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Ma Mathematics tests KEY STAGE 3 for Paper 1 Tiers 3–5, 4–6, 5–7 and 6–8 2008 ALL TIERS Mark scheme National curriculum assessments Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 1 http://www.SATs-Papers.co.uk 30/11/07 21:39:51 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 inform teachers. 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 identiﬁer irrespective of tier. The structure of the mark schemes The marking information for questions is set out in the form 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 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 are independent or cumulative examples of some different types of correct 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. For 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 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 2 http://www.SATs-Papers.co.uk 30/11/07 21:39:52 2008 KS3 Mathematics test mark scheme: Paper 1 General guidance General guidance Using the mark schemes Answers that are numerically equivalent or algebraically equivalent are acceptable unless the mark scheme states otherwise. In order to ensure consistency of marking, the most frequent procedural queries are listed on the following two pages with the prescribed correct action. This is followed by further guidance relating speciﬁcally to the marking of questions that involve money, negative numbers, algebra, time, coordinates or probability. Unless otherwise speciﬁed in the mark scheme, markers should apply the following guidelines in all cases. 3 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 3 http://www.SATs-Papers.co.uk 30/11/07 21:39:52 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. Markers should use their judgement in deciding whether the response corresponds with the statement of requirements given in the Correct response column. Refer also to the Additional guidance. The pupil has responded in a non-standard way. Calculations, formulae and written responses do not have to be set out in any particular format. Pupils may provide evidence in any form as long as its meaning can be understood. Diagrams, symbols or words are acceptable for explanations or for indicating a response. Any correct method of setting out working, however idiosyncratic, is acceptable. Provided there is no ambiguity, condone the continental practice of using a comma for a decimal point. The pupil has made a conceptual error. In some questions, a method mark is available provided the pupil has made a computational, rather than conceptual, error. A computational error is a ‘slip’ such as writing 4 × 6 = 18 in an otherwise correct long multiplication. A conceptual error is a more serious misunderstanding of the relevant mathematics; when such an error is seen, no method marks may be awarded. Examples of conceptual errors 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 45 – 26 to give the answer 21; incorrect signs when working with negative numbers. The pupil’s accuracy is marginal according to the overlay provided. Overlays can never be 100% accurate. However, provided the answer is within, or touches, the boundaries given, the mark(s) should be awarded. The pupil’s answer correctly follows through from earlier incorrect work. 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 correct response or an acceptable follow-through response should be marked as correct. There appears to be a misreading affecting the working. This is when the pupil misreads the information given in the question and uses different information. If the original intention or difﬁculty level of the question is not reduced, deduct one mark only. If the original intention or difﬁculty level is reduced, do not award any marks for the question part. The correct answer is in the wrong place. Where a pupil has shown understanding of the question, the mark(s) should be given. In particular, where a word or number response is expected, a pupil may meet the requirement by annotating a graph or labelling a diagram elsewhere in the question. 4 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 4 http://www.SATs-Papers.co.uk 30/11/07 21:39:52 2008 KS3 Mathematics test mark scheme: Paper 1 General guidance What if … Marking procedure The ﬁnal answer is wrong but the correct answer is shown in the working. 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 incorrect answer is due to a transcription error If so, award the mark. in questions not testing accuracy, the correct answer has been given but then rounded or truncated If so, award the mark. the pupil has continued to give redundant extra working which does not contradict work already done If so, award the mark. the pupil has continued, in the same part of the question, to give redundant extra working which does contradict work already done. If so, do not award the mark. Where a question part carries more than one mark, only the ﬁnal mark should be withheld. The pupil’s answer is correct but the wrong working is seen. A correct response should always be marked as correct unless the mark scheme states otherwise. The correct response has been crossed or rubbed out and not replaced. Mark, according to the mark scheme, any legible crossed or rubbed out work that has not been replaced. More than one answer is given. The answer is correct but, in a later part of the question, the pupil has contradicted this response. If all answers given are correct or a range of answers is given, all of which are correct, the mark should be awarded unless prohibited by the mark scheme. If both correct and incorrect responses are given, no mark should be awarded. A mark given for one part should not be disallowed for working or answers given in a different part, unless the mark scheme speciﬁcally states otherwise. 