Final. Mark Scheme. Linear Mathematics 4365H. (Specification 4365) Paper 1 Higher Tier 43651H. General Certificate of Secondary Education June 2013

Transcription

1 Versio 1.0 Geeral Certificate of Secodary Educatio Jue 013 Liear Mathematics 4365H (Specificatio 4365) Paper 1 Higher Tier 43651H Fial Mark Scheme

2 Mark schemes are prepared by the Pricipal Examier ad cosidered, together with the relevat questios, by a pael of subject teachers. This mark scheme icludes ay amedmets made at the stadardisatio evets which all examiers participate i ad is the scheme which was used by them i this examiatio. The stadardisatio process esures that the mark scheme covers the studets resposes to questios ad that every examier uderstads ad applies it i the same correct way. As preparatio for stadardisatio each examier aalyses a umber of studets scripts: alterative aswers ot already covered by the mark scheme are discussed ad legislated for. If, after the stadardisatio process, examiers ecouter uusual aswers which have ot bee raised they are required to refer these to the Pricipal Examier. It must be stressed that a mark scheme is a workig documet, i may cases further developed ad expaded o the basis of studets reactios to a particular paper. Assumptios about future mark schemes o the basis of oe year s documet should be avoided; whilst the guidig priciples of assessmet remai costat, details will chage, depedig o the cotet of a particular examiatio paper. Further copies of this Mark Scheme are available from: aqa.org.uk Copyright 013 AQA ad its licesors. All rights reserved. Copyright AQA retais the copyright o all its publicatios. However, registered schools/colleges for AQA are permitted to copy material from this booklet for their ow iteral use, with the followig importat exceptio: AQA caot give permissio to schools/colleges to photocopy ay material that is ackowledged to a third party eve for iteral use withi the cetre. Set ad published by the Assessmet ad Qualificatios Alliace. The Assessmet ad Qualificatios Alliace (AQA) is a compay limited by guaratee registered i Eglad ad Wales (compay umber ) ad a registered charity (registered charity umber ). Registered address: AQA, Devas Street, Machester M15 6EX.

3 AQA GCSE Mathematics (Liear) 43651H Jue 013 Glossary for Mark Schemes GCSE examiatios are marked i such a way as to award positive achievemet wherever possible. Thus, for GCSE Mathematics papers, marks are awarded uder various categories. M M dep A B B dep Q ft SC oe [a, b] [a, b) Method marks are awarded for a correct method which could lead to a correct aswer. A method mark depedet o a previous method mark beig awarded. Accuracy marks are awarded whe followig o from a correct method. It is ot ecessary to always see the method. This ca be implied. Marks awarded idepedet of method. A mark that ca oly be awarded if a previous idepedet mark has bee awarded. Marks awarded for quality of writte commuicatio. Follow through marks. Marks awarded for correct workig followig a mistake i a earlier step. Special case. Marks awarded for a commo misiterpretatio which has some mathematical worth. Or equivalet. Accept aswers that are equivalet. 1 eg accept 0.5 as well as Accept values betwee a ad b iclusive. Accept values betwee a ad b with a icluded but b ot icluded 5.3 Allow aswers which begi 5.3 e.g. 5.3, 5.31, Use of brackets It is ot ecessary to see the bracketed work to award the marks. Nms No method show 3

4 AQA GCSE Mathematics (Liear) 43651H Jue B1 Oly outlie eeded. Ca be aywhere o grid Iteral lies ot ecessary (may be A dashed). Shape may be shaded (eve i chequerboard fashio) B B1 Oly outlie eeded. Ca be aywhere o grid Iteral lies ot ecessary (may be dashed). Shape may be shaded (eve i chequerboard fashio) C B1 Ay orietatio (as show) Oly outlie eeded. Ca be aywhere o grid Iteral lies ot ecessary (may be dashed). Shape may be shaded (eve i chequerboard fashio) 4

5 AQA GCSE Mathematics (Liear) 43651H Jue M1 M1 for ay two show i the appropriate calculatio M1 for ad ad clearly stated if ot used i a calculatio 100 Correct aswer oly see is M1, but must use correct approximatios if workig is see 3 Substitutes 10 ito at least two expressios ad evaluates correctly or = 10 substituted ito all five expressios ie. 1, 10 1, , ad 10 Evaluates all 5 expressios correctly ( 10 ca be left as 10) or 1, 10, 10 1, , writte i either order M1 1 (oe), 9, 11, 100, [3, 4] 10 If 10 evaluated ad ot i rage [3, 4] the this is A0 If 10 substituted but ot evaluated oly the expressios order or reverse order will get 1 or 9 or 10 1 ft Do ot ft if 3 expressios evaluated icorrectly ft o M1, A0 if 10 give a value ad 5 expressios evaluated, with at least 3 correct. or ft o M1, A0 if 10 ot evaluated, with at least three correct out of 1, 9, 11 or 100, 10 but the media give implies that 10 used i the correct place if the umbers were arraged i order Media may be give as a value, a expressio i or a uevaluated expressio usig 10 5

