FP2 Mark Schemes from old P4, P5, P6 and FP1, FP2, FP3 papers (back to June 2002)
|
|
- Felix Hoover
- 5 years ago
- Views:
Transcription
1 FP Mark Schemes from old P, P5, P6 and FP, FP, FP papers (back to June 00) Please note that the following pages contain mark schemes for questions from past papers. The standard of the mark schemes is variable, depending on what we still have many are scanned, some are handwritten and some are typed. The questions are available on a separate document, originally sent with this one. FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009
2 . [P January 00 Qn ]. [P January 00 Qn 6] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009
3 . [P January 00 Qn 7] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009
4 . [P January 00 Qn 8] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009
5 5. ( > 0) 5 > or 5 = ( + )( ), critical values ½ and A, A > A ft < 0 5 < Using critical value 0: ½ < < 0, A ft Alt. 5 0 or ( 5) > ( )( ) 0 or ( + )( ) > 0, A Critical values ½ and, > A, A ft Using critical value 0, ½ < < 0, A ft (7 marks) [P June 00 Qn ] d 6. (a) y sin y cos d cos Int. factor Integrate: e tan d ln(cos ) e sec, A ysec cos d, A ysec sin C A ( y sin cos C cos ) (6) (b) When y = 0, cos (sin C) 0, cos 0 solutions for this ( = /, /) A () (c) y = 0 at = 0: C = 0 : y sin cos ( y ½sin ) Shape A A () Scales ( marks) [P June 00 Qn 6] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 5
6 7. (a) m + 7m + = 0 (m + )(m + ) = 0 m = ½, ½t C.F. is y Ae t Be, A P.I. y = at + bt + c y at b, y a B (a) + 7(at + b) + (at + bt + c) t + t a =, a = + b =, b = A 7 + c = 0, c =, A ½t t General solution: y Ae Be ( t t ) A ft (8) ½t t (b) y ½Ae Be (t ) t = 0, y : = ½A B t = 0, y = : = + A + B one of, A these Solve: A + B = 0, A + 6B = A = /5, B = /5 y 5 ½t t ( t t ) (e e ) A (5) ½ (c) t = : y (e e ) (=.5 ) B () 5 ( marks) [P June 00 Qn 7] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 6
7 8. (a) y r sin a(sin 5 sin cos ) dy a(cos d 5 cos ), A 5 cos cos cos, cos 5 5, A =.07 A ft r = a A ft (6) (b) r sin 0 8a sin 0, 0 a =.795 8sin, A () (c) ( 5 cos ) cos 5cos B sin Integrate: sin 5 Limits used: [...] (or upper limit:, A 5 9 ) A ½ 0 r d a ( ) 8 m, A (6) (5 marks) [P June 00 Qn 8] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 7
8 9. (a)(i) + (y )i = + (y + i) + (y ) = ( + (y + ) ) (ii) so + y + y = 0 any correct from; terms; isw A () y Sketch circle B Centre (0, ) B r = or touches ais B () (b) w = (z 7 + i) B = z + i B () (7 marks) [P6 June 00 Qn ] d y dy d y dy d y dy 0. (a) y ; ; 0 marks can be awarded in(b) A; B;B d d d d d d dy d y dy d y d d d or sensible correct alternative d y B (5) (b) When = 0 d y d y, and 5 d d A, A ft 5 y... 6, A ft (5) (c) Could use for = 0. but not for = 50 as B approimation is best at values close to = 0 B () ( marks) [P6 June 00 Qn ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 8
9 . zw = cos cos sin sin = cos i sin B + isin cos cos sin A ( marks) [P January 00 Qn ]. (a) r r (b) n r r = B B () + n n + n n = n n A A 5 5n 5n 0 n 0 = 6 6( n )( n ) n(5n ) = 6( n )( n ) * A cso (5) (7 marks) [P January 00 Qn ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 9
10 . (a) y y 5 y shape points on aes B B () 5 (b) + = 5 - = 7 > 7 A A ft () (5 marks). (a) (b) [P January 00 Qn ] d v v +,= ( + v)( + v), d d v = v + 5v + v A d d v = (v + ) * A () d dv = ( v ) d B, (c) y = v + v = v = = ln + c must have + c A ln c ln c A (5) B () ln c (0 marks) [P January 00 Qn 5] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 0
11 5. (a) y = cos d y = cos sin A d d d y = sin sin 9 cos 6 sin 9 cos + 9 cos = sin = A A cso () (b) 9 = 0 = ()i A y = A sin + B cos form y = A sin + B cos + cos A ft on s () (c) y =, = 0 B = B d y Aft on = A cos B sin + cos 6 sin d s = A + A = 0 y = cos + cos A () (d) y aes shape B B () ( marks) [P January 00 Qn 7] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009
12 6. (a) a cos cos d Acorrect with limits = cos a cos d A = a sin sin A 0 a = a = A (6) (b) = a cos + a cos r cos d = a sin a cos sin d A d = 0 cos = d finding = r = a or = or r = a a A: r =, = finding r a B: r =, = both A and B A (5) (c) = a WX = a + a = a A () (d) WXYZ = 7 a 8 B ft () (e) Area = =. cm A () (6 marks) [P January 00 Qn 8] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009
13 7. (a) r r r r r r r A () (b) n r r r ( r ) n r ( r ) r ( n ) n =... = n (*) A cso () [P June 00 Qn ] 8. Identifying as critical values, B, B Establishing there are no further critical values Obtaining + or equivalent = 6 < 0 A Using eactly two critical values to obtain inequalities < < A Graphical alt. Identifying = and = as vertical asymptotes Two rectangular hyperbolae oriented correctly with respect to asymptotes in the correct half-planes. Two correctly drawn curves with no intersections As above y (6 marks) B, B A, A O [P June 00 QN n] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009
