KEY STAGE Mark Scheme 3 For Paper 1 ALL TIERS Tiers 3-5, 4-6, 5-7 And 6-8

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MaKEY STAGE3Mark schemefor Paper 1Tiers 3–5, 4–6, 5–75–7 andand 6–86–82009ALL TIERSMathematics testsNational curriculum assessments

2009 KS3 Mathematics test mark scheme: Paper 1IntroductionIntroductionThis booklet contains the mark scheme for paper 1 at all tiers. The paper 2 mark schemeis printed in a separate booklet. Questions have been given names so that each one hasa unique identifier irrespective of tier.The structure of the mark schemesThe marking information for each question is set out in the form of tables, which start onpage 10 of this booklet. The columns on the left-hand side of each table provide a quickreference to the tier, question number, question part and the total number of marksavailable for that question part.The ‘Correct response’ column usually includes two types of information:a statement of the requirements for the award of each mark, with an indication of whether credit can be given for correct working, and whether the marks areindependent or cumulativeexamples of some different types of correct response, including the most common.The ‘Additional guidance’ column indicates alternative acceptable responses, andprovides details of specific types of response that are unacceptable. Other guidance,such as when ‘follow-through’ is allowed, is provided as necessary.Questions with a Using and applying mathematics (UAM) element are identified in themark scheme by the symbol U1 . The number indicates the significance of using andapplying mathematics in answering the question. The U number can be any wholenumber from 1 to the number of marks in the question.For graphical and diagrammatic responses, including those in which judgements onaccuracy are required, marking overlays have been provided as the centre pages of thisbooklet.The 2009 key stage 3 mathematics tests and mark schemes were developed bythe Test Development Team at Pearson Research and Assessment.2

2009 KS3 Mathematics test mark scheme: Paper 1General guidanceGeneral guidanceUsing the mark schemesAnswers that are numerically equivalent or algebraically equivalent are acceptable unlessthe mark scheme states otherwise.In order to ensure consistency of marking, the most frequent procedural queries arelisted on the following two pages with the prescribed correct action. This is followed byfurther guidance relating specifically to the marking of questions that involve money,negative numbers, time, measures, coordinates, probability or algebra. Unless otherwisespecified in the mark scheme, markers should apply the following guidelines in all cases.Recording marks awarded on the test paperAll questions, even those not attempted by the pupil, should be marked, with a1 or a 0 entered in each marking space. Where 2m can be split into 1m gainedand 1m lost, with no explicit order, then this will be recorded by the marker as 10The total marks awarded for a double page should be written in the box at the bottomof the right-hand page, and the total number of marks obtained on the paper should berecorded on the front of the test paper.A total of 120 marks is available in each of tiers 3–5, 4–6, 5–7 and 6–8.Awarding levelsThe sum of the marks gained on paper 1, paper 2 and the mental mathematicspaper determines the level awarded. Level threshold tables, which show themark ranges for the award of different levels, will be available on the NAAwebsite www.naa.org.uk/tests from April 2009.3

