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Mathematics tests Ma KEY STAGE 3 ALL TIERS 2002 Mark scheme for Paper 1 Tiers 3–5, 4–6, 5–7 and 6–8 KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST KEY STAGE 3 KEY STAGE 3 KEY STAG 3 KEY STAGE 3 KEY STAGE 3 KEY ST Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 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 and the extension paper mark schemes are printed in separate booklets. 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 11 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 and the minimum acceptable. 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. 2 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 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 to marking of questions that involve money, time, coordinates, algebra or probability. Unless otherwise specified in the mark scheme, markers should apply the following guidelines in all cases. Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 3 2002 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 t 6 e 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 t 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. The correct answer is in the wrong place. 4 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. 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. Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 The final answer is wrong but the correct answer is shown in the working. General guidance 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; in questions not testing accuracy, the correct answer has been given but then rounded or truncated; 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 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. The correct response has been crossed (or rubbed) out and not replaced. If so, award the mark. the pupil has continued to give redundant extra working which does not contradict work already done; The pupil’s answer is correct but the wrong working is seen. If so, award the mark. If so, do not award the mark. Where a question part carries more than one mark, only the final mark should be withheld. A correct response should always be marked as correct unless the mark scheme states otherwise. Mark, according to the mark scheme, any legible crossed (or rubbed) out work that has not been replaced. 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. Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 5 2002 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 use of pounds or pence eg £320, £320p or £700p, or 3.20 or 3.20p not in the answer space. Incorrect placement of decimal points, spaces, etc or incorrect use or omission of 0 The £ sign is usually already printed in the answer space. Where the pupil writes an answer other than in the answer space, or crosses out the £ sign, accept an answer with correct units in pounds and/or pence eg 320p, 700p eg £3.2, £3 200, £32 0, £3-2-0, £7.0 Responses involving time A time interval For example: 2 hours 30 mins Accept Take care ! Do not accept Any unambiguous indication eg 2.5 (hours), 2h 30 Digital electronic time ie 2:30 Incorrect or ambiguous time interval eg 2.3(h), 2.30, 2-30, 2h 3, 2.30min ! The time unit, hours or minutes, is usually printed in the answer space. Where the pupil writes an answer other than in the answer space, or crosses out the given unit, accept an answer with correct units in hours or minutes, unless the question has asked for a specific unit to be used. A specific time For example: 8.40am, 17:20 Accept Any unambiguous, correct indication eg 08.40, 8.40, 8:40, 0840, 8 40, 8-40, twenty to nine, 8,40 Unambiguous change to 12 or 24 hour clock eg 17:20 as 5:20pm, 17:20pm 6 Sourced from SATs-Papers.co.uk Do not accept Incorrect time eg 8.4am, 8.40pm Incorrect placement of separators, spaces, etc or incorrect use or omission of 0 eg 840, 8:4:0, 084, 84 http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 General guidance Responses involving coordinates For example: ( 5, 7 ) Accept Do not accept Unambiguous but unconventional notation eg ( 05, 07 ) ( five, seven ) x y ( 5, 7 ) ( x e5, y e7 ) Incorrect or ambiguous notation eg ( 7, 5 ) ( 5x, 7y ) ( x5, y7 ) ( 5x, 7y ) Responses involving the use of algebra For example: 2 p n n p 2 2n Accept The unambiguous use of a different case eg N used for n Unconventional notation for multiplication eg n t 2 or 2 t n or n2 or n p n for 2n n t n for n2 Multiplication by 1 or 0 eg 2 p 1n for 2 p n 2 p 0n for 2 Words used to precede or follow equations or expressions eg t e n p 2 tiles or tiles e t e n p 2 for t e n p 2 Unambiguous letters used to indicate expressions eg t e n p 2 for n p 2 Embedded values given when solving equations eg 3 t 10 p 2 e 32 for 3x p 2 e 32 Sourced from SATs-Papers.co.uk Take care ! Do not accept ! Words or units used within equations or expressions should be ignored if accompanied by an acceptable response, but should not be accepted on their own eg do not accept n tiles p 2 n cm p 2 Change of variable eg x used for n Ambiguous letters used to indicate expressions eg n e n p 2 However, to avoid penalising any of the three types of error above 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. Embedded values that are then contradicted eg for 3x p 2 e 32, 3 x 10 p 2 e 32, x e 5 http://www.SATs-Papers.co.uk 7 2002 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. For example: 0.7 Accept Take care ! Do not accept A correct probability that is correctly expressed as a decimal, fraction or percentage. Equivalent decimals, fractions or percentages 70 35 eg 0.700, , , 70.0% 100 50 A probability correctly expressed in one acceptable form which is then incorrectly converted, but is still less than 1 and greater than 0 eg 70 18 e 100 25 The following four categories of error should be ignored if accompanied by an acceptable response, but should not be accepted on their own. ! A probability that is incorrectly expressed eg 7 in 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. However, each of the three types of error above should not be penalised 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 expressed as a ratio eg 7 : 10, 7 : 3, 7 to 10 A probability greater than 1 or less than 0 8 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 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. The extension paper carries 42 marks. Awarding levels The sum of the marks gained on paper 1, paper 2 and the mental arithmetic paper determines the level awarded. Level threshold tables, which show the mark ranges for the award of different levels, will be available on the QCA website (www.qca.org.uk) from Wednesday, 26 June 2002. QCA will also send a copy to each school in July. Schools will be notified of pupils’ results by means of a marksheet, which will be returned to schools by the External Marking Agency with the pupils’ marked scripts. The marksheet will include pupils’ scores on the test papers and the levels awarded. The 2002 key stage 3 mathematics tests and mark schemes were developed by the Mathematics Test Development Team at QCA. Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 9 2002 KS3 Mathematics Test Mark Scheme: Paper 1 BLANK PAGE 10 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tier 3–5 only Tier & Question Half 3-5 4-6 5-7 6-8 1 Correct response 1m Additional guidance Both correct, ie more than half half Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 11 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tier 3–5 only Tier & Question Robot 3-5 4-6 5-7 6-8 2 a Correct response 1m Correct diagram, ie Additional guidance Unambiguous indication eg N ! Arrows incorrect or omitted Ignore b c 1m 1m A correct route, showing 2 Norths and 1 East eg I North North East I N E N I East N N A different correct route, also showing 2 Norths and 1 East Identical steps combined eg, in part (b) N Move 2m north, then 1m east ! Other compass points used eg, in part (b) N North-east East West-north Penalise only the first occurrence ! More than the specified number of steps used Do not accept in part (d). Otherwise penalise only the first occurrence, unless this error occurs alongside the error given above (other compass points used) in which case ignore ! Follow through from part (b) to part (c) d 12 1m A correct route, showing one step in any direction and its inverse eg I North South I W E Sourced from SATs-Papers.co.uk If the compass directions in part (b) are incorrect, accept the same directions used in part (c) but in a different order eg, from part (b) as W, N, N N N W N Compass directions not specified Do not accept the route shown only by lines on the diagram, or other ways of specifying directions eg N Forward Right Forward http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tier & Question Tier 3–5 only Computation 3-5 4-6 5-7 6-8 3 Correct response a 1m 573 b 1m 446 c 1m 168 d 1m Additional guidance 26 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 13 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tier & Question Tier 3–5 only Olympic Games 3-5 4-6 5-7 6-8 4 Correct response 3m or 2m Additional guidance 103 Shows or implies correct totals of 131 and 28 and the intention to subtract, even if the notation is incorrect eg I 41 p 43 p 47 e 131, 11 p 10 p 7 e 28 131 m 28 e 117 (error) I 28 m 131 e 117 (error) I 117 given as the answer ! Intention to subtract not explicit Accept implicit intention to subtract eg N 131 and 28 seen, with 102 given as the answer or Shows or implies correct differences of 30, 33 and 40 and the intention to add eg I 41 m 11 e 30, 43 m 10 e 33, 47 m 7 e 40 30 p 33 p 40 ! Intention to add not explicit Accept implicit intention to add eg N 30, 33 and 40 seen, with 113 given as the answer or Shows a complete correct method with not more than one error, that is followed through correctly to an answer eg I 41 p 43 p 47 e 132 (error), 132 m 28 e 104 I 30 p 23 (error) p 40 e 93 or 1m ! Method not explicit Accept implicit methods eg N 121 (error) and 28 seen, with 93 given as the answer but no other working shown Shows the totals 131 and 28 or Shows the differences 30 and 33 and 40 or Shows a complete correct method with not more than two errors 14 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 3–5 only Tier & Question Pictogram key 3-5 4-6 5-7 6-8 5 Correct response 2m Correct for both male and female, ie 2 circles for male, 1 1 circles for female 2 Additional guidance ! Drawings not accurate or the same size, or the half circle is not closed Accept provided the pupil’s intention is clear ! Symbol other than circle used to or 1m Correct for either male or female represent 4 people Do not accept multiple symbols, eg circles and squares used. However, if the only error is to use a different symbol consistently for both male and female, mark as 1, 0 Tier & Question Two steps 3-5 4-6 5-7 6-8 6 a Correct response 40 1m b 1m 46 1m 12 Additional guidance ! Units given Ignore eg, accept N 12 cm ! Step size shown on diagram Accept if unambiguous, but do not accept incorrect further working eg, do not accept N 12 shown correctly on the diagram, but 24 given as the answer ! Both step sizes shown Accept if unambiguous eg, accept N 12, 12 N 12 and 12 Do not accept if ambiguous eg N 12 p 12 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 15 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tier & Question Tiers 3–5, 4–6 Calculations 3-5 4-6 5-7 6-8 7 Correct response 2m Additional guidance All four decisions correct, ie or 1m Any three correct decisions or Both crosses are left blank, ie Tier & Question Areas 3-5 4-6 5-7 6-8 8 1 Correct response a a 1m 12 b b 1m 3 Additional guidance Follow through as part (a) d 4 If their (a) d 4 is not an integer, accept values rounded or truncated to one or more decimal places c c 1m 12 Follow through as part (b) t 4, or as part (a) Note that follow through from part (b) must be exact eg, from 3.2 in part (b), accept 12.8 only 16 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 3–5, 4–6 Tier & Question Signs 3-5 4-6 5-7 6-8 9 2 Correct response 1m 5 p 2 e 10 m 3 1m 12 m3e3t3 1m 2 6 Other correct signs eg, for the first mark N 5 p p2 e 10 p m3 eg, for the first mark N 6 d m6 e 7 d m7 p1e9d3 1m Additional guidance m6e7m7 or 6 d6e7d7 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 17 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 3–5, 4–6 Tier & Question Angles 3-5 4-6 5-7 6-8 10 3 a a Correct response 1m Additional guidance Indicates ‘acute’, ie b b 1m Indicates ‘No’ and gives a correct explanation The most common correct explanations: State the angles are the same eg I They are both 45° I They both have the same amount of turn I The first diagram