =. b) t dt (Idtrmiat). L H.R. lim t dt lim lim. f ()d f ()d f ()d f ()d. a) z z z ral th which givs z.z z z z.z z z z z z ad z z. Thrfor, M movs o th -ais cpt poit with affi. b) c) QII Aswrs N For t = ; E is a poit o (d). (t ) (t + ) + = + + = ; F yf thus F (P) th th giv quatio is that of (P). a FHt ;t ; t ; FH V(d) ; (t ) (t ) t ; t th 9 H ; ; b H is th midpoit of EL thus L ; ; c 8 (FH) is th bisctor of EFL. FM mfh m, y m, z m A dirctor vctor of th prpdicular bisctor is P (; ;) ad th prpdicular bisctor passs i poit H; th systm of paramtric quatios is: ; y ;z whr λ is a ral paramtr
6 QIII Aswrs N PE 7 C W C ; P E P(F) P(F W) P(F W) 7 7 P W 6 C 6 ; P(E) P(W E) P(W E). W C ; P(G) P(E) P(F) C G. P W G P(W).P 7 C 8 W G PG P(G) P(S ) P(S ) 7 7 QIV Aswrs N y. L ;, N ; M ;. a b sic L is o (C). Thus M movs o (E). c a p SF thus p =.y-ais is th focal ais, thrfor OR: Th dirctri is th li (D) with quatio y y. y. Dist(R,(D)) = RF with R(; y) (P) y y y. b S figur i c. a d. b Ara = ab d. y = f() = thus f '( ) =, f '( H) thus H ;. 6 GH GF thrfor G, H t F ar colliar.
7 QV Aswrs N a b CÔD DÔD 9 th C, O, D ar colliar ad OC = OD = OD, th O is th midpoit of [CD ]. OB = OC = OD thrfor triagl CBD is right at B. Pythagoras givs : CB CD' BD'. a R(C) = D t R(A) = B (AC) is prpdicular to (BD) ad AC = BD. b R(D) = D, R(A) =B thus AD prpdicular to BD ad (BC) is prpdicular to (BD ), th (AD) ad (BC) ar paralll. a h(a) = C ad (AD) ar paralll to (BC), thrfor h(d) = B. b BC KDA So: K. F midpoit of [BC] ; E, F ad L ar colliar. (OF) ad (OL) ar prpdicular to (BC) O, F ad L ar colliar. a S is th similitud S (E,, ). b S (A) = hr (A) h(r (A)) h(d) Bsic EAD is a right isoscls triagl. QVI Aswrs N a lim h() lim. A b lim h() lim ( ) ad (d) is a asymptot to (C). lim[h() y] lim, a h ().
8 b h() lim thus(c) has a vrtical asymptotic dirctio. c Th miimum of h() is, so h(), th, thus. h() ; so thus D f lim f () lim, lim f () lim. Doc ls droits d'équatios y = t y = sot du asymptots à C. f (). a y = +. b ( )( ) ( ) f () ( ) ( ). c For ; f() ( ),, C itrcpt (T). For ; f() ( ) For = ; C is abov (T). C is blow (T). B d C. u u f d f d f d f d f d kowig f th a b f d ; So (u ) is icrasig. f () thus f () for all. f ()d d si c th u ; lim u lim ; lim u thrfor u is divrgt.
9
Deduce, from this equality, the area of the region bounded by (E).
وزارة التربية والتعليم العالي المديرية العامة للتربية دائرة االمتحانات امتحانات شهادة الثانوية العامة فرع العلوم العامة دورة سنة العادية مسابقة في الرياضيات عدد المسائل : ستة المدة : أربع ساعات مالحظة
More informationدورة الؼام اهتحا ات الشهادة الثا ىية الؼاهة وزارة التربية والتؼلين الؼالي اإلنث يي 07 حسيراى 7102 فرع: الؼلىم الؼاهة
70 الؼادي ة دورة الؼام اهتحا ات الشهادة الثا ىية الؼاهة وزارة التربية والتؼلين الؼالي اإلنث يي 07 حسيراى 70 فرع: الؼلىم الؼاهة الوديرية الؼاهة للتربية دائرة االهتحا ات الرسوية االسن: هسابقة في هادة الرياضيات
More informationامتحانات الشھادة الثانویة العامة الفرع: علوم عامة المدة أربع ساعات
وزارة التربیة والتعلیم العالي المدیریة العامة للتربیة داي رة الامتحانات عدد المساي ل: ست امتحانات الشھادة الثانویة العامة الفرع: علوم عامة مسابقة في مادة الریاضیات المدة أربع ساعات الاسم: الرقم: دورة سنة
More informationPURE MATHEMATICS A-LEVEL PAPER 1
-AL P MATH PAPER HONG KONG EXAMINATIONS AUTHORITY HONG KONG ADVANCED LEVEL EXAMINATION PURE MATHEMATICS A-LEVEL PAPER 8 am am ( hours) This papr must b aswrd i Eglish This papr cosists of Sctio A ad Sctio
More information1985 AP Calculus BC: Section I
985 AP Calculus BC: Sctio I 9 Miuts No Calculator Nots: () I this amiatio, l dots th atural logarithm of (that is, logarithm to th bas ). () Ulss othrwis spcifid, th domai of a fuctio f is assumd to b
More informationTime : 1 hr. Test Paper 08 Date 04/01/15 Batch - R Marks : 120
