{... expansion. January Core Mathematics C4 Mark Scheme. Question Number ** represents a constant
|
|
- Jack Watts
- 5 years ago
- Views:
Transcription
1 January Core Mathematics C Mark Question ** represents a constant. 5x 5x f(x) ( 5x) Takes outside the bracket to give any of () - or. B + ( )(* * x); + (* * x) + (* * x) +...!! Expands ( + * * x) to give an unsimplified + ( )(* * x); A correct unsimplified {... expansion } with candidate s (**x) A ( )( ) ( )( )( ) ;... 5x 5x 5x !! 75x 5x 5x; x 75x 5x + ; Anything that cancels to 5x + ; 75x Simplified 5x + A; 6 8 A 5 + x; + x + 5 x [5] 5 marks 9
2 Aliter. Way f(x) ( 5x) ( )( ) () + () (* * x); + () (* * x)! ( )( )( ) 5 + () (* * x) +...! or () Expands ( 5x) to give an unsimplifed () + ( )() (* * x); A correct unsimplified {... expansion } with candidate s (**x) B A ( )( ) () + ( )() ( 5x); + () ( 5x)! ( )( )( ) 5 + () ( 5x) +...! + ( )( 5x); + ()(5x ) ( )( 5x ) x 75x 5x + ; Anything that cancels to 5x + ; 75x Simplified 5x + A; 6 8 A 5 + x; + x + 5 x [5] 5 marks Attempts using Maclaurin expansions need to be referred to your team leader. 0
3 . (a) Volume x 9 x ( + ) ( + ) Use of V y. Can be implied. Ignore limits. B 9 ( + ) x Moving their power to the top. (Do not allow power of -.) Can be implied. Ignore limits and 9 (+ x) 9 ( )() Integrating to give ± p( + x) ( x) + A + 9 ( x) 9 () ( ) 9 Use of limits to give exact values of or or or aef 6 (b) From Fig., AB ( ) units A aef [5] As units cm then scale factor k. Hence Volume of paperweight ( ) (their answer to part (a)) V 6 cm cm 6 or awrt or or aef A [] Note: 9 (or implied) is not needed for the middle three marks of question (a). 7 marks
4 Aliter. (a) Volume Way x 6x ( + ) ( + ) ( ) ( + ) 6x Use of V y. Can be implied. Ignore limits. Moving their power to the top. (Do not allow power of -.) Can be implied. Ignore limits and B ( + 6x) ( )(6) Integrating to give ± p( + 6x) ( + 6x) 6 A + ( 6 6x) 6(6) 6 ( ) 6 9 Use of limits to give exact values of or or aef or 6 A aef [5] Note: is not needed for the middle three marks of question (a).
5 . (a) x 7cos t cos7t, y 7 sin t sin7t, 7sint + 7sin7t, 7cost 7cos7t Attempt to differentiate x and y with respect to t to give in the form ± A sin t ± B sin7t in the form ± Ccost ± Dcos7t Correct and A 7cos t 7cos7t 7 sin t + 7 sin7t Candidate s B [] (b) 7 7cos 7cos When t, m(t) sin 7sin ; Substitutes t 6 or 0 o into their awrt to give any of the four underlined expressions oe (must be correct solution only) A cso Hence m(n) or awrt 0.58 Uses m(t) to correctly find m(n). Can be ft from their tangent gradient. A oe. When t 6, 7 x 7cos cos y 7sin sin N: y ( ) x The point (, ) or ( awrt 6.9, ) Finding an equation of a normal with their point and their normal gradient or finds c by using y (their gradient)x + "c ". B N: y x or y x or y x Correct simplified EXACT equation of normal. This is dependent on candidate using correct (, ) A oe or + c c 0 Hence N: y x or y x or y x [6] 9 marks
6 Aliter. (a) x 7cos t cos7t, y 7 sin t sin7t, Way 7sint + 7sin7t, 7cost 7cos7t Attempt to differentiate x and y with respect to t to give in the form ± A sin t ± B sin7t in theform ± Ccost ± Dcos7t Correct and A 7cost 7cos7t 7( sint sint) tant 7sint + 7sin7t 7(cost sint) Candidate s B [] (b) When t, m(t) tan ; 6 6 Substitutes t 6 or 0 o into their ( ) ( ) awrt.7 () to give any of the three underlined expressions oe (must be correct solution only) A cso Hence m(n) or awrt 0.58 Uses m(t) to correctly find m(n). Can be ft from their tangent gradient. A oe. When t 6, 7 x 7cos cos y 7sin sin N: y ( ) x The point (, ) or ( awrt 6.9, ) Finding an equation of a normal with their point and their normal gradient or finds c by using y (their gradient)x + "c ". B N: y x or y x or y x Correct simplified EXACT equation of normal. This is dependent on candidate using correct (, ) A oe or + c c 0 Hence N: y x or y x or y x [6] 9 marks
7 Beware: A candidate finding an m(t) 0 can obtain Aft for m(n), but obtains M0 if they write y (x ). If they write, however, N: x, then they can score. Beware: A candidate finding an m(t) can obtain Aft for m(n) 0, and also obtains if they write y 0(x ) or y. 5