is an enlargement of the second diagram I Angle B fits onto angle A exactly I They are the same, you just see more of A ! Angles measured Accept as 45 ± 2° provided both angles are the same, but do not accept incorrect measurements eg, do not accept N Both are 45° or 135° Minimally acceptable explanation eg N They are the same A and B used to refer to the diagram rather than the angle eg N If you enlarge B it is the same as A ! Response refers to the squares Accept if there is unambiguous reference to the angles eg N They both go through the diagonal Do not accept if ambiguous eg N They both have the same number of squares within them (could be referring to area) Address the misconception eg I It’s how much turn, not how long the lines are I Just because the arms are longer it doesn’t make it bigger Minimally acceptable explanation eg N N It’s just that the lines are longer Because one is smaller in size doesn’t mean the angle is smaller Implicit reference to the length of the lines eg N N 18 Sourced from SATs-Papers.co.uk B is a bit smaller but it’s the same angle A has been drawn bigger than B http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 3–5, 4–6 Tier & Question Factors 3-5 4-6 5-7 6-8 11 4 a a Correct response 2m Additional guidance All five correct factor pairs, in any order, with none duplicated or incorrect eg I 1, 16 2, 8 4, 4 8, 2 16, 1 or 1m b b At least three factor pairs correct 2m All correct, ie 1 3 4 5 6 7 or 1m 2 8 9 10 11 12 At least four correct and none incorrect or At least five correct and not more than one incorrect or Identifies all numbers that are not factors of 12, ie 1 2 3 4 5 6 7 8 9 10 11 12 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 19 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 3–5, 4–6 Tier & Question Thinking of rules 3-5 4-6 5-7 6-8 12 5 a a Correct response 1m Additional guidance Multiple steps 12 eg, for the first rule N 2, then add another 10 N 3, then t 2 1m 3 1m Correct response eg I Add 6 I p6 ! The starting value of 6 is repeated 3 2 I t I Add the number you first thought of Ignore if inserted before the given operation eg, accept N first rule: 6 add 12 If 6 is inserted immediately after the given operation, penalise only the first occurrence eg N first rule: add 6 p 12 Do not accept 6 repeated after their rule eg N first rule: add 12 p 6 For the third rule, the operation is not specified eg N 6 b b 1m Gives a correct rule eg I Divide by 2 I d2 I Halve the first number I Take half of the first number away ! Embedded rule Accept provided both calculations are shown and use the same rule eg N 10 d 2 and 8 d 2 Use of ‘half’ for halve eg N Half Incorrect rule eg N m 1 2 Inverse rule eg N Double Result used to define the rule eg N Take the smaller number away from the bigger N 10 m 5 e 5, 8 m 4 e 4 20 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 3–5, 4–6 Tier & Question Car parking 3-5 4-6 5-7 6-8 13 6 Correct response 2m or 1m Additional guidance 75 p Shows a correct multiplicative method even if there are computational errors eg I 15 d 8 t 40 I 40 d 8 t 15 I 15 t 5 I 15 t 10 d 2 or Shows a correct additive method with not more than one computational error eg I 15 p 15 p 15 p 15 p 15 I 8 15 16 30 24 45 32 50 (error) 40 65 Tier & Question Heights 3-5 4-6 5-7 6-8 14 7 a a Correct response 1m 1.2(0) Additional guidance Correct height in centimetres, with units given b b 1m 1.15 c 1m 170 c Sourced from SATs-Papers.co.uk Height in metres http://www.SATs-Papers.co.uk 21 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 3–5, 4–6, 5–7 Tier & Question Spinning 3-5 4-6 5-7 6-8 15 8 1 a a a Correct response 1m Gives a correct probability eg I 1 4 I 2 8 I 1m Additional guidance 25% Gives a correct probability eg I 1 I 100% Equivalent fractions eg N 8 8 N 1 1 ! Probability not quantified Ignore descriptors alongside correct probabilities, but do not accept on their own eg, do not accept N Certain N Definite b b b 2m Shows exactly two fours, exactly two even numbers other than four, and any two odd numbers eg ! Use of zero Note zero is defined as an even number I I or 1m Shows exactly two fours or Shows exactly four even numbers, even if the other two entries are left blank 22 Sourced from SATs-Papers.co.uk Four fours http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tier & Question Tiers 3–5, 4–6, 5–7 Interpreting algebra 3-5 4-6 5-7 6-8 16 9 3 Correct response 1m Gives a correct interpretation, by referring to at least 3 of the 4 aspects listed below 1. The meaning of a and b (eg by using Ann and Ben, or A and B) 2. The meaning of the p and e signs (eg by using key words such as ‘sum of’ or ‘total’ or ‘altogether’ or ‘add’) 3. The value 69 4. The given context (eg by referring to age or years) eg, accept I The sum of the ages of Ben and Ann is 69 (all aspects shown) I Altogether A and B are 69 years old (all aspects shown) I Altogether, a and b are 69 years old (1st aspect missing) I Ann’s p Ben’s age e 69 (2nd aspect missing) I The sum of the ages of A and Ben (3rd aspect missing) I Together, Ann and Ben are 69 (4th aspect missing) 1m Gives a correct interpretation, by referring to the given context (eg by referring to age or years) and at least 1 of the 2 aspects listed below Additional guidance ! Ben’s age taken to be 30 Accept Ann’s age unambiguously shown as 39, with reference to both the meaning of a and the given context eg, accept N Ann is 39 years old N A’s age e 39 N A is 9 years older than B In English, ages are commonly referred to without years, so also accept the following N A is 39 However, do not accept other responses that do not refer to both the meaning of a and the given context eg N Ann e 39 Also, do not accept incorrect computation eg N Ann is 29 years old ! Ben’s age taken to be 30 Accept Cindy’s age unambiguously shown as 15, with reference to both the meaning of c and the given context, and applying the additional guidance as given in part (a) 1. The meaning of b and c (eg by using Ben and Cindy, or B and C) 2. The meaning of the ‘2’ or ‘2 t’ (eg by using key words such as ‘twice’ or ‘half’ or ‘two times’) eg, accept I Ben is twice as old as C I C is half B’s age I B is twice C’s age I b is twice c’s age (1st aspect missing) I B e 2 t C’s age (2nd aspect missing) Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 23 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tier & Question Tiers 3–5, 4–6, 5–7 Interpreting algebra (cont) 3-5 4-6 5-7 6-8 16 9 3 Correct response 1m Gives a correct interpretation by referring to the mean and either the given context, or 28, or both eg I The mean age of Ann, Ben and Cindy is 28 I 28 is the mean age I 28 is the mean (no reference to the given context) I The mean age (no reference to 28) Additional guidance Use of ‘average’ for mean or Gives a correct interpretation by referring to the total of 84 and the given context eg I The total age of Ann, Ben and Cindy is 84 I 84 is the sum of their ages Partial or incorrect processing eg N The total of their ages is 3 t 28 N 3 t 28 e 82 (error) which is the sum of their ages or Gives a correct interpretation, by referring to the given context and the denominator of 3 (eg by showing d 3) and at least 2 of the 3 aspects listed below 1. The meaning of a, b and c (eg by using Ann, Ben and Cindy, or A, B and C, or by using inclusive key words such as ‘their’ or, minimally, ‘the’) 2. The meaning of the p signs (eg by using key words such as ‘sum of’ or ‘total’ or ‘altogether’ or ‘add’) 3. The value 28 eg, accept I The sum of their ages divided by 3 is 28 I Add A’s age to B’s age to C’s age then divide by 3 gives the answer 28 I Their total age d 3 is 28 I The ages of A p B p C, then divide by three equals 28 (2nd aspect missing) I Add up the ages then divide by 3 (3rd aspect missing) 24 Sourced from SATs-Papers.co.uk ! Ambiguity as to whose age is divided by 3 Pupils who reproduce the statement in the order shown can introduce ambiguity Do not accept such responses eg, accept N (Ann p Ben p Cindy’s age) d 3 e 28 N Ann p Ben p Cindy’s ages d 3 e 28 eg, do not accept N Ann p Ben p Cindy’s age d 3 e 28 N Ann’s p Ben’s p Cindy’s age d 3 e 28 ! Ben’s age taken to be 30 Ignore if accompanying a correct response, otherwise do not accept eg, do not accept N (39 p 30 p 15) d 3 e 28 ! Within the question, two equations solved correctly but with no credit given eg N a e 39, c e 15 Mark as 0, 0, 1 http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 3–5, 4–6, 5–7 Tier & Question Growing shapes 3-5 4-6 5-7 6-8 17 10 2 a a a Correct response 1m Completes the bigger triangle, ie Additional guidance ! Lines not ruled or accurate Accept provided the pupil’s intention is clear or b b b 1m Completes the trapezium, ie ! Parts (b) and (c) transposed Mark part (b) as 0, then part (c) as 1 or ! Internal lines missing eg, for part (b) N Penalise only the first occurrence c c c 1m Completes the parallelogram, ie Incorrect internal lines eg, for part (c) N or ! Four more congruent triangles or trapezia joined eg, for part (b) N eg, for part (c) N Penalise only the first occurrence Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 25 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 3–5, 4–6, 5–7, 6–8 Tier & Question Halfway 3-5 4-6 5-7 6-8 18 11 4 1 a a Correct response 9.2 or equivalent value 1m b b 1m 24 2m Additional guidance 1140 or 1m Shows a correct efficient method eg I 30 t 38 or Shows both 1026 and 1254 ! 30 t 38 or 1140 seen in the working Note that some pupils show 30 t 38 or 1140 as part of their calculation of 33 t 38 eg N 30 t 38 e 1140 3 t 38 e 114 1140 p 114 Do not accept as evidence of a correct efficient method or Shows one of 1026 or 1254, but makes error(s) when finding the other value, then follows through correctly to give a final answer eg I 27 t 38 e 1026, 33 t 38 e 1354 (error) 1026 p 1354 e 2380 2380 d 2 e 1190 I 27 t 38 e 926 (error) 1254 m 926 e 328 328 d 2 e 164 926 p 164 e 1090 I 1026 d 2 e 513 1250 (error) d 2 e 625 513 p 625 e 1138 I 27 t 38 e 1034 (error), 33 t 38 e 1254 1034 p 220 e 1254 1034 p 110 e 1144 26 Sourced from SATs-Papers.co.uk ! Their incorrect value is odd Accept rounding or truncation to an integer value eg N 27 t 38 e 1023 (error), 33 t 38 e 1254 1023 p 231 e 1254 1023 p 115 e 1138 http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 3–5, 4–6, 5–7 Tier & Question Survey 3-5 4-6 5-7 6-8 19 12 5 a a a Correct response 1m English Additional guidance Unambiguous indication eg, for English N 2 eg, for Maths N 7 b b b 1m Maths c 1m Gives a correct explanation c c The most common correct explanations: Calculate the percentages to show they are different eg I 30% for boys, but only 15% for girls Show that the totals are different eg I It’s 3 out of 10 for boys but 3 out of 20 for girls I There are more girls so it’s a smaller percentage I The total for girls is 20, but for boys it is 10 I There are twice as many girls as boys I Take the boys to be 100%, then the girls will be 200% Percentages calculated incorrectly Incomplete explanation eg N The percentages are different for boys and girls Minimally acceptable explanation eg N N N N N N There are more girls It’s out of different numbers It depends on how many boys and girls there are You need to look at the percentage, not just the number The percentage for boys is higher There are 10 boys and 20 girls (implicit comparison) Incorrect explanation accompanying a correct statement eg N Because he asked 20 girls and 10 boys and that is not a fair thing to do in a survey N There are more girls than boys so girls (error) have a bigger percentage than the boys N There are 10 boys and 20 girls so it couldn’t be equally popular Incomplete explanation eg N The total for girls is 20 d d d 1m English Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 27 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 3–5, 4–6, 5–7, 6–8 Tier & Question Solving 3-5 4-6 5-7 6-8 20 15 6 2 a a a Correct response 2m Any two correct 2m 3 or 1m c c Incorrect notation eg N 23x for 23 All three correct, ie 23 20 33 or 1m b b b Additional guidance 2m ! Ambiguous notation eg Equivalent fraction or decimal Correct value eg 1 I 2 eg I 2.5 2 N 5 2 I 2 4 N 2 or 1m t3 Mark as 1, 0 N Subtracts 11 from both sides to give a correct algebraic equation eg I 2y e 17 m 11 I 2y p 11 m 11 e 17 m 11 I 2y e 6 10 4 For 2m, incomplete processing eg N 10 d 4 Collects together like terms eg I 9y m 5y e 13 m 3 I 4y e 10 I y e 10 d 4 Simplified expressions which are not equated eg N 9y m 5y e 4y 13 m 3 e 10 ! Method used is trial and improvement or Shows working in which the only error is to add, rather than subtract, 3 to the right-hand side, resulting in the solution y e 4 eg I 9y p 3 e 5y p 