satspapers.org Mathematics tests Mark scheme KEY STAGE 3 for Paper 1 Tiers 3 5, 4 6, 5 7 and 6 8 ALL TIERS National curriculum assessments

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1 Ma KEY STAGE 3 ALL TIERS Mathematics tests Mark scheme f Paper 1 Tiers 3 5, 4 6, 5 7 and National curriculum assessments

2 2008 KS3 Mathematics test mark scheme: Paper 1 Introduction Introduction The test papers will be marked by external markers. The markers will follow the mark scheme in this booklet, which is provided here to infm teachers. This booklet contains the mark scheme f 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 identifier irrespective of tier. The structure of the mark schemes The marking infmation f questions is set out in the fm of tables, which start on page 12 of this booklet. The columns on the left-hand side of each table provide a quick reference to the tier, question number, question part and the total number of marks available f that question part. The Crect response column usually includes two types of infmation: a statement of the requirements f the award of each mark, with an indication of whether credit can be given f crect wking, and whether the marks are independent cumulative examples of some different types of crect response, including the most common. The Additional guidance column indicates alternative acceptable responses, and provides 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 UAM element are identified in the mark scheme by an encircled U with a number that indicates the significance of using and applying mathematics in answering the question. The U number can be any whole number from 1 to the number of marks in the question. F graphical and diagrammatic responses, including those in which judgements on accuracy are required, marking overlays have been provided as the centre pages of this booklet. The 2008 key stage 3 mathematics tests and mark schemes were developed by the Test Development Team at Edexcel. 2

3 2008 KS3 Mathematics test mark scheme: Paper 1 General guidance General guidance Using the mark schemes Answers that are numerically equivalent algebraically equivalent are acceptable unless the mark scheme states otherwise. In der to ensure consistency of marking, the most frequent procedural queries are listed on the following two pages with the prescribed crect action. This is followed by further guidance relating specifically to the marking of questions that involve money, native numbers, algebra, time, codinates probability. Unless otherwise specified in the mark scheme, markers should apply the following guidelines in all cases. 3

4 2008 KS3 Mathematics test mark scheme: Paper 1 General guidance What if The pupil s response does not match closely any of the examples given. The pupil has responded in a non-standard way. The pupil has made a conceptual err. The pupil s accuracy is marginal accding to the overlay provided. The pupil s answer crectly follows through from earlier increct wk. There appears to be a misreading affecting the wking. The crect answer is in the wrong place. Markers should use their judgement in deciding whether the response cresponds with the statement of requirements given in the Crect response column. Refer also to the Additional guidance. Calculations, fmulae and written responses do not have to be set out in any particular fmat. Pupils may provide evidence in any fm as long as its meaning can be understood. Diagrams, symbols wds are acceptable f explanations f indicating a response. Any crect method of setting out wking, however idiosyncratic, is acceptable. Provided there is no ambiguity, condone the continental practice of using a comma f a decimal point. In some questions, a method mark is available provided the pupil has made a computational, rather than conceptual, err. A computational err is a slip such as writing 4 6 = 18 in an otherwise crect long multiplication. A conceptual err is a me serious misunderstanding of the relevant mathematics; when such an err is seen, no method marks may be awarded. Examples of conceptual errs are: misunderstanding of place value, such as multiplying by 2 rather than 20 when calculating 35 27; subtracting the smaller value from the larger in calculations such as to give the answer 21; increct signs when wking with native numbers. Overlays can never be 100% accurate. However, provided the answer is within, touches, the boundaries given, the mark(s) should be awarded. Follow-through marks may be awarded only when specifically stated in the mark scheme, but should not be allowed if the difficulty level of the question has been lowered. Either the crect response an acceptable follow-through response should be marked as crect. This is when the pupil misreads the infmation given in the question and uses different infmation. If the iginal intention difficulty level of the question is not reduced, deduct one mark only. If the iginal intention difficulty level is reduced, do not award any marks f the question part. Where a pupil has shown understanding of the question, the mark(s) should be given. In particular, where a wd number response is expected, a pupil may meet the requirement by annotating a graph labelling a diagram elsewhere in the question. 4