8 . (a) x A B + (x )(x ) (x ) (x ) x A(x ) + B(x ) Let x, ( ) B B Forming this identity. NB: A & B are not assigned in this question Let x, A A either one of A or B. A both correct for their A, B. A giving + (x ) (x ) [] (b) & (c) (x ) y (x )(x ) Separates variables as shown Can be implied B + (x ) (x ) Replaces RHS with their partial fraction to be integrated. ln y ln(x ) + ln(x ) + c At least two terms in ln s At least two ln terms correct All three terms correct and + c A A [5] y 0, x gives c ln0 c ln0 B ln y ln(x ) + ln(x ) + ln0 ln y ln(x ) + ln(x ) + ln0 Using the power law for logarithms (x ) ln y ln + ln0 or (x ) 0(x ) ln y ln (x ) Using the product and/or quotient laws for logarithms to obtain a single RHS logarithmic term with/without constant c. y 0(x ) (x ) y 0(x ) (x ) or aef. isw A aef [] marks 6
9 Aliter. (b) & (c) Way (x ) y (x )(x ) + (x ) (x ) Separates variables as shown Can be implied Replaces RHS with their partial fraction to be integrated. B ln y ln(x ) + ln(x ) + c At least two terms in ln s At least two ln terms correct All three terms correct and + c A A See below for the award of B decide to award B here!! B ln y ln(x ) + ln(x ) + c (x ) ln y ln + c x Using the power law for logarithms Using the product and/or quotient laws for logarithms to obtain a single RHS logarithmic term with/without constant c. ln y A(x ) ln x where c lna or (x ) (x ) ln + c ln x x lny e e e e c y A(x ) (x ) y 0, x gives A 0 A 0 for B award above y 0(x ) (x ) y 0(x ) (x ) or aef & isw A aef [5] & [] Note: The B mark (part (c)) should be awarded in the same place on epen as in the Way approach. 7
10 Aliter (b) & (c) Way (x ) y (x )(x ) Separates variables as shown Can be implied + Replaces RHS with their partial (x ) (x ) fraction to be integrated. B ln y ln(x ) + ln(x ) + c At least two terms in ln s At least two ln terms correct All three terms correct and + c A A [5] y 0, x gives c ln0 ln ln 0 c ln0 ln( ) or c ln0 B oe ln y ln(x ) + ln(x ) + ln 0 ln y ln(x ) ln(x ) ln0 + + Using the power law for logarithms (x ) ln y ln + ln 0 or (x ) 0(x ) ln y ln (x ) Using the product and/or quotient laws for logarithms to obtain a single RHS logarithmic term with/without constant c. y 0(x ) (x ) y 0(x ) (x ) or aef. isw A aef [] Note: Please mark parts (b) and (c) together for any of the three ways. 8
11 5. (a) sin x + cos y 0.5 ( eqn ) cos x sin y 0 ( eqn # ) Differentiates implicitly to include ± sin y. (Ignore ( ).) cos x sin y cos x sin y A cso [] (b) cos x 0 0 cosx 0 sin y Candidate realises that they need to solve their numerator 0 or candidate sets 0 in their (eqn #) and attempts to solve the resulting equation. giving x or x both x o, or x ± 90 or awrt x ±.57 required here A When x When x, ( ), sin + cos y 0.5 sin + cos y 0.5 x Substitutes either their or x into eqn cos y.5 y has no solutions cos y 0.5 y or Only one of y o or or 0 or 0 or awrt -.09 or awrt.09 A In specified range ( x, y, ) and (, ) Only exact coordinates of, and, Do not award this mark if candidate states other coordinates inside the required range. A [5] 7 marks 9
12 6. x x ln y e (a) Way Aliter ln.e ln.e xln xln Hence x (a) ln y ln( ) Way x x ln. ln AG x ln AG A cso leads to ln y x ln Takes logs of both sides, then uses the power law of logarithms ln y and differentiates implicitly to give ln y [] Hence x yln ln AG x ln AG A cso [] (b) (x ) y (x ) x..ln (x ) Ax (x ) x..ln or x.y.ln if y is defined A When x, () ln Substitutes x into their which is of the form ± k x or Ax (x ) 6ln ln or awrt. A [] 6 marks 50
13 Aliter 6. (b) ln y ln( ) x Way leads to x.ln y ln y x ln Ax.ln y x.ln y A When x, () ln Substitutes x into their which is of the form ± k x or Ax (x ) 6ln ln or awrt. A [] 5
14 7. a OA i + j + k OA b OB i + j k OB 8 BC ± ( i + j + k) BC AC ± i + j k AC 8 (a) c OC i + j k i + j k B cao [] (b) OA OB + 0 or BO BC + 0 or AC BC + 0 or AO AC + 0 An attempt to take the dot product between either OA and OB OA and AC, AC and BC or OB and BC Showing the result is equal to zero. A and therefore OA is perpendicular to OB and hence OACB is a rectangle. perpendicular and OACB is a rectangle A cso Area (c) OD d ( i + j k ) Using distance formula to find either the correct height or wih. Multiplying the rectangle s height by its wih. exact value of 8, 9, 6 or aef ( + ) A i j k B [6] [] 5