2009 KS3 Mathematics test mark scheme: Paper 1What if Marking procedureThe pupil’s response isnumerically or algebraicallyequivalent to the answer inthe mark scheme.Markers should award the mark unless the mark scheme states otherwise.The pupil’s response doesnot match closely any of theexamples given.Markers should use their judgement in deciding whether the response correspondswith the statement of the requirements given in the ‘Correct response’ column.Refer also to the ‘Additional guidance’.The pupil has respondedin a non-standard way.Calculations, formulae and written responses do not have to be set out in anyparticular format. Pupils may provide evidence in any form as long as its meaningcan be understood. Diagrams, symbols or words are acceptable for explanationsor for indicating a response. Any correct method of setting out working, howeveridiosyncratic, should be accepted. Provided there is no ambiguity, condone thecontinental practice of using a comma for a decimal point.There appears to be amisreading affectingthe working.This is when the pupil misreads the information given in the question and usesdifferent information without altering the original intention or difficulty level of thequestion. For each misread that occurs, deduct one mark only.No answer is given in theexpected place, but thecorrect answer is givenelsewhere.Where a pupil has shown understanding of the question, the mark(s) should begiven. In particular, where a word or number response is expected, a pupil maymeet the requirement by annotating a graph or labelling a diagram elsewhere inthe question.The final answer is wrong,but the correct answer isshown in the working.Where appropriate, detailed guidance will be given in the mark scheme and mustbe adhered to. If no guidance is given, markers will need to examine each caseto decide whether:The pupil’s answer iscorrect but the wrongworking is shown.4General guidance the incorrect answer is due to a transcription errorIf so, award the mark. in questions not testing accuracy, the correctanswer has been given but then rounded ortruncatedIf so, award the mark. the pupil has continued to give redundant extraworking which does not contradict work already doneIf so, award the mark. the pupil has continued, in the same part of thequestion, to give redundant extra working whichdoes contradict work already done.If so, do not awardthe mark. Where aquestion part carriesmore than one mark,only the final markshould be withheld.A correct response should always be marked as correct unless the mark schemestates otherwise.

2009 KS3 Mathematics test mark scheme: Paper 1What if General guidanceMarking procedureThe pupil has madea conceptual error.In some questions, a method mark is available provided the pupil has made acomputational, rather than conceptual, error. A computational error is a ‘slip’ suchas writing 4 6 18 in an otherwise correct long multiplication. A conceptual erroris a more serious misunderstanding of the relevant mathematics; when such an erroris seen, no method marks may be awarded. Examples of conceptual errors are: misunderstanding of place value, such as multiplying by 2 rather than 20 whencalculating 35 27 subtracting the smaller value from the larger in calculations such as 45 – 26 togive the answer 21 incorrect signs when working with negative numbers.The correct response hasbeen crossed or rubbed outand not replaced.Any legible crossed or rubbed out work that has not been replaced should bemarked according to the mark scheme. If the work is replaced, then crossed orrubbed out work should not be considered.More than oneanswer is given.If all answers given are correct (or a range of answers is given, all of which arecorrect), the mark should be awarded unless prohibited by the mark scheme.If both correct and incorrect responses are given, no mark should be awarded.The pupil’s answercorrectly followsthrough from earlierincorrect work.Follow-through marks may be awarded only when specifically stated in the markscheme, but should not be allowed if the difficulty level of the question has beenlowered. Either the correct response or an acceptable follow-through responseshould be marked as correct.The answer is correctbut, in a later part of thequestion, the pupil hascontradicted this response.A mark given for one part should not be disallowed for working or answers given ina different part, unless the mark scheme specifically states otherwise.The pupil’s accuracy ismarginal according to theoverlay provided.Overlays can never be 100% accurate. However, provided the answer is within ortouches the boundaries given, the mark(s) should be awarded.The pupil has drawn lineswhich do not meet at thecorrect point.Markers should interpret the phrase ‘lines not accurate’ to mean meeting within oron a circle of radius 2mm with centre at the correct point.within the circleacceptedon the circleacceptedoutside the circlenot accepted5

2009 KS3 Mathematics test mark scheme: Paper 1General guidanceResponses involving moneyWhere the signis given9Accept9 3.20 7 7.00Any unambiguous indication of thecorrect amount, eg 3.20p 3 20 pence 3 20 3,20 3-20 3:20320p with sign crossed outfor example: 3.20, 7Where the p signis given9for example:40pWhere no signis given9for example: 3.20, 40p40pAny unambiguous indication of thecorrect amount, eg 0.40p .40p 0.40 with p sign crossed out8Do not accept8Incorrect placement of pounds orpence, eg 320 320pIncorrect placement of decimal point,or incorrect use or omission of 0, eg 3.2 3 200 32 0 3-2-08Incorrect or ambiguous use of poundsor pence, eg0.40p 40p8Omission of final zero, eg3.20.48Do not accept 3.20320p40p 0.40Any unambiguous indication of thecorrect amount in or p as shownaboveAt levels 3 and 4 only also acceptomission of units, eg3.20320400.40Responses involving negative numbers9AcceptFor example:–2To avoid penalising the error belowmore than once within each question,do not award the mark for the firstoccurence of the error within eachquestion. Where a question part carriesmore than one mark, only the final markshould be withheld.86Incorrect notation, eg2–