13 so 4y e 16 (error) so y e 4 Note that no partial credit can be given Also note that the correct solution must be explicitly stated rather than embedded eg, do not accept N 5 t 2.5 p 13 e 9 t 2.5 p 3 without 2.5 identified as the solution or Shows working in which the only error is to add, rather than subtract, 5y to the left-hand side, resulting in the solution y e 5 , or 7 equivalent fraction or decimal between 0.71 and 0.72 inclusive eg I 9y p 3 e 5y p 13 14y (error) e 10 so y e 28 Sourced from SATs-Papers.co.uk 10 14 http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 4–6, 5–7, 6–8 Tier & Question Dropping litter 3-5 4-6 5-7 6-8 13 7 3 Correct response a a a 1m Gives a correct reason The most common correct reasons are: Additional guidance Question would be difficult to answer eg N The sample size is too small eg I They should ask more than 10 I Not enough people I 10 is too small, he should ask 100 People might not respond honestly eg I They might be embarrassed so won’t be honest I They will lie I They are not likely to admit to it I They might ignore the pupils People might not remember eg I They might not remember doing it People might not be consistent eg I They might only drop it on some days so they would say they don’t drop it every day I They might not drop it every day but still drop it sometimes No-one would know if they did drop it every day Implicit reference to the sample size being too small eg N Those 10 might not drop litter but others might N Those people might not have any litter to drop In part (a) or part (b), conceptual misunderstanding The most common of these imply that everyone in the country should be asked, or that the figure of 93% must be proved exactly, or that the exact conditions applied by the newspaper must be replicated, or that you should select the people being surveyed according to the desired outcome eg N 10 people is not all of us N There are a lot more than 10 people in England N It is not possible to get a figure of 93% with only 10 people N 10 is too difficult, he should ask 100 N You don’t know how many people the newspaper asked N You might ask the wrong people ! In part (a) or part (b), more than one reason The sampling method may lead to bias eg I They might only ask people in a clean area with not much litter I He might only ask young people 1m given within one response Do not accept a correct response accompanied by an incorrect response from the same category. Otherwise ignore irrelevant or incorrect further responses. If two correct reasons from different categories are given in the first response space, both marks should be awarded Gives a correct reason from a different category to one already credited Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 29 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 4–6, 5–7, 6–8 Tier & Question Dropping litter (cont) 3-5 4-6 5-7 6-8 13 7 3 Correct response b b b 1m Gives a correct reason The most common correct reasons are: The sample might be biased due to the time of week or the time of day Additional guidance Method is time consuming eg N It would take too long Minimally acceptable correct reason eg N N Recording people walking past may produce an inappropriate sample size, ie too big to be practical or too small to be of use Minimally acceptable correct reason eg N N Some people may be counted more than once They might drop more at the weekend At lunchtime there will be more litter You can’t observe everyone Not enough people are around then Minimally acceptable correct reason eg N People might change their behaviour if they are being observed Minimally acceptable correct reason eg N The sample might be biased because only one position is used They’ll see the pupils and stop Minimally acceptable correct reason eg N N The sample might be biased due to the type of shop People may pass more than once The shop may be in a clean area People drop more in towns Minimally acceptable correct reason eg N N It might be a burger shop Children might not go to that shop The results might be affected by whether there is a bin nearby People may not have litter to drop Although people have litter, they may drop it elsewhere/ at a different time Minimally acceptable correct reason eg N N Although people drop litter, accurate observation may be difficult Minimally acceptable correct reason eg N 1m 30 They won’t all drop it outside one shop A person is only observed for 30 seconds Will they always see the person who is dropping it? Gives a correct reason from a different category to one already credited Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 4–6, 5–7, 6–8 Tier & Question Negatives 3-5 4-6 5-7 6-8 14 8 4 Correct response 1m Gives two negative numbers, the second of which is 5 less than the first eg I m8 – m13 Additional guidance Zero used as a negative eg N m0 ! Incorrect notation eg 15 m Penalise only the first occurrence N I m1 1m – m6 Gives two negative numbers, the second of which is 5 more than the first eg I m6 – m1 m15 – m10 I Sourced from SATs-Papers.co.uk ! Neither calculation is correct but the numbers used in the second set of boxes are the same as in the first set, but in reverse order If all the numbers are negative, mark as 0, 1 eg N m7 then m3 in the first, m3 then m7 in the second http://www.SATs-Papers.co.uk 31 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 4–6, 5–7, 6–8 Tier & Question Puzzle 3-5 4-6 5-7 6-8 16 9 5 Correct response 2m Writes three correct algebraic expressions, the first two of which may be unsimplified eg, for the first box I 2n p 4 I n p 4 p n eg, for the second box I n p 2 I (2n p 4) d 2 eg, for the third box I n Additional guidance ! Expression for the third box not fully simplified Given the context of the question, this expression must be simplified at least as far 2n as n p 2 m 2 or 2 eg, do not accept 2np 4 N m2 2 For 2m, incorrect algebraic notation eg, for the second box N 2n p 4 d 2 or 1m Writes correct algebraic expressions for the first two boxes, even if unsimplified or Writes correct algebraic expressions for the last two boxes and fully simplifies, indicating that the pupil has worked upwards eg I n p 9 (error) np2 n or Within an otherwise correct response, the only error is in the notation for the expression for the second box eg I 2n p 4 2n p 4 d 2 (error in notation only) n or The expression