14 9. (a) d t = d or equivalent I = te t dt complete substitution = te t dt + e t dt A = te t e t ( + c) A = e e ( + c) A (6) (b) I.F. = e d = (or multiplying equation by ) B d ( y) = e d y = e or y = e e + C Alts (a) (i) mark t = similarly (ii).(e d ) d with evidence of attempt at integration by parts Aft A () (0 marks) = ( e = e (iii) u = e ) +.e e, du d (+ c) d = e = ln u hence I = ln u du A + A A (6) = u ln u u. u du A = u ln u u ( + c) A = e e ( + c) A (6) (The result ln u du = u ln u u may be quoted, gaining A A but must be completely correct.) [P June 00 Qn 6] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009
15 0. (a) A: (5a, 0) B: (a, 0) allow on a sketch (b) + cos = 5 cos cos = B, B () = 5, (allow ) A 5 Points are (a, ), (a, ) A () (c) ( ) r d = ( ) (5 cos ) d = ( ) (5 0 cos + cos ) d = ( ) (5 0 cos + cos + ) d = ( )[7 0 sin + sin ] A ( ) r d = ( ) ( + cos ) d = ( ) (9 + cos + cos ) d = ( ) ( + cos + cos ) d = ( ) [ + sin + sin ] nd integration A Area = (5 cos ) d + ( + cos ) d = 0 + (addition; condone /½) correctly identifying limits with s A = a [7 0 + ] + a [( ) 6 ] d = a [9 8] (*) A cso (8) ( marks) [P June 00 Qn 7] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 5
16 . (a) y = kt.e t + kt e t use of product rule y = ke t + kt e t + 9t e t product rule, twice substituting k + kt + 9kt kt 8kt + 9kt = k = A () (b) Au. eqn. (if used) (m ) = 0 m =, repeated yc.f. = (A + Bt) e t required form (allow just written down) A G.S. y = (A + Bt) e t + t e t (ft on t e t ) A ft () (c) t = 0, y = A = B y = Be t + (A + Bt) e t + te t + 6t e t y = 0, t = 0 = B + A B = 8 A y = ( 8t + t )e t () (d) y shape crossing +ve -ais B, B y = ( + t)e t + ( t + t )e t = 0 6t 5t = 0 t = 6 5 A y = e.5 (.5) 9 awrt.5 A (5) (6 marks) [P June 00 Qn 8] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 6
17 . (i)(a) Circle A One half line correct B Second half line B () [SC Allow B for two full lines in correct position] (b) shading correct region A ft () (ii)(a) Rearrange z w Completion (b) z w to give z f w or z fw z w z, or z z w z w A w z w w w A () Correct line shown Correct shading A () [0] [P6 June 00 Qn ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 7
18 . (a) (cos + i sin ) 5 = cos 5 + i sin 5 (cos + i sin ) 5 = cos cos (i sin ) + 0 cos (i sin ) + 0 cos (i sin ) + 5 cos (i sin ) + (i sin ) 5 A cos 5 = cos 5 0 cos sin + 5 cos sin = cos 5 0 cos ( cos ) + 5 cos ( cos + cos ) = 6 cos 5 0 cos + 5 cos (*) A cso (6) (b) cos 5 = (or, or 0) 5 = (n )80 = (n )6 = cos =, 0.09, A A [0] () [P6 June 00 Qn 5] n. ( 6r ) = 0 attempt to use an identity r n r = : : (n ) (n ) n (n ) (n + ) (n ) differences (must see) = (n + ) + n A 6 r = (n + ) + n n n or equiv. B n r = n + n + n r = 6 n(n + )(n + ) () Sub. and 6 or equiv. c.s.o., A [P January 00 Qn ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 8
19 5. (a) IF = = d e ln e A = e e (b) e y = y = ln must see = e A () e d = e d = e e + c by parts A c e o.e. A () (c) I = ce c = e y = - e.e 8 8 = 8 ( + e ) A () or = or better (0 marks) [P January 00 Qn] 6. (a) y y = ( )( ) Line crosses aes B 8 Curve shape B 6 Aes contacts 6, 8, y = 6 B Cusps at and B () (b) 6 = ( )( ) and 6 + = ( )( ), + = = 0 either = = A, A (5) (c) < <, A () ( marks) [P January 00 Qn5] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 9
20 7. (a) m + m + 5 = 0 m = i A y = e (Acos Bsin ) PI = sin + cos PI & attempt diff. y = cos sin y = sin cos A = = 0 subst. in eqn. & equate 8 = = 0 solving sim. eqn = 0 65 = 65 =, = 8 A y = e (Acos + Bsin ) + sin 8 cos ft on their and Aft (9) (b) As, e 0 y sin 8 cos y R sin( + ) Bft R = 65 = tan 8 =.6 or 8.9 A () (marks) [P January 00 Qn6] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 0
21 8. (a) Shape + horiz. ais B B () (b) Area = r d = 9 cos d use of r 9 cos = d use of cos = cos = 9 sin 8 d, A 6 9 = 8 6 subst. and 6 9 = or 0.0 A (6) 6 (c) r sin = sin cos dy = cos cos 6 sin sin diff. r sin, A d dy = 0 6 cos cos sin cos = 0 d use of dy = 0 d 6 cos cos ( cos )cos = 0 use double angle formula 8 cos 5 cos = 0 solving cos = 0 or cos = 6 5 or tan = 5 or sin = 6 A r = ( 65 ) = r sin = 6 use of d = r sin d = 6 A (8) (6 marks) [P January 00 Qn 7] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009
22 9. [P June 00 Qn ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009
23 0. [P June 00 Qn 6] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009
24 . [P June 00 Qn 7] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009
25 . [P June 00 Qn 8] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 5
26 . (a) f ( ) sec f ( ) sec (sec tan ) (or equiv.) A f ( ) sec (sec ) tan (sec tan ) (or equiv.) A () (sec (sec 6sec tan ) sec tan ), (6sec sec ), ( 8tan 6tan ) (b) tan or sec (,,, 6) B tan f f f f 6 (c) 8 (Allow equiv. fractions A(cso) (), souse tan (*) A(cso) () [P6 June 00 Qn ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 6
27 FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March [P6 June 00 Qn ]. (a) n = : sin e cos e cos e d d (Use of product rule) sin cos sin sin cos cos cos cos e cos e d d True for n = (cso + comment) A Suppose true for n = k. cos e d d cos e d d k k k k sin e cos e k k k A cos e cos e k k k k A True for n = k +, so true (by induction) for all n. ( ) A(cso) (8) (b) cos cos 6 cos cos () (0) ( ) ( ) 6 cos e (or equiv. fractions) A(,0) ().