5 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 5 http://www.SATs-Papers.co.uk 30/11/07 21:39:52 2008 KS3 Mathematics test mark scheme: Paper 1 General guidance Marking speciﬁc types of question Responses involving money For example: £ 3.20 £7 Accept Do not accept Any unambiguous indication of the correct amount eg £ 3.20(p), £3 20, £3,20, 3 pounds 20, £3-20, £ 3 20 pence, £3:20, £ 7.00 Incorrect or ambiguous indication of the amount eg £320, £320p or £700p The unit, £ or 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 eg with £ given in the answer space, accept 3.20 7 or 7.00 Ambiguous use of units outside the answer space eg with £ given in the answer space, do not accept 3.20p outside the answer space Given units amended eg with £ crossed out in the answer space, accept 320p 700p Incorrect placement of decimal points, spaces, etc or incorrect use or omission of 0 eg £3.2, £3 200, £32 0, £3-2-0, £7.0 Responses involving negative numbers For example: Accept –2 Do not accept To avoid penalising the error below more than once within each question, do not award the mark for the ﬁrst occurrence of the error within each question. Where a question part carries more than one mark, only the ﬁnal mark should be withheld. Incorrect notation eg 2 – 6 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 6 http://www.SATs-Papers.co.uk 30/11/07 21:39:52 2008 KS3 Mathematics test mark scheme: Paper 1 General guidance Responses involving the use of algebra For example: 2+n n+2 2n n n2 2 Take care ! Do not accept Accept Unambiguous use of a different case or variable eg N used for n x used for n ! Unconventional notation eg n × 2 or 2 × n or n2 or n + n for 2n n × n for n2 n ÷ 2 for n or 1 n 2 2 2 + 1n for 2 + n 2 + 0n for 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, or within an explanation or general working. Embedded values given when solving equations eg in solving 3x + 2 = 32, 3 × 10 + 2 = 32 for x = 10 To avoid penalising the two types of error below more than once within each question, do not award the mark for the ﬁrst occurrence of each type within each question. Where a question part carries more than one mark, only the ﬁnal mark should be withheld. Words used to precede or follow equations or expressions eg t = n + 2 tiles or tiles = t = n + 2 for t = n + 2 Unambiguous letters used to indicate expressions eg t = n + 2 for n + 2 ! Words or units used within equations or expressions eg n tiles + 2 n cm + 2 Do not accept on their own. Ignore if accompanying an acceptable response. Ambiguous letters used to indicate expressions eg n = n + 2 for n + 2 7 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 7 http://www.SATs-Papers.co.uk 30/11/07 21:39:53 2008 KS3 Mathematics test mark scheme: Paper 1 General guidance Responses involving time A time interval For example: 2 hours 30 minutes Accept Take care ! Do not accept Any unambiguous indication eg 2.5 (hours), 2h 30 Incorrect or ambiguous time interval eg 2.3(h), 2.30, 2-30, 2h 3, 2.30min ! Digital electronic time ie 2:30 A speciﬁc time For example: 8:40am The unit, hours and/or minutes, is usually printed in the answer space. Where the pupil writes an answer outside the answer space, or crosses out the given unit, accept answers with correct units, unless the question has speciﬁcally asked for other units to be used. 17:20 Accept Do not accept Any unambiguous, correct indication eg 08.40, 8.40, 8:40, 0840, 8 40, 8-40, twenty to nine, 8,40 Incorrect time eg 8.4am, 8.40pm Unambiguous change to 12 or 24 hour clock eg 17:20 as 5:20pm, 17:20pm Incorrect placement of separators, spaces, etc or incorrect use or omission of 0 eg 840, 8:4:0, 084, 84 Responses involving coordinates For example: ( 5, 7 ) Accept Do not accept Unconventional notation eg ( 05, 07 ) ( ﬁve, seven ) Incorrect or ambiguous notation eg ( 7, 5 ) x y ( 5, 7 ) ( x = 5, y = 7 ) y x ( 7, 5 ) ( 5x, 7y ) ( 5x, 7y ) ( x – 5, y – 7 ) 8 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 8 http://www.SATs-Papers.co.uk 30/11/07 21:39:53 2008 KS3 Mathematics test mark scheme: Paper 1 General guidance Responses involving probability A numerical probability should be expressed as a decimal, fraction or percentage only. 7 70% For example: 0.7 10 Accept Take care ! Do not accept Equivalent decimals, fractions and percentages 70 35 , 70.0% eg 0.700, , 100 50 The ﬁrst four categories of error below should be ignored if accompanied by an acceptable response, but should not be accepted on their own. However, to avoid penalising the ﬁrst three types of error below more than once within each question, do not award the mark for the ﬁrst occurrence of each type of error unaccompanied by an acceptable response. Where a question part carries more than one mark, only the ﬁnal mark should be withheld. ! A probability that is incorrectly expressed eg 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 integers in the numerator and/or denominator. ! A probability