15 (d) Way using dot product formula 5 DA ± ( i + j + k ) BA ± i + j + 5k or & DC ± ( i + j k ) & OC ± ( i + j k) cos D ( ± ) ( ± ) ( ± ) Identifies a set of two relevant vectors Correct vectors ± Applies dot product formula on multiples of these vectors. Correct ft. application of dot product formula. A d A D cos Attempts to find the correct angle D rather than 80 D. dd Aliter o D using dot product formula and direction vectors (d) d BA ± ( i + j + 5k) Way & d OC ± ( i + j k) cos D ( ± ) ( ± ) ( ± ) or awrt09 or.9 c Identifies a set of two direction vectors Correct vectors ± Applies dot product formula on multiples of these vectors. Correct ft. application of dot product formula. A A d A [6] D cos Attempts to find the correct angle D rather than 80 D. dd o D or awrt09 or.9 c A [6] 5
16 Aliter using dot product formula and similar triangles (d) doa ( i + j + k) Way cos ( D) & d OC ( i + j k) Identifies a set of two direction vectors Correct vectors A Applies dot product formula on multiples of these vectors. Correct ft. application of dot product formula. d A D cos Attempts to find the correct angle D by doubling their angle for D. dd o D or awrt09 or.9 c A [6] Aliter using cosine rule 5 (d) DA i + j + k Way DA 7,, DC + DC 7 i j k, AC 8, AC i + j k Attempts to find all the lengths of all three edges of ADC All Correct A ( 8 ) cos D 7 7 Using the cosine rule formula with correct subtraction. Correct ft application of the cosine rule formula d A D cos Attempts to find the correct angle D rather than 80 D. dd o D or awrt09 or.9 c A [6] 5
17 Aliter using trigonometry on a right angled triangle 5 (d) DA i + j + k OA i + j + k AC i + j k Way 5 Let X be the midpoint of AC 7 DA, DX OA, AX AC 8 (hypotenuse), (adjacent), (opposite) Attempts to find two out of the three lengths in ADX Any two correct A 8 7 sin( D), 7 cos( D) or 8 tan( D) Uses correct sohcahtoa to find D Correct ft application of sohcahtoa d A eg. 8 D tan Attempts to find the correct angle D by doubling their angle for D. dd o D or awrt09 or.9 c A [6] Aliter using trigonometry on a right angled similar triangle OAC (d) OC i + j k OA i + j + k AC i + j k Way 6 OC 7, OA, AC 8 (hypotenuse), (adjacent), (opposite) Attempts to find two out of the three lengths in OAC Any two correct A 8 sin( D), cos( D) or tan( D) Uses correct d sohcahtoa to find D Correct ft application of sohcahtoa A eg. 8 D tan Attempts to find the correct angle D by doubling their angle for D. dd o D or awrt09 or.9 c A [6] 55
18 Aliter 7. (b) (i) Way c OC ± i + j k AB ± 5 ( i j k) A complete method of proving that the diagonals are equal. OC () + () + ( ) () + () + ( 5) AB As OC AB 7 Correct result. A then the diagonals are equal, and OACB is a rectangle. a OA i + j + k OA b OB i + j k OB 8 BC ± ( i + j + k) BC AC ± ( i + j k) AC 8 c OC ± ( i + j k) OC 7 AB ± i j 5k AB 7 diagonals are equal and OACB is a rectangle A cso [] Aliter ( OA) + ( AC) ( OC) 7. (b) (i) or ( BC) + ( OB) ( OC) or ( OA) + ( OB) ( AB) or equivalent Way or ( BC) + ( AC) ( AB) + () ( 8) 7 A complete method of proving that Pythagoras holds using their values. Correct result A and therefore OA is perpendicular to OB or AC is perpendicular to BC and hence OACB is a rectangle. perpendicular and OACB is a rectangle A cso [] marks 56
19 8. (a) x 0 5 y e e e 7 0 e e e or y Either e, e and e or awrt.,.6 and 6.8 or e to the power awrt.65,.6,.6 (or mixture of decimals and e s) At least two correct All three correct B B [] (b) { 7 0 } I ; e + e + e + e + e + e Outside brackets For structure of trapezium rule{...} ; B; (sf) 0.6 A cao [] Beware: In part (b) candidates can add up the individual trapezia: (b) ( + ) + ( + ) + ( + ) + ( + ) + ( + ) I.e e.e e.e e.e e.e e 57