Tim : hr. Tst Papr 8 D 4//5 Bch - R Marks : SINGLE CORRECT CHOICE TYPE [4, ]. If th compl umbr z sisfis th coditio z 3, th th last valu of z is qual to : z (A) 5/3 (B) 8/3 (C) /3 (D) o of ths 5 4. Th itgral,
More informationامتحانات الشھادة الثانویة العامة الفرع : علوم عامة مسابقة في مادة الریاضیات المدة أربع ساعات
سنة ۲۰۰۷ الا كمالیة الا ستثناي یة I ( points) وزارة التربیة والتعلیم العالي المدیریة العامة للتربیة داي رة الامتحانات امتحانات الشھادة الثانویة العامة الفرع : علوم عامة دورة الاسم: الرقم: مسابقة في مادة
More informationاهتحانات الشهادة الثانىية العاهة الفرع : علىم عاهة هسابقت في هادة الزياضياث االسن: الودة أربع ساعاث
وزارة التربية والتعلين العالي الوديرية العاهة للتربية دائرة االهتحانات اهتحانات الشهادة الثانىية العاهة الفرع : علىم عاهة الدورة العادية للعام هسابقت في هادة الزياضياث االسن: الودة أربع ساعاث عدد الوسائل:سث
More informationMONTGOMERY COLLEGE Department of Mathematics Rockville Campus. 6x dx a. b. cos 2x dx ( ) 7. arctan x dx e. cos 2x dx. 2 cos3x dx
MONTGOMERY COLLEGE Dpartmt of Mathmatics Rockvill Campus MATH 8 - REVIEW PROBLEMS. Stat whthr ach of th followig ca b itgratd by partial fractios (PF), itgratio by parts (PI), u-substitutio (U), or o of
More informationاهتحانات الشهادة الثانىية العاهة الفرع : علىم عاهة هسابقت في هادة الزياضياث الودة أربع ساعاث
9 وزارة التربية والتعلين العالي الوديرية العاهة للتربية دائرة االهتحانات عدد الوسائل : سث اهتحانات الشهادة الثانىية العاهة الفرع : علىم عاهة هسابقت في هادة الزياضياث الودة أربع ساعاث االسن: الرقن: الدورة
More information+ x. x 2x. 12. dx. 24. dx + 1)
INTEGRATION of FUNCTION of ONE VARIABLE INDEFINITE INTEGRAL Fidig th idfiit itgrals Rductio to basic itgrals, usig th rul f ( ) f ( ) d =... ( ). ( )d. d. d ( ). d. d. d 7. d 8. d 9. d. d. d. d 9. d 9.
More information07 - SEQUENCES AND SERIES Page 1 ( Answers at he end of all questions ) b, z = n
07 - SEQUENCES AND SERIES Pag ( Aswrs at h d of all qustios ) ( ) If = a, y = b, z = c, whr a, b, c ar i A.P. ad = 0 = 0 = 0 l a l
More informationChapter 2 Infinite Series Page 1 of 11. Chapter 2 : Infinite Series
Chatr Ifiit Sris Pag of Sctio F Itgral Tst Chatr : Ifiit Sris By th d of this sctio you will b abl to valuat imror itgrals tst a sris for covrgc by alyig th itgral tst aly th itgral tst to rov th -sris
More informationReview Exercises. 1. Evaluate using the definition of the definite integral as a Riemann Sum. Does the answer represent an area? 2
MATHEMATIS --RE Itgral alculus Marti Huard Witr 9 Rviw Erciss. Evaluat usig th dfiitio of th dfiit itgral as a Rima Sum. Dos th aswr rprst a ara? a ( d b ( d c ( ( d d ( d. Fid f ( usig th Fudamtal Thorm
More informationامتحانات الشهادة الثانوية العامة الفرع : العلوم العامة مسابقة في مادة الفيزياء الرقم:
وزارة التربية والتعليم العالي المديرية العامة للتربية دائرة االمتحانات امتحانات الشهادة الثانوية العامة الفرع : العلوم العامة دورة العام 5 االستثنائية الخميس اب 5 االسم: مسابقة في مادة الفيزياء الرقم:
More informationThis exam is formed of three exercises in three pages numbered from 1 to 3. The use of a non-programmable calculator is recommended.
0 وزارة التربية والتعليم العالي المديرية العامة للتربية دائرة االمتحانات امتحانات الشهادة الثانوية العامة الفرع : علوم الحياة الدورة العادية للعام مسابقة في مادة الفيزياء المدة ساعتان االسم: الرقم: This
More informationWBJEEM MATHEMATICS. Q.No. μ β γ δ 56 C A C B
WBJEEM - MATHEMATICS Q.No. μ β γ δ C A C B B A C C A B C A B B D B 5 A C A C 6 A A C C 7 B A B D 8 C B B C 9 A C A A C C A B B A C A B D A C D A A B C B A A 5 C A C B 6 A C D C 7 B A C A 8 A A A A 9 A
More informationThis exam is formed of three exercises in three pages. The Use of non-programmable calculators is allowed.