correctly expressed in one acceptable form which is then incorrectly converted, but is still less than 1 and greater than 0 70 = 18 eg 100 25 A probability expressed as a ratio eg 7 : 10, 7 : 3, 7 to 10 A probability greater than 1 or less than 0 9 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 9 http://www.SATs-Papers.co.uk 30/11/07 21:39:53 2008 KS3 Mathematics test mark scheme: Paper 1 General guidance Recording marks awarded on the test paper All questions, even those not attempted by the pupil, will be marked, with a 1 or a 0 entered in each marking space. Where 2m can be split into 1m gained and 1m lost, with no explicit order, then this will be recorded by the marker as 1 0 The total marks awarded for 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 recorded 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 for the award of different levels, will be available on the NAA website www.naa.org.uk/tests from Monday 23 June 2008. 10 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 10 http://www.SATs-Papers.co.uk 30/11/07 21:39:54 2008 KS3 Mathematics test mark scheme: Paper 1 BLANK PAGE 11 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 11 http://www.SATs-Papers.co.uk 30/11/07 21:39:54 2008 KS3 Mathematics test mark scheme: Paper 1 Tier 3–5 only Tier & Question Symbols 3-5 4-6 5-7 6-8 1 Correct response 1m Gives two of the symbols to make a correct calculation, ie 12 ÷ 3 = Other numbers or operations used 4 × Additional guidance 4 or 12 1m = 3 Gives two of the symbols to make a different correct calculation from any credited for the ﬁrst mark U1 12 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 12 http://www.SATs-Papers.co.uk 30/11/07 21:39:54 2008 KS3 Mathematics test mark scheme: Paper 1 Tier & Question Tier 3–5 only Rhino crisis 3-5 4-6 5-7 6-8 2 Correct response a 1m African (rhino) b 1m 110 c 1m Completes the pie chart labels correctly, ie Additional guidance Unambiguous indication of type eg A I A d 1m Numbers used as labels Do not accept numbers as the only labels, but ignore alongside correct labels B W Gives a correct explanation eg There are no Javan rhinos in the captive population The captive number for J was zero Minimally acceptable explanation eg There aren’t any Zero (or 0) They’re only in the wild It has got no captive population Incomplete or incorrect explanation eg There is no section for that type It’s so small you can’t see that section It has been missed out U1 Tier & Question Units 3-5 4-6 5-7 6-8 3 Correct response 1m Gives the most appropriate unit, ie metres 1m Gives the most appropriate unit, ie feet Additional guidance ! Unit abbreviated Accept only if unambiguous eg, for the ﬁrst mark do not accept m eg, for the second mark accept f 13 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 13 http://www.SATs-Papers.co.uk 30/11/07 21:39:54 2008 KS3 Mathematics test mark scheme: Paper 1 Tier 3–5 only Tier & Question Sports 3-5 4-6 5-7 6-8 4 Correct response 2m Completes both bars correctly, ie Additional guidance ! Bars not ruled, accurate or shaded Accept provided the pupil’s intention is clear Running ! Bars inaccurately positioned or of incorrect widths Condone Tennis 0 2 4 6 8 10 12 14 16 or 1m Completes one bar correctly or Indicates the values 14 and 6 eg Bars transposed but otherwise correct Values 14 and 6 highlighted on the horizontal scale Tier & Question Euro 3-5 4-6 5-7 6-8 5 Correct response a 2m Completes all three ways of paying correctly, ie Additional guidance Responses in ﬁgures four eight forty or 1m 1m b Completes two ways of paying correctly 500, 200, 200 and 100, in any order 14 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 14 http://www.SATs-Papers.co.uk 30/11/07 21:39:54 2008 KS3 Mathematics test mark scheme: Paper 1 Tier & Question Tier 3–5 only Shape statements 3-5 4-6 5-7 6-8 6 Correct response 2m Makes correct decisions for all four statements, ie True False Additional guidance Unambiguous indication eg for true and for false or 1m Makes correct decisions for three of the statements Tier & Question Anniversaries 3-5 4-6 5-7 6-8 7 Correct response a 1m 2002 b 1m 1960 c 1m Additional guidance 1987 Unambiguous indication of year eg, for 2002 02 eg, for 1960 60 U1 15 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 15 http://www.SATs-Papers.co.uk 30/11/07 21:39:55 2008 KS3 Mathematics test mark scheme: Paper 1 Tier & Question Tiers 3–5, 4–6 Calculations 3-5 4-6 5-7 6-8 8 1 Correct response 1m 1891 1m 493 1m 585 1m Additional guidance 22 Tier & Question Number line 3-5 4-6 5-7 6-8 9 2 Correct response 1m –3 1m 3 1m Additional guidance –2 Tier & Question Competition 3-5 4-6 5-7 6-8 10 3 Correct response a a 1m H b b 1m 0 c 1m Additional guidance 4 c Unambiguous indication of 0 eg None U1 16 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 16 http://www.SATs-Papers.co.uk 30/11/07 21:39:55 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 3–5, 4–6 Tier & Question Eight times 3-5 4-6 5-7 6-8 11 4 Correct response 1m 100 1m Additional guidance 10 Tier & Question Adding 3-5 4-6 5-7 6-8 12 5 Correct response 2m Additional guidance Gives all three correct digits in the correct positions, ie 4 3 7 + 2 3 8 = 6 7 5 or 1m Gives two correct digits in the correct positions U1 17 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 17 http://www.SATs-Papers.co.uk 30/11/07 21:39:55 2008 KS3 Mathematics test mark