5 2008 KS3 Mathematics test mark scheme: Paper 1 General guidance What if The final answer is wrong but the crect answer is shown in the wking. Marking procedure Where appropriate, detailed guidance will be given in the mark scheme and must be adhered to. If no guidance is given, markers will need to examine each case to decide whether: the increct answer is due to a transcription err If so, award the mark. in questions not testing accuracy, the crect answer has been given but then rounded truncated the pupil has continued to give redundant extra wking which does not contradict wk already done the pupil has continued, in the same part of the question, to give redundant extra wking which does contradict wk already done. If so, award the mark. If so, award the mark. If so, do not award the mark. Where a question part carries me than one mark, only the final mark should be withheld. The pupil s answer is crect but the wrong wking is seen. The crect response has been crossed rubbed out and not replaced. Me than one answer is given. The answer is crect but, in a later part of the question, the pupil has contradicted this response. A crect response should always be marked as crect unless the mark scheme states otherwise. Mark, accding to the mark scheme, any lible crossed rubbed out wk that has not been replaced. If all answers given are crect a range of answers is given, all of which are crect, the mark should be awarded unless prohibited by the mark scheme. If both crect and increct responses are given, no mark should be awarded. A mark given f one part should not be disallowed f wking answers given in a different part, unless the mark scheme specifically states otherwise. 5

6 2008 KS3 Mathematics test mark scheme: Paper 1 General guidance Marking specific types of question Responses involving money F example: Accept Do not accept Any unambiguous indication of the crect amount 3.20(p), 3 20, 3,20, 3 pounds 20, 3-20, 3 20 pence, 3:20, 7.00 The unit, p, is usually printed in the answer space. Where the pupil writes an answer outside the answer space with no units, accept responses that are unambiguous when considered alongside the given units with given in the answer space, accept Given units amended with crossed out in the answer space, accept 320p 700p Increct ambiguous indication of the amount 320, 320p 700p Ambiguous use of units outside the answer space with given in the answer space, do not accept 3.20p outside the answer space Increct placement of decimal points, spaces, etc increct use omission of 0 3.2, 3 200, 32 0, 3-2-0, 7.0 Responses involving native numbers F example: 2 Accept Do not accept To avoid penalising the err below me than once within each question, do not award the mark f the first occurrence of the err within each question. Where a question part carries me than one mark, only the final mark should be withheld. Increct notation 2 6

7 2008 KS3 Mathematics test mark scheme: Paper 1 General guidance Responses involving the use of algebra F example: 2 + n n + 2 2n n n 2 2 Accept Take care! Do not accept Unambiguous use of a different case variable N used f n x used f n! Unconventional notation n 2 2 n n2 n + n f 2n n n f n 2 n 2 f n n 2 + 1n f 2 + n 2 + 0n f 2 Within a question that demands simplification, do not accept as part of a final answer involving algebra. Accept within a method when awarding partial credit, within an explanation general wking. Embedded values given when solving equations in solving 3x + 2 = 32, = 32 f x = 10 To avoid penalising the two types of err below me than once within each question, do not award the mark f the first occurrence of each type within each question. Where a question part carries me than one mark, only the final mark should be withheld. Wds used to precede follow equations expressions t = n + 2 tiles tiles = t = n + 2 f t = n + 2 Unambiguous letters used to indicate expressions t = n + 2 f n + 2! Wds units used within equations expressions n tiles + 2 n cm + 2 Do not accept on their own. Igne if accompanying an acceptable response. Ambiguous letters used to indicate expressions n = n + 2 f n + 2 7