20 (c) t (x + )..(x + ) or t x+ t A(x ) + or t A (x + ) or t A so.(x + ) t t Candidate obtains either or in terms of t (x+ ) I e e t. t t e.. and moves on to substitute this into I to convert an integral wrt x to an integral wrt t. d I t te t te A change limits: when x 0, t & when x 5, t changes limits x t so that 0 and 5 B t Hence I te ; where a, b, k [5] (d) du u t dv t t e v e Let k be any constant for the first three marks of this part. k te t k te t e t. t t k te e + c { } t te e e e e Use of integration by parts formula in the correct direction. Correct expression with a constant factor k. Correct integration with/without a constant factor k Substitutes their changed limits into the integrand and subtracts oe. A A d oe (e ) e either e or awrt 09. A [5] 5 marks Note: d denotes a method mark which is dependent upon the award of the previous method mark dd denotes a method mark which is dependent upon the award of the previous two method marks. 58
Mark Scheme (Results) January 2007
Mark (Results) January 007 GCE GCE Mathematics Core Mathematics C (6666) Edexcel Limited. Registered in England and Wales No. 96750 Registered Office: One90 High Holborn, London WCV 7BH ** represents a
More informationPhysicsAndMathsTutor.com
Edecel GCE Core Mathematics C4 (6666) PhysicsAndMathsTutor.com GCSE Edecel GCE Core Mathematics C4 (6666) Summer 005 Mark (Results) Final Version June 005 6666 Core C4 Mark. ( ) 4 9 9 = 4 B 9 ( ) 9 ( )(
More informationGCE Edexcel GCE. Core Mathematics C4 (6666) June Edexcel GCE. Mark Scheme (Final) Core Mathematics C4 (6666)
GCE Edecel GCE Core Mathematics C4 (6666) June 006 Mark (Final) Edecel GCE Core Mathematics C4 (6666) June 006 6666 Pure Mathematics C4 Mark Question. dy dy dy = 6 4y + = 0 d d d Differentiates implicitly
More informationMark Scheme (Results) Summer 2008
Mark (Results) Summer 008 GCE GCE Mathematics (6666/0) Edecel Limited. Registered in England and Wales No. 4496750 Registered Office: One90 High Holborn, London WCV 7BH June 008 6666 Core Mathematics C4
More informationMark Scheme (Final) January 2009
Mark (Final) January 009 GCE GCE Core Mathematics C (6666/0) Edecel Limited. Registered in England and Wales No. 96750 Registered Office: One90 High Holborn, London WCV 7BH General Marking Guidance All
More informationPhysicsAndMathsTutor.com
. A curve C has parametric equations x sin t, y tan t, 0 t < (a) Find in terms of t. (4) The tangent to C at the point where t cuts the x-axis at the point P. (b) Find the x-coordinate of P. () (Total
More informationMark Scheme (Results) January GCE Core Mathematics C4 (6666) Paper 1
Mark Scheme (Results) January 0 GCE Core Mathematics C4 (6666) 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
More informationPhysicsAndMathsTutor.com
. A curve C has parametric equations x = sin t, y = tan t, 0 t < (a) Find in terms of t. (4) The tangent to C at the point where t = cuts the x-axis at the point P. (b) Find the x-coordinate of P. () (Total
More informationMark Scheme (Results) June GCE Core Mathematics C2 (6664) Paper 1
Mark (Results) June 0 GCE Core Mathematics C (6664) 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 informationTime: 1 hour 30 minutes
Paper Reference(s) 6666/ Edexcel GCE Core Mathematics C4 Gold Level (Harder) G3 Time: hour 3 minutes Materials required for examination Mathematical Formulae (Green) Items included with question papers
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education. Published
Cambridge International Examinations Cambridge International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/ Paper October/November 06 MARK SCHEME Maximum Mark: 80 Published This
More informationA-LEVEL Mathematics. Pure Core 4 MPC4 Mark scheme June Version 1.1: Final
A-LEVEL Mathematics Pure Core MPC Mark scheme 0 June 05 Version.: Final Mark schemes are prepared by the Lead Assessment Writer and considered, together with the relevant questions, by a panel of subject
More informationMark Scheme (Results) Summer Pearson Edexcel GCE in Core Mathematics 4 (6666/01)
Mark Scheme (Results) Summer 05 Pearson Edexcel GCE in Core Mathematics 4 (6666/0) Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK s largest awarding bo.