28 5. (a) arg z = z i (or putting and y equal at some stage) B ( ) i w, and attempt modulus of numerator or denominator. ( )i (Could still be in terms of and y) ) i ( )i ( ), ( (b) w (*) A, Acso () z wi w zw wi z z z i w z wi w A For w a ib, ( b) ai ( a ) ib ( b b) a ( a ) (c) b = a Image is (line) y = A (6) B B () (d) z = i marked (P) on z-plane sketch. B i i z i w i marked (Q) on w-plane sketch. B () i [P6 June 00 Qn 7] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 8
29 6. [FP/P January 005 Qn ] 7. [FP/P January 005 Qn ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 9
30 8. [FP/P January 005 Qn 5] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 0
31 9. [FP/P January 005 Qn 6] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009
32 0. [FP/P January 005 Qn 7].(a) [FP/P June 005 Qn ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009
33 . [FP/P June 005 Qn ].(a) [FP/P June 005 Qn 6] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009
34 .(a) [FP/P June 005 Qn 7] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009
35 5. [FP/P June 005 Qn 7] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 5
36 6. [FP/P6 June 005 Qn ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 6
37 7. [FP/P6 June 005 Qn 5] 8. [FP/P January 006 Qn ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 7
38 9. [FP/ P January 006 Qn ] 50. [FP/P January 006 Qn 6] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 8
39 5. [FP/P January 006 Qn 7] 5. [FP/P6 January 006 Qn ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 9
40 5. [FP/P6 January 006 Qn 6] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 0
41 5. [FP/P6 January 006 Qn 8] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009
42 55. Use of r d B Limits are 8 and B 6a cos 8a cos sin cos d A Aa sin 8 a 0 8 a a cso A (7) [7] [FP June 006 Qn ] 56. (a) y sin 6 cos y cos sin A Substituting cos sin sin k cos k A () (b) General solution is y Acos B sin sin B 0, A B, B B y cos sin sin Needs y A () [8] [FP June 006 Qn ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009
43 57. (a) (r ) 8r r 6r (r ) 8r r 6r A, B (r ) (r ) r Accept r 0 B and r A B 6 A for both A () (b) (c) 5 n n n n r n ft their B A Aft n r n 8n n n r r 0 0 r r nn n nn n cso A (5) 6 6 (r ) (9r 6r ) A () [0] [FP June 006 Qn 5] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009
44 58. (a) 6 6 Leading to surds required A 6 6 Leading to 0 0, A, A (6) (b) Accept if parts (a) and (b) done in reverse order y Curved shape B Line B At least intersections B () O (c) Using all CVs and getting all into inequalities, both Aft ft their greatest positive and their least negative CVs 0 A () [] [FP June 006 Qn 7] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009
45 59. (a) dt ln 0 t B 0 t ln0 t e 0 t A ds S 0 t dt 0 t 0 t d S dt 0 t 0 t S 0 t 0 t C 0, C C or integral equivalent A t 0 t S accept C = awrt A (8) 600 (b) Substituting ds 0 t dt 600 ds 0 t 5 dt A 8 S 9 (kg) A () [] [FP June 006 Qn 8] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 5
46 60. (a) f cos, f 0, f sin, f cos f f 0, f 8sin iv f 6cos v, f sin, f 8 A iv f 0 v f A f f cos f f...! Three terms are sufficient to establish method 5 cos... A (5) 5 (b) Substitute = 0.60 B 5 cos cao A () [8] [FP June 006 Qn ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 6
47 6. (a) In this solution cos c and sin s c s 5 cos5 isin5 i 5 ( c 5c is 0c is 0c is 5c is is ) 5 sin c s c s s equate A 5c s 0c c s c s s = c s 6c c A (5) (b) sin 6cos cos cos sin 0 sin 0 0 B 6c 0c 8c c 0 c, c any two A.,.9;, any two A all four A (6) accept awrt 0.79,.,.9,.6 [] Ignore any solutions out of range. [FP June 006 Qn ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 7
48 6. (a) Let z iy Leading to 6 y 9 y 8 8y 8 y 0 A This is a circle; the coefficients of there is no y term. and y are the same and Allow equivalent arguments and ft their f, y if appropriate. y y 6 0 Aft 5 y Leading to Centre:, A Radius: 5 or equivalent A (7) (b) Circle B centre in correct quadrant B ft through origin B Line cuts ve and +ve y aes B 6 O intersects with circle on aes and all correct B (5) (c) Shading inside circle B and above line with all correct B () [] [FP June 006 Qn 6] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 8
49 6. [FP January 007 Qn ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 9
50 6. [FP Jan 007 Qn ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March
51 65. FP January 007 Qn 5] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 5
52 66. [FP January 007 Qn 7] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 5
53 67. [FP January 007 Qn 8] 68. [FP June 007 Qn ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 5
54 69. [FP June 007 Qn ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 5
55 70. [FP June 007 Qn ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March
56 7. [FP June 007 Qn 5] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March
57 7. [FP June 007 Qn 7] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March
58 7. (a) d y d y d y dy dy 0 d d d d d At 0, d y d dy d A cso () (b) d y d 0 f 0 f 0 y 6, + 6 f 0 f 0 Allow anywhere B Aft, A (dep) () [FP June 007 Qn ] [7] n n 7. (a) z cos isin cos n isin n n n both Adding cso z cos i sin cos n i sin n cos n i sin n z n cos n n z A () (b) two correct 6 z z 6z 5z 0 5z 6z z z z z 6 z z 5 z z 0 6 6cos cos 6 cos 0cos 0 6 cos cos 6 6cos 5cos 0 A, A p, q 6, r 5, s 0 A any (5) 6 (c) cos d cos 6 6cos 5cos 0 d sin 6 6sin 5sin equivalent or eact Aft A () [] [FP June 007 Qn ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March
59 75. (a) Let z i ; i w i i i i i uiv i A u, v Eliminating gives a line with equation vu or equivalent A (5) (b) Let z i; u i w i i i i i i uiv, v u v u v u v v Reducing to the circle with equation u v u v A 0 cso A (7) (c) v O ft their line Bft Circle through origin, centre in correct quadrant B u Intersections correctly placed B () [5] [FP June 007 Qn 8] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March
60 76. [FP January 008 Qn ] 77.(a) [FP January 008 Qn ] 78.(a) [FP January 008 Qn 5] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March
61 79.(a) [FP January 008 Qn 7] 80.(a) [FP January 008 Qn 8] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 6
62 8. [FP June 008 Qn ] 8. [FP June 008 Qn 5] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 6
63 8. [FP June 008 Qn 6] 8. [FP June 008 Qn 7] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 6
64 85. [FP June 008 Qn 8] 86. [FP June 008 QN ] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March 009 6
65 87. [FP June 008 Qn ] 88. [FP June 008 Qn 6] FP question mark schemes from old P, P5, P6 and FP, FP, FP papers Version March
FP2 Mark Schemes from old P4, P5, P6 and FP1, FP2, FP3 papers (back to June 2002)
FP Mark Schemes from old P, P5, P6 and FP, FP, FP papers (back to June 00) Please note that the following pages contain mark schemes for questions from past papers. The standard of the mark schemes is
More informationCandidates sitting FP2 may also require those formulae listed under Further Pure Mathematics FP1 and Core Mathematics C1 C4. e π.