2009 KS3 Mathematics test mark scheme: Paper 1General guidanceResponses involving timeA time interval9Accept8Do not accept92 hours 30 minutesAny unambiguous, correct indication,eg8Incorrect or ambiguous time interval,eg2.3 hours2.3h2h 32.30 min2.302-302,302.38Incorrect time, eg8.4am8.40pmIncorrect placement of separators,spaces, etc or incorrect use or omissionof 0, eg8408:4:08.4084848Do not accept8Incorrect or ambiguous use of units, eg8600kgfor example:2 hours 30 minutes12 2 hours2.5 hours2h 302h 30 min2 30Digital electronic time, ie2:30A specific time9for example:8:40am, 17:208:40am8:40twenty to nineAny unambiguous, correct indication,eg08.408.4008408 408-408,40Unambiguous change to 12 or 24 hourclock, eg17:20 as 5:20pm or 17:20pmResponses involving measuresWhere unitsare given(eg kg, m, l)for example:8.6kg9Accept98.6kgAny unambiguous indication of thecorrect measurement, eg8.60kg8.6000kg8kg 600gNoteIf a pupil leaves the answer box empty but writes the answer elsewhere on the page, then that answer must be consistentwith the units given in the answer box and the conditions listed above.If a pupil changes the unit given in the answer box, then their answer must be equivalent to the correct answer, using theunit they have chosen, unless otherwise indicated in the mark scheme.7

2009 KS3 Mathematics test mark scheme: Paper 1General guidanceResponses involving coordinatesFor example:(5, 7)9Accept8Do not accept9Unconventional notation, eg(05, 07)8Incorrect or ambiguous notation, eg(7, 5)y x(five, seven)(7, 5)x y(5 x , 7 y )(5, 7)xy(5 , 7 )(x 5, y 7)( x 5, y 7)Responses involving probabilityA numerical probabilityshould be expressed asa decimal, fraction orpercentage only.9Accept9Equivalent decimals, fractions andpercentages, eg0.700710355070%70.0%9A probability correctly expressed inone acceptable form which is thenincorrectly converted, but is still lessthan 1 and greater than 0, eg7018 100 258Do not acceptThe first four categories of error belowshould be ignored if accompanied byan acceptable response, but should notbe accepted on their own.However, to avoid penalising the firstthree types of error below more thanonce within each question, do notaward the mark for the first occurrenceof each type of error unaccompaniedby an acceptable response. Where aquestion part carries more than onemark, only the final mark should bewithheld.70100for example:0.7! Take care! A probability that is incorrectlyexpressed, eg7 in 107 over 107 out of 107 from 10! A probability expressed as apercentage without a percentage sign.! A fraction with other than integers inthe numerator and/or denominator.! A probability expressed as a ratio, eg7:107:37 to 1088A probability greater than 1or less than 0