008 وزارة التربية والتعليم العالي المديرية العامة للتربية دائرة االمتحانات امتحانات الشهادة الثانوية العامة الفرع : علوم الحياة مسابقة في مادة الفيزياء المدة ساعتان االسم: الرقم: الدورة اإلستثنائية للعام
More informationH2 Mathematics Arithmetic & Geometric Series ( )
H Mathmatics Arithmtic & Gomtric Sris (08 09) Basic Mastry Qustios Arithmtic Progrssio ad Sris. Th rth trm of a squc is 4r 7. (i) Stat th first four trms ad th 0th trm. (ii) Show that th squc is a arithmtic
More informationChapter At each point (x, y) on the curve, y satisfies the condition
Chaptr 6. At ach poit (, y) o th curv, y satisfis th coditio d y 6; th li y = 5 is tagt to th curv at th poit whr =. I Erciss -6, valuat th itgral ivolvig si ad cosi.. cos si. si 5 cos 5. si cos 5. cos
More informationامتحانات الشهادة الثانوية العامة الفرع: علوم عامة مسابقة في مادة الكيمياء المدة: ساعتان
وزارة التربية والتعليم العالي المديرية العامة للتربية دائرة االمتحانات الرسمية امتحانات الشهادة الثانوية العامة الفرع: علوم عامة مسابقة في مادة الكيمياء المدة: ساعتان االسم: الرقم: دورة العام 72 العادي
More informationامتحانات الشهادة الثانوية العامة فرع العلوم العامة مسابقة في مادة الفيزياء المدة ثالث ساعات
وزارة التربية والتعليم العالي المديرية العامة للتربية دائرة االمتحانات امتحانات الشهادة الثانوية العامة فرع العلوم العامة مسابقة في مادة الفيزياء المدة ثالث ساعات االسم: الرقم: دورة سنة 008 العادية This
More informationThis exam is formed of four exercises in four pages numbered from 1 to 4. The use of non-programmable calculator is recommended,
وزارة التربية والتعليم العالي المديرية العامة للتربية دائرة االمتحانات الرسمية امتحانات الشهادة الثانوية العامة الفرع : علوم عامة مسابقة في مادة الفيزياء المدة ثالث ساعات االسم: الرقم: دورة العام 6 العادي
More informationChapter Five. More Dimensions. is simply the set of all ordered n-tuples of real numbers x = ( x 1
Chatr Fiv Mor Dimsios 51 Th Sac R W ar ow rard to mov o to sacs of dimsio gratr tha thr Ths sacs ar a straightforward gralizatio of our Euclida sac of thr dimsios Lt b a ositiv itgr Th -dimsioal Euclida
More informationOption 3. b) xe dx = and therefore the series is convergent. 12 a) Divergent b) Convergent Proof 15 For. p = 1 1so the series diverges.
Optio Chaptr Ercis. Covrgs to Covrgs to Covrgs to Divrgs Covrgs to Covrgs to Divrgs 8 Divrgs Covrgs to Covrgs to Divrgs Covrgs to Covrgs to Covrgs to Covrgs to 8 Proof Covrgs to π l 8 l a b Divrgt π Divrgt
More information1973 AP Calculus BC: Section I
97 AP Calculus BC: Scio I 9 Mius No Calculaor No: I his amiaio, l dos h aural logarihm of (ha is, logarihm o h bas ).. If f ( ) =, h f ( ) = ( ). ( ) + d = 7 6. If f( ) = +, h h s of valus for which f
More informationامتحانات الشهادة الثانوية العامة الفرع : علوم الحياة مسابقة في مادة الفيزياء المدة: ساعتان
وزارة التربية والتعليم العالي المديرية العامة للتربية دائرة االمتحانات الرسمية امتحانات الشهادة الثانوية العامة الفرع : علوم الحياة مسابقة في مادة الفيزياء المدة: ساعتان االسم: الرقم: دورة العام 06 اإلستثنائية
More informationStudent s Printed Name:
Studt s Pritd Nam: Istructor: CUID: Sctio: Istructios: You ar ot prmittd to us a calculator o ay portio of this tst. You ar ot allowd to us a txtbook, ots, cll pho, computr, or ay othr tchology o ay portio
More informationProblem Value Score Earned No/Wrong Rec -3 Total
GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL & COMPUTER ENGINEERING ECE6 Fall Quiz # Writt Eam Novmr, NAME: Solutio Kys GT Usram: LAST FIRST.g., gtiit Rcitatio Sctio: Circl t dat & tim w your Rcitatio
More informationSOLVED EXAMPLES. Ex.1 If f(x) = , then. is equal to- Ex.5. f(x) equals - (A) 2 (B) 1/2 (C) 0 (D) 1 (A) 1 (B) 2. (D) Does not exist = [2(1 h)+1]= 3
SOLVED EXAMPLES E. If f() E.,,, th f() f() h h LHL RHL, so / / Lim f() quls - (D) Dos ot ist [( h)+] [(+h) + ] f(). LHL E. RHL h h h / h / h / h / h / h / h As.[C] (D) Dos ot ist LHL RHL, so giv it dos
More informationاالسن: الرقن: This exam is formed of three obligatory exercises in two pages. Non- programmable calculators are allowed.