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 informationADDITIONAL MATHEMATICS 4037/12 Paper 1 October/November 2016 MARK SCHEME Maximum Mark: 80. Published
Cambridge International Eaminations Cambridge Ordinary Level ADDITIONAL MATHEMATICS 07/ Paper October/November 06 MARK SCHEME Maimum Mark: 80 Published This mark scheme is published as an aid to teachers
More informationMark Scheme (Results) Summer Pearson Edexcel GCE in Core Mathematics 2R (6664_01R)
Mark (Results) Summer 014 Pearson Edexcel GCE in Core Mathematics R (6664_01R) Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK s largest awarding body. We
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 informationMark Scheme (Results) January 2008
Mark Scheme (Results) January 008 GCE GCE Mathematics (6664/01) Edecel Limited. Registered in England and Wales No. 4496750 Registered Office: One90 High Holborn, London WC1V 7BH January 008 6664 Core
More informationMark Scheme (Results) Summer GCE Core Mathematics C4 6666/01 Original Paper
Mark Scheme (Results) Summer 0 GCE Core Mathematics C 6666/0 Original Paper Edexcel and BTEC Qualifications Edexcel and BTEC qualifications come from Pearson, the world s leading learning company. We provide
More informationMark Scheme (Results) January 2007
Mark Scheme (Results) January 007 GCE GCE Mathematics Core Mathematics C (666) Edexcel Limited. Registered in England and Wales No. 96750 Registered Office: One90 High Holborn, London WCV 7BH January 007
More informationPMT. Mark Scheme (Results) Summer Pearson Edexcel International A Level in Core Mathematics C34 (WMA02/01)
Mark Scheme (Results) Summer 04 Pearson Edexcel International A Level in Core Mathematics C4 (WMA0/0) Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK s largest
More informationPhysicsAndMathsTutor.com
. A curve C has equation x + y = xy Find the exact value of at the point on C with coordinates (, ). (Total marks). The curve C has the equation cosx + cosy =, π π x, 4 4 0 π y 6 (a) Find in terms of x
More informationAS Level / Year 1 Edexcel Maths / Paper 1
AS Level / Year Edexcel Maths / Paper March 8 Mocks 8 crashmaths Limited 4x + 4x + 3 = 4( x + x) + 3 Takes out a factor of 4 from first two terms or whole expression = 4 x + + 3 4 Completes the square
More informationTime: 1 hour 30 minutes
Paper Reference(s) 6666/0 Edexcel GCE Core Mathematics C4 Silver Level S Time: hour 30 minutes Materials required for examination papers Mathematical Formulae (Green) Items included with question Nil Candidates
More informationMark Scheme (Results) June GCE Further Pure FP1 (6667) Paper 1
Mark Scheme (Results) June 0 GCE Further Pure FP (6667) 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 informationPMT. Mark Scheme (Results) Summer Pearson Edexcel International A Level in Core Mathematics C34 (WMA02/01)
Mark Scheme (Results) Summer 04 Pearson Edexcel International A Level in Core Mathematics C4 (WMA0/0) Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK s largest
More informationMark Scheme (Results) Summer GCE Core Mathematics 4 (6666/01R)
Mark Scheme (Results) Summer 0 GCE Core Mathematics 4 (6666/0R) Edexcel and BTEC Qualifications Edexcel and BTEC qualifications come from Pearson, the world s leading learning company. We provide a wide
More informationJanuary 2015 (IAL) PhysicsAndMathsTutor.com. Mark Scheme (Results) January Pearson Edexcel International A Level Core Mathematics 12 (WMA01_01)