for the first or second box is incorrect, but is then followed through correctly including full simplification of the expression for the third box eg I n p 9 (error) np9 2 n p 5 (or 0.5n p 2.5) 2 I 2n p 4 n p 4 (error) np2 32 Sourced from SATs-Papers.co.uk For the third box, incorrect simplification to n eg N n p 9 (error) np9 2 n p 9 – 2 e n (error) 2 http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 5–7, 6–8 Tier & Question Rectangle rest 3-5 4-6 5-7 6-8 10 6 Correct response a a 2m or 1m Additional guidance 50 Calculates, or shows on the diagram, that the other acute angle in the white triangle is 40 eg 40 seen without being located on the diagram or without supporting working I I 180 m 60 e 120, 120 p 20 e 140, 180 m 140 e 40 or Shows a complete correct method with not more than one computational error eg I 180 m (20 p 120) e 50 (error), 90 m 50 e 40 I 20 p 90 e 110, 110 m 60 I b b 2m or 1m 180 d 3 e 60, 60 m 20 e 50 (error) 180 m 90 m 50 e 40 Gives a correct justification eg I ∠DEB is 120 (180 m 60), ∠EBD is 30 (180 m 90 m 60), so ∠BDE is 30 (180 m 120 m 30) As ∠BDE e ∠EBD then triangle BDE is isosceles Shows working to justify that ∠DBE is 30 eg I 180 m (90 p 60) e 30 Sourced from SATs-Papers.co.uk Minimally acceptable justification eg N Angle at B e 180 m 90 m 60 e 30, so the angles in the triangle are 120, 30, 30 For 2m or 1m, angle of 30 not justified, or justified only by assuming the triangle is isosceles eg N The angles in triangle BDE are 30, 30 and 120 N 180 m 60 e 120, 180 m 120 e 60, 60 d 2 e 30 http://www.SATs-Papers.co.uk 33 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 4–6, 5–7, 6–8 Tier & Question Mice 3-5 4-6 5-7 6-8 17 11 7 Correct response a a a 1m 50 ± 2 b b b 1m 55 ± 2 c Indicates ‘No’ and gives a correct explanation Additional guidance c c 1m The most common correct explanations: Refer to the fact that the number of mice is unknown eg I It’s only percentages, the real data is not shown I You need to know the actual numbers I It may be out of different amounts of mice I There may be more mice in homes close to woodland Refer to the limitations of percentage bar charts eg I The charts only allow you to compare the proportions Indicates ‘Yes’ and qualifies their decision by stating the assumption needed eg N Provided the total number of mice is about the same Minimally acceptable explanation eg N N N They’ve used % so you can’t tell They only show the percentage You don’t know how many mice were found altogether ! Explanation specifies which location gets more mice The explanation must be the correct way round, ie less more Far Close eg, do not accept N There may be more mice in homes far from woodland ! Explanation refers to number of homes or people, rather than number of mice Condone these errors eg, accept N It may be out of different amounts of homes N They might have asked different amounts of people who lived close to or far from woodland ! Irrelevant explanation If accompanied by a correct explanation, ignore eg, accept N There may be more mice close to woodland or the homes could be dirtier ! Explanation interprets the percentages in terms of probability, or states that the percentages may not be accurate eg N It doesn’t mean there must be more, just that it is more likely N There could be more mice that weren’t found Ignore if accompanying a correct response, otherwise do not accept 34 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 4–6, 5–7, 6–8 Tier & Question Straight lines Marking overlay available 3-5 4-6 5-7 6-8 18 12 8 Correct response a a 1m Indicates ‘Yes’ and gives a correct explanation eg I When x e 25, 3x e 75 I 3 t 25 e 75 I y must be 3 t x Additional guidance Explanation does not explicitly state that the line goes through the origin eg N (2.5, 7.5) is on the line and you can times them both by 10 N The line goes up three for every one it goes across N 25 d 25 e 1, 75 d 25 e 3 and (1, 3) is on the line Minimally acceptable explanation eg N N ye3tx You multiply the number on the x-axis by three Equation restated but not interpreted eg N y e 3x Incomplete explanation eg N It goes (1, 3), (2, 6) and so on N (2.5, 7.5) is on the line b b 3m or 2m (2 1 , 11) 2 Shows x e 2 Equivalent fraction or decimal 1 or y e 11 2 or Shows a complete correct method for solving algebraically with not more than one error eg I 4x p 1 e 6x m 4 so 3 (error) e 2x x e 1.5 so y e 4 t 1.5 p 1 e 7 I y m 4x e 1, y m 6x e m4, so 2x e 3 (error), so x e 1.5 and y e 6 t 1.5 m 4 e 5 I 3y e 12x p 3 2y e 12x m 8 y e m5 (error) m5 e 4x p 1 so x e m1.5 or For at least 4cm, draws both lines on the graph within the tolerance as shown on the overlay Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 35 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 5–7, 6–8 Tier & Question 12 8 b b Straight lines (cont) Marking overlay available 3-5 4-6 5-7 6-8 Correct response or 1m Additional guidance Shows 4x p 1 e 6x m 4 or equivalent cont or Attempts to solve simultaneously and forms two correct equations that would allow elimination of x, or subtracts the two given equations to eliminate y eg I 3y e 12x p 3 2y e 12x m 8 I 6y e 24x p 6 4y e 24x m 16 I 0 e 2x m 5 or Indicates, on the graph or elsewhere, at least two correct points on each of the lines or Draws one line on the graph within the tolerance as shown on the overlay, and at least of length 4cm c c 1m Gives a correct explanation eg 1 I Both have gradient of but they pass 2 I I through (0, 3) and (0, 5) Same gradient, different intercepts The lines are parallel but are not the same I 2 N N Same slope The lines are parallel eg Gives a correct algebraic interpretation eg I different eg 1 N Both have gradient of Minimally acceptable explanation or I Implicit assumption that the lines are 1 1 x p 3 ≠ x p 5 because 3 ≠ 5 2 2 The difference will always be 2 No matter what value you put in for x, the ys will never be the same N N The equations are the same except for the 3 and the 5 The second line will always be higher Incomplete or no interpretation eg N Because the lines do not cross N Different intercepts N Because of the p 3 and the p 5 N They have the same number of x 1 2 N Both have N The difference is 2 One value only considered eg N When x e 10, in the first line y e 8 but in the second line y e 10 36 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 4–6, 5–7, 6–8 