00 اإلستثنائية وزارة التربية والتعلين العالي الوديرية العاهة للتربية دائرة االهتحانات الشهادة الوتىسطة هسابقة في هادة الفيسياء الودة: ساعة واحدة االسن: الرقن: دورة العام This exam is formed of three obligatory
More information1973 AP Calculus AB: Section I
97 AP Calculus AB: Sction I 9 Minuts No Calculator Not: In this amination, ln dnots th natural logarithm of (that is, logarithm to th bas ).. ( ) d= + C 6 + C + C + C + C. If f ( ) = + + + and ( ), g=
More informationNET/JRF, GATE, IIT JAM, JEST, TIFR
Istitut for NET/JRF, GATE, IIT JAM, JEST, TIFR ad GRE i PHYSICAL SCIENCES Mathmatical Physics JEST-6 Q. Giv th coditio φ, th solutio of th quatio ψ φ φ is giv by k. kφ kφ lφ kφ lφ (a) ψ (b) ψ kφ (c) ψ
More information( ) ( ) ( ) 2011 HSC Mathematics Solutions ( 6) ( ) ( ) ( ) π π. αβ = = 2. α β αβ. Question 1. (iii) 1 1 β + (a) (4 sig. fig.
HS Mathmatics Solutios Qustio.778.78 ( sig. fig.) (b) (c) ( )( + ) + + + + d d (d) l ( ) () 8 6 (f) + + + + ( ) ( ) (iii) β + + α α β αβ 6 (b) si π si π π π +,π π π, (c) y + dy + d 8+ At : y + (,) dy 8(
More informationASSERTION AND REASON
ASSERTION AND REASON Som qustios (Assrtio Rso typ) r giv low. Ech qustio cotis Sttmt (Assrtio) d Sttmt (Rso). Ech qustio hs choics (A), (B), (C) d (D) out of which ONLY ONE is corrct. So slct th corrct
More informationA Review of Complex Arithmetic
/0/005 Rviw of omplx Arithmti.do /9 A Rviw of omplx Arithmti A omplx valu has both a ral ad imagiary ompot: { } ad Im{ } a R b so that w a xprss this omplx valu as: whr. a + b Just as a ral valu a b xprssd
More informationDTFT Properties. Example - Determine the DTFT Y ( e ) of n. Let. We can therefore write. From Table 3.1, the DTFT of x[n] is given by 1
DTFT Proprtis Exampl - Dtrmi th DTFT Y of y α µ, α < Lt x α µ, α < W ca thrfor writ y x x From Tabl 3., th DTFT of x is giv by ω X ω α ω Copyright, S. K. Mitra Copyright, S. K. Mitra DTFT Proprtis DTFT
More informationNational Quali cations
PRINT COPY OF BRAILLE Ntiol Quli ctios AH08 X747/77/ Mthmtics THURSDAY, MAY INSTRUCTIONS TO CANDIDATES Cdidts should tr thir surm, form(s), dt of birth, Scottish cdidt umbr d th m d Lvl of th subjct t
More informationLECTURE 13 Filling the bands. Occupancy of Available Energy Levels
LUR 3 illig th bads Occupacy o Availabl rgy Lvls W hav dtrmid ad a dsity o stats. W also d a way o dtrmiig i a stat is illd or ot at a giv tmpratur. h distributio o th rgis o a larg umbr o particls ad
More informationNational Quali cations
Ntiol Quli ctios AH07 X77/77/ Mthmtics FRIDAY, 5 MAY 9:00 AM :00 NOON Totl mrks 00 Attmpt ALL qustios. You my us clcultor. Full crdit will b giv oly to solutios which coti pproprit workig. Stt th uits
More informationمسابقة في الكيمياء االسم: المدة ساعتان الرقم:
امتحانات شهادة الثانوية العامة فرع العلوم العامة دورة سنة 4002 العادية وزارة التربية و التعليم العالي المديرية العامة للتربية دائرة االمتحانات مسابقة في الكيمياء االسم: المدة ساعتان الرقم: This Exam Includes
More informationSession : Plasmas in Equilibrium
Sssio : Plasmas i Equilibrium Ioizatio ad Coductio i a High-prssur Plasma A ormal gas at T < 3000 K is a good lctrical isulator, bcaus thr ar almost o fr lctros i it. For prssurs > 0.1 atm, collisio amog
More informationz 1+ 3 z = Π n =1 z f() z = n e - z = ( 1-z) e z e n z z 1- n = ( 1-z/2) 1+ 2n z e 2n e n -1 ( 1-z )/2 e 2n-1 1-2n -1 1 () z
Sris Expasio of Rciprocal of Gamma Fuctio. Fuctios with Itgrs as Roots Fuctio f with gativ itgrs as roots ca b dscribd as follows. f() Howvr, this ifiit product divrgs. That is, such a fuctio caot xist
More information1997 AP Calculus AB: Section I, Part A
997 AP Calculus AB: Sction I, Part A 50 Minuts No Calculator Not: Unlss othrwis spcifid, th domain of a function f is assumd to b th st of all ral numbrs for which f () is a ral numbr.. (4 6 ) d= 4 6 6
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) by D. Klain Vrsion 207.0.05 Corrctions and commnts ar wlcom. Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix A A k I + A + k!