F Further IAL Pure PAPERS: Mathematics FP 04-6 AND SPECIMEN Candidates sitting FP may also require those formulae listed under Further Pure Mathematics FP and Core Mathematics C C4. Area of a sector A
More informationFP3 mark schemes from old P4, P5, P6 and FP1, FP2, FP3 papers (back to June 2002)
FP mark schemes from old P, P5, P6 and FP, FP, FP papers (back to June ) Please note that the following pages contain mark schemes for questions from past papers. Where a question reference is marked with
More informationMark Scheme (Results) Summer 2009
Mark (Results) Summer 009 GCE GCE Mathematics (6668/0) June 009 6668 Further Pure Mathematics FP (new) Mark Q (a) = rr ( + ) r ( r+ ) r ( r+ ) B aef () (b) n n r = r = = rr ( + ) r r+ = + +...... + + n
More informationMark Scheme Summer 2009
Mark Summer 009 GCE GCE Mathematics (6668/0) Edecel is one of the leading eamining and awarding bodies in the UK and throughout the world. We provide a wide range of qualifications including academic,
More informationFP1 PAST EXAM QUESTIONS ON NUMERICAL METHODS: NEWTON-RAPHSON ONLY
FP PAST EXAM QUESTIONS ON NUMERICAL METHODS: NEWTON-RAPHSON ONLY A number of questions demand that you know derivatives of functions now not included in FP. Just look up the derivatives in the mark scheme,
More informationFP1 Mark Schemes from old P4, P5, P6 and FP1, FP2, FP3 papers (back to June 2002)
FP Mar Schemes from old P4, P5, P6 and FP, FP, FP papers (bac to June 00) Please note that the following pages contain mar schemes for questions from past papers which were not written at an AS standard
More informationFP1 Mark Schemes from old P4, P5, P6 and FP1, FP2, FP3 papers (back to June 2002)
FP1 Mar Schemes from old P4, P5, P6 and FP1, FP, FP papers (bac to June 00) Please note that the following pages contain mar schemes for questions from past papers which were not written at an AS standard
More informationPMT. Mark Scheme (Results) Summer Pearson Edexcel GCE in Further Pure Mathematics FP2 (6668/01)
Mark (Results) Summer 04 Pearson Edecel GCE in Further Pure Mathematics FP (6668/0) Edecel and BTEC Qualifications Edecel and BTEC qualifications come from Pearson, the world s leading learning company.
More informationOCR Maths FP1. Topic Questions from Papers. Complex Numbers. Answers
OCR Maths FP1 Topic Questions from Papers Complex Numbers Answers PhysicsAndMathsTutor.com . 1 (i) i Correct real and imaginary parts z* = i 1i Correct conjugate seen or implied Correct real and imaginary
More informationPMT. Mark Scheme (Results) Summer Pearson Edexcel GCE in Further Pure Mathematics FP2R (6668/01R)
Mark Scheme (Results) Summer 04 Pearson Edecel GCE in Further Pure Mathematics FPR (6668/0R) Edecel and BTEC Qualifications Edecel and BTEC qualifications come from Pearson, the world s leading learning
More informationMark Scheme (Results) Summer GCE Core Mathematics 3 (6665/01R)
Mark Scheme (Results) Summer GCE Core Mathematics (6665/R) Question Number Scheme Marks. (a) + ( + 4)( ) B Attempt as a single fraction (+ 5)( ) ( + ) ( + )( ) or + 5 ( + 4) M ( + 4)( ) ( + 4)( ), ( +
More informationMark Scheme (Results) Summer Pearson Edexcel International A Level in Further Pure Mathematics F2 (WFM02/01)
Mark Scheme (Results) Summer 015 Pearson Edexcel International A Level in Further Pure Mathematics F (WFM0/01) Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the
More informationMark Scheme (Results) Summer Pearson Edexcel GCE In Further Pure Mathematics FP2 (6668/01)
Mark Scheme (Results) Summer 017 Pearson Edexcel GCE In Further Pure Mathematics FP (6668/01) Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK s largest awarding
More informationMathematics (JAN13MPC301) General Certificate of Education Advanced Level Examination January Unit Pure Core TOTAL
Centre Number Candidate Number For Eaminer s Use Surname Other Names Candidate Signature Eaminer s Initials Mathematics Unit Pure Core Wednesday January General Certificate of Education Advanced Level
More informationPMT. A-LEVEL Mathematics. MFP3 Further Pure 3 Mark scheme June Version: 1.0 Final
A-LEVEL Mathematics MFP Further Pure Mark scheme 0 June 0 Version:.0 Final Mark schemes are prepared by the Lead Assessment Writer and considered, together with the relevant questions, by a panel of subject
More informationabc Mathematics Further Pure General Certificate of Education SPECIMEN UNITS AND MARK SCHEMES
abc General Certificate of Education Mathematics Further Pure SPECIMEN UNITS AND MARK SCHEMES ADVANCED SUBSIDIARY MATHEMATICS (56) ADVANCED SUBSIDIARY PURE MATHEMATICS (566) ADVANCED SUBSIDIARY FURTHER
More informationA-LEVEL Mathematics. MFP2 Further Pure 2 Mark scheme June Version: 1.0 Final
A-LEVEL Mathematics MFP Further Pure Mark scheme 660 June 0 Version:.0 Final Mark schemes are prepared by the Lead Assessment Writer and considered, together with the relevant questions, by a panel of
More informationMark Scheme Summer 2009
Mark Summer 009 GCE Core Mathematics C (666) Edecel is one of the leading eamining and awarding bodies in the UK and throughout the world. We provide a wide range of qualifications including academic,
More informationJune Further Pure Mathematics FP1 (new) Mark Scheme
June 009 6667 Further Pure Mathematics FP (new) Mar Q (a) Mars B () (c) (d) z + ( ) 5 (or awrt.4) α arctan or arctan arg z 0.46 or 5.8 (awrt) (answer in degrees is A0 unless followed by correct conversion)
More informationJune Further Pure Mathematics FP1 (new) Mark Scheme
June 009 6667 Further Pure Mathematics FP (new) Mar Question Q (a) Mars B () (c) (d) z! # (" ) 5 (or awrt.4)! ) & ) & *! arctan' $ or arctan ' " $ ( % ( % arg z! "0.46 or 5.8 (awrt) (answer in degrees
More informationAS Mathematics MPC1. Unit: Pure Core 1. Mark scheme. June Version: 1.0 Final
AS Mathematics MPC1 Unit: Pure Core 1 Mark scheme June 017 Version: 1.0 Final FINAL MARK SCHEME AS MATHEMATICS MPC1 JUNE 017 Mark schemes are prepared by the Lead Assessment Writer and considered, together
More informationMark Scheme (Results) Summer Pearson Edexcel GCE in Further Pure Mathematics FP2R (6668/01R)
Mark Scheme (Results) Summer 04 Pearson Edexcel GCE in Further Pure Mathematics FPR (6668/0R) Edexcel and BTEC Qualifications Edexcel and BTEC qualifications come from Pearson, the world s leading learning