8 2008 KS3 Mathematics test mark scheme: Paper 1 General guidance Responses involving time A time interval F example: 2 hours 30 minutes Accept Take care! Do not accept Any unambiguous indication 2.5 (hours), 2h 30 Digital electronic time ie 2:30 Increct ambiguous time interval 2.3(h), 2.30, 2-30, 2h 3, 2.30min! The unit, hours and/ minutes, is usually printed in the answer space. Where the pupil writes an answer outside the answer space, crosses out the given unit, accept answers with crect units, unless the question has specifically asked f other units to be used. A specific time F example: 8:40am 17:20 Accept Do not accept Any unambiguous, crect indication 08.40, 8.40, 8:40, 0840, 8 40, 8-40, twenty to nine, 8,40 Unambiguous change to hour clock 17:20 as 5:20pm, 17:20pm Increct time 8.4am, 8.40pm Increct placement of separats, spaces, etc increct use omission of 0 840, 8:4:0, 084, 84 Responses involving codinates F example: ( 5, 7 ) Accept Do not accept Unconventional notation ( 05, 07 ) ( five, seven ) x y ( 5, 7 ) ( x = 5, y = 7 ) Increct ambiguous notation ( 7, 5 ) y x ( 7, 5 ) ( 5x, 7y ) ( 5 x, 7 y ) ( x 5, y 7 ) 8

9 2008 KS3 Mathematics test mark scheme: Paper 1 General guidance Responses involving probability A numerical probability should be expressed as a decimal, fraction percentage only. 7 F example: % 10 Accept Take care! Do not accept Equivalent decimals, fractions and percentages 0.700, , 35 50, 70.0% A probability crectly expressed in one acceptable fm which is then increctly converted, but is still less than 1 and greater than = The first four caties of err below should be igned if accompanied by an acceptable response, but should not be accepted on their own. However, to avoid penalising the first three types of err below me than once within each question, do not award the mark f the first occurrence of each type of err unaccompanied by an acceptable response. Where a question part carries me than one mark, only the final mark should be withheld.! A probability that is increctly expressed 7 in 10 7 over 10 7 out of 10 7 from 10! A probability expressed as a percentage without a percentage sign.! A fraction with other than inters in the numerat and/ denominat.! A probability expressed as a ratio 7 : 10, 7 : 3, 7 to 10 A probability greater than 1 less than 0 9

10 2008 KS3 Mathematics test mark scheme: Paper 1 General guidance Recding marks awarded on the test paper All questions, even those not attempted by the pupil, will be marked, with a 1 a 0 entered in each marking space. Where 2m can be split into gained and lost, with no explicit der, then this will be recded by the marker as 1 0 The total marks awarded f a double page will be written in the box at the bottom of the right-hand page, and the total number of marks obtained on the paper will be recded 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 levels The sum of the marks gained on paper 1, paper 2 and the mental mathematics paper determines the level awarded. Level threshold tables, which show the mark ranges f the award of different levels, will be available on the NAA website from Monday 23 June

11 2008 KS3 Mathematics test mark scheme: Paper 1 BLANK PAGE 11

12 2008 KS3 Mathematics test mark scheme: Paper 1 Tier 3 5 only 1 Crect response Additional guidance Symbols Gives two of the symbols to make a crect calculation, ie 12 3 = 4 12 = 3 4 Other numbers operations used U1 Gives two of the symbols to make a different crect calculation from any credited f the first mark 12

13 2008 KS3 Mathematics test mark scheme: Paper 1 Tier 3 5 only 2 Crect response Additional guidance a African (rhino) Unambiguous indication of type A Rhino crisis b 110 c Completes the pie chart labels crectly, ie I B Numbers used as labels Do not accept numbers as the only labels, but igne alongside crect labels A W d Gives a crect explanation There are no Javan rhinos in the captive population The captive number f J was zero Minimally acceptable explanation There aren t any Zero ( 0) They re only in the wild It has got no captive population Incomplete increct explanation There is no section f that type It s so small you can t see that section It has been missed out U1 3 Crect response Additional guidance Units Gives the most appropriate unit, ie metres Gives the most appropriate unit, ie feet! Unit abbreviated Accept only if unambiguous, f the first mark do not accept m, f the second mark accept f 13