More informationالمادة: الریاضیات الشھادة: المتوسطة نموذج رقم -۱- قسم : الریاضیات
الھیي ة الا كادیمی ة المشتركة قسم : الریاضیات المادة: الریاضیات الشھادة: المتوسطة نموذج رقم -۱- المد ة : ساعتان I - ( points) نموذج مسابقة (یراعي تعلیق الدروس والتوصیف المعد ل للعام الدراسي ۲۰۱۷-۲۰۱٦ وحتى
More informationSTIRLING'S 1 FORMULA AND ITS APPLICATION
MAT-KOL (Baja Luka) XXIV ()(08) 57-64 http://wwwimviblorg/dmbl/dmblhtm DOI: 075/МК80057A ISSN 0354-6969 (o) ISSN 986-588 (o) STIRLING'S FORMULA AND ITS APPLICATION Šfkt Arslaagić Sarajvo B&H Abstract:
More informationEAcos θ, where θ is the angle between the electric field and
8.4. Modl: Th lctric flux flows out of a closd surfac around a rgion of spac containing a nt positiv charg and into a closd surfac surrounding a nt ngativ charg. Visualiz: Plas rfr to Figur EX8.4. Lt A
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) by Dan Klain Vrsion 28928 Corrctions and commnts ar wlcom Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix () A A k I + A + k!
More informationMATHEMATICS PAPER IIB COORDINATE GEOMETRY AND CALCULUS. Note: This question paper consists of three sections A, B and C.
MATHEMATICS PAPER IIB COORDINATE GEOMETRY AND CALCULUS. Tim: 3hrs Ma. Marks.75 Not: This qustion papr consists of thr sctions A, B and C. SECTION -A Vry Short Answr Typ Qustions. 0 X = 0. Find th condition
More information2008 AP Calculus BC Multiple Choice Exam
008 AP Multipl Choic Eam Nam 008 AP Calculus BC Multipl Choic Eam Sction No Calculator Activ AP Calculus 008 BC Multipl Choic. At tim t 0, a particl moving in th -plan is th acclration vctor of th particl
More informationIntroduction to Quantum Information Processing. Overview. A classical randomised algorithm. q 3,3 00 0,0. p 0,0. Lecture 10.
Itroductio to Quatum Iformatio Procssig Lctur Michl Mosca Ovrviw! Classical Radomizd vs. Quatum Computig! Dutsch-Jozsa ad Brsti- Vazirai algorithms! Th quatum Fourir trasform ad phas stimatio A classical
More informationGRADE 12 JUNE 2016 MATHEMATICS P2
NATIONAL SENIOR CERTIFICATE GRADE 1 JUNE 016 MATHEMATICS P MARKS: 150 TIME: 3 hours *MATHE* This questio paper cosists of 11 pages, icludig 1 iformatio sheet, ad a SPECIAL ANSWER BOOK. MATHEMATICS P (EC/JUNE
More information5. B To determine all the holes and asymptotes of the equation: y = bdc dced f gbd
1. First you chck th domain of g x. For this function, x cannot qual zro. Thn w find th D domain of f g x D 3; D 3 0; x Q x x 1 3, x 0 2. Any cosin graph is going to b symmtric with th y-axis as long as
More informationVICTORIA JUNIOR COLLEGE Preliminary Examination. Paper 1 September 2015
VICTORIA JUNIOR COLLEGE Prelimiary Eamiatio MATHEMATICS (Higher ) 70/0 Paper September 05 Additioal Materials: Aswer Paper Graph Paper List of Formulae (MF5) 3 hours READ THESE INSTRUCTIONS FIRST Write
More informationCalculus & analytic geometry
Calculus & aalytic gomtry B Sc MATHEMATICS Admissio owards IV SEMESTER CORE COURSE UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION CALICUT UNIVERSITYPO, MALAPPURAM, KERALA, INDIA 67 65 5 School of Distac
More informationpage 11 equation (1.2-10c), break the bar over the right side in the middle
I. Corrctios Lst Updtd: Ju 00 Complx Vrils with Applictios, 3 rd ditio, A. Dvid Wusch First Pritig. A ook ought for My 007 will proly first pritig With Thks to Christi Hos of Swd pg qutio (.-0c), rk th
More informationAdditional Math (4047) Paper 2 (100 marks) y x. 2 d. d d
Aitional Math (07) Prpar b Mr Ang, Nov 07 Fin th valu of th constant k for which is a solution of th quation k. [7] Givn that, Givn that k, Thrfor, k Topic : Papr (00 marks) Tim : hours 0 mins Nam : Aitional
More informationCOLLECTION OF SUPPLEMENTARY PROBLEMS CALCULUS II
COLLECTION OF SUPPLEMENTARY PROBLEMS I. CHAPTER 6 --- Trscdtl Fuctios CALCULUS II A. FROM CALCULUS BY J. STEWART:. ( How is th umbr dfid? ( Wht is pproimt vlu for? (c ) Sktch th grph of th turl potil fuctios.