2009 KS3 Mathematics test mark scheme: Paper 1General guidanceResponses involving the use of algebraFor example:89Accept! Take care9Unambiguous use of a different case orvariable, egN used for nx used for n! Unconventional notation, egn 2, or 2 n, or n 22 nn 2Do not acceptor n n for 2nn n for n2n 2 for n2 or 12 n2 1n for 2 n2 0 n for 22nn2n2Within a question that demandssimplification, do not accept as part ofa final answer involving algebra. Acceptwithin a method when awarding partialcredit, or within an explanation orgeneral working.8Embedded values given when solvingequations, egin solving 3 x 2 32,3 10 2 32 for x 10To avoid penalising the two types oferror below more than once withineach question, do not award the markfor the first occurrence of each typewithin each question. Where a questionpart carries more than one mark, onlythe final mark should be withheld.9Words used to precede or followequations or expressions, eg! Words or units used within equationsor expressions, egn tiles 2n cm 2t n 2 tiles or tiles t n 2for t n 2Do not accept on their own. Ignore ifaccompanying an acceptable response.9Unambiguous letters used to indicateexpressions, egt n 2 for n 28Ambiguous letters used to indicateexpressions, egn n 2 for n 29

2009 KS3 Mathematics test mark scheme: Paper 1Tier 3–5 onlyTier & QuestionCircle totals3–5 4–6 5–7 6–81Mark Correct response2mAdditional guidanceCompletes the diagram correctly, ie2540203045or1mU110Gives two correct values351045! For 1m, follow-through from their 25Accept follow-through for their 30 as55 – their 25

2009 KS3 Mathematics test mark scheme: Paper 1Tier 3–5 onlyTier & QuestionDishes3–5 4–6 5–7 6–82Mark Correct responsea1m 11b2mor1m 2.50Additional guidanceGives the answer 2.5 or 250orShows the value 7.5(0) or 750orShows or implies a complete correct method with notmore than one computational erroreg 1.50 2.50 3.50 7.00 (error)Answer given as 3c1mGives a correct pair of colours, in any order, ieGreen and OrangeorBlue and Red1m9Unambiguous indication of coloureg G and O B and R! Response gives costs rather than coloursWithhold 1 mark only for the first occurrence.Allow costs given in penceeg 1.50 and 3(.00)2(.00) and 2.50 150 and 300200 and 250Mark as 0, 1Gives a correct pair of colours, other than anypreviously creditedU111

2009 KS3 Mathematics test mark scheme: Paper 1Tier 3–5 onlyTier & QuestionFive squares3–5 4–6 5–7 6–83Mark Correct responseAdditional guidancea1mDraws the correct line of symmetry, ie! Line not ruled, accurate or extendedAccept lines of at least 3 diagonals in lengthprovided the pupil’s intention is clearb1mCompletes the diagram correctly, ie! Squares not shadedAccept provided indication of squares isunambiguousTier & QuestionJavelin3–5 4–6 5–7 6–84Mark Correct responsea1m16 to 18 inclusiveb1m4c1m17 to 19 inclusive12Additional guidance

2009 KS3 Mathematics test mark scheme: Paper 1Tier 3–5 onlyTier & QuestionDigit cards3–5 4–6 5–7 6–85Mark Correct response1mGives four of the digits to make a correct calculationeg 7 8 15 5 6 11 9 9 181mGives four of the digits to make a correct calculationeg 6 7 42 7 5 35 9 9 811m1mU1Gives five of the digits to make a correct calculationeg 23 – 4 19 67 – 5 62 24 – 2 22Additional guidance! Zero used at the end of a numbereg, for the first mark 2 8 10Penalise only the first occurrence8 Zero used or card left blank at thebeginning of a two-digit numbereg, for the second mark, do not accept 2 3 068 Card left blank at the end of a numbereg, for the third mark, do not accept 2–1 18 Extra digit insertedeg, for the fourth mark, do not accept 36 2 18Gives four of the digits to make a correct calculationeg 14 2 7 24 4 6 36 6 6Tier & QuestionHeights3–5 4–6 5–7 6–86Mark Correct responsea1mIndicates 1.8 metres, ieb1mIndicates 7 metres, ieAdditional guidance13