January 05 (IAL) Mark (Results) January 05 Pearson Edexcel International A Level Core Mathematics (WMA0_0) January 05 (IAL) Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by
More informationMark Scheme (Results) Summer 2010
Mark (Results) Summer 010 GCE Core Mathematics C (6664) Edexcel Limited. Registered in England and Wales No. 4496750 Registered Office: One90 High Holborn, London WC1V 7BH Edexcel is one of the leading
More informationPhysicsAndMathsTutor.com
PhysicsAndMathsTutor.com 47 Mark Scheme June 00 (i) u =, u =, u = 8 The sequence is an Arithmetic Progression B B B For the correct value of u For both correct values of u and u For a correct statement
More informationVersion 1.0: abc. General Certificate of Education. Mathematics MPC4 Pure Core 4. Mark Scheme examination - January series
Version.0: 007 abc General Certificate of Education Mathematics 0 MPC Pure Core Mark Scheme 007 examination - January series Mark schemes are prepared by the Principal Examiner and considered, together
More informationPhysicsAndMathsTutor.com. Mark Scheme (Results) Summer Pearson Edexcel GCE in Core Mathematics 2 (6664/01)
Mark Scheme (Results) Summer 06 Pearson Edexcel GCE in Core Mathematics (666/0) Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK s largest awarding body. We
More informationC4 QUESTIONS FROM PAST PAPERS DIFFERENTIATION
C4 QUESTIONS FROM PAST PAPERS DIFFERENTIATION. A curve C has equation + y = y Find the eact value of at the point on C with coordinates (, ). (Total 7 marks). The diagram above shows a cylindrical water
More informationTime: 1 hour 30 minutes
Paper Reference(s) 6666/0 Edexcel GCE Core Mathematics C4 Silver Level S5 Time: hour 0 minutes Materials required for examination papers Mathematical Formulae (Green) Items included with question Nil Candidates
More informationTime: 1 hour 30 minutes
Paper Reference(s) 6666/0 Edexcel GCE Core Mathematics C4 Silver Level S Time: hour 0 minutes Materials required for examination papers Mathematical Formulae (Green) Items included with question Nil Candidates
More informationPaper 1 (Edexcel Version)
AS Level / Year 1 Paper 1 (Edexcel Version) Set A / Version 1 017 crashmaths Limited 1 y = 3x 4 + x x +1, x > 0 (a) ydx = 3x 3 3 3 + x 3 / x + x {+c} Attempts to integrate, correct unsimplified integration
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 informationADDITIONAL MATHEMATICS 4037/23 Paper 2 October/November 2016 MARK SCHEME Maximum Mark: 80. Published
Cambridge International Examinations Cambridge Ordinary Level ADDITIONAL MATHEMATICS 407/ Paper October/November 016 MARK SCHEME Maximum Mark: 80 Published This mark scheme is published as an aid to teachers
More informationMark scheme. 65 A1 1.1b. Pure Mathematics Year 1 (AS) Unit Test 5: Vectors. Pearson Progression Step and Progress descriptor. Q Scheme Marks AOs
Pure Mathematics Year (AS) Unit Test : Vectors Makes an attempt to use Pythagoras theorem to find a. For example, 4 7 seen. 6 A.b 4th Find the unit vector in the direction of a given vector Displays the
More informationMark Scheme (Results) October Pearson Edexcel IAL in Core Mathematics 12 (WMA01/01)
Mark Scheme (Results) October 06 Pearson Edexcel IAL in Core Mathematics (WMA0/0) Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK s largest awarding body.