scheme: Paper 1 Tier & Question Tiers 3–5, 4–6 Grid patterns 3-5 4-6 5-7 6-8 13 6 a a Correct response 1m Indicates squares to make a pattern with exactly two lines of symmetry eg Additional guidance ! Squares not shaded Accept any unambiguous indication of squares ! Response uses part squares Accept provided the intended symmetry is clearly correct eg, for part (b) ! Line(s) of symmetry drawn Ignore, even if incorrect b b 1m Indicates square(s) to make a pattern with exactly one line of symmetry eg 18 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 18 http://www.SATs-Papers.co.uk 30/11/07 21:39:56 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 3–5, 4–6 Tier & Question Think of a number 3-5 4-6 5-7 6-8 14 7 a a Correct response 1m Additional guidance Indicates the correct decisions for all three questions, ie Yes Unambiguous indication eg for yes and for no No … even number? … multiple of 3? … factor of 18? b b 1m 15 U1 Tier & Question Dial 3-5 4-6 5-7 6-8 15 8 Correct response a a 1m 2 b b 1m 135 Additional guidance Answers of 135 + any multiple of 360 Tier & Question Temperatures 3-5 4-6 5-7 6-8 16 9 Correct response a a 1m 6 b b 1m Additional guidance –3 19 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 19 http://www.SATs-Papers.co.uk 30/11/07 21:39:56 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 3–5, 4–6, 5–7 Tier & Question Making ten 3-5 4-6 5-7 6-8 17 10 1 Correct response 1m Gives two numbers, one positive and one negative, that add to 10 eg –10 and 20 15 and –5 –1 and 11 –0.5 and 10.5 Tier & Question Additional guidance Fractions or decimals Addition symbol amended eg 20 – 10 = 10 Decimals 3-5 4-6 5-7 6-8 18 11 2 Correct response 1m 7.2 1m Additional guidance Equivalent fractions or decimals 0.2 20 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 20 http://www.SATs-Papers.co.uk 30/11/07 21:39:56 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 3–5, 4–6, 5–7 Tier & Question Duckweed 3-5 4-6 5-7 6-8 20 12 3 Correct response a a a 1m 34 b b b 1m 26 c c 1m 16 d d d 1m Gives a correct interpretation eg When salt is added, the number of leaves decreases and the more salt there is, the quicker the number of leaves will be zero With no salt, the plant grows but the more 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 Additional guidance c ! Follow-through Accept follow-through as 60 – their (a), provided their (a) was not 0 Minimally acceptable interpretation eg The more salt, the faster the number of leaves goes down As the amount of salt increases, the plant dies more quickly The more salt there is, the fewer leaves the plant will have The less salt, the more leaves the plant will have Incomplete or incorrect interpretation eg Adding salt makes it lose leaves rather than grow them Salt kills the plants The more salt, the more chance the plant will die U1 Tier & Question Six cubes 3-5 4-6 5-7 6-8 19 13 4 Correct response 1m Indicates both correct shapes, ie Additional guidance Unambiguous indication 21 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 21 http://www.SATs-Papers.co.uk 30/11/07 21:39:57 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 3–5, 4–6, 5–7 Tier & Question Substituting 3-5 4-6 5-7 6-8 21 14 5 Correct response 2m Completes all three statements correctly eg 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 Additional guidance Negatives, fractions or decimals ! Decimal answers rounded or truncated Accept answers rounded or truncated to two decimal places or better Incomplete processing eg, for the last part 3 3, 3 6 6, 3 or 1m Completes two statements correctly Tier & Question Boxes 3-5 4-6 5-7 6-8 22 15 6 Correct response 2m Additional guidance 925 or 1m Shows a complete correct method with not more than one computational error eg 37 × 100 = 3700 3700 ÷ 2 = 1850 1850 ÷ 2 30 7 20 600 140 5 150 Conceptual error eg 37 ×25 185 74 259 45 (error) so 600 + 150 + 140 + 45 = 935 37 ×25 185 640 (error) 825 22 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 22 http://www.SATs-Papers.co.uk 30/11/07 21:39:57 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 3–5, 4–6, 5–7 1 3 times table 2 Tier & Question 3-5 4-6 5-7 6-8 24 16 7 a a a Correct response 1m 14 1m Additional guidance 1 17 or equivalent 2 ! For the second mark, follow-through Accept as their value for the ﬁrst mark + 3 1m b b b 210 1m Indicates No and gives a correct explanation 1 2 ! Incorrect statement alongside a correct explanation Ignore eg, accept 1 1 11 is an odd number, 11 × = 6 2 2 The most common correct explanations: Reason about odd and/or even multiples of 3 1 2 eg 11 is an odd number so you will get a half left over 1 1 2 × = 1, so only an even number of 3 s 2 2 will give a whole number Minimally acceptable explanation eg 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 eg 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 or imply the correct product or a relevant portion of it eg 1 1 11 × 3 = 38 2 2 1 17 + 21 2 1 33 + 5 2 Minimally acceptable explanation eg 1 38 2 1 1 11 × = 5 2 2 1 1 11 ends in 1 and 1 × = 2 2 Incomplete or incorrect explanation eg 1 11 × 3 does not give a whole number 2 1 It will end in a 2 1 1 11 × 3 = 33 2 2 U1 23 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 23 http://www.SATs-Papers.co.uk 30/11/07 21:39:58 2008 KS3 Mathematics test mark scheme: Paper 1 Tier & Question Tiers 3–5, 4–6, 5–7 Solving 3-5 4-6 5-7 6-8 