14 2008 KS3 Mathematics test mark scheme: Paper 1 Tier 3 5 only 4 Crect response Additional guidance Spts 2m Completes both bars crectly, ie Running Tennis ! Bars not ruled, accurate shaded Accept provided the pupil s intention is clear! Bars inaccurately positioned of increct widths Condone Completes one bar crectly Indicates the values 14 and 6 Bars transposed but otherwise crect Values 14 and 6 highlighted on the hizontal scale 5 Crect response Additional guidance Euro a 2m Completes all three ways of paying crectly, ie Responses in figures four eight fty Completes two ways of paying crectly b 500, 200, 200 and 100, in any der 14

15 2008 KS3 Mathematics test mark scheme: Paper 1 Tier 3 5 only Shape statements 6 Crect response Additional guidance 2m Makes crect decisions f all four statements, ie True False Unambiguous indication f true and f false Makes crect decisions f three of the statements Anniversaries 7 Crect response Additional guidance a b Unambiguous indication of year, f , f c U

16 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 3 5, Crect response Additional guidance 1891 Calculations Crect response Additional guidance 3 Number line Crect response Additional guidance a a H Competition b b 0 Unambiguous indication of 0 None c c U1 4 16

17 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 3 5, Crect response Additional guidance 100 Eight times Crect response Additional guidance Adding 2m Gives all three crect digits in the crect positions, ie + = U1 Gives two crect digits in the crect positions 17

18 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 3 5, Crect response Additional guidance Grid patterns a a Indicates squares to make a pattern with exactly two lines of symmetry! Squares not shaded Accept any unambiguous indication of squares! Response uses part squares Accept provided the intended symmetry is clearly crect, f part (b)! Line(s) of symmetry drawn Igne, even if increct b b Indicates square(s) to make a pattern with exactly one line of symmetry 18

19 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 3 5, 4 6 Think of a number 14 7 Crect response Additional guidance a a Indicates the crect decisions f all three questions, ie Yes No Unambiguous indication f yes and f no even number? multiple of 3? fact of 18? b b U Crect response Additional guidance Dial a a 2 b b 135 Answers of any multiple of 360 Temperatures 16 9 Crect response Additional guidance a a 6 b b 3 19

20 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 3 5, 4 6, Crect response Additional guidance Making ten Gives two numbers, one positive and one native, that add to and and 5 1 and and 10.5 Fractions decimals Addition symbol amended = Crect response Additional guidance 7.2 Equivalent fractions decimals Decimals

21 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 3 5, 4 6, Crect response Additional guidance a a a 34 Duckweed b b b 26! Follow-through Accept follow-through as 60 their (a), provided their (a) was not 0 c c c 16 d d d Gives a crect interpretation When salt is added, the number of leaves decreases and the me salt there is, the quicker the number of leaves will be zero With no salt, the plant grows but the me salt you put in, the faster the plant dies With no salt the leaves increased, with a little salt they decreased slowly, and with a lot of salt they decreased quickly Minimally acceptable interpretation The me salt, the faster the number of leaves goes down As the amount of salt increases, the plant dies me quickly The me salt there is, the fewer leaves the plant will have The less salt, the me leaves the plant will have U1 Incomplete increct interpretation Adding salt makes it lose leaves rather than grow them Salt kills the plants The me salt, the me chance the plant will die Crect response Additional guidance Indicates both crect shapes, ie Unambiguous indication Six cubes 21

22 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 3 5, 4 6, Crect response Additional guidance Substituting 2m Completes all three statements crectly 3, 6 3, 9 3, 1 1, 4 2, 6 6, 2 4, 7 4, 12 4, 4 3 0, 3 0, 0 0, 0 Natives, fractions decimals! Decimal answers rounded truncated Accept answers rounded truncated to two decimal places better Incomplete processing, f the last part 3, 3 3 6, 6 3 Completes two statements crectly Crect response Additional guidance Boxes 2m 925 Shows a complete crect method with not me than one computational err = = (err) (err) 825 so = 935 Conceptual err