2009 KS3 Mathematics test mark scheme: Paper 1Tiers 3–5, 4–6Tier & QuestionChange3–5 4–6 5–7 6–8Mark Correct response7Additional guidancea1m3b2mCompletes all three rows of the table correctly inany ordereg or1mNumber of50p coinsNumber of20p coinsNumber of10p coins2302222142069Cell that should contain zero left blankCompletes two rows of the table correctlyTier & QuestionDoctors3–5 4–6 5–7 6–8Mark Correct response81aa1mGives a value between 49 and 53 inclusiveb b1mGives a value between 23 and 27 inclusivec1mGives a possible reasoneg They might think their doctor’s treatment is sometimes very good, but not at other times They might not think that any of the possibleanswers is what they think They don’t have a doctor They might not want to comment They could be worried about giving an opinion They may have only ever had one doctor They don’t always see the same doctor14cAdditional guidance9Value qualifiedeg, for part (a) About 509Minimally acceptable reasoneg Could be sometimes one category and sometimes another They may not like the choices If they’re not sure They don’t see their doctor very often They have just got a new doctor Not relevant They don’t want to answer They can’t tell what is meant by good8Incomplete reasoneg They don’t know

2009 KS3 Mathematics test mark scheme: Paper 1Tiers 3–5, 4–6Tier & QuestionUsing tens3–5 4–6 5–7 6–892Mark Correct response1m 101m 10– 101m 10 10Additional guidance! Correct operation indicated, but 10 omittedeg, for the first mark Penalise only the first occurrenceTier & QuestionCard shape3–5 4–6 5–7 6–810 3Mark Correct response2mAdditional guidanceIndicates only the three correct shapes, ie999Unambiguous indicationeg for yes andfor no9or1mIndicates any two of the correct shapes with the thirdincorrect or omitted! For 1 mark, response indicates only the threeshapes showing the grey side of the shape, egor9Indicates the three correct shapes with not more thanone other incorrect99CondoneTier & QuestionNumber lines3–5 4–6 5–7 6–811 4Mark Correct response1mGives both the values 2 and 8 in the correct positions1mGives the value – 4 in the correct position1mGives the value ( )6 in the correct positionAdditional guidance! Follow-through from their –4Accept the sum of their –4 and 10 providedtheir –4 is a negative number15

2009 KS3 Mathematics test mark scheme: Paper 1Tiers 3–5, 4–6Tier & QuestionRhombus grid3–5 4–6 5–7 6–812 5aMark Correct responsea1m12b b1mDraws a correct triangleeg Additional guidance! Lines not ruled or accurate, or triangle notshadedAccept provided the pupil’s intention is clear! Vertices of triangle not on the intersectionsof the gridAccept vertices within 2mm of the intersectionsof the grid! Other shapes drawnAs these may be trials, ignore 16

2009 KS3 Mathematics test mark scheme: Paper 1Tiers 3–5, 4–6Tier & QuestionMissing digits3–5 4–6 5–7 6–813 6Mark Correct response1mAdditional guidanceCompletes the second calculation correctly, ie17 3 51! Both digits placed in the same boxeg 17 3 51Condone1mCompletes the third calculation correctly, ie14 3 4215 3 4516 3 48ororU1Tier & QuestionClocks3–5 4–6 5–7 6–814 7aMark Correct responsea1m10amb b1m6pmAdditional guidance! Indication of am or pm incorrect or omittedCondone omission of am or pm but do notaccept incorrect timeseg, for part (a) accept 10 (o’clock)eg, for part (a) do not accept 10pm 22:00eg, for part (b) accept 6 (o’clock) 18:00eg, for part (b) do not accept 6am 06:0017

