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1 PhysicsAdMthsTuto.com

2 PhysicsAdMthsTuto.com Jue Fid the geel solutio of the diffeetil equtio blk d si y ycos si si, d givig you swe i the fom y = f(). (8) 6 *M3544A068*

3 PhysicsAdMthsTuto.com Jue 00 blk 7. () Show tht the tsfomtio z = y tsfoms the diffeetil equtio dy 4yt y d = (I) ito the diffeetil equtio dz zt d = (II) (5) (b) Solve the diffeetil equtio (II) to fid z s fuctio of. (6) (c) Hece obti the geel solutio of the diffeetil equtio (I). () 8 *N35388A084*

4 PhysicsAdMthsTuto.com Jue 00 Questio 7 cotiued blk *N35388A094* 9 Tu ove

5 PhysicsAdMthsTuto.com Jue 0 3. Fid the geel solutio of the diffeetil equtio blk givig you swe i the fom. (8) 6 *P3543A068*

6 PhysicsAdMthsTuto.com Jue 0 7. () Show tht the substitutio tsfoms the diffeetil equtio blk (I) ito the diffeetil equtio (II) (3) (b) By solvig diffeetil equtio (II), fid geel solutio of diffeetil equtio (I) i the fom y = f ( ). (6) Give tht y = t =, (c) fid the vlue of d y d t = () 0 *P4004A008*

7 PhysicsAdMthsTuto.com Jue 0 Questio 7 cotiued blk *P4004A08* Tu ove

8 PhysicsAdMthsTuto.com Jue 03 (R) 5. () Fid, i the fom y = f(), the geel solutio of the equtio blk dy d π Give tht y = t = 3 y t = si, 0 < < π (6) (b) fid the vlue of y t = 6 π, givig you swe i the fom k l b, whee d b e iteges d k is tiol. (4) 6 *P4955A063*

9 PhysicsAdMthsTuto.com Jue 03 (R) Questio 5 cotiued blk *P4955A073* 7 Tu ove

10 PhysicsAdMthsTuto.com Jue () Fid the geel solutio of the diffeetil equtio d y y d = 4 (5) blk (b) Fid the pticul solutio fo which y = 5 t =, givig you swe i the fom y = f(). () (c) (i) Fid the ect vlues of the coodites of the tuig poits of the cuve with equtio y = f(), mkig you method cle. (ii) Sketch the cuve with equtio y = f(), showig the coodites of the tuig poits. (5) *P4349A08*

11 PhysicsAdMthsTuto.com Jue 03 Questio 5 cotiued blk *P4349A038* 3 Tu ove

12 Futhe Pue Mthemtics FP Cdidtes sittig FP my lso equie those fomule listed ude Futhe Pue Mthemtics FP d Coe Mthemtics C C4. Ae of secto A = dθ (pol coodites) Comple umbes θ e i = cosθ isiθ { (cosθ isiθ )} = (cos θ isi θ ) k i e π The oots of z = e give by z =, fo k = 0,,,, Mclui s d Tylo s Seies ( ) f( ) = f(0) f (0) f (0) f (0)!! ( ) ( ) ( ) f( ) = f( ) ( ) f ( ) f ( ) f ( )!! ( ) f( ) = f( ) f ( ) f ( ) f ( )!! e = ep( ) =!! 3 l ( ) = ( ) 3 fo ll 3 5 si = ( ) 3! 5! ( )! 4 cos = ( )! 4! ()! 3 5 ct = ( ) 3 5 ( < ) fo ll fo ll ( ) Edecel AS/A level Mthemtics Fomule List: Futhe Pue Mthemtics FP Issue Septembe 009 9

13 Futhe Pue Mthemtics FP Cdidtes sittig FP my lso equie those fomule listed ude Coe Mthemtics C d C. Summtios = = 3 = = 6 4 ( )( ) ( ) Numeicl solutio of equtios The Newto-Rphso itetio fo solvig f( ) = 0 : f( ) = f ( ) Coics Pbol Rectgul Hypebol Stdd Fom y = 4 y = c Pmetic Fom (t, t) ct, c t Foci (, 0) Not equied Diectices = Not equied Mti tsfomtios Aticlockwise ottio though θ bout O: cosθ siθ siθ cosθ Reflectio i the lie cos θ si θ y = (tθ ) : si θ cos θ I FP, θ will be multiple of Edecel AS/A level Mthemtics Fomule List: Futhe Pue Mthemtics FP Issue Septembe 009

14 Coe Mthemtics C4 Cdidtes sittig C4 my lso equie those fomule listed ude Coe Mthemtics C, C d C3. Itegtio ( costt) f() f( ) d sec k t cot t k k l sec l si cosec l cosec cot, l t( ) sec l sec t, l t( 4 π ) dv du u d = uv v d d d Edecel AS/A level Mthemtics Fomule List: Coe Mthemtics C4 Issue Septembe 009 7

15 Coe Mthemtics C3 Cdidtes sittig C3 my lso equie those fomule listed ude Coe Mthemtics C d C. Logithms d epoetils e l = Tigoometic idetities si ( A ± B) = si Acos B ± cos Asi B cos( A ± B) = cos Acos B si Asi B t A ± t B t ( A ± B) = ( A ± B ( k ) t A t B A B A B si A si B = si cos A B A B si A si B = cos si A B A B cos A cos B = cos cos A B A B cos A cos B = si si π ) Diffeetitio f() t k sec cot cosec f( ) g( ) f () k sec k sec t cosec cosec cot f ( )g( ) f( )g ( ) (g( )) 6 Edecel AS/A level Mthemtics Fomule List: Coe Mthemtics C3 Issue Septembe 009

16 Edecel AS/A level Mthemtics Fomule List: Coe Mthemtics C Issue Septembe Coe Mthemtics C Cdidtes sittig C my lso equie those fomule listed ude Coe Mthemtics C. Cosie ule = b c bc cos A Biomil seies ) ( b b b b b = ( ) whee )!!(! C = = < =, ( ) ( ) ( ) ( ) ( ) Logithms d epoetils b b log log log = Geometic seies u = S = ) ( S = fo < Numeicl itegtio The tpezium ule: b y d h{(y 0 y ) (y y... y )}, whee b h =

17 Coe Mthemtics C Mesutio Sufce e of sphee = 4π Ae of cuved sufce of coe = π slt height Aithmetic seies u = ( )d S = ( l) = [ ( )d] 4 Edecel AS/A level Mthemtics Fomule List: Coe Mthemtics C Issue Septembe 009