Tier & Question Egyptians 3-5 4-6 5-7 6-8 19 13 9 Correct response a a a 1m Additional guidance 7 or equivalent fraction 10 Incorrect notation or incorrect further working eg N a a a 1m or or or b b b 31⁄2 5 In part (a) or (b), shows a correct method that enables addition or subtraction of fractions The most common correct methods: Show or imply correct common denominators eg, in part (a) I 5 2 p 10 10 I 1 25 1 10 e , e 2 50 5 50 I 31⁄2 5 eg, in part (b) I 1 5 e seen with no attempt to change 4 20 the denominator of the fraction 9 20 I 1 20 9 36 e , e 4 80 20 80 I The answer is a fraction equivalent to 1 5 Convert correctly to decimals or percentages, even if their value is subsequently incorrectly converted back to a fraction eg, in part (a) I 0.5 p 0.2 eg, in part (b) I 0.45 and 0.25 seen b b b 1m c c 2m or 1m 1 1 p 4 5 1 5 Answer as 5 or equivalent fraction 6 Correct working and answer shown, but the Shows or implies the fractions are eg I 1 1 p 2 3 Sourced from SATs-Papers.co.uk two unit fractions are given on the answer line 1 1 and 2 3 Minimally acceptable implication eg N 0.5 p 0.33 1 as a unit fraction 1 http://www.SATs-Papers.co.uk 37 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tier 5–7, 6–8 Tier & Question Rearrange 3-5 4-6 5-7 6-8 14 10 Correct response a 2m Rearranges correctly to make e the subject eg Minimally acceptable correct rearrangement eg N I p m 2f ee 2 I ee 1 (p m 2f) 2 I ee p mf 2 I or 1m Additional guidance eemfp N e e (p m 2f) d 2 eepd2mf For 2m, incorrect equation eg N ee 1 p m 2f 2 1 p 2 Expands the brackets correctly eg I p e 2e p 2f seen or p incorrectly multiplied by 2 at the same time as the brackets expanded eg N 2p e 2e p 2f Divides by 2 throughout eg p I e e p f seen 2 or Expands incorrectly to give p e 2e p f, then follows through correctly eg I p e 2e p f (error) and so e e b 2m ee p mf without previous working shown 2 As there is no way of knowing how many errors were made, do not accept p mf 2 Rearranges correctly to make d the subject eg I d e c m 2r Minimally acceptable correct rearrangement eg 1 1 Shows 2r m c e md or d e c m r 2 2 d e (2c m 4r) d 2 N or 1m N decm N d e c m 1r r 0.5 ⁄2 or As a correct first step, multiplies by 2, or divides by a half, throughout eg I 2r e c m d seen I I 38 r e c m d seen 0.5 r ⁄2 1 e c m d seen Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 6–8 only Tier & Question What number? 3-5 4-6 5-7 6-8 11 Correct response a 1m Additional guidance Minimally acceptable explanation Gives a correct explanation eg The most common correct explanations: N N Refer to blue counters being non-integers eg I If 0.2 represented 10, 0.05 would represent 2 I I I 1 which is not an integer 2 N ! Number of yellow counters stated to be a 2.5 blue is not possible As the probability for yellow is 4 t blue, the number of yellow counters would have to be a multiple of four If Y is 10, the total would be 50 but 1 of 20 50 is a decimal number not a whole number Refer to green counters being non-integers eg I There would be 22.5 green counters multiple of four Accept if it is clear that this is an example eg N The blue and green wouldn’t be integers, there could be 20 yellow counters Do not accept if the statement is definitive eg N The blue and green wouldn’t be integers, there must be 20 yellow counters Incorrect calculation or statement eg N You can’t have half counters but there would be 1.5 blue N b 2m There would be 2 1 green 2 ! Answers given as probabilities Completes the table correctly ie Blue Red Green Yellow 1 or 1m There would be half counters The numbers of counters would not be whole numbers You’d have half blues – not possible 6 9 4 If the numerators are the correct values and the denominators are 20, mark as 1, 0 eg N 1 6 9 4 , , , 20 20 20 20 Shows the number of blue counters is 1 or Shows R, G, Y are 6, 9, 4 respectively Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 39 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tiers 5–7, 6–8 Tier & Question Locus Marking overlay available 3-5 4-6 5-7 6-8 15 12 Correct response a a 1m Correct line, ie x e m 1, ruled, ie Additional guidance ! Line not full length Do not accept lines that are less than 8 units in length ! Shading Within the question, ignore ! Line not continuous Within the question, accept lines that are shown as dotted or dashed but do not accept series of points b b 1m Both lines correct, ie ! Lines not ruled or full length Accept provided there is no ambiguity and each line goes at least 2cm from the origin into each of the relevant quadrants ! Lines ‘bounded’ If boundary lines are drawn along one or more of x e 5, x e m 5, y e 5, y e m 5, ignore c c 2m or 1m Locus completed that fulfils the four conditions below 1. Ruled 2. Within the tolerance as shown on the overlay 3. At least 5cm in length 4. Evidence of correct construction arcs that are centred on C and on D, and are of equal radii, and show both intersections ! Use of construction arcs on overlay Note that these are to give a visual guide as to whether the correct centres have been used, and do not indicate tolerance Spurious construction arcs Do not accept as correct arcs that do not show two distinct intersections, eg arcs that just touch Locus completed with all of the conditions 1 to 3 fulfilled or Condition 4 fulfilled even if the locus is incorrect or omitted 40 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tier 5–7, 6–8 Tier & Question MOT 3-5 4-6 5-7 6-8 16 13 Correct response Additional guidance a a 1m Lower value between 150 and 151 inclusive Upper value between 260 and 270 inclusive b b 1m Correct straight line, ruled, within ± 2mm at (400, 0) and (0, 400) ! Line not full length Correct region, ie below the line, shaded Only the white section on the graph within 1m Accept provided the line is at least of length to cross the white ‘pass’ section of the graph, and would not be more than ± 2mm from (250, 150) and (150, 250) the correct region shaded ! Follow through Accept provided their boundary is a straight line, ruled or unruled, with a negative gradient c c 1m Lower value between 200 and 201 inclusive Upper value between 260 and 270 inclusive ! Follow through from parts (a) and (b) Follow through can be awarded only if at least one mark was awarded in part (b), and their (b) allows follow through for two values of R Mark follow through