2009 KS3 Mathematics test mark scheme: Paper 1Tiers 3–5, 4–6Tier & QuestionSum of 803–5 4–6 5–7 6–815 8Mark Correct response1mIndicates Set Aandgives a correct explanationeg A 74 and 80 – 74 6B 90 and 90 – 80 10 A is –3, –2, –1, (0) and B is 1, 2, 3, 4,so A is only 6 less than 80, but B is 10 moreAdditional guidance9Minimally acceptable explanationeg 6 and 10 seen 74 and 90 seen (–)3, (–)2, (–)1, (0) and 1, 2, 3, 4 seen8Incomplete or incorrect explanationeg A adds up to 74 B is 10 more than 80 A adds up to 74, B adds up to 110 17, 18 and 19 are all under 20 so A is smallerU1Tier & QuestionNumber chains3–5 4–6 5–7 6–816 9aMark Correct responsea1mGives the values 14 and 41 in the correct positionsb b1mShows a correct ruleeg 3 Multiply by 3 Triple 3 then 0Additional guidance9Minimally acceptable ruleeg Add the number 3 times Add on double itself Double then add the number It’s the next power of 3 3 ! Rule embedded or shown in workingAccept provided a correct rule is shown explicitly,even if an incorrect value for the next number inthe chain is shown on the answer lineeg, accept 81 3 seen (4 – 1) 81eg, do not accept 81 81 81 81 2 81818Incomplete or incorrect ruleeg 3 54 3n

2009 KS3 Mathematics test mark scheme: Paper 1Tiers 3–5, 4–6, 5–7Tier & QuestionMaking 13–5 4–6 5–7 6–817 10 1aaab b bMark Correct response2mAdditional guidanceJoins all four pairs of numbers correctly, s at least two pairs of numbers correctly2mJoins all four pairs of numbers correctly, ieor1m120.540.2510.1200.05108Number matched to more than one otherFor 2m or 1m, do not accept as a correct matchJoins at least two pairs of numbers correctlyTier & QuestionT-shirts3–5 4–6 5–7 6–818 11 2Mark Correct responseAdditional guidancea1m15or equivalent probabilityb b b1m23or equivalent probability! Value roundedAccept 0.66( ) or 0.67 or the percentageequivalentsc1m13or equivalent probability! Value roundedAccept 0.33( ) or the percentage equivalentaacc19

2009 KS3 Mathematics test mark scheme: Paper 1Tiers 3–5, 4–6, 5–7Tier & QuestionWater3–5 4–6 5–7 6–819 12 3Mark Correct response1mAdditional guidanceIndicates the value 500 on the jug, iemillilitres10009Unambiguous indication! Inaccurate indicationAccept provided the pupil’s intention is clear800600400200U1Tier & QuestionBoxes3–5 4–6 5–7 6–820 13 4Mark Correct response2mor1mU1Additional guidance90Shows or implies a complete correct method with notmore than one computational erroreg 72 4 16 (error)72 16 88 72 4 1818 5 80 (error)Tier & QuestionPercentages3–5 4–6 5–7 6–821 14 5aAdditional guidancea1m18! Throughout the question, incorrect use of% signeg 18%54%Penalise only the first occurrenceb b b1m54! For part (b) follow-throughAccept follow-through as their (a) 3, or as36 their (a) provided the result is less than 36020aMark Correct response

2009 KS3 Mathematics test mark scheme: Paper 1Tiers 3–5, 4–6, 5–7Tier & QuestionNumber grids3–5 4–6 5–7 6–822 15 6Mark Correct response1mAdditional guidanceCompletes the first grid correctly, ie221335417521mCompletes the second grid correctly, ie7183412U1Tier & QuestionAngles in a triangle3–5 4–6 5–7 6–823 16 7Mark Correct response3mor2mAdditional guidanceGives all three correct angles, iex 90y 20z 20Gives any two correct anglesoror1mGives x 90 and y z, provided this value is 90 and 0Gives any one correct angleorGives y z, provided this value is 90 and 021

