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1 physicsadmathstuto.com

2 physicsadmathstuto.com Jue 005. A cuve has equatio blak x + xy 3y + 16 = 0. dy Fid the coodiates of the poits o the cuve whee 0. dx = (7) Q (Total 7 maks) *N03B034* 3 Tu ove

3 physicsadmathstuto.com Jauay A cuve C is descibed by the equatio blak 3x +4y x +6xy 5=0. Fid a equatio of the taget to C at the poit (1, ), givig you aswe i the fom ax + by + c = 0, whee a, b ad c ae iteges. (7) *N3553A00*

4 physicsadmathstuto.com Jue A cuve C is descibed by the equatio blak 3x y +x 3y +5=0. Fid a equatio of the omal to C at the poit (0, 1), givig you aswe i the fom ax + by + c = 0, whee a, b ad c ae iteges. (7) *N3563A00*

5 physicsadmathstuto.com Jauay A cuve has paametic equatios x =7cost cos 7t, y =7sit si7t, <t <. 8 3 d y (a) Fid a expessio fo i tems of t. You eed ot simplify you aswe. dx (b) Fid a equatio of the omal to the cuve at the poit whee t. 6 Give you aswe i its simplest exact fom. (3) (6) blak 6 *N356A060*

6 physicsadmathstuto.com Jauay A set of cuves is give by the equatio si x +cosy = 0.5. d y (a) Use implicit diffeetiatio to fid a expessio fo. dx Fo <x< ad <y<, d y (b) fid the coodiates of the poits whee 0. dx () (5) blak 10 *N356A0100*

7 physicsadmathstuto.com Jauay (a) Give that y = x, ad usig the esult x =e xl d y x, o othewise, show that l. dx () blak (b) Fid the gadiet of the cuve with equatio y = (x) at the poit with coodiates (,16). (4) 1 *N356A010*

8 physicsadmathstuto.com Jauay A cuve is descibed by the equatio blak. (a) Fid the coodiates of the two poits o the cuve whee x = 8. (3) (b) Fid the gadiet of the cuve at each of these poits. (6) 10 *N68A0104*

9 physicsadmathstuto.com Jue A cuve has equatio 3x y + xy = 4. The poits P ad Q lie o the cuve. The gadiet of the taget to the cuve is at P ad at Q. 8 3 blak (a) Use implicit diffeetiatio to show that y x = 0 at P ad at Q. (6) (b) Fid the coodiates of P ad Q. (3) 10 *H3047A0108*

10 physicsadmathstuto.com Jauay A cuve C has the equatio y 3y = x dy (a) Fid i tems of x ad y. dx (b) Hece fid the gadiet of C at the poit whee y = 3. (4) (3) blak *N31013A08*

11 physicsadmathstuto.com Jue The cuve C has the equatio ye x = x + y. blak (a) Fid d y dx i tems of x ad y. (5) The poit P o C has coodiates (0, 1). (b) Fid the equatio of the omal to C at P, givig you aswe i the fom ax + by + c = 0, whee a, b ad c ae iteges. (4) 10 *H3465A0108*

12 physicsadmathstuto.com Jue 009 Questio 4 cotiued blak *H3465A0118* 11 Tu ove

13 physicsadmathstuto.com Jauay The cuve C has the equatio cos x + cos 3y = 1, x, 0 y (a) Fid d y dx i tems of x ad y. (3) blak The poit P lies o C whee x 6. (b) Fid the value of y at P. (3) (c) Fid the equatio of the taget to C at P, givig you aswe i the fom ax + by + c = 0, whee a, b ad c ae iteges. (3) 8 *N3538A088*

14 physicsadmathstuto.com Jauay 010 Questio 3 cotiued blak *N3538A098* 9 Tu ove

15 physicsadmathstuto.com Jue A cuve C has equatio x + y = Fid the exact value of d y dx at the poit o C with coodiates (3, ). (7) xy blak 8 *H35386A083*