More informationMark Scheme (Results) Summer 2007
Mark Scheme (Results) Summer 007 GCE GCE Mathematics Core Mathematics C (666) Edecel Limited. Registered in England and Wales No. 96750 Registered Office: One90 High Holborn, London WCV 7BH June 007 666
More informationA-LEVEL Mathematics MPC3
A-LEVEL Mathematics MPC UNIT: Pure Core Mark scheme 660 June 07 Version:.0 Final MARK SCHEME A LEVEL MATHEMATICS MPC JUNE 07 Mark schemes are prepared by the Lead Assessment Writer and considered, together
More informationabc Mathematics Pure Core General Certificate of Education SPECIMEN UNITS AND MARK SCHEMES
abc General Certificate of Education Mathematics Pure Core SPECIMEN UNITS AND MARK SCHEMES ADVANCED SUBSIDIARY MATHEMATICS (56) ADVANCED SUBSIDIARY PURE MATHEMATICS (566) ADVANCED SUBSIDIARY FURTHER MATHEMATICS
More informationA-LEVEL Mathematics. Further Pure 2 MFP2 Mark scheme June Version/Stage: 1.0 Final
A-LEVEL Mathematics Further Pure MFP Mark scheme 660 June 0 Version/Stage:.0 Final Mark schemes are prepared by the Lead Assessment Writer and considered, together with the relevant questions, by a panel
More informationPMT. Version. General Certificate of Education (A-level) January 2013 MPC3. Mathematics. (Specification 6360) Pure Core 3. Final.
Version General Certificate of Education (A-level) January Mathematics MPC (Specification 66) Pure Core Final Mark Scheme Mark schemes are prepared by the Principal Eaminer and considered, together with
More informationCore Mathematics C3 Advanced Subsidiary
Paper Reference(s) 6665/0 Edecel GCE Core Mathematics C Advanced Subsidiary Thursday June 0 Morning Time: hour 0 minutes Materials required for eamination Mathematical Formulae (Pink) Items included with
More informationPhysicsAndMathsTutor.com. Mark Scheme (Results) Summer GCE Further Pure FP2 (6668) Paper 1
Mark (Results) Summer 01 GCE Further Pure FP (6668) Paper 1 Edexcel and BTEC Qualifications Edexcel and BTEC qualifications come from Pearson, the world s leading learning company. We provide a wide range
More informationVersion 1.0. General Certificate of Education (A-level) January 2011 MPC3. Mathematics. (Specification 6360) Pure Core 3.
Version.0 General Certificate of Education (A-level) January 0 Mathematics MPC (Specification 660) Pure Core Mark Scheme Mark schemes are prepared by the Principal Eaminer and considered, together with
More informationCore Mathematics C1 Advanced Subsidiary
Paper Reference(s) 666/0 Edexcel GCE Core Mathematics C Advanced Subsidiary Monday 0 January 0 Morning Time: hour 0 minutes Materials required for examination Mathematical Formulae (Pink) Items included
More informationMark Scheme (Results) June GCE Further Pure FP2 (6668) Paper 1
Mark (Results) June 0 GCE Further Pure FP (6668) Paper Edexcel is one of the leading examining and awarding bodies in the UK and throughout the world. We provide a wide range of qualifications including
More information2 nd ORDER O.D.E.s SUBSTITUTIONS
nd ORDER O.D.E.s SUBSTITUTIONS Question 1 (***+) d y y 8y + 16y = d d d, y 0, Find the general solution of the above differential equation by using the transformation equation t = y. Give the answer in
More informationMark Scheme (Results) Summer Pearson Edexcel IAL in Further Pure Mathematics 2 (WFM02/01)
Mark Scheme (Results) Summer 06 Pearson Edexcel IAL in Further Pure Mathematics (WFM0/0) dexcel and BTEC Qualifications dexcel and BTEC qualifications are awarded by Pearson, the UK s largest awarding
More informationMark Scheme (Results) Summer GCE Further Pure Mathematics 2 (6668/01)
Mark Scheme (Results) Summer 0 GCE Further Pure Mathematics (6668/0) Edecel and BTEC Qualifications Edecel and BTEC qualifications come from Pearson, the world s leading learning company. We provide a
More informationMark Scheme (Results) January 2011
Mark (Results) January 0 GCE GCE Core Mathematics C3 (6665) Paper Edecel Limited. Registered in England and Wales No. 4496750 Registered Office: One90 High Holborn, London WCV 7BH Edecel is one of the
More informationPhysicsAndMathsTutor.com
GCE Edecel GCE Core Mathematics C(666) Summer 005 Mark Scheme (Results) Edecel GCE Core Mathematics C (666) June 005 666 Core Mathematics C Mark Scheme Question Number. (a) Scheme Penalise ± B Marks ()
More informationC4 mark schemes - International A level (150 minute papers). First mark scheme is June 2014, second mark scheme is Specimen paper
C4 mark schemes - International A level (0 minute papers). First mark scheme is June 04, second mark scheme is Specimen paper. (a) f (.).7, f () M Sign change (and f ( ) is continuous) therefore there
More informationEdexcel GCE Final. Further Pure Maths Unit no. 6674/01. June Mark Scheme (Results) Further Pure Maths 6674/01. Edexcel GCE
Edexcel GCE Final Further Pure Maths Unit no. 667/0 June 006 (Results) Edexcel GCE Further Pure Maths 667/0 General Instructions. The total number of marks for the paper is 75.. Method (M) marks are awarded
More informationGeneral Certificate of Education Advanced Level Examination January 2010
General Certificate of Education Advanced Level Eamination January 00 Mathematics MPC3 Unit Pure Core 3 Friday 5 January 00.30 pm to 3.00 pm For this paper you must have: an 8-page answer book the blue
More informationMark Scheme (Results) Summer 2009
Mark (Results) Summer 009 GCE GCE Mathematics (666/01) June 009 666 Core Mathematics C1 Mark Q1 (a) ( 7) = 6 B1 (1) (b) (8 + )( ) = 16 + 8 = 11, 6 A1, A1 (a) B1 for 6 only (b) for an attempt to epand their
More informationMark Scheme (Results) January Pearson Edexcel International Advanced Level. Core Mathematics 3 (6665A) January 2014 (IAL)
January 014 (IAL) Mark (Results) January 014 Pearson Edecel International Advanced Level Core Mathematics (6665A) January 014 (IAL) Edecel and BTEC Qualifications Edecel and BTEC qualifications are awarded
More informationFormulae to Learn. The Rules for Differentiation are. The instructions are to either: Find ( or ), or
Differentiation Formulae to Learn The Rules for Differentiation are The instructions are to either: Find ( or ), or Differentiate, or Find the derived function, or Find the derivative. the curve. finds
More informationVersion 1.0. General Certificate of Education (A-level) June Mathematics MPC3. (Specification 6360) Pure Core 3. Final.
