Methods Higher Tier Practice Paper Unit 1 Markscheme

Transcription

1 Methods Higher Tier Pratie Paper Unit Marksheme

2 GCSE MATHEMATICS LINKED PAIR METHODS FOUNDATION NOTES ON MARKING PRINCIPLES Types of mark M marks: method marks A marks: auray marks B marks: unonditional auray marks (independent of M marks) Areviations ao orret answer only isw ignore susequent working oe or equivalent (and appropriate) indep - independent ft follow through SC: speial ase dep dependent No working If no working is shown then orret answers normally sore full marks If no working is shown then inorret (even though nearly orret) answers sore no marks. 4 With working If there is a wrong answer indiated on the answer line always hek the working in the ody of the sript (and on any diagrams), and award any marks appropriate from the mark sheme. If working is rossed out and still legile, then it should e given any appropriate marks, as long as it has not een replaed y alternative work. If it is lear from the working that the orret answer has een otained from inorret working, award 0 marks. Send the response to review, and disuss eah of these situations with your Team Leader. If there is no answer on the answer line then hek the working for an ovious answer. Any ase of suspeted misread loses A (and B) marks on that part, ut an gain the M marks. Disuss eah of these situations with your Team Leader. If there is a hoie of methods shown, then no marks should e awarded, unless the answer on the answer line makes lear the method that has een used. 5 Follow through marks Follow through marks whih involve a single stage alulation an e awarded without working sine you an hek the answer yourself, ut if amiguous do not award. Follow through marks whih involve more than one stage of alulation an only e awarded on sight of the relevant working, even if it appears ovious that there is only one way you ould get the answer given. Ignoring susequent work Paper: Methods F

3 GCSE MATHEMATICS LINKED PAIR METHODS FOUNDATION It is appropriate to ignore susequent work when the additional work does not hange the answer in a way that is inappropriate for the question: e.g. inorret aneling of a fration that would otherwise e orret It is not appropriate to ignore susequent work when the additional work essentially makes the answer inorret e.g. algera. Transription errors our when andidates present a orret answer in working, and write it inorretly on the answer line; mark the orret answer. Proaility Proaility answers must e given a frations, perentages or deimals. If a andidate gives a deimal equivalent to a proaility, this should e written to at least deimal plaes (unless tenths). Inorret notation should lose the auray marks, ut e awarded any implied method marks. If a proaility answer is given on the answer line using oth inorret and orret notation, award the marks. If a proaility fration is given then anelled inorretly, ignore the inorretly anelled answer. 8 Linear equations Full marks an e gained if the solution alone is given on the answer line, or otherwise unamiguously indiated in working (without ontradition elsewhere). Where the orret solution only is shown sustituted, ut not identified as the solution, the auray mark is lost ut any method marks an e awarded. 9 Parts of questions Unless allowed y the mark sheme, the marks alloated to one part of the question CANNOT e awarded in another. Paper: Methods F

4 GCSE MATHEMATICS LINKED PAIR METHODS FOUNDATION Question Working Answer Mark Notes a M A ao a Corret refletion 5 B ao (B refletion in any line parallel to y = x) B ao B ao 9 B ao d AU B = {,5,,8,9,0} a Squares at end are x eah Square in the middle is x Retangles are y eah 4 a 0 = y = + 4y But y annot e negative = d = 0; + = 0 8 M n(au B) 8 A Explanation M Sight of either x or x or y C The 4y or 8x otained onviningly C the 8x + 4y otained onviningly Explanation M 0 = y M 4y = - C y annot e negative 0.45 M A ao 0. M A ao 50 M A ao Eri eause she threw it more. 0 0 B ao M uses no of sixes total numer A 0 0 oe Question Working Answer Mark Notes Paper: Methods F 4