16 physicsadmathstuto.com Jue Fid the gadiet of the cuve with equatio blak l y = x l x, x 0, y 0 at the poit o the cuve whee x =. Give you aswe as a exact value. (7) 1 *P38160A014*

17 physicsadmathstuto.com Jauay The cuve C has the equatio x + 3y + 3x y = 4x. The poit P o the cuve has coodiates ( 1, 1). blak (a) Fid the gadiet of the cuve at P. (5) (b) Hece fid the equatio of the omal to C at P, givig you aswe i the fom ax + by + c = 0, whee a, b ad c ae iteges. (3) *P40085A08*

18 physicsadmathstuto.com Jue The cuve C has equatio blak 3 16y + 9x y 54x = 0 (a) Fid d y dx i tems of x ad y. (5) (b) Fid the coodiates of the poits o C whee d y dx = 0. (7) 16 *P41484A0163*

19 physicsadmathstuto.com Jue 013 (R)

20 physicsadmathstuto.com Jue A cuve is descibed by the equatio blak x + 4xy + y + 7 = 0 (a) Fid d y dx i tems of x ad y. (5) A poit Q lies o the cuve. The taget to the cuve at Q is paallel to the y-axis. Give that the x coodiate of Q is egative, (b) use you aswe to pat (a) to fid the coodiates of Q. (7) 4 *P43137A043*

21 physicsadmathstuto.com Jue 013 Questio 7 cotiued blak *P43137A053* 5 Tu ove

22 Coe Mathematics C4 Cadidates sittig C4 may also equie those fomulae listed ude Coe Mathematics C1, C ad C3. Itegatio (+ costat) f(x) f( x) dx sec kx ta x cot x 1 ta kx k l sec x l si x cosec x l cosec x + cot x, l ta( 1 x) 1 1 sec x l sec x + ta x, l ta( x + 4 π ) dv du u dx = uv v dx dx dx Edexcel AS/A level Mathematics Fomulae List: Coe Mathematics C4 Issue 1 Septembe 009 7

23 Coe Mathematics C3 Cadidates sittig C3 may also equie those fomulae listed ude Coe Mathematics C1 ad C. Logaithms ad expoetials e x l a = a x Tigoometic idetities si ( A ± B) = si Acos B ± cos Asi B cos( A ± B) = cos Acos B si Asi B ta A ± ta B ta ( A ± B) = ( A ± B ( k + ) 1 ta A ta 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 1 π ) Diffeetiatio f(x) ta kx sec x cot x cosec x f( x) g( x) f (x) k sec kx sec x ta x cosec x cosec x cot x f ( x )g( x) f( x)g ( x) (g( x)) 6 Edexcel AS/A level Mathematics Fomulae List: Coe Mathematics C3 Issue 1 Septembe 009

24 Edexcel AS/A level Mathematics Fomulae List: Coe Mathematics C Issue 1 Septembe Coe Mathematics C Cadidates sittig C may also equie those fomulae listed ude Coe Mathematics C1. Cosie ule a = b + c bc cos A Biomial seies 1 ) ( 1 b b a b a b a a b a = + ( ) whee )!!(! C = = < = + x x x x x 1, ( 1 1) ( 1) ( 1 1) ( 1 ) (1 ) Logaithms ad expoetials a x x b b a log log log = Geometic seies u = a 1 S = a 1 ) (1 S = a 1 fo < 1 Numeical itegatio The tapezium ule: b a x y d 1 h{(y 0 + y ) + (y 1 + y y 1 )}, whee a b h =

25 Coe Mathematics C1 Mesuatio Suface aea of sphee = 4π Aea of cuved suface of coe = π slat height Aithmetic seies u = a + ( 1)d S = 1 (a + l) = 1 [a + ( 1)d] 4 Edexcel AS/A level Mathematics Fomulae List: Coe Mathematics C1 Issue 1 Septembe 009