6 AQA GCSE Mathematics (Liear) 43651H Jue 013 4(a) Eve B1 4(b) Odd B1 4(c) Either B1 5(a) Correct straight (if ot draw with a ruler the itetio to be straight) lie graph from (0, 1) to (4, 7) with 1mm (½ square) tolerace Allow a dashed lie B3 B correct lie but ot from (0, 1) to (4, 7) for at least a cotiuous x distace of. B all iteger poits (ay others must also be correct) betwee 0 ad 4 plotted but lie ot draw B correct but more tha ½ square from tolerace Oly oe of these may be awarded. B1 straight lie graph through (0, 1) of ay legth eve if crooked later but ot x = 0 or y = 1 B1 Sigle straight lie graph with gradiet of ay legth B1 two correct poits calculated (eg i table) or plotted Ay lie that is ot straight is B0 although the B1 for two poits calculated or plotted may still be gaied 5(b) 1.5 B1 Correct (eg from algebra) or ft their graph if y = draw to the graph ad the a vertical lie to x-axis 6

7 AQA GCSE Mathematics (Liear) 43651H Jue 013 6(a) Histogram or frequecy polygo with mid-poits of bars ad vertices of polygo at (5, 36), (15, 34), (5, 18) ad (35, 1) B B1 oe error Igore lies before (5, 36) ad after (35, 1) if polygo draw 6(b) 6 (18 + 1) NB table ca be see if ecessary. M1 oe SC1 30% stated as aswer SC1 for 40 as aswer or M1 has to come from correct workig (30 their ) 4 M1Dep Their + 4a = 30 First M must be scored 7 Alt 1 Guess a value for a ad correctly works out xf Guesses a secod value earer to the correct aswer ad correctly works out xf M1 M1Dep First M must be scored 7

8 AQA GCSE Mathematics (Liear) 43651H Jue 013 8(a) 3(x 5) B1 8(b) 5y + 0t 10 B B1 for correct terms. Pealise ay icorrect further workig. Eg 5y + 0t 10 = 5yt 10 is B1 5y + 0t 1 = 5yt 1 is B0 (error i expasio ad icorrect further work) 5y + 0t 10 = 5(y + 4t ) give as aswer is B1 as shows a misuderstadig of expadig brackets. 8(c) 3w + 6 = w 1 M1 w + = 3 w 1 3 3w w = 1 6 M1 This mark is for rearragig their expasio correctly to get w terms oe side ad umber terms o the other. w 3 w = 1 3 (oe) 7 ft ft o oe error 8

9 AQA GCSE Mathematics (Liear) 43651H Jue (550 50) 3 M1 J + W = 50 or J + 4W = W = 300 or W = their 100 M1Dep J = 50 or J = Alt (= 3 5 ) M1 Their 3 5 = 300 or 1 = their 100 M1Dep Alt 550 marked by top divisio ad 50 marked by bottom divisio o same diagram M1 300 idicated as differece o diagram or 350 ad 450 writte by itermediate divisios 100 marked betwee ay two divisios is M1, 150 marked at bottom M1Dep 150 stated as aswer 9 Alt 3 Guesses a value for weight of jug, subtracts from 50, multiplies aswer by 4 ad adds to their value Correct calculatios Guesses a secod value for weight of jug earer to 150 ad correctly calculates all values M1 M1Dep 150 9

10 AQA GCSE Mathematics (Liear) 43651H Jue y 5 or 5 y B1 Ay order. Pealise first use of > or < oly. Pealise first use of >= or => or =< or <= oly. Accept < y 5 or y 5 x or x B1 Accept x < 5 or x 5 y x or x y B1 oe Sc1 y = 5 ad x = ad y = x or Sc1 y 5 ad x ad y x (= 1) B1 3 ad 4 must be used 48 their 1 (= 4) M1 Their 1 meas their additio of or their total if they thik that a petago does ot have 5 sides 0 ft ft o B0 Accept 1 : 16 : 0 1 a + c = 5a 5b or a + c = 5(a b) c = 5a a 5b or c = 5(a b) a c 3a 5b or equivalet expressio M ft M1 if oe expasio, sig or rearragemet error o ay lie c = is OK if rest correct ft o oe error Must have c = o aswer lie If questio simplified by a icorrect expasio a + c to give c = (see exemplar below) the they must simplify their aswer Do ot award if icorrect further work 1 Alt a + c =.5(a b) c =.5(a b) a M M1 if oe expasio, sig or rearragemet error o ay lie c =.5(a b) a or equivalet expressio ft ft o oe error Must have c = o aswer lie Do ot award if icorrect further work 10