Version.0 General Certificate of Education (A-level) June 0 Mathematics MPC3 (Specification 6360) Pure Core 3 Final Mark Scheme Mark schemes are prepared by the Principal Eaminer and considered, together
More informationVersion 1,0. General Certificate of Education (A-level) June 2012 MPC3. Mathematics. (Specification 6360) Pure Core 3. Mark Scheme
Version,0 General Certificate of Education (A-level) June 0 Mathematics MPC (Specification 660) Pure Core Mark Scheme Mark schemes are prepared by the Principal Eaminer and considered, together with the
More informationGCE Mathematics. Mark Scheme for June Unit 4727: Further Pure Mathematics 3. Advanced GCE. Oxford Cambridge and RSA Examinations
GCE Mathematics Unit 477: Further Pure Mathematics 3 Advanced GCE Mark Scheme for June 04 Oxford Cambridge and RSA Examinations OCR (Oxford Cambridge and RSA) is a leading UK awarding body, providing a
More informationGCE Core Mathematics C1 (6663) Paper 1
Mark Scheme (Results) January 01 GCE Core Mathematics C1 (666) Paper 1 Edexcel is one of the leading examining and awarding bodies in the UK and throughout the world. We provide a wide range of qualifications
More informationMark Scheme (Results) Summer Pearson Edexcel International GCSE Further Pure Mathematics (4PM0) Paper 1
. Mark Scheme (Results) Summer 05 Pearson Edexcel International GCSE Further Pure Mathematics (4PM0) Paper Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK
More informationCore Mathematics C1 Advanced Subsidiary
Paper Reference(s) 666/0 Edecel GCE Core Mathematics C Advanced Subsidiary Monday May 00 Afternoon Time: hour 0 minutes Materials required for eamination papers Mathematical Formulae (Pink) Items included
More informationPMT GCE. Edexcel GCE Core Mathematics C1 (6663) January Mark Scheme (Results) Core Mathematics C1 (6663) Edexcel GCE
GCE Edexcel GCE Core Mathematics C (666) January 006 Mark Scheme (Results) Edexcel GCE Core Mathematics C (666) January 006 666 Core Mathematics C Mark Scheme. x( x 4x + ) Factor of x. (Allow ( x 0) )
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education. Published
Cambridge International Eaminations Cambridge International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/ Paper March 07 MARK SCHEME Maimum Mark: 80 Published This mark scheme
More informationPMT. Version 1.0. General Certificate of Education (A-level) June 2013 MPC3. Mathematics. (Specification 6360) Pure Core 3. Final.
Version.0 General Certificate of Education (A-level) June 0 Mathematics MPC (Specification 660) Pure Core Final Mark Scheme Mark schemes are prepared by the Principal Eaminer and considered, together with
More informationeliminate e x [3] dx B1dep dep correct derivative
753/01 Mark Scheme January 013 1 (i) y = e x sin x Product rule u their v + v their u dy/dx = e x.cos x + (e x )sin x B1 d/dx(sin x) = cos x Any correct expression but mark final answer [3] 1 (ii) ft their
More informationQ Scheme Marks AOs. Attempt to multiply out the denominator (for example, 3 terms correct but must be rational or 64 3 seen or implied).
1 Attempt to multiply the numerator and denominator by k(8 3). For example, 6 3 4 8 3 8 3 8 3 Attempt to multiply out the numerator (at least 3 terms correct). M1 1.1b 3rd M1 1.1a Rationalise the denominator
More informationPhysicsAndMathsTutor.com
. (a) Simplify fully + 9 5 + 5 (3) Given that ln( + 9 5) = + ln( + 5), 5, (b) find in terms of e. (Total 7 marks). (i) Find the eact solutions to the equations (a) ln (3 7) = 5 (3) (b) 3 e 7 + = 5 (5)
More informationSeparate sum (may be implied) ( 1)(2 1) ( 1) 6 n n n n n A1,A1 1 mark for each part oe
4755 Mark Scheme June 04 n n n (i) (ii) 0 0 (iii) r( r ) r r Separate sum (may be implied) ( )( ) ( ) 6 n n n n n A,A mark for each part oe ( )[( ) 6] 6 n n n nn ( )(linear factor) ( )( 5) 6 n n n A Or
More informationMark Scheme (Results) January Pearson Edexcel International Advanced Level. Further Pure Mathematics 1 (WFM01/01)
Mar (Results) January 0 Pearson Edexcel International Advanced Level Further Pure Mathematics (WFM0/0) Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK s largest
More informationMark Scheme (Results) June GCE Further Pure FP3 (6669) Paper 1
Mark (Results) June 0 GCE Further Pure FP (6669) Paper Edexcel is one of the leading examining and awarding bodies in the UK and throughout the world. We provide a wide range of qualifications including
More information4751 Mark Scheme June Mark Scheme 4751 June 2005
475 Mark Scheme June 005 Mark Scheme 475 June 005 475 Mark Scheme June 005 Section A 40 subst of for x or attempt at long divn with x x seen in working; 0 for attempt at factors by inspection 6y [ x =
More information2 grad AB = 8/4 or 2 or y = 2x 10 grad BC = 1/ 2 or ½ or y = ½ x product of grads = 1 [so perp] (allow seen or used) ii midpt E of AC = (6, 4.