More informationThis exam is formed of three exercises The use of a non-programmable calculator is recommended
وزارة التربیة والتعلیم العالي المدیریة العامة للتربیة داي رة الامتحانات امتحانات الشھادة الثانویة العامة فرع علوم الحیاة مسابقة في مادة الفیزیاء المدة: ساعتان الاسم: الرقم: دورة سنة ۲۰۰٦ العادیة This exam
More informationChapter 3 Fourier Series Representation of Periodic Signals
Chptr Fourir Sris Rprsttio of Priodic Sigls If ritrry sigl x(t or x[] is xprssd s lir comitio of som sic sigls th rspos of LI systm coms th sum of th idividul rsposs of thos sic sigls Such sic sigl must:
More informationSection 11.6: Directional Derivatives and the Gradient Vector
Sction.6: Dirctional Drivativs and th Gradint Vctor Practic HW rom Stwart Ttbook not to hand in p. 778 # -4 p. 799 # 4-5 7 9 9 35 37 odd Th Dirctional Drivativ Rcall that a b Slop o th tangnt lin to th
More informationPhysics 302 Exam Find the curve that passes through endpoints (0,0) and (1,1) and minimizes 1
Physis Exam 6. Fid th urv that passs through dpoits (, ad (, ad miimizs J [ y' y ]dx Solutio: Si th itgrad f dos ot dpd upo th variabl of itgratio x, w will us th sod form of Eulr s quatio: f f y' y' y
More informationMock Exam 2 Section A
Mock Eam Mock Eam Sction A. Rfrnc: HKDSE Math M Q ( + a) n n n n + C ( a) + C( a) + C ( a) + nn ( ) a nn ( )( n ) a + na + + + 6 na 6... () \ nn ( ) a n( n )( n ) a + 6... () 6 6 From (): a... () n Substituting
More informationProbability & Statistics,
Probability & Statistics, BITS Pilai K K Birla Goa Campus Dr. Jajati Kshari Sahoo Dpartmt of Mathmatics BITS Pilai, K K Birla Goa Campus Poisso Distributio Poisso Distributio: A radom variabl X is said
More informationln x = n e = 20 (nearest integer)
H JC Prlim Solutios 6 a + b y a + b / / dy a b 3/ d dy a b at, d Giv quatio of ormal at is y dy ad y wh. d a b () (,) is o th curv a+ b () y.9958 Qustio Solvig () ad (), w hav a, b. Qustio d.77 d d d.77
More informationENJOY MATHEMATICS WITH SUHAAG SIR
R-, OPPOSITE RAILWAY TRACK, ZONE-, M. P. NAGAR, BHOPAL :(0755) 00 000, 80 5 888 IIT-JEE, AIEEE (WITH TH, TH 0 TH, TH & DROPPERS ) www.tkoclasss.com Pag: SOLUTION OF IITJEE 0; PAPER ; BHARAT MAIN SABSE
More informationOrdinary Differential Equations
Basi Nomlatur MAE 0 all 005 Egirig Aalsis Ltur Nots o: Ordiar Diffrtial Equatios Author: Profssor Albrt Y. Tog Tpist: Sakurako Takahashi Cosidr a gral O. D. E. with t as th idpdt variabl, ad th dpdt variabl.
More informationMixed Mode Oscillations as a Mechanism for Pseudo-Plateau Bursting
Mixd Mod Oscillatios as a Mchaism for Psudo-Platau Burstig Richard Brtram Dpartmt of Mathmatics Florida Stat Uivrsity Tallahass, FL Collaborators ad Support Thodor Vo Marti Wchslbrgr Joël Tabak Uivrsity
More informationPart B: Transform Methods. Professor E. Ambikairajah UNSW, Australia
Part B: Trasform Mthods Chaptr 3: Discrt-Tim Fourir Trasform (DTFT) 3. Discrt Tim Fourir Trasform (DTFT) 3. Proprtis of DTFT 3.3 Discrt Fourir Trasform (DFT) 3.4 Paddig with Zros ad frqucy Rsolutio 3.5
More informationOn the approximation of the constant of Napier
Stud. Uiv. Babş-Bolyai Math. 560, No., 609 64 O th approximatio of th costat of Napir Adri Vrscu Abstract. Startig from som oldr idas of [] ad [6], w show w facts cocrig th approximatio of th costat of
More information1 1 1 p q p q. 2ln x x. in simplest form. in simplest form in terms of x and h.
NAME SUMMER ASSIGNMENT DUE SEPTEMBER 5 (FIRST DAY OF SCHOOL) AP CALC AB Dirctions: Answr all of th following qustions on a sparat sht of papr. All work must b shown. You will b tstd on this matrial somtim
More informationDiscrete Mathematics and Probability Theory Fall 2014 Anant Sahai Homework 11. This homework is due November 17, 2014, at 12:00 noon.