11 AQA GCSE Mathematics (Liear) 43651H Jue (a) 0 B1 13(b) 9 B1 13(c) 11 ad 3 see M1 Could be writte o diagram 8 13(d) Commet o average ad the implicatio, eg waitig times decreased after ew widow as media lower B1 ft their medias if valid coclusio reached Commet o rage or iter-quartile rage ad the implicatio, eg Spread of waitig times decreased after ew widow as rage decreased or Not much effect o waitig times as IQR about the same B1 ft their values if a valid coclusio reached 14(a) 35 B1 *14(b) 100 B1 Agle at cetre twice agle o circumferece Q1 Must use words cetre ad circumferece (or perimeter ) Allow poor spellig eve though both words give oe (strad) (i) 15(a) 6x + 4x + 15x + 10 M1 Allow oe sig or arithmetic error. Must see 4 terms icludig term i x, terms i x ad a costat term 6x + 19x + 10 NB Aswer oly 6x + 19x + b implies M1 ax + 19x + 10 implies M1 Do ot award if icorrect further work 11

12 AQA GCSE Mathematics (Liear) 43651H Jue (b) 9x 4 y 8 B B1 for two of 9, x 4 or y 8 B1 maximum for ay use of sigs B0 for ay additio eg 9 + x 4 + y 8 Deduct oe mark for icorrect further work *16 Ay side chose for square ad squared, eg 10 = 100 Half the side squared ad multiplied by, eg 5 must be [3.1, 3.14] or 7 Work out 75% of their square ad a correct calculatio of the circle area, or works out what percetage the circle area is of the square area A method mark gaied ad correct coclusio based o 75% of their square with their circle M Q1 M is for both square ad circle areas attempted with correct umerical values (eg if 10 chose for side of square, the 5 must be used as radius of circle, or if 4 chose as radius the 8 used as side of square) M1 if both square ad circle area attempted with oe icorrect umerical value (eg if 10 chose for side of square, the 10 used as radius of circle, or if 4 chose as radius the 4 used as side of square) This ca be awarded eve if oly M1 awarded. Allow π used if a clear compariso, eg π 5 > 3 5 Strad (ii). Do ot award if their circle area > square area, eg 78.5 > 5 *16 Alt r legth of side of square givig 4r as area r as radius of circle givig r as area of circle M M is for both square ad circle area attempted with correct umerical values (eg r if r chose for side of square, the must be used as radius of circle, or if r chose as radius the r used as side of square) M1 if both square ad circle area attempted with oe icorrect umerical value (eg if x chose for side of square, the x used as radius of circle, or if x chose as radius the x used as side of square) 75% of their square (= 3r ) ad correct expressio for area of circle with their chose radius A method mark gaied ad correct coclusio based o 75% of their square with their circle. eg π > 3 Q1 Strad (ii). Do ot award if their circle area > square area, eg πr > r 1

13 AQA GCSE Mathematics (Liear) 43651H Jue ( 1 ) ( 1) B1 This mark is for combiig fractios or if fractios dealt with separately, for combiig terms correctly 4 of fractios is B0 as icorrect combiig B1 This mark is for elimiatig ad either by showig by crossig or writig o same lie ad writig ext lie without them B1 This mark is for cacellig top ad bottom = = 17 Alt (( 1) ( 1)) B1 This mark is for factorisig out a commo factor. ( 1 1) is B0 as icorrect 4 factorisatio ( ) B1 This mark is for combiig terms iside bracket correctly B1 1 is OK 18 (x + x 3) (x + x 3) M1 Or attempt to balace equatios y = x.3 ad 1.3 ft ft if M awarded ad their lie draw 13

14 AQA GCSE Mathematics (Liear) 43651H Jue (a) 3 3 = 9 ad 3 3 = 3 1 or = 3 B1 3 3 is essetial see or implied Accept (3 1.5 ) = 3 3 = 7 oe 19(b) (3 3) (3 ) (= 7 18) or (3 ) + AD = (3 3) M1 Ivisible brackets must be recovered for M1 9 or (= 4 ) M1Dep Dep o M1, ot o as well 0.5 their base their 3 M1Dep 6 19(b) Alt 1 (3 3) (3 ) (= 7 18) M1 Ivisible brackets must be recovered for M1 9 or 3 Area ABD = 0.5 their 3 3 ad area ADC = 0.5 their 3 Area ABD = 0.5 their area ADC = 0.5 their 3 6 M1Dep M1Dep Dep o M1, ot o as well Sum of two correct areas for their AD 19(b) Alt (3 3) (3 ) (= 7 18) M1 Ivisible brackets must be recovered for M1 9 or (= 4 ) M1Dep Dep o M1, ot o as well Si ABD = their ad Area = Their 4 their 3 6 M1Dep 14