5 GCSE MATHEMATICS LINKED PAIR METHODS FOUNDATION 5 a 84 = 4 = = a a Width of square = x Area of square = x x Area of BCDE = xy Width of square = x Length of ACDF = (x + y) 0 M for a method that if arried out orretly would lead to the orret answer ( steps) A ao M for a produt of 4 numers, at least of whih are prime. A a orret answer M a fully orret proess A ao 0. M for any two of 0, 0.09, 9, 8 x + xy x(x + y) A A 0. oe p 8q B ao B Width of square B Area of square = x x B x + xy B Width of square B Length of ACDF = (x + y) B x(x + y) 8 x 8 = x + 0 x x = x = 8 a M x - M Rearrange ax + = x + 0 orretly A ao 8.04 B ao B ao 4 B ao Question Working Answer Mark Notes Paper: Methods F 5

6 GCSE MATHEMATICS LINKED PAIR METHODS FOUNDATION 9 a X y Corret line B any orret value pair in the tale B any other orret value pair in the tale B orret line 0 a(i) y = x or Height ase from their line M Rearrange to y = x A ao M or Height ase from their line A ao (SC B for as answer) B ao (ii) 8 x 8 + = x - 4 B ao 8 M x A ao a 0 4 B ao M A ao a x x B ao y y + 5y -5 y + y 5 (t + 5)(t 5) M 4 term expansion with all 4 terms orret ignoring signs or with out of 4 terms orret with orret signs A ao B ao d x x x M x x A, M (p a)(p ) with either a = or a + Paper: Methods F

7 GCSE MATHEMATICS LINKED PAIR METHODS FOUNDATION e (p )(p ) = 0 =5 A (p )(p ) A ao a(i) o 5 B ao (ii) Angle DBC = o (angle at entre is twie angle at irumferene) Angle ABC = o + 0 o Angle ADC = 80 o 9 o (opposite angles in a yli quadrilateral are supplementary) 88 o M Angle DBC = 4 M Angle ABC = o + 0 o M Angle ADC = 80 o 9 o C 88 and supported with oth reasons Paper: Methods F

8 GCSE MATHEMATICS LINKED PAIR METHODS FOUNDATION Question Working Answer Mark Notes 4 a 0 B ao n +n + 5 M set up differene tale to nd diff M use nth term = a + Δa(n-) + Δ (n-)(n- )/ A fully orret 5 a nth term = + 9(n ) + (n-)(n-) Angle EDC = angle ABD (alternate angles) Angle DEC = angle DAB (given) Angle ECD = angle ADB (angle sum of a triangle) Proof B Angle EDC = angle ABD B Angle DEC = angle DAB C ompleted with reasons CE AD CD BD ; CE 5 a Corret enlargement area of shape U.5 5 area of shape T 4 area of shape V 0.5 area of shape U Area of shape U = 5 0 Area of shape V = M CE CD AD BD A 0 oe B fully orret (B enlargement with SF.5, wrong entre or orret entre, wrong SF) (B enlargement, wrong entre, wrong SF) M M area of shape U.5 area of shape T A 5 oe M Area of shape U = 5 0 M Area of shape V =.5 5 Paper: Methods F 8

9 GCSE MATHEMATICS LINKED PAIR METHODS FOUNDATION a Area of shape T = 4 A oe 4 M any one orret expression for a pro that the tile Nellie piks has a igger 4 numer than the tile John piks M All orret expressions M All orret expression added C oe and orret reasoning M ' ' 4 0 A oe 4 8 A 5 + = 5 + = B ao n( n ) ( n )( n ) = n n n = n n =( n )( n ) 4 B for M for ( n )( n ) n n n or n n n n 9 a Msimplify or ollet terms A fully orret M Corret or 4 out of 4 terms orret A fully orret Paper: Methods F 9

10 8 GCSE MATHEMATICS LINKED PAIR METHODS FOUNDATION Sustitute in LHS = QED M Sustitute in LHS A ao B ao. 9. y y 5 4 y = x S x x. (a) y 0 Paper: Methods F 0 9

11 GCSE MATHEMATICS LINKED PAIR METHODS FOUNDATION () y V U 5 4 Paper: Methods F T