EECS 70 Discrt Mathmatics ad Probability Thory Fall 2014 Aat Sahai Homwork 11 This homwork is du Novmbr 17, 2014, at 12:00 oo. 1. Sctio Rollcall! I your slf-gradig for this qustio, giv yourslf a 10, ad
More informationThis exam is formed of three exercises in three pages. The use of non-programmable calculators is recommended.
011 وزارة التربية والتعلين العالي الوديرية العاهة للتربية دائرة االهتحانات اهتحانات الشهادة الثانىية العاهة الفرع : علىم الحياة مسابقة في مادة الفيزياء المدة ساعتان االسن: الرقن: الدورة العادية للعام This
More information10. Joint Moments and Joint Characteristic Functions
0 Joit Momts ad Joit Charactristic Fctios Followig sctio 6 i this sctio w shall itrodc varios paramtrs to compactly rprst th iformatio cotaid i th joit pdf of two rvs Giv two rvs ad ad a fctio g x y dfi
More informationRestricted Factorial And A Remark On The Reduced Residue Classes
Applid Mathmatics E-Nots, 162016, 244-250 c ISSN 1607-2510 Availabl fr at mirror sits of http://www.math.thu.du.tw/ am/ Rstrictd Factorial Ad A Rmark O Th Rducd Rsidu Classs Mhdi Hassai Rcivd 26 March
More informationGRADE 12 JUNE 2017 MATHEMATICS P2
NATIONAL SENIOR CERTIFICATE GRADE 1 JUNE 017 MATHEMATICS P MARKS: 150 TIME: 3 hours *JMATHE* This questio paper cosists of 14 pages, icludig 1 page iformatio sheet, ad a SPECIAL ANSWER BOOK. MATHEMATICS
More information(HELD ON 22nd MAY SUNDAY 2016) MATHEMATICS CODE - 2 [PAPER -2]
QUESTION PAPER WITH SOLUTION OF JEE ADVANCED - 6 7. Lt P (HELD ON d MAY SUNDAY 6) FEEL THE POWER OF OUR KNOWLEDGE & EXPERIENCE Our Top clss IITi fculty tm promiss to giv you uthtic swr ky which will b
More informationWashington State University
he 3 Ktics ad Ractor Dsig Sprg, 00 Washgto Stat Uivrsity Dpartmt of hmical Egrg Richard L. Zollars Exam # You will hav o hour (60 muts) to complt this xam which cosists of four (4) problms. You may us
More informationAn Introduction to Asymptotic Expansions
A Itroductio to Asmptotic Expasios R. Shaar Subramaia Asmptotic xpasios ar usd i aalsis to dscrib th bhavior of a fuctio i a limitig situatio. Wh a fuctio ( x, dpds o a small paramtr, ad th solutio of
More informationSolution to 1223 The Evil Warden.
Solutio to 1 Th Evil Ward. This is o of thos vry rar PoWs (I caot thik of aothr cas) that o o solvd. About 10 of you submittd th basic approach, which givs a probability of 47%. I was shockd wh I foud
More informationQuantum Mechanics & Spectroscopy Prof. Jason Goodpaster. Problem Set #2 ANSWER KEY (5 questions, 10 points)
Chm 5 Problm St # ANSWER KEY 5 qustios, poits Qutum Mchics & Spctroscopy Prof. Jso Goodpstr Du ridy, b. 6 S th lst pgs for possibly usful costts, qutios d itgrls. Ths will lso b icludd o our futur ms..
More informationLinear Algebra Existence of the determinant. Expansion according to a row.
Lir Algbr 2270 1 Existc of th dtrmit. Expsio ccordig to row. W dfi th dtrmit for 1 1 mtrics s dt([]) = (1) It is sy chck tht it stisfis D1)-D3). For y othr w dfi th dtrmit s follows. Assumig th dtrmit
More informationWorksheet: Taylor Series, Lagrange Error Bound ilearnmath.net
Taylor s Thorm & Lagrag Error Bouds Actual Error This is th ral amout o rror, ot th rror boud (worst cas scario). It is th dirc btw th actual () ad th polyomial. Stps:. Plug -valu ito () to gt a valu.
More informationThis exam is formed of three exercises in three pages. The use of a non-programmable calculator is allowed
وزارة التربية والتعلين العالي الوديرية العاهة للتربية دائرة االهتحانات اهتحانات الشهادة الثانىية العاهة الفرع : علىم الحياة مسابقة في مادة الفيزياء المدة ساعتان االسن: الرقن: الدورة اإلستثنائية للعام 0
More informationSOLUTIONS TO CHAPTER 2 PROBLEMS
SOLUTIONS TO CHAPTER PROBLEMS Problm.1 Th pully of Fig..33 is composd of fiv portios: thr cylidrs (of which two ar idtical) ad two idtical co frustum sgmts. Th mass momt of irtia of a cylidr dfid by a
More informationMATHEMATICS PAPER IB COORDINATE GEOMETRY(2D &3D) AND CALCULUS. Note: This question paper consists of three sections A,B and C.