2009 KS3 Mathematics test mark scheme: Paper 1Tiers 3–5, 4–6, 5–7, 6–8Tier & QuestionFinding b3–5 4–6 5–7 6–8Mark Correct response24 17 82mor1mAdditional guidance2Shows or implies that a 5 and shows the intentionto substitute this value into the second equationeg 5 7 10 b b 12 – 10orShows a complete correct method with not morethan one computational erroreg b 11 – 6 7 – 10 a 11 – 6 6 (error)6 7 10 bb 38Conceptual erroreg a 11 6 17Tier & QuestionMatching3–5 4–6 5–7 6–818 91Mark Correct response1mAdditional guidance8Matches both instructions on the left to theequivalent instruction on the right, ieSubtract 01Add 0Add 2Add 2Subtract 2Subtract 2Add –21Subtract –222Instruction on the left matched to more thanone instruction on the right

2009 KS3 Mathematics test mark scheme: Paper 1Tiers 4–6, 5–7, 6–8Tier & QuestionOak leaves3–5 4–6 5–7 6–819 10 2Mark Correct response1mGives a correct reason from one of the five categoriesbelow that states or implies the problem, or suggestsan improvementAdditional guidance9The most common correct reasons:Category 1: Refer to the number of leaves in thesample being too smalleg, problem The sample is too small Those 10 leaves might all be diseasedeg, improvement They should pick more than 10Category 2: Refer to the number of trees in thesample being too smalleg, problem One oak tree might be different from others May be something wrong with that treeeg, improvement They should use more than one treeCategory 3: Refer to the conditions in which thetree is growing being too uniformeg, problem Different conditions may affect the leaves onother trees The soil might be very bad in that areaeg, improvement They should choose trees in different areasCategory 4: Refer to the area of the tree from whichthe leaves are picked being too smalleg, problem The leaves on higher branches might be different Those branches may not get enough lighteg, improvement They need leaves from all over the treeMinimally acceptable reasoneg, problem Too small Only 10 Not enough Just one Same growing conditions for the tree Other branches might be different Only the lowest brancheseg, improvement 100 is better More than one Need different areas Use other branches Collect at other times! For the first or the second reason, more thanone reason given within one responseDo not accept a correct response accompaniedby an incorrect response from the same category.Otherwise ignore irrelevant or incorrect furtherresponses.If two correct reasons from different categoriesare given in one response space, both marksshould be awardedeg They need more trees from more areasMark as 1, 18Incomplete reason that repeats theinformation given with no further explanationeg They are taking 10 leaves They are using one oak tree They are taking them from one part ofthe treeCategory 5: Refer to the period for picking thesample being too shorteg, problem The leaves may be different at different times ofyear It may be wintereg, improvement They should collect throughout the year1mGives a correct reason from a different category fromone already creditedU123

2009 KS3 Mathematics test mark scheme: Paper 1Tiers 4–6, 5–7, 6–8Tier & QuestionMissing lengths3–5 4–6 5–7 6–820 11 3Mark Correct response2mor1mGives both correct lengths, iex 10 and y 3.9 or equivalentGives y 3.9 or equivalentorGives the two values transposed, iex 3.9 or equivalent and y 10orShows a complete correct method with not morethan one computational erroreg x 10, 10 – 6.1 4.9 (error) 4 6.1 24.4, 40 – 24.4 16.6 (error)16.6 4 4.15, 4.15 6.1 10.25 40 4 20 (error)20 – 6.1 13.924Additional guidance