More informationMark Scheme (Results) Summer GCE Core Mathematics 2 (6664/01)
Mark (Results) Summer 0 GCE Core Mathematics (666/0) Edexcel and BTEC Qualifications Edexcel and BTEC qualifications come from Pearson, the world s leading learning company. We provide a wide range of
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 informationPhysicsAndMathsTutor.com. GCE Edexcel GCE. Core Mathematics C2 (6664) January Mark Scheme (Results) Core Mathematics C2 (6664) 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. (a) +-5 + c = 0 or - + c = 0 c = A () (b)
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 informationVersion 1.0. klm. General Certificate of Education June Mathematics. Pure Core 4. Mark Scheme
Version.0 klm General Certificate of Education June 00 Mathematics MPC4 Pure Core 4 Mark Scheme Mark schemes are prepared by the Principal Examiner and considered, together with the relevant questions,
More informationMark Scheme (Results) January Pearson Edexcel International GCSE In Further Pure Mathematics (4PM0) Paper 1
Mark Scheme (Results) January 07 Pearson Edexcel International GCSE In Further Pure Mathematics (4PM0) Paper Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the
More information0606 ADDITIONAL MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the May/June 5 series 66 ADDITIONAL MATHEMATICS 66/ Paper, maximum raw mark 8 This
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) January Pearson Edexcel International Advanced Level Core Mathematics C12 (WMA01/01)
Mark (Results) January 04 Pearson Edexcel International Advanced Level Core Mathematics C (WMA0/0) Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK s largest
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 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 informationTime: 1 hour 30 minutes
Paper Reference(s) 6664/01 Edexcel GCE Core Mathematics C Silver Level S3 Time: 1 hour 30 minutes Materials required for examination Mathematical Formulae (Green) Items included with question papers Nil
More informationTime: 1 hour 30 minutes
Paper Reference(s) 6666/ Edecel GCE Core Mathematics C4 Gold Level (Hardest) G4 Time: hour minutes Materials required for eamination Mathematical Formulae (Green) Items included with question papers Nil
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 informationMark Scheme (Results) January International Advanced Level in Core Mathematics C12 (WMA01/01)
Mark (Results) January 06 International Advanced Level in Core Mathematics C (WMA0/0) Edexcel and BTEC Qualifications Edexcel and BTEC qualifications come from Pearson, the world s leading learning company.
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 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 information4754A Mark Scheme June 2014 BUT
4754A Mark Scheme June 04 3x A Bx C ( x)(4 x ) x 4 x correct form of partial fractions ( condone additional coeffs eg A B BUT x 4 x ** is M0 ) Ax B Cx D x 4 x * for 3x = A(4 + x ) + (Bx + C)( x) Multiplying
More informationMark Scheme (Results) Summer 2009
Mark Scheme (Results) Summer 009 GCSE GCSE Mathematics (Linear) - 1380 Paper: NOTES ON MARKING PRINCIPLES 1 Types of mark M marks: method marks A marks: accuracy marks B marks: unconditional accuracy marks
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 informationWednesday 18 June 2014 Afternoon
Wednesday 8 June 04 Afternoon A GCE MATHEMATICS (MEI) 4754/0A Applications of Advanced Mathematics (C4) Paper A QUESTION PAPER * 4 3 4 5 9 5 9 * Candidates answer on the Printed Answer Book. OCR supplied
More informationTABLE OF CONTENTS 2 CHAPTER 1
TABLE OF CONTENTS CHAPTER 1 Quadratics CHAPTER Functions 3 CHAPTER 3 Coordinate Geometry 3 CHAPTER 4 Circular Measure 4 CHAPTER 5 Trigonometry 4 CHAPTER 6 Vectors 5 CHAPTER 7 Series 6 CHAPTER 8 Differentiation
More informationMark Scheme (Results) June GCE Core Mathematics C3 (6665) Paper 1
Mark Scheme (Results) June 2011 GCE Core Mathematics C3 (6665) 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 informationTime: 1 hour 30 minutes
Paper Reference (complete below) Centre No. Surname Initial(s) Candidate No. Signature Paper Reference(s) 6663 Edexcel GCE Pure Mathematics C Advanced Subsidiary Specimen Paper Time: hour 30 minutes Examiner
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 informationPMT. Mark Scheme (Results) Summer Pearson Edexcel GCE in Core Mathematics 4 (6666/01)
Mark Scheme (Results) Summer 04 Pearson Edecel GCE in Core Mathematics 4 (6666/0) Edecel and BTEC Qualifications Edecel and BTEC qualifications come from Pearson, the world s leading learning company.