MATHEMATICS PAPER IB COORDINATE GEOMETRY(D &D) AND CALCULUS. TIME : hrs Ma. Marks.75 Not: This qustion papr consists of thr sctions A,B and C. SECTION A VERY SHORT ANSWER TYPE QUESTIONS. 0X =0.If th portion
More informationChapter 1. Chapter 10. Chapter 2. Chapter 11. Chapter 3. Chapter 12. Chapter 4. Chapter 13. Chapter 5. Chapter 14. Chapter 6. Chapter 7.
Chaptr Binomial Epansion Chaptr 0 Furthr Probability Chaptr Limits and Drivativs Chaptr Discrt Random Variabls Chaptr Diffrntiation Chaptr Discrt Probability Distributions Chaptr Applications of Diffrntiation
More informationاهتحانات الشهادة الثانىية العاهة الفرع: علىم الحياة هسابقة في هادة الفيسياء الرقن:
وزارة التربية والتعلين العالي الوذيرية العاهة للتربية دائرة االهتحانات الرسوية اهتحانات الشهادة الثانىية العاهة الفرع: علىم الحياة دورة العام 70 العادية الخويس 0 حسيراى 70 االسن: هسابقة في هادة الفيسياء
More informationChapter 4 - The Fourier Series
M. J. Robrts - 8/8/4 Chaptr 4 - Th Fourir Sris Slctd Solutios (I this solutio maual, th symbol,, is usd for priodic covolutio bcaus th prfrrd symbol which appars i th txt is ot i th fot slctio of th word
More informationExercises for lectures 23 Discrete systems
Exrciss for lcturs 3 Discrt systms Michal Šbk Automatické říí 06 30-4-7 Stat-Spac a Iput-Output scriptios Automatické říí - Kybrtika a robotika Mols a trasfrs i CSTbx >> F=[ ; 3 4]; G=[ ;]; H=[ ]; J=0;
More informationThis exam is formed of four exercises in four pages The use of non-programmable calculator is recommended
وزارة التربية والتعلين العالي الوديرية العاهة للتربية دائرة االهتحانات اهتحانات الشهادة الثانىية العاهة الفرع : علىم عاهة مسابقة في مادة الفيزياء المدة ثالث ساعات االسن: الرقن: الدورة اإلستثنائية للعام
More informationCalculus II (MAC )
Calculus II (MAC232-2) Tst 2 (25/6/25) Nam (PRINT): Plas show your work. An answr with no work rcivs no crdit. You may us th back of a pag if you nd mor spac for a problm. You may not us any calculators.
More information(Reference: sections in Silberberg 5 th ed.)
ALE. Atomic Structur Nam HEM K. Marr Tam No. Sctio What is a atom? What is th structur of a atom? Th Modl th structur of a atom (Rfrc: sctios.4 -. i Silbrbrg 5 th d.) Th subatomic articls that chmists
More informationMath 34A. Final Review
Math A Final Rviw 1) Us th graph of y10 to find approimat valus: a) 50 0. b) y (0.65) solution for part a) first writ an quation: 50 0. now tak th logarithm of both sids: log() log(50 0. ) pand th right
More information(A) 1 (B) 1 + (sin 1) (C) 1 (sin 1) (D) (sin 1) 1 (C) and g be the inverse of f. Then the value of g'(0) is. (C) a. dx (a > 0) is
[STRAIGHT OBJECTIVE TYPE] l Q. Th vlu of h dfii igrl, cos d is + (si ) (si ) (si ) Q. Th vlu of h dfii igrl si d whr [, ] cos cos Q. Vlu of h dfii igrl ( si Q. L f () = d ( ) cos 7 ( ) )d d g b h ivrs
More informationSolution: APPM 1360 Final (150 pts) Spring (60 pts total) The following parts are not related, justify your answers:
APPM 6 Final 5 pts) Spring 4. 6 pts total) Th following parts ar not rlatd, justify your answrs: a) Considr th curv rprsntd by th paramtric quations, t and y t + for t. i) 6 pts) Writ down th corrsponding
More informationStatistics 3858 : Likelihood Ratio for Exponential Distribution
Statistics 3858 : Liklihood Ratio for Expotial Distributio I ths two xampl th rjctio rjctio rgio is of th form {x : 2 log (Λ(x)) > c} for a appropriat costat c. For a siz α tst, usig Thorm 9.5A w obtai
More informationCLASS XI CHAPTER 3. Theorem 1 (sine formula) In any triangle, sides are proportional to the sines of the opposite angles. That is, in a triangle ABC
CLSS XI ur I CHPTER.6. Proofs d Simpl pplictios of si d cosi formul Lt C b trigl. y gl w m t gl btw t sids d C wic lis btw 0 d 80. T gls d C r similrly dfid. T sids, C d C opposit to t vrtics C, d will
More informationThis exam is formed of four exercises in four pages numbered from 1 to 4 The use of non-programmable calculator is recommended
وزارة التربية والتعلين العالي الوديرية العاهة للتربية دائرة االهتحانات اهتحانات الشهادة الثانىية العاهة الفرع : علىم عاهة مسابقة في مادة الفيزياء المدة ثالث ساعات االسن: الرقن: الدورة العادية للعام This
More information