23 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 3 5, 4 6, times table Crect response Additional guidance a a a equivalent! F the second mark, follow-through 2 Accept as their value f the first mark b b b Indicates No and gives a crect explanation The most common crect explanations:! Increct statement alongside a crect explanation Igne, accept 11 is an odd number, = 61 2 Reason about odd and/ even multiples of is an odd number so you will get a half left over = 1, so only an even number of 31 2 s will give a whole number Minimally acceptable explanation 11 is odd The first number needs to be even All the odd ones are not whole numbers Only the even numbers are whole numbers Incomplete explanation Every other multiple is a whole number It is an odd number It is not an even number 10 is whole so 11 is not Show imply the crect product a relevant ption of it = Minimally acceptable explanation = ends in 1 and = 1 2 Incomplete increct explanation does not give a whole number 2 It will end in a 1 2 U =

24 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 3 5, 4 6, Crect response Additional guidance 3 5! Increct notation, as an answer f the first mark 3 3x Penalise only the first occurrence Solving! Incomplete processing, as an answer f the first mark 15 5 Penalise only the first occurrence Crect response Additional guidance Codinates 2m Gives A as (3, 4) Gives A as (4, 3) Shows implies that the side length of the square is = 4 (5, 2) seen (1, 6) seen , 2, 3, 4, 5 2, 3, 4, 5, 6 5 U1 24

25 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 4 6, 5 7, Crect response Additional guidance Expressions 2m Matches all three expressions crectly, ie 3! Expression on the left matched with me than one expression on the right F 2m, do not accept as a crect match 2d 3d 4d 2d 2 3d 2 2d 3 Matches any two of the expressions crectly 25

26 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 4 6, 5 7, Crect response Additional guidance Views 2m Draws both views crectly using the grid, ie FRONT SIDE! Lines not ruled accurate Accept provided the pupil s intention is clear! Shading used Igne! Crect view from the side in a different ientation Condone, f 2m accept FRONT SIDE Draws one of the views crectly using the grid Draws both views crectly using the grid but transposes their positions Draws both views crectly either without using the grid of increct sizes, provided the length and width of each view are clearly intended to be equal! F 2m, their side view omits the middle section of the diagonal line Condone FRONT SIDE Crect response Additional guidance Multiple of 6 1, 2 and 3, in any der 26

27 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 4 6, 5 7, Crect response Additional guidance a a a 11 Test results b b b U Crect response Additional guidance Square tiles U1 Gives a crect value f the area of the rectangle Shows the crect unit f their area cm² [with 54] mm² [with 5400]! Area increct omitted, but units given If the mark f their crect area has not been awarded, condone cm² seen f the second mark 27

28 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 4 6, 5 7, 6 8 Walking to school Crect response Additional guidance a a a 20 b b b 2m 28 Gives an answer of 72 U1 Shows implies a crect method out of Crect response Additional guidance a a a metres b b b 2m 2.8 equivalent Identifies the values 13.6 and 16.4 equivalent Shows a complete crect method with not me than one computational err = 3, = 0.2, 3 0.2! F, key not interpreted Condone only if the crect range has been evaluated, accept 2 8, do not accept F, conceptual err = 3, = 0.2, = 3.2 c c 15.3 equivalent 28

29 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 4 6, 5 7, Crect response Additional guidance Sequences a a 2m Makes all four crect decisions, ie increasing decreasing neither Makes three crect decisions b b Gives all four crect terms in any der 1 4, 1 9, 1 16, 1 25 Equivalent fractions! Equivalent decimals F 1, accept F 1, accept 0.11 better 9 F 1, accept F 1, accept ! Increct further wking Condone provided the four crect terms have been given Answer of 1, 1 4, 1 9, 1 16 Incomplete processing, f

30 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 4 6, 5 7, Crect response Additional guidance Equation 2m 12 Shows implies a crect first step of algebraic manipulation that either reduces the number of terms collects unknowns on one side of the equation and numbers on the other 2x = x x = x 6 + x = 6 2x x = x = 0! Method used is trial and improvement Note that no partial credit can be given Crect response Additional guidance 20 Cancelling 400! Incomplete processing Penalise only the first occurrence, provided all redundant values have been cancelled, f both marks 4 5 (4 5) 2 Mark as 0, 1! Follow-through F the second mark, accept the square of their 20 evaluated 30