More informationMark Scheme (Results) Summer 2007
Mark (Results) Summer 007 GCE GCE Mathematics Core Mathematics C (6665) Edexcel Limited. Registered in England and Wales No. 4496750 Registered Office: One90 High Holborn, London WCV 7BH June 007 6665
More information(b) find the possible values of a. (2) (Total 6 marks) and simplify each term. (Total 4 marks)
1. (a) Find the first 4 terms, in ascending powers of x, of the binomial expansion of (1 + ax) 7, where a is a constant. Give each term in its simplest form. (4) Given that the coefficient of x in this
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 informationMARK SCHEME for the October/November 2013 series 9709 MATHEMATICS. 9709/11 Paper 1, maximum raw mark 75
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the October/November 013 series 9709 MATHEMATICS 9709/11 Paper 1, maximum raw mark 75 This mark
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 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 informationVersion General Certificate of Education. Mathematics MPC1 Pure Core 1. Mark Scheme examination - January series
Version.0 00 General Certificate of Education Mathematics 660 MPC Pure Core Mark Scheme 00 examination - January series Mark schemes are prepared by the Principal Examiner and considered, together with
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) 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 informationMark Scheme (Results) Summer Pearson Edexcel GCE in Core Mathematics 1 (6663_01)
Mark Scheme (Results) Summer 0 Pearson Edexcel GCE in Core Mathematics (666_0) Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK s largest awarding body. We
More informationGCSE (9-1) Paper 2H (Calculator)
GCSE (9-1) Paper H (Calculator) Practice set A 017 crashmaths Limited CM GCSE Practice Papers / Set A / Paper H (V1 FINAL) 1 (a) (1, 0) 1 B1 : cao (b) rotation 3 B1 : correct orientation of the shape (m
More informationPhysicsAndMathsTutor.com
. The diagram above shows a cylindrical water tank. The diameter of a circular cross-section of the tank is 6 m. Water is flowing into the tank at a constant rate of 0.48π m min. At time t minutes, the
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 informationM A1. 4 M1 for listing at least three multiples for any two of 25, 12, (i) 24
MA Practice papers Set : Paper H (Regular) mark scheme Version.0. 3 M 500 (00 00) (=0.5) 87 A M 8 0.5. (i) 4 50 75 4 M for listing at least three multiples for any two of 5,, 8 M for listing at least three
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 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 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 informationMark Scheme (Results) January Pearson Edexcel International GCSE Mathematics B (4MB0) Paper 02
Mark Scheme (Results) January 017 Pearson Edexcel International GCSE Mathematics B (4MB0) Paper 0 Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK s largest
More information0606 ADDITIONAL MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the October/November 0 series 0606 ADDITIONAL MATHEMATICS 0606/ Paper, maimum raw
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 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 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 informationMark Scheme (Results) January Pearson Edexcel International GCSE In Further Pure Mathematics (4PM0) Paper 2
Mark (Results) Januar 07 Pearson Edexcel International GCSE In Further Pure Mathematics (4PM0) Paper Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded b Pearson, the UK s largest
More informationMARK SCHEME for the November 2004 question paper 9709 MATHEMATICS 8719 HIGHER MATHEMATICS
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary and Advanced Level MARK SCHEME for the November 004 question paper 9709 MATHEMATICS 879 HIGHER MATHEMATICS 9709/03, 879/03 Paper
More informationGCSE. Edexcel GCSE Mathematics A Summer Mark Scheme (Results)
GCSE Edexcel GCSE Mathematics A 387 Summer 006 Mark Scheme (Results) NOTES ON MARKING PRINCIPLES Types of mark M marks: method marks A marks: accuracy marks B marks: unconditional accuracy marks (independent
More information5w 3. 1MA0 Higher Tier Practice Paper 2H (Set D) Question Working Answer Mark Notes 1 (a) 5w 8 = 3(4w + 2) 5w 8 = 12w = 12w 5w 14 = 7w
(a) 5w 8 = (4w + ) 5w 8 = w + 6 8 6 = w 5w 4 = 7w M for attempting to multiply both sides by as a first step (this can be implied by equations of the form 5w 8 = w +? or 5w 8 =?w + 6 i.e. the LHS must
More information9709 MATHEMATICS. 9709/13 Paper 1, maximum raw mark 75
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the May/June 0 series 9709 MATHEMATICS 9709/ Paper, maximum raw mark 75 This mark scheme is published
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 informationCambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level. Published
Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level MATHEMATICS 9709/1 Paper 1 October/November 016 MARK SCHEME Maximum Mark: 75 Published This mark scheme
More informationMark Scheme (Results) Summer Pearson Edexcel International GCSE In Mathematics B (4MB0) Paper 02
Mark Scheme (Results) Summer 017 Pearson Edexcel International GCSE In Mathematics B (4MB0) Paper 0 Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK s largest
More informationEdexcel GCE. Mathematics. Pure Mathematics P Summer FINAL Mark Scheme. Mathematics. Edexcel GCE
Edexcel GCE Mathematics Pure Mathematics P 667 Summer 00 FINAL Mark Scheme Edexcel GCE Mathematics General Instructions. The total number of marks for the paper is 7.. Method (M) marks are awarded for
More informationCambridge Assessment International Education Cambridge International General Certificate of Secondary Education. Published
Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/ Paper 07 MARK SCHEME Maximum Mark: 80 Published This mark scheme
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 information