25 17 8 Correct response 1m 3 1m –5 Additional guidance ! Incorrect notation eg, as an answer for the ﬁrst mark ×3 3x Penalise only the ﬁrst occurrence ! Incomplete processing eg, as an answer for the ﬁrst mark 15 5 Penalise only the ﬁrst occurrence Tier & Question Coordinates 3-5 4-6 5-7 6-8 23 18 9 Correct response 2m Additional guidance Gives A as (3, 4) or 1m Gives A as (4, 3) or Shows or implies that the side length of the square is 4 eg 5–1=4 (5, 2) seen (1, 6) seen 6 2 1 5 1, 2, 3, 4, 5 2, 3, 4, 5, 6 U1 24 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 24 http://www.SATs-Papers.co.uk 30/11/07 21:39:58 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 4–6, 5–7, 6–8 Tier & Question Expressions 3-5 4-6 5-7 6-8 19 10 1 Correct response 2m Additional guidance Matches all three expressions correctly, ie 3 ! Expression on the left matched with more than one expression on the right For 2m or 1m, do not accept as a correct match 2d 3d 4d 2d 2 3d 2 2d 3 or 1m Matches any two of the expressions correctly 25 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 25 http://www.SATs-Papers.co.uk 30/11/07 21:39:58 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 4–6, 5–7, 6–8 Tier & Question Views 3-5 4-6 5-7 6-8 20 11 2 Correct response 2m Draws both views correctly using the grid, ie … FRONT … SIDE Additional guidance ! Lines not ruled or accurate Accept provided the pupil’s intention is clear ! Shading used Ignore ! Correct view from the side in a different orientation Condone eg, for 2m accept … FRONT ! For 2m or 1m, their side view omits the middle section of the diagonal line Condone eg or 1m … SIDE Draws one of the views correctly using the grid … FRONT … SIDE or Draws both views correctly using the grid but transposes their positions or Draws both views correctly either without using the grid or of incorrect sizes, provided the length and width of each view are clearly intended to be equal Tier & Question Multiple of 6 3-5 4-6 5-7 6-8 21 12 3 Correct response 1m Additional guidance 1, 2 and 3, in any order 26 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 26 http://www.SATs-Papers.co.uk 30/11/07 21:39:59 2008 KS3 Mathematics test mark scheme: Paper 1 Tier & Question Tiers 4–6, 5–7, 6–8 Test results 3-5 4-6 5-7 6-8 22 13 4 Correct response a a a 1m 11 b b b 1m Additional guidance 12 U1 Tier & Question Square tiles 3-5 4-6 5-7 6-8 23 14 5 Correct response 1m Additional guidance Gives a correct value for the area of the rectangle eg 54 5400 U1 1m Shows the correct unit for their area eg cm² [with 54] mm² [with 5400] ! Area incorrect or omitted, but units given If the mark for their correct area has not been awarded, condone cm² seen for the second mark 27 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 27 http://www.SATs-Papers.co.uk 30/11/07 21:39:59 2008 KS3 Mathematics test mark scheme: Paper 1 Tier & Question Tiers 4–6, 5–7, 6–8 Walking to school 3-5 4-6 5-7 6-8 24 15 6 Correct response a a a 1m 20 b b b 2m Additional guidance 28 or 1m Gives an answer of 72 or Shows or implies a correct method eg 7×4 0.28 7 out of 25 7 25 U1 Tier & Question 100 metres 3-5 4-6 5-7 6-8 25 16 7 Correct response a a a 1m 4 b b b 2m Additional guidance 2.8 or equivalent or 1m Identiﬁes the values 13.6 and 16.4 or equivalent or Shows a complete correct method with not more than one computational error eg 16 – 13 = 3, 0.6 – 0.4 = 0.2, 3 – 0.2 c c 1m ! For 1m, key not interpreted Condone only if the correct range has been evaluated eg, accept 2|8 eg, do not accept 16|4 – 13|6 For 1m, conceptual error eg 16 – 13 = 3, 0.6 – 0.4 = 0.2, 3 + 0.2 = 3.2 15.3 or equivalent 28 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 28 http://www.SATs-Papers.co.uk 30/11/07 21:39:59 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 4–6, 5–7, 6–8 Tier & Question Sequences 3-5 4-6 5-7 6-8 26 17 8 Correct response a a 2m Additional guidance Makes all four correct decisions, ie increasing decreasing neither or 1m b b 1m Makes three correct decisions Gives all four correct terms in any order eg 1 1 1 1 , , , 4 9 16 25 Equivalent fractions ! Equivalent decimals 1 For , accept 0.25 4 1 For , accept 0.11 or better 9 1 , accept 0.0625 For 16 1 , accept 0.04 For 25 ! Incorrect further working Condone provided the four correct terms have been given Answer of 1, 1 1 1 , , 4 9 16 Incomplete processing 1 eg, for 4 1 22 29 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 29 http://www.SATs-Papers.co.uk 30/11/07 21:40:00 2008 KS3 Mathematics test mark scheme: Paper 1 Tier & Question Tiers 4–6, 5–7, 6–8 Equation 3-5 4-6 5-7 6-8 27 18 9 Correct response 2m Additional guidance –12 or 1m Shows or implies a correct ﬁrst step of algebraic manipulation that either reduces the number of terms or collects unknowns on one side of the equation and numbers on the other eg 2x = x – 12 12 + 2x = x 6 + x = –6 2x – x = –6 – 6 12 + x = 0 Tier & Question ! Method used is trial and improvement Note that no partial credit can be given Cancelling 3-5 4-6 5-7 6-8 28 19 10 Correct response 1m 20 1m 400 Additional guidance ! Incomplete processing Penalise only the ﬁrst occurrence, provided all redundant values have been cancelled eg, for both marks 4×5 (4 × 5)2 Mark as 0, 1 ! Follow-through For the second mark, accept the square of their 20 evaluated 30 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 30 http://www.SATs-Papers.co.uk 