x 2 + 9x 2 = 25 0x 2 = 25 x= ±( 0)/2 or.± (5/2) or ±5/ 0 oe y = [±] (5/2) o.e. eg y = [±] 22.5 A2 B for subst for x or y attempted or x 2 = 2.5 o.e.; condone one error from start [allow 0x 2 25 = 0 + correct
More informationQ Scheme Marks AOs Pearson Progression Step and Progress descriptor. and sin or x 6 16x 6 or x o.e
1a A 45 seen or implied in later working. B1 1.1b 5th Makes an attempt to use the sine rule, for example, writing sin10 sin 45 8x3 4x1 States or implies that sin10 3 and sin 45 A1 1. Solve problems involving
More informationA-LEVEL Mathematics. MPC4 Pure Core 4 Mark scheme June Version: 1.0 Final
A-LEVEL Mathematics MPC4 Pure Core 4 Mark scheme 660 June 06 Version:.0 Final Mark schemes are prepared by the Lead Assessment Writer and considered, together with the relevant questions, by a panel of
More informationVersion 1.0. General Certificate of Education (A-level) June 2012 MPC2. Mathematics. (Specification 6360) Pure Core 2. Mark Scheme
Version.0 General Certificate of Education (A-level) June 0 Mathematics MPC (Specification 660) Pure Core Mark Scheme Mark schemes are prepared by the Principal Eaminer and considered, together with the
More informationCondensed. Mathematics. General Certificate of Education Advanced Subsidiary Examination January 2012
General Certificate of Education Advanced Subsidiary Examination January 01 Mathematics MPC1 Unit Pure Core 1 Friday 13 January 01 9.00 am to 10.30 am For this paper you must have: the blue AQA booklet
More informationMark Scheme (Results) Summer 2009
Mark (Results) Summer 009 GCE GCE Mathematics (6664/0) June 009 6664 Core Mathematics C Mark Question Q x x x x dx 4 x x dx x x 6 8 4 = 9 (9 + C scores A0) M AA M A (5) [5] st M for attempt to integrate
More informationVersion : klm. General Certificate of Education. Mathematics MPC3 Pure Core 3. Mark Scheme examination - June series
Version :. 69 klm General Certificate of Education Mathematics 66 MPC Pure Core Mark Scheme 9 examination - June series Mark schemes are prepared by the Principal Examiner and considered, together with
More informationabc Mark Scheme Mathematics 6360 General Certificate of Education 2006 examination - January series MPC3 Pure Core 3
Version.0: 006 General Certificate of Education abc Mathematics 660 MPC Pure Core Mark Scheme 006 eamination - January series Mark schemes are prepared by the Principal Eaminer and considered, together
More informationMark Scheme. Mathematics General Certificate of Education examination June series. MPC2 Pure Core 2
Version.0: 0606 abc General Certificate of Education Mathematics 660 MPC Pure Core Mark Scheme 006 examination June series Mark schemes are prepared by the Principal Examiner and considered, together with
More informationGCE. Mathematics. Mark Scheme for June Advanced GCE. Unit 4727: Further Pure Mathematics 3. Oxford Cambridge and RSA Examinations
GCE Mathematics Advanced GCE Unit 477: Further Pure Mathematics Mark Scheme for June 0 Oxford Cambridge and RSA Examinations OCR (Oxford Cambridge and RSA) is a leading UK awarding body, providing a wide
More informationVersion abc. General Certificate of Education. Mathematics MPC2 Pure Core 2. Mark Scheme examination - January series
Version.0 007 abc General Certificate of Education Mathematics 660 Pure Core Mark Scheme 007 eamination - January series Mark schemes are prepared by the Principal Eaminer and considered, together with
More information3 x 2 / 3 2. PhysicsAndMathsTutor.com. Question Answer Marks Guidance 1 5x(x + 1) 3(2x + 1) = (2x + 1)(x + 1) M1*
Question Answer Marks Guidance 5( + ) 3( + ) ( + )( + ) * 3 4 4 0 dep* Multiplying throughout by ( + )( + ) or combining fractions and multiplying up oe (eg can retain denominator throughout) Condone a
More informationMark Scheme (Results) January 2011
Mark (Results) January 0 GCE GCE Core Mathematics C (6664) Paper Edecel Limited. Registered in England and Wales No. 4496750 Registered Office: One90 High Holborn, London WCV 7BH Edecel is one of the leading
More informationVersion 1.0. General Certificate of Education (A-level) January Mathematics MPC2. (Specification 6360) Pure Core 2. Final.
Version 1.0 General Certificate of Education (A-level) January 01 Mathematics MPC (Specification 660) Pure Core Final Mar Scheme Mar schemes are prepared by the Principal Eaminer and considered, together
More informationPhysicsAndMathsTutor.com PMT
PhysicsAndMathsTutor.com PMT Version.0: 006 General Certificate of Education abc Mathematics 660 MPC Pure Core Mark Scheme 006 eamination - January series Mark schemes are prepared by the Principal Eaminer
More informationTime: 1 hour 30 minutes
Paper Reference(s) 6665/01 Edecel GCE Core Mathematics C Silver Level S Time: 1 hour 0 minutes Materials required for eamination papers Mathematical Formulae (Green) Items included with question Nil Candidates
More informationMark Scheme (Results) Summer Pearson Edexcel GCE in Core Mathematics 3 (6665_01)
Mark Scheme (Results) Summer 04 Pearson Edecel GCE in Core Mathematics 3 (6665_0) Edecel and BTEC Qualifications Edecel and BTEC qualifications are awarded by Pearson, the UK s largest awarding body. We
More informationVersion 1.0: abc. General Certificate of Education. Mathematics MPC3 Pure Core 3. Mark Scheme examination - January series
Version.0: 008 abc General Certificate of Education Mathematics 660 MPC Pure Core Mark Scheme 008 eamination - January series Mark schemes are prepared by the Principal Eaminer and considered, together
More informationMATHEMATICS (New Specification)
MS WELSH JOINT EDUCATION COMMITTEE. CYD-BWYLLGOR ADDYSG CYMRU General Certificate of Education Advanced Subsidiary/Advanced Tystysgrif Addysg Gyffredinol Uwch Gyfrannol/Uwch MARKING SCHEMES JANUARY 6 MATHEMATICS
More informationCondensed. Mathematics. General Certificate of Education Advanced Subsidiary Examination January Unit Pure Core 2.