31 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 5 7, 6 8 Marking overlay available Finding Atlanta Crect response Additional guidance 2m Indicates a point within the rion shown on the overlay and shows crect intersecting construction arcs with radii within the tolerances as shown on the overlay Indicates a point within the rion shown on the overlay, even if the construction arcs are increct omitted Draws at least one crect construction arc with radius within the tolerance as shown on the overlay The only err is to transpose the distances, ie indicates a point within the rion shown on the overlay when turned over and shows their two crect intersecting construction arcs! F 2m, intersecting arcs shown but point not otherwise labelled Condone! Arcs extended extra arcs Igne inaccuracies in sections of arcs extending beyond the tolerances as shown on the overlay, arcs not indicated on the overlay, even if increct! Spurious arcs Do not accept arcs drawn without compasses Crect response Additional guidance Twice as far 2m Gives both crect pairs of codinates, ie (16, 3) and (8, 3) in either der Gives one crect pair of codinates with the other pair increct omitted Identifies both crect points on the graph, even if the codinates are increct omitted! Crect points marked on the graph, but alongside other points marked F, do not accept unless the two crect points are clearly identified 31

32 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 5 7, Crect response Additional guidance Functions 2m Makes crect decisions f all four functions, ie q increases r increases s increases t increases q decreases r decreases s decreases t decreases Makes three crect decisions Red and blue cubes Crect response Additional guidance 2m Gives the number of blue cubes as 35 Shows the value 5, with no evidence of an increct method f that value Shows the values 20 and 35, 30 and : 35 35, 30 Shows a complete crect method 10 (6 4) U1 32

33 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 5 7, Crect response Additional guidance a a Indicates No and gives a crect explanation The most common crect explanations: Straight lines Show how (7, 12) fails to follow the rule y = 2x + 1 It should be x to get y but = 15, not 12 It s double 7 then subtract 2, but it should be double 7 then add 1 It should be 12 1 then 2 but this gives 5 1 2, not 7 If the x-codinate is a whole number, the y-codinate will always be an odd number Minimally acceptable explanation (12 1) 2 7 y = 2x 2 Incomplete explanation = 15 (12 1) 2 the y-codinate will always be odd Show imply that the point (7, 15) (5 1, 12) is on the straight line 2 It should be (7, 15) since = 15 (5 1, 12) is on the line because 12 1 = 11 2 and 11 2 = It s not one of these codinates: x y Minimally acceptable explanation (7, 15) (5 1 2, 12) 15, not , not 7 (4 + 3, 9 + 6) (6, 13) is on the line so (7, 12) can t be since 12 is less than 13 When x goes up 1, y goes up 2 Incomplete increct explanation It doesn t fit the equation The y codinate is too low You don t get to (7, 12) Only (6, 13) and (8, 17) are on the line b b Gives a crect equation y = 3x + 1 3x y = 1! Unconventional notation 1y = 3 x + 1 Condone U1! Incomplete processing y = 2x x Condone 33

34 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 5 7, Crect response Additional guidance Square root a a Gives a crect explanation 9 2 = 81 and 10 2 = 100 and 89 is between 81 and < 89 and > 89 Minimally acceptable explanation 81, , < 89 < is between the squares of 9 and 10 Value f 89 given 9.4( ) seen! Explanation refers to native values Igne alongside a crect explanation, accept 81 = 9 9 and 100 = U1 Incomplete increct explanation 89 is between 9 and 10 The square root of 9 is 81 and the square root of 10 is = 81 and 9 10 = 90 so it s between 9 and 10 b b 19 and 20, in either der! Native values given 19 and and 20 Condone! Answer embedded and seen Condone Incomplete response 361 and

35 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 5 7, 6 8 Heads tails Crect response Additional guidance 2m both! F 2m, value(s) qualified, f 2m About 31 Condone U1 Shows implies a crect method with not me than one computational err, even if their final value is not a whole number equivalents seen , 250, 175 (err), 87.5, 43.75! F, value(s) rounded truncated Condone crect rounding truncation at any stage within a crect method, f accept 500, 250, 175 (err), 88, 44 Codinate net Crect response Additional guidance Gives L as ( 10, 0) Gives M as (30, 20)! Answers f L and M transposed but otherwise completely crect If this is the only err, ie gives L as (30, 20) and gives M as ( 10, 0), mark as 0, 1 35