as shown below Correct line in (b) and correct shading lower value: 200 to 201 inclusive upper value: their upper value from (a) Correct line in (b) but no shading lower value: 200 to 201 inclusive upper value: their upper value from (a) Correct line in (b), incorrect side shaded lower value: their lower value from (a) upper value: 199 to 200 inclusive Incorrect line in (b), 1m for shading lower value: their lower value from the graph upper value: their upper value from (a) Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 41 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tier 6–8 only Tier & Question Similarity 3-5 4-6 5-7 6-8 14 Correct response a 1m Gives a correct explanation eg Additional guidance Values not explicitly stated to be different eg N I 10 14 ≠ 8 12 10 8 ≠ 14 12 N I I 8 h e so h e (14 t 8) d 10 ≠ 12 14 10 I I b 2m or 1m N 14 d 10 e 1.4 12 d 8 e 1.5 Picture is in the ratio 4 : 5, board is in the ratio 6 : 7 8 : 12 e 2 : 3 10 : 14 e 5 : 7 1.25 t 12 e 15 not 14 Depth of board is 1.5 times the depth of the picture, but the length isn’t 11.2 or equivalent value Shows a correct method eg I part (a) 4 14 t 5 I Correct method for part (b) shown in 14 h e 8 10 Tier & Question Robotic 3-5 4-6 5-7 6-8 15 Correct response a 2m or 1m 1 , or equivalent probability 64 Shows a correct method eg ! Non-exact decimal or percentage The exact value is 0.015625 For 2m, accept rounding to 2sf or better For 1m, accept rounding or truncation to 0.01, 0.02 or 0.015, or the equivalent percentage values 1 3 4 I ( ) I b 1m Additional guidance 0.25 t 0.25 t 0.25 3 , or equivalent probability 64 ! Follow through as 3 t part (a) Accept provided the resulting value is less than 1 Incomplete processing eg N 42 Sourced from SATs-Papers.co.uk 1 t3 64 http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tier 6–8 only Tier & Question Rectangles 3-5 4-6 5-7 6-8 16 Correct response 1m 1m 1m 1m Additional guidance Multiplies out one of the pairs of brackets correctly eg 2 I (y p 5)(y p 1) e y p 6y p 5 seen 2 I (y p 10)(y m 3) e y p 7y m 30 seen ! Expansion is not simplified Forms an equation equating the two areas and multiplies out the other pair of brackets correctly eg I (y p 5)(y p 1) e (y p 10)(y m 3) 2 2 I y p 6y p 5 e y p 7y m 30 Implicit equating Simplifies their equation by at least removing 2 terms in y eg I 6y p 5 e 7y m 30 I 30 p 5 e y I y e 35 ! Follow through from their incorrect 35, with no incorrect algebra shown eg, for (y p 5)(y p 1) 2 N y p 5y p 1y p 5 Accept unsimplified expansions for the first two marks, but do not accept for the third mark eg N A e (y p 5)(y p 1) A e (y p 10)(y m 3) equation 2 Accept provided it has terms in both y and y For this mark, do not follow through ! 35 with no supporting algebra If there is no incorrect algebra, this final mark may be awarded. Do not accept 35 from incorrect algebra eg 2 2 N y p 6y p 5 e y p 7y m 30 2 2 7y p 5 e 8y m 30 (error) 35 e y Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 43 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tier 6–8 only Tier & Question Oranges and lemons 3-5 4-6 5-7 6-8 17 Correct response 3m Correct simplified ratio, ie 2 : 3 Additional guidance Ratio simplified to the form 1 : n or n : 1 Accept if exact eg N 1 : 1.5 N or 2m Shows a correct but unsimplified ratio 2 :1 3 ! The only error is to interpret 1 : 4 as 25% to 75% If the pupil follows through correctly to give the ratio of 7 : 9, mark as 1, 1, 0 or Shows 3 : 2 or Shows a correct method that includes the proportion added eg I 20% : 80% becomes 15% : 60%, then add 25% of orange I Suppose the glass holds 500ml, that’s 100 orange, 400 lemonade. After you’ve drunk, it’s 75 orange, 300 lemonade then add 125 ml of orange or 1m Indicates that the proportions after drinking are still 1 : 4 or equivalent eg 1 I Glass holds 200, drink so 150 left, 4 I I 44 which is still 1 : 4 15% : 60% 1 : 4 then Sourced from SATs-Papers.co.uk 3 :3 4 http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Tier 6–8 only Tier & Question Prism 3-5 4-6 5-7 6-8 18 Correct response a 1m Correct justification eg 2 I 24x p 3xy e (2 t 6x t 2x) p (3x t y) 2 I 6x t 2x e 12x , 3x t y e 3xy, 2 2 2 12x p 12x p 3xy e 24x p 3xy 2 I Area would be 6x t (4x p y) e 24x p 6xy, but 3xy is missing I b 2m or 1m Additional guidance Minimally acceptable justification eg N N 6x t 2x p 6x t 2x p 3x t y (6x t 4x) p 3x t y Incorrect algebra eg N 6x t 2x e 12x, 2 12x p 12x e 24x 1x x 2 Multiplies out 3x (8x p y) correctly eg 3 2 I 24x p 3x y or 2 Factorises 24x p 3xy correctly eg I 3x (8x p y) Sourced from SATs-Papers.co.uk Partial factorisation eg 2 N 3(8x p xy) http://www.SATs-Papers.co.uk 45 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Index Index to mark schemes Tier Question 3–5 4–6 5–7 6–8 Page 1 Half 11 2 Robot 12 3 Computation 13 4 Olympic Games 14 5 Pictogram key 15 6 Two steps 15 7 Calculations 16 8 1 Areas 16 9 2 Signs 17 10 3 Angles 18 11 4 Factors 19 12 5 Thinking of rules 20 13 6 Car parking 21 14 7 Heights 21 15 8 1 Spinning 22 16 9 3 Interpreting algebra 23 17 10 2 Growing shapes 25 18 11 4 Halfway 26 19 12 5 Survey 27 20 15 6 2 Solving 28 13 7 3 Dropping litter 29 14 8 4 Negatives 31 16 9 5 Puzzle 32 10 6 Rectangle rest 33 17 11 7 Mice 34 18 12 8 Straight lines 35 19 13 9 Egyptians 37 14 10 Rearrange 38 11 What number? 39 12 Locus 40 15 46 Sourced from SATs-Papers.co.uk 1 http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 1 Index Index to mark schemes Tier Question 3–5 4–6 5–7 6–8 16 Page MOT 41 14 Similarity 42 15 Robotic 42 16 Rectangles 43 17 Oranges and lemons 44 18 Sourced from SATs-Papers.co.uk 13 Prism 45 http://www.SATs-Papers.co.uk 47 EARLY YEARS NATIONAL CURRICULUM 5 –16 GCSE GNVQ GCE A LEVEL NVQ First published in 2002 © Qualifications and Curriculum Authority 2002 Reproduction, storage, adaptation or translation, in any form or by any means, of OTHER VOCATIONAL QUALIFICATIONS 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, provided full acknowledgement is given. Produced 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/ Further teacher packs may be purchased (for any purpose other than statutory assessment) by contacting: QCA Publications, PO Box 99, Sudbury, Suffolk CO10 2SN (tel: 01787 884444; fax: 01787 312950) SourcedOrderSATs-Papers.co.uk from ref: QCA/02/831 http://www.SATs-Papers.co.uk 01-8633/11