General Certificate of Education Advanced Subsidiary Examination January 0 Mathematics MPC Unit Pure Core Monday January 0 9.00 am to 0.0 am For this paper you must have: the blue AQA booklet of formulae
More informationGeneral Certificate of Education examination - January series
Version.: 6 General Certificate of Education abc Mathematics 66 MFP Further Pure Mark Scheme 6 eamination - January series Mark schemes are prepared by the Principal Eaminer and considered, together with
More information4751 Mark Scheme June fraction line; accept to power ½ with denominator appropriate brackets answer M1 for a triple decker fraction or for
1 Question Answer Marks Guidance A A 2 square root symbol must extend below condone missing end bracket in [ r ] or [ r ] as final fraction line; accept to power ½ with denominator x y x y appropriate
More informationMark Scheme (Results) January 2011
Mark (Results) January 0 GCE GCE Core Mathematics C (666) Paper Edexcel Limited. Registered in England and Wales No. 96750 Registered Office: One90 High Holborn, London WCV 7BH Edexcel is one of the leading
More informationJanuary Further Pure Mathematics FP1 Mark Scheme
January 6667 Further Pure Mathematics FP Mar Q z + 8i + i (a) z i + i + i + 8i 8 + 5i z (b) ( ) + 5 z (or awrt 5.8) () ft () (c) 5 5 tan α or z arg π.... z + i (a) and attempt to multiply out for + i -
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education. Published
Cambridge International Eaminations Cambridge International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/ Paper October/November 06 MARK SCHEME Maimum Mark: 80 Published This
More informationPhysicsAndMathsTutor.com
PhysicsAndMathsTutor.com EDEXCEL PURE MATHEMATICS P (667) JUNE 00 PROVISIONAL MARK SCHEME Number Scheme. (a) 7 + 7 + a = 7, d = 7, n = 4 n = 4 B n( n + ) Sn = n(a + b) or
More informationPMT. Version 1.0. General Certificate of Education (A-level) June 2013 MPC1. Mathematics. (Specification 6360) Pure Core 1. Final.
Version 1.0 General Certificate of Education (A-level) June 01 Mathematics MPC1 (Specification 660) Pure Core 1 Final Mark Scheme Mark schemes are prepared by the Principal Eaminer and considered, together
More informationMark Scheme (Results) Summer Pearson Edexcel Advanced Extension Award in Mathematics (9801/01)
Mark Scheme (Results) Summer 05 Pearson Edexcel Advanced Extension Award in Mathematics (80/0) Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK s largest awarding
More informationCore Mathematics C3 Advanced Level
Paper Reference(s) 666/0 Edecel GCE Core Mathematics C Advanced Level Wednesda 0 Januar 00 Afternoon Time: hour 0 minutes Materials required for eamination Mathematical Formulae (Pink or Green) Items included
More informationMark Scheme (Results) January Pearson Edexcel Level 3 Award In Algebra (AAL30)
Mark Scheme (Results) January 0 Pearson Edexcel Level 3 Award In Algebra (AAL30) Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK s largest awarding body.
More informationPRACTICE PAPER 6 SOLUTIONS
PRACTICE PAPER 6 SOLUTIONS SECTION A I.. Find the value of k if the points (, ) and (k, 3) are conjugate points with respect to the circle + y 5 + 8y + 6. Sol. Equation of the circle is + y 5 + 8y + 6
More informationThis document consists of 15 printed pages.
Cambridge International Examinations Cambridge International Advanced Level FURTHER MATHEMATICS 93/ Paper MARK SCHEME Maximum Mark: 00 Published This mark scheme is published as an aid to teachers and
More informationPhysicsAndMathsTutor.com. Mark Scheme (Results) June GCE Core Mathematics 4 (6666/01)
Mark Scheme (Results) June 03 GCE Core Mathematics 4 (6666/0) Edecel and BTEC Qualifications Edecel and BTEC qualifications come from Pearson, the world s leading learning company. We provide a wide range
More informationand in each case give the range of values of x for which the expansion is valid.
α β γ δ ε ζ η θ ι κ λ µ ν ξ ο π ρ σ τ υ ϕ χ ψ ω Mathematics is indeed dangerous in that it absorbs students to such a degree that it dulls their senses to everything else P Kraft Further Maths A (MFPD)
More informationVersion 1.0: abc. General Certificate of Education. Mathematics MFP2 Further Pure 2. Mark Scheme examination June series
Version.0: 0608 abc General Certificate of Education Mathematics 6360 MFP Further Pure Mark Scheme 008 examination June series Mark schemes are prepared by the Principal Examiner and considered, together
More informationMark Scheme (Results) Summer Pearson Edexcel International A Level in Core Mathematics C34 (WMA02/01)
Mark Scheme (Results) Summer 05 Pearson Edecel International A Level in Core Mathematics C4 (WMA0/0) Edecel and BTEC Qualifications Edecel and BTEC qualifications are awarded by Pearson, the UK s largest
More informationVersion 1.0: hij. General Certificate of Education. Mathematics MFP2 Further Pure 2. Mark Scheme examination - June series
Version.0: 0609 hij General Certificate of Education Mathematics 6360 MFP Further Pure Mark Scheme 009 examination - June series Mark schemes are prepared by the Principal Examiner and considered, together
More informationCondensed. Mathematics. General Certificate of Education Advanced Subsidiary Examination January Unit Pure Core 2.
General Certificate of Education Advanced Subsidiary Eamination January 0 Mathematics MPC Unit Pure Core Monday 0 January 0 9.00 am to 0.0 am For this paper you must have: the blue AQA booklet of formulae
More information2014 HSC Mathematics Extension 2 Marking Guidelines
04 HSC Mathematics Extension Marking Guidelines Section I Multiple-choice Answer Key Question Answer D A 3 B 4 C 5 C 6 D 7 B 8 B 9 A 0 D BOSTES 04 HSC Mathematics Extension Marking Guidelines Section II
More information