36 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 5 7, Crect response Additional guidance a Gives a crect justification The most common crect justifications: Halving Evaluate 1 2 of 103 and is 1000, so half is 500 but 5 3 is = 1000, 5 3 = 125 but 1 of 1000 is not Minimally acceptable justification 500, , 125 Incomplete increct justification Express the two sides of the equation in a fm that enables comparison = , not Minimally acceptable justification , Incomplete increct justification 5 3 is too small It should be Address the misconception You only divide one of the tens by 2 not all of them Minimally acceptable justification You just halve one of the tens It s only one 5 and two 10s Incomplete justification You don t halve all of the tens 36

37 2008 KS3 Mathematics test mark scheme: Paper 1 Tier 6 8 only Halving (cont) 19 Crect response Additional guidance b Gives a crect justification The most common crect justifications: Calculate 1 of of is not It should be not not is bigger than Minimally acceptable justification of Incomplete increct justification is too small 1 2 of 108 isn t 10 4 It should be Address the misconception You only halve the six not the power of 10 The number will still have nine digits It should keep 8 zeros Minimally acceptable justification You only halve the 6 The power of 10 stays the same Incomplete justification You don t halve both values c 2m ! Zero(s) given after the last decimal place within standard fm notation Condone, f 2m accept Shows a value equivalent to Makes an err in halving 1.65, but follows through crectly giving their answer in standard fm =

38 2008 KS3 Mathematics test mark scheme: Paper 1 Tier 6 8 only 20 Crect response Additional guidance Pay a Indicates only the third statement, ie me than twice as much exactly twice as much less than twice as much U1 not enough infmation b Indicates only the second statement, ie me than twice as much exactly twice as much less than twice as much U1 not enough infmation 21 Crect response Additional guidance Factisation Completes the factisation crectly x 2 + 7x + 6 = (x + 1)(x + 6) x 2 + 7x + 10 = (x + 2)(x + 5) x 2 + 7x + 12 = (x + 4)(x + 3) x 2 + 7x + 18 = (x + 9)(x + 2) x 2 + 7x = (x )(x ) x 2 + 7x + 0 = (x + 7)(x + 0) Completes the factisation crectly in a different way from any previously credited Factisation given f the first mark repeated, but the der of the facts reversed, from x 2 + 7x + 6 = (x + 1)(x + 6) f the first mark x 2 + 7x + 6 = (x + 6)(x + 1) 38

39 2008 KS3 Mathematics test mark scheme: Paper 1 Tier 6 8 only 22 Crect response Additional guidance a 2m 1 equivalent probability 20 Shape cards Shows the values 1 5 and 1 equivalent 4 probabilities Gives the answer 1 equivalent probability 25 [ie the only err is to assume the first card is replaced] b U1 1 equivalent probability! Follow-through 10 Accept 2 their (a) provided this gives a value greater than 0 and less than 1 39

40 2008 KS3 Mathematics test mark scheme: Paper 1 Tier 6 8 only 23 Crect response Additional guidance Lines a 2m Completes all three rows of the table crectly, ie Point Above On Below (6, 3) (8, 5) (100, 60) ( 4, 3) Completes any two of the rows crectly b Gives a crect equation equivalent to y = 1 2 x + c where c < 1 y = 1 2 x 1 2y = x! Unconventional notation y = 1 2 x 1 1y = 1 2 x + 0 Condone 24 Crect response Additional guidance Dimensions 2m Makes all three crect decisions, ie area area volume Makes two crect decisions 40