2009 KS3 Mathematics test mark scheme: Paper 1Tiers 4–6, 5–7, 6–8Tier & QuestionCounters3–5 4–6 5–7 6–821 12 4aaaMark Correct response2mor1mb b bGives the value 3, with no evidence of an incorrectmethodShows or implies a correct equation for the bagsand shows or implies a correct first step of algebraicmanipulation that either reduces the numberof terms or collects variables on one side of theequation and numbers on the othereg 6y 1 4y 76y – 4y 7 – 1 –2y 7 1 6y – 6 4y 2y 62m5or1mGives an answer of 4.( )orU1Additional guidance! Method used is trial and improvementNote that no partial credit can be given! Method used is trial and improvementNote that no partial credit can be givenShows or implies a correct inequality using theexpressions for the bagseg 4k k 12 3k 12 k 4Tier & QuestionPrize money3–5 4–6 5–7 6–822 13 5Mark Correct response2m 490 000or1mShows the value 980 000Additional guidance9 490k8For 1m, one million taken to be 100 000eg 100 000 – 20 000 80 000,80 000 2 40 0008For 1m, computational error that simplifiesthe divisioneg 1 000 000 – 20 000 800 000,800 000 2 400 000orShows a complete correct method with not morethan one erroreg 1 000 000 – 20 000 98 000 (error),98 000 2 49 00025

2009 KS3 Mathematics test mark scheme: Paper 1Tiers 4–6, 5–7, 6–8Tier & QuestionCorrelation3–5 4–6 5–7 6–823 14 6aaaMark Correct response1mAdditional guidanceIndicates B and gives a correct explanationThe most common correct explanations:9Minimally acceptable explanationeg It slopes upwards It goes up It’s like this8Incomplete explanationeg It slopes the positive way9Minimally acceptable explanationeg As one amount gets bigger, so does the other It could be the higher the temperature,the more ice creams are sold8Incomplete explanationeg They both increase It goes from the left-hand corner It is slanted towards the rightRefer to the points being closer to a line of best fiteg The points are practically in a straight line,so the correlation is very strong If you drew the line of best fit, the points in Awould all be close to it but many would be furtheraway in B9Minimally acceptable explanationeg They are closer to one line In B they are less bunched together in a line8Incomplete explanationeg The points are closer together In B they are more spread outRefer to the ‘line’ or sloping pattern being clearerto seeeg You can see the pattern of a very clear,almost straight line In B you can see a pattern sloping upward,but it’s not as clear9Minimally acceptable explanationeg They are in a straight line The pattern sloping downwards is clear In B the line is less easy to see B’s points are sloping upwards, but notas definitely as in A8Incomplete explanationeg The pattern is clearer They are in a lineRefer to the ‘slope’ or ‘gradient’ of the pointseg The points make a pattern that is sloping upwardsfrom left to right The line of best fit would have a positive gradientDescribe the

Mark scheme for Paper 1 Tiers 3-5, 4-6, 5-7 and 6-8 National curriculum assessments ALL TIERS Ma KEY STAGE 3 2009. 2009 KS3 Mathematics test mark scheme: Paper 1 Introduction 2 Introduction This booklet contains the mark scheme for paper 1 at all tiers. The paper 2 mark scheme is printed in a separate booklet. Questions have been given names so that each one has a unique identifi er .

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the mark scheme, the own figure rule can be used with the accuracy mark. Of Own Figure rule Accuracy marks can be awarded where the candidates’ answer does not match the mark scheme, though is accurate based on their valid method. cao Correct Answer Only rule Accuracy marks will only be awarded if the candidates’ answer is correct, and in line with the mark scheme. oe Or Equivalent rule .

50 TRX mining cost), with stage 2 beginning once total mined reaches 2M tokens. The mining cost breakdown for each stage is the following: Stage #: Mining Cost, Stage Beginning Token Supply Stage 1 (beginning): 50 TRX, 100K Stage 1: 50 TRX, 1M Stage 2: 200 TRX, 2M Stage 3: 450 TRX, 3M Stage 4: 800 TRX, 4M Stage 5: 1.25K TRX, 5M

Fedrico Chesani Introduction to Description Logic(s) Some considerations A Description Language DL Extending DL Description Logics Description Logics and SW A simple logic: DL Concept-forming operators Sentences Semantics Entailment Sentences d 1: d 2 Concept d 1 is equivalent to concept d 2, i.e. the individuals that satisfy d 1 are precisely those that satisfy d 2 Example: PhDStudent .