30/11/07 21:40:00 2008 KS3 Mathematics test mark scheme: Paper 1 Tier & Question Marking overlay available Tiers 5–7, 6–8 Finding Atlanta 3-5 4-6 5-7 6-8 20 11 Correct response 2m or 1m Additional guidance Indicates a point within the region shown on the ! For 2m, intersecting arcs shown but point overlay not otherwise labelled and Condone shows correct intersecting construction arcs with radii within the tolerances as shown on the overlay ! Arcs extended or extra arcs Ignore inaccuracies in sections of arcs extending beyond the tolerances as shown on the overlay, or arcs not indicated on the Indicates a point within the region shown on the overlay, even if incorrect overlay, even if the construction arcs are incorrect or omitted ! Spurious arcs Do not accept arcs drawn without compasses or Draws at least one correct construction arc with radius within the tolerance as shown on the overlay or The only error is to transpose the distances, ie indicates a point within the region shown on the overlay when turned over and shows their two correct intersecting construction arcs Tier & Question Twice as far 3-5 4-6 5-7 6-8 21 12 Correct response 2m Additional guidance Gives both correct pairs of coordinates, ie (16, 3) and (8, 3) in either order or 1m Gives one correct pair of coordinates with the other pair incorrect or omitted or Identiﬁes both correct points on the graph, even if the coordinates are incorrect or omitted ! Correct points marked on the graph, but alongside other points marked For 1m, do not accept unless the two correct points are clearly identiﬁed 31 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 31 http://www.SATs-Papers.co.uk 30/11/07 21:40:00 2008 KS3 Mathematics test mark scheme: Paper 1 Tier & Question Tiers 5–7, 6–8 Functions 3-5 4-6 5-7 6-8 22 13 Correct response 2m Additional guidance Makes correct decisions for all four functions, ie q increases q decreases r increases r decreases s increases s decreases t increases t decreases or 1m Makes three correct decisions Tier & Question Red and blue cubes 3-5 4-6 5-7 6-8 23 14 Correct response 2m Additional guidance Gives the number of blue cubes as 35 or 1m Shows the value 5, with no evidence of an incorrect method for that value or Shows the values 20 and 35, or 30 and 35 eg 20 : 35 35, 30 or Shows a complete correct method eg 10 ÷ (6 – 4) × 7 7 × 10 2 U1 32 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 32 http://www.SATs-Papers.co.uk 30/11/07 21:40:01 2008 KS3 Mathematics test mark scheme: Paper 1 Tier & Question Tiers 5–7, 6–8 Straight lines 3-5 4-6 5-7 6-8 24 15 Correct response a a 1m Additional guidance Indicates No and gives a correct explanation The most common correct explanations: Show how (7, 12) fails to follow the rule y = 2x + 1 eg It should be x × 2 + 1 to get y but 7 × 2 + 1 = 15, not 12 It’s double 7 then subtract 2, but it should be double 7 then add 1 1 It should be 12 – 1 then ÷ 2 but this gives 5 , 2 not 7 If the x-coordinate is a whole number, the y-coordinate will always be an odd number Show or imply that the point (7, 15) or 1 (5 , 12) is on the straight line 2 eg It should be (7, 15) since 7 × 2 + 1 = 15 1 (5 , 12) is on the line because 12 – 1 = 11 2 1 and 11 ÷ 2 = 5 2 It’s not one of these coordinates: x 4 5 6 7 b b 1m Gives a correct equation eg y = 3x + 1 3x – y = –1 y 9 11 13 15 Minimally acceptable explanation eg 7 × 2 + 1 12 (12 – 1) ÷ 2 7 y = 2x – 2 Incomplete explanation eg 7 × 2 + 1 = 15 (12 – 1) ÷ 2 the y-coordinate will always be odd Minimally acceptable explanation eg (7, 15) 1 (5 , 12) 2 15, not 12 1 5 , not 7 2 (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 or incorrect explanation eg It doesn’t ﬁt the equation The y coordinate is too low You don’t get to (7, 12) Only (6, 13) and (8, 17) are on the line ! Unconventional notation eg 1y = 3 × x + 1 Condone ! Incomplete processing eg y = 2x + 1 + x Condone U1 33 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 33 http://www.SATs-Papers.co.uk 30/11/07 21:40:01 2008 KS3 Mathematics test mark scheme: Paper 1 Tiers 5–7, 6–8 Tier & Question Square root 3-5 4-6 5-7 6-8 25 16 Correct response a a 1m Gives a correct explanation eg 92 = 81 and 102 = 100 and 89 is between 81 and 100 9 × 9 < 89 and 10 × 10 > 89 Additional guidance Minimally acceptable explanation eg 81, 100 81, 100 92 < 89 < 102 89 is between the squares of 9 and 10 Value for 89 given eg 9.4(…) seen ! Explanation refers to negative values Ignore alongside a correct explanation eg, accept 81 = 9 or –9 and 100 = 10 or –10 Incomplete or incorrect explanation eg 89 is between 9 and 10 The square root of 9 is 81 and the square root of 10 is 100 9 × 9 = 81 and 9 × 10 = 90 so it’s between 9 and 10 U1 b b 1m 19 and 20, in either order ! Negative values given eg 19 and 20 –19 and –20 Condone ! Answer embedded eg 19 × 19 and 20 × 20 seen Condone Incomplete response eg 361 and 400 34 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 34 http://www.SATs-Papers.co.uk 30/11/07 21:40:01 2008 KS3 Mathematics test mark scheme: Paper 1 Tier & Question Tiers 5–7, 6–8 Heads or tails 3-5 4-6 5-7 6-8 26 17 Correct response 2m Additional guidance 31 or 32 or both ! For 2m or 1m, value(s) qualiﬁed eg, for 2m About 31 Condone Shows or implies a correct method with not more than one computational error, even if their ﬁnal value is not a whole number eg 31.25 or 31.5 or equivalents seen 1000 ÷ 2 ÷ 2 ÷ 2 ÷ 2 ÷ 2 500, 250, 175 (error), 87.5, 43.75 ! For 1m, value(s) rounded or truncated Condone correct rounding or truncation at any stage within a correct method eg, for 1m accept 500, 250, 175 (error), 88, 44 or 1m U1 Tier & Question Coordinate net 3-5 4-6 5-7 6-8 27 18 Correct response 1m Gives L as (–10, 0) 1m Gives M as (30, –20) Additional guidance ! Answers for L and M transposed but otherwise completely correct If this is the only error, ie gives L as (30, –20) and gives M as (–10, 0), mark as 0, 1 35 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 35 http://www.SATs-Papers.co.uk 30/11/07 21:40:02 2008 KS3 Mathematics test mark scheme: Paper 1 Tier & Question Tiers 5–7, 6–8 Halving 3-5 4-6 5-7 6-8 28 19 a 1m Correct response Additional guidance Gives a correct justiﬁcation The most common correct justiﬁcations: Evaluate 1 of 103 and 53 2 eg 103 is 1000, so half is 500 but 53 is 125 103 = 1000, 53 = 125 1 but of 1000 is not 125 2 Express the two sides of the equation in a form that enables comparison eg 0.5 × 10 × 10 × 10 = 5 × 10 × 10, not 5 × 5 × 5 Minimally acceptable justiﬁcation eg 500, 125 1000, 125 Incomplete or incorrect justiﬁcation eg 500 1000 125 Minimally acceptable justiﬁcation eg 5 × 10 × 10, 5 × 5 × 5 5 × 102 5 × 52 0.5 × 10 × 10 × 10 5 × 5 × 5 Incomplete or incorrect justiﬁcation eg 53 is too small It should be 101.5 Address the misconception eg You only divide one of the tens by 2 not all of them Minimally acceptable justiﬁcation eg You just halve one of the tens It’s only one 5 and two 10s Incomplete justiﬁcation eg You don’t halve all of the tens 36 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 36 http://www.SATs-Papers.co.uk 30/11/07 21:40:02 2008 KS3 Mathematics test mark scheme: Paper 1 Tier & Question Tier 6–8 only Halving (cont) 3-5 4-6 5-7 6-8 19 Correct response b 1m Additional guidance Gives a correct justiﬁcation The most common correct justiﬁcations: Calculate 1 of 6 × 108 2 eg 1 of 6 × 108 is 3 × 108 not 3 × 104 2 It should be 6 × 5 × 107 not 3 × 104 300 000 000 not 30 000 0.5 × 600 000 000 is bigger than 30 000 Minimally acceptable justiﬁcation eg 3 × 108 6 × 5 × 107 300 000 000 1 of 600 000 000 30 000 2 Incomplete or incorrect justiﬁcation eg 3 × 104 is too small 1 of 108 isn’t 104 2 It should be 6 × 104 Address the misconception eg 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 eg You only halve the 6 The power of 10 stays the same Incomplete justiﬁcation eg You don’t halve both values c 2m 8.25 × 105 ! Zero(s) given after the last decimal place within standard form notation Condone eg, for 2m accept 8.25000 × 105 or 1m Shows a value equivalent to 8.25 × 105 eg 0.825 × 106 825 000 or Makes an error in halving 1.65, but follows through correctly giving their answer in standard form eg 0.325 × 106 = 3.25 × 105 37 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 37 http://www.SATs-Papers.co.uk 30/11/07 21:40:02 2008 KS3 Mathematics test mark scheme: Paper 1 Tier 6–8 only Tier & Question Pay 3-5 4-6 5-7 6-8 20 Correct response a 1m Additional guidance Indicates only the third statement, ie … more than twice as much… … exactly twice as much… … less than twice as much… … not enough information… U1 b 1m Indicates only the second statement, ie … more than twice as much… … exactly twice as much… … less than twice as much… … not enough information… U1 Tier & Question Factorisation 3-5 4-6 5-7 6-8 21 Correct response 1m Completes the factorisation correctly eg 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) 1 1 1 x 2 + 7x + 3 = (x + )(x + 6 ) 4 2 2 x 2 + 7x + 0 = (x + 7)(x + 0) 1m Completes the factorisation correctly in a different way from any previously credited Additional guidance Factorisation given for the ﬁrst mark repeated, but the order of the factors reversed eg, from x 2 + 7x + 6 = (x + 1)(x + 6) for the ﬁrst mark x 2 + 7x + 6 = (x + 6)(x + 1) 38 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 38 http://www.SATs-Papers.co.uk 30/11/07 21:40:03 2008 KS3 Mathematics test mark scheme: Paper 1 Tier & Question Tier 6–8 only Shape cards 3-5 4-6 5-7 6-8 22 Correct response a 2m Additional guidance 1 or equivalent probability 20 or 1m 1 1 Shows the values and or equivalent 5 4 probabilities or Gives the answer 1 or equivalent probability 25 [ie the only error is to assume the ﬁrst card is replaced] b 1m 1 or equivalent probability 10 ! Follow-through Accept 2 × their (a) provided this gives a value greater than 0 and less than 1 U1 39 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 39 http://www.SATs-Papers.co.uk 30/11/07 21:40:03 2008 KS3 Mathematics test mark scheme: Paper 1 Tier 6–8 only Tier & Question Lines 3-5 4-6 5-7 6-8 23 Correct response a 2m Additional guidance Completes all three rows of the table correctly, ie Point Above On Below (6, 3) (8, 5) (100, 60) (–4, –3) or 1m b 1m Completes any two of the rows correctly Gives a correct equation equivalent to 1 y = x + c where c < 1 2 eg 1 y= x–1 2 2y = x Tier & Question ! Unconventional notation eg 1 y= ×x–1 2 1 1y = x + 0 2 Condone Dimensions 3-5 4-6 5-7 6-8 24 Correct response 2m Additional guidance Makes all three correct decisions, ie area area volume or 1m Makes two correct decisions 40 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 40 http://www.SATs-Papers.co.uk 30/11/07 21:40:03 2008 KS3 Mathematics test mark scheme: Paper 1 Tier 6–8 only Tier & Question Speed 3-5 4-6 5-7 6-8 25 Correct response a 1m 0.65 to 0.67 inclusive Additional guidance Equivalent fractions, decimals or percentages Value of 65 to 67 inclusive without a percentage sign b 1m Indicates Thursday and gives a correct explanation The most common correct explanations: Refer to the relative speeds of the cars on the two days eg 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 more 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 eg 71.5, 55 Lower median They were generally slower Most went more slowly More were under the speed limit ! Value(s) given for the median(s) Accept 71 to 72 inclusive for Monday Accept 55 to 55.5 inclusive for Thursday ! Irrelevant information eg There was also more variation in the speeds on Thursday as some people take more care than others Ignore alongside a correct explanation Incomplete or incorrect explanation eg 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 eg Most of the Thursday line is to the left of the Monday line, so the speeds are lower The line for Monday is further along the speed axis, showing higher values Minimally acceptable explanation eg 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 for Monday is below the other, ie at faster speeds Incomplete or incorrect explanation eg Thursday’s line is higher up The line for Monday is below the other U1 41 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 41 http://www.SATs-Papers.co.uk 30/11/07 21:40:04 2008 KS3 Mathematics test mark scheme: Paper 1 Tier 6–8 only Tier & Question Inequalities 3-5 4-6 5-7 6-8 26 Correct response 1m Gives a pair of values such that k < n and k + n < 0 eg k = –3, n = –2 k = –8, n = 7 k = –1, n = 0 Tier & Question Additional guidance Fractions or decimals Two more numbers 3-5 4-6 5-7 6-8 27 Correct response 2m Gives x = 3y Additional guidance ! Unconventional notation eg x=3×y x = y3 Condone or 1m Shows a correct equation in x and y eg 2(x – y) = x + y 1 x – y = (x + y) 2 2x = x + 3y y= x 3 42 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 42 http://www.SATs-Papers.co.uk 30/11/07 21:40:04 2008 KS3 Mathematics test mark scheme: Paper 1 BLANK PAGE 43 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 43 http://www.SATs-Papers.co.uk 30/11/07 21:40:04 2008 KS3 Mathematics test mark scheme: Paper 1 Tier Index Question Page 1 Symbols 12 2 Rhino crisis 13 3 Units 13 4 Sports 14 5 Euro 14 6 Shape statements 15 7 Anniversaries 15 3–5 4–6 5–7 6–8 8 1 Calculations 16 9 2 Number line 16 10 3 Competition 16 11 4 Eight times 17 12 5 Adding 17 13 6 Grid patterns 18 14 7 Think of a number 19 15 8 Dial 19 16 9 Temperatures 19 17 10 1 Making ten 20 18 11 2 Decimals 20 20 12 3 Duckweed 21 19 13 4 Six cubes 21 21 14 5 Substituting 22 22 15 6 Boxes 22 24 16 7 3½ times table 23 25 17 8 Solving 24 23 18 9 Coordinates 24 44 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 44 http://www.SATs-Papers.co.uk 30/11/07 21:40:04 2008 KS3 Mathematics test mark scheme: Paper 1 Tier 3–5 Index Question Page 4–6 5–7 6–8 19 10 1 Expressions 25 20 11 2 Views 26 21 12 3 Multiple of 6 26 22 13 4 Test results 27 23 14 5 Square tiles 27 24 15 6 Walking to school 28 25 16 7 100 metres 28 26 17 8 Sequences 29 27 18 9 Equation 30 28 19 10 Cancelling 30 20 11 Finding Atlanta 31 21 12 Twice as far 31 22 13 Functions 32 23 14 Red and blue cubes 32 24 15 Straight lines 33 25 16 Square root 34 26 17 Heads or tails 35 27 18 Coordinate net 35 28 19 Halving 36 20 Pay 38 21 Factorisation 38 22 Shape cards 39 23 Lines 40 24 Dimensions 40 25 Speed 41 26 Inequalities 42 27 Two more numbers 42 45 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 45 http://www.SATs-Papers.co.uk 30/11/07 21:40:05 2008 KS3 Mathematics test mark scheme: Paper 1 BLANK PAGE 46 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 46 http://www.SATs-Papers.co.uk 30/11/07 21:40:05 2008 KS3 Mathematics test mark scheme: Paper 1 BLANK PAGE 47 Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 47 http://www.SATs-Papers.co.uk 30/11/07 21:40:05 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: 08700 60 60 40 Minicom: 020 7509 6546 Fax: 020 7509 5908 Email: tests@naa.org.uk Website: www.naa.org.uk/tests First published 2008 © Qualifications and Curriculum Authority 2008 ISBN 1-84721-491-6 Reproduction, storage, adaptation or translation, in any form or by any means, of this publication is prohibited without prior written permission of the publisher, unless within the terms of licences issued by the Copyright Licensing Agency. Excerpts may be reproduced for the purpose of research, private study, criticism or review, or by educational institutions solely for educational purposes, without permission, providing full acknowledgement is given. Printed in Great Britain by the Qualifications and Curriculum Authority under the authority and superintendence of the Controller of Her Majesty’s Stationery Office and Queen’s Printer of Acts of Parliament. The Qualifications and Curriculum Authority is an exempt charity under Schedule 2 of the Charities Act 1993. Qualifications and Curriculum Authority 83 Piccadilly London W1J 8QA www.qca.org.uk Sourced from SATs-Papers.co.uk 282675_MS_P1.06.indd 48 For more copies: QCA Orderline, PO Box 29, Norwich NR3 1GN www.qca.org.uk/orderline email: orderline@qca.org.uk Tel: 08700 60 60 15 Fax: 08700 60 60 17 QCA/08/3286 282675 http://www.SATs-Papers.co.uk 30/11/07 21:40:05