41 2008 KS3 Mathematics test mark scheme: Paper 1 Tier 6 8 only 25 Crect response Additional guidance Speed a 0.65 to 0.67 inclusive Equivalent fractions, decimals percentages Value of 65 to 67 inclusive without a percentage sign b Indicates Thursday and gives a crect explanation The most common crect explanations: Refer to the relative speeds of the cars on the two days The median was 71.5mph on Monday, but only 55mph on Thursday due to the rain That day had a lower median speed because people drive me carefully in the rain People drove slower on average on this day, probably because of the wet roads It s dangerous to go too quickly in the rain, so most cars went slower on Thursday Only about 2 cars broke the speed limit on Thursday, but 33 did on Monday Minimally acceptable explanation 71.5, 55 Lower median They were generally slower Most went me slowly Me were under the speed limit! Value(s) given f the median(s) Accept 71 to 72 inclusive f Monday Accept 55 to 55.5 inclusive f Thursday! Irrelevant infmation There was also me variation in the speeds on Thursday as some people take me care than others Igne alongside a crect explanation Incomplete increct explanation The cars were slower on Thursday There were no cars going faster than about 77mph on Thursday Refer to the relative positions of the graphs Most of the Thursday line is to the left of the Monday line, so the speeds are lower The line f Monday is further along the speed axis, showing higher values Minimally acceptable explanation Its line is on the left Monday s graph is further right Thursday s line is higher up so is showing lower values The line f Monday is below the other, ie at faster speeds U1 Incomplete increct explanation Thursday s line is higher up The line f Monday is below the other 41

42 2008 KS3 Mathematics test mark scheme: Paper 1 Tier 6 8 only 26 Crect response Additional guidance Inequalities Gives a pair of values such that k < n and k + n < 0 k = 3, n = 2 k = 8, n = 7 k = 1, n = 0 Fractions decimals Two me numbers 27 Crect response Additional guidance 2m Gives x = 3y! Unconventional notation x = 3 y x = y3 Condone Shows a crect equation in x and y 2(x y) = x + y x y = 1 (x + y) 2 2x = x + 3y y = x 3 42

43 2008 KS3 Mathematics test mark scheme: Paper 1 BLANK PAGE 43

44 2008 KS3 Mathematics test mark scheme: Paper 1 Index Tier Question Page Symbols 12 2 Rhino crisis 13 3 Units 13 4 Spts 14 5 Euro 14 6 Shape statements 15 7 Anniversaries Calculations Number line Competition Eight times Adding Grid patterns Think of a number Dial Temperatures Making ten Decimals Duckweed Six cubes Substituting Boxes ½ times table Solving Codinates 24 44

45 2008 KS3 Mathematics test mark scheme: Paper 1 Index Tier Question Page Expressions Views Multiple of Test results Square tiles Walking to school metres Sequences Equation Cancelling Finding Atlanta Twice as far Functions Red and blue cubes Straight lines Square root Heads tails Codinate net Halving Pay Factisation Shape cards Lines Dimensions Speed Inequalities Two me numbers 42 45

46 2008 KS3 Mathematics test mark scheme: Paper 1 BLANK PAGE 46

47 2008 KS3 Mathematics test mark scheme: Paper 1 BLANK PAGE 47

48 QCA wishes to make its publications widely accessible. Please contact us if you have any specific accessibility requirements. 29 Bolton Street London W1J 8BT Telephone: Minicom: Fax: Website: First published 2008 Qualifications and Curriculum Authity 2008 ISBN Reproduction, stage, adaptation translation, in any fm by any means, of this publication is prohibited without pri written permission of the publisher, unless within the terms of licences issued by the Copyright Licensing Agency. Excerpts may be reproduced f the purpose of research, private study, criticism review, by educational institutions solely f educational purposes, without permission, providing full acknowledgement is given. Printed in Great Britain by the Qualifications and Curriculum Authity under the authity and superintendence of the Controller of Her Majesty s Stationery Office and Queen s Printer of Acts of Parliament. The Qualifications and Curriculum Authity is an exempt charity under Schedule 2 of the Charities Act Qualifications and Curriculum Authity 83 Piccadilly London W1J 8QA F me copies: QCA Orderline, PO Box 29, Nwich NR3 1GN derline@qca.g.uk Tel: Fax: QCA/08/