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2002 KS3 Mathematics Test Mark Scheme: Paper 2 Index Index to mark schemes Tier Question 3–5 4–6 5–7 6–8 21 Page 14 Percentage change 38 15 Star 39 16 Trigonometry 40 17 Satellite 41 18 Simplify 42 First published in 2002 © Qualifications and Curriculum Authority 2002 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, 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) Order ref: QCA/02/831 Sourced from SATs-Papers.co.uk © Qualifications and Curriculum Authority 2002 QCA, Key Stage 3 Team, 83 Piccadilly, London W1J 8QA http://www.SATs-Papers.co.uk 01-8633/12 Mathematics tests Ma KEY STAGE 3 ALL TIERS 2002 Mark scheme for Paper 2 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 2 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 2 at all tiers. The paper 1 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 10 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: I 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; I 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. 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. 2 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 2 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 2 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 2 General guidance What if … 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. 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. The answer is correct but, in a later part of the question, the pupil has contradicted this response. 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 2 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 2 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 = 5, y=7) Incorrect or ambiguous notation eg ( 7, 5 ) ( 5x, 7y ) ( x5, y7 ) ( 5x, 7y ) Responses involving the use of algebra For example: 2 + n n + 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 + n for 2n n t n for n2 Multiplication by 1 or 0 eg 2 + 1n for 2 + n 2 + 0n for 2 Words used to precede or follow equations or expressions eg t = n + 2 tiles or tiles = t = n + 2 for t = n + 2 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 + 2 n cm + 2 Change of variable eg x used for n Ambiguous letters used to indicate expressions eg n = n + 2 Unambiguous letters used to indicate expressions eg t = n + 2 for n + 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 given when solving equations eg 3 t 10 + 2 = 32 for 3x p 2 e 32 Embedded values that are then contradicted eg for 3x + 2 = 32, 3 t 10 + 2 = 32, x = 5 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 7 2002 KS3 Mathematics Test Mark Scheme: Paper 2 General guidance Responses involving probability A numerical probability should be expressed as a decimal, fraction or percentage only. For example: 0.7 Accept A correct probability that is correctly expressed as a decimal, fraction or percentage. Equivalent decimals, fractions or percentages eg 70 35 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 Take care ! Do not accept 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 2 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 2 Tier 3–5 only Tier & Question Game 3-5 4-6 5-7 6-8 1 Correct response a 1m 430 b 1m 609 c 1m 391 Additional guidance ! Follow through as 1000 – their (b) Accept, provided their (b) < 1000 Tier & Question Marking overlay available 3-5 4-6 5-7 6-8 2 Correct response a 1m 1m 6 c 1m 4 d 1m Indicates the triangle west of the school Additional guidance 5 b Travelling to school ! More than one symbol ringed Do not accept if more than one triangle is ringed. Accept if the only triangle ringed is the correct one, as some pupils may mark the diagram to help with other parts of the question e 2m Draws a square, within the angle tolerance as shown on the overlay, touching the 3km line ! Square not accurate Accept, including in any orientation, provided there is no ambiguity within the context of the question ! Square touches the lines indicating the angle or 1m 10 tolerance Accept, provided the square does not extend beyond the dashed lines shown on the overlay Fulfils any two of the three conditions below. The symbol drawn is a square; has direction within the angle tolerance as shown on the overlay; touches the 3km line Sourced from SATs-Papers.co.uk ! Rings round existing symbols Ignore in part (e) http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tier 3–5 only Tier & Question Holiday 3-5 4-6 5-7 6-8 3 Correct response a 1m £ 10 b 3m Additional guidance £ 22 or 2m Incorrect response eg N – 10 Shows the digits 22 eg I 220 I 2.20 or Shows the values 586 and 608 or Shows one of the values 586 and 608 and correctly subtracts using their incorrect total eg I Woman 586, man 648 (error), 648 m 586 e 62 I 194 p 196 p 196 e 486 (error) 289 p 319 e 608 so it’s 122 more or Shows a complete correct method with the only error in the final answer eg I 289 p 319 m (194 p 196 p 196) e 32 (error) or 1m Shows one of the values 586 or 608 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 11 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tier & Question Describing shapes 3-5 4-6 5-7 6-8 4 a Tier 3–5 only Correct response 1m Draws a square Additional guidance ! Lines not ruled, or internal lines drawn Accept provided the pupil’s intention is clear b 1m Draws a rectangle, or draws a square that is a different size from the one in part (a) c 1m Draws a parallelogram with no right angles eg I I I d 2m or 1m 12 All four entries correct, ie 4 4 2 4 Unambiguous indication that the sides are the same length eg, for the final value of 4 N All N The N Yes At least two entries correct Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tier & Question Tiers 3–5, 4–6 School trip 3-5 4-6 5-7 6-8 5 Correct response a 1m 60 b 2m Additional guidance All three correct, ie 5 6 10 or 1m Any two correct Tier & Question Place names 3-5 4-6 5-7 6-8 6 1 Correct response a a 1m 49 b b 1m Additional guidance 30 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 13 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 3–5, 4–6 Tier & Question Dinner time 3-5 4-6 5-7 6-8 7 2 a a Correct response 2m Additional guidance ! Frequencies shown All three rows correct, ie For 2m or 1m, if the correct box for a row has been identified ignore any frequencies shown, even if incorrect. If the correct box for a row has not been identified, and all 9 frequencies are correct, mark as 1, 0 eg N 2m or 1m 18 42 26 44 36 b b 38 36 or 1m 28 30 Any two rows correct 12 Shows at least one of the following totals: 106 (or 70), 94 (or 58) or Shows both of the differences 2 and 14, with no evidence of an incorrect method 14 Sourced from SATs-Papers.co.uk ! Signs incorrect Ignore http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 3–5, 4–6 Tier & Question Which calculation? 3-5 4-6 5-7 6-8 8 3 a a Correct response Joins the first to 4 m 3 1m Joins the third to (4 t 25) m (3 t 27) 1m The question refers to the total number of pupils in year 9 eg I Altogether, how many people are in year 9? I How many pupils are there in year 9? The following shows the correct responses: Joins the second to (3 t 27) p (4 t 25) 1m b b 1m Additional guidance or The question refers to both 4 and 25, and interprets the significance of the multiplication sign eg I How many pupils are there altogether in 4 classes of 25? or Interprets the calculation in a valid way whilst still referring to year 9 eg I If there were always 4 classes in year 9, how many classes would there have been in 25 years? Sourced from SATs-Papers.co.uk Response is a statement rather than a question eg, for the first category N It’s the total number of people in year 9 N All the pupils in all the classes in the oldest year Incomplete response eg N How many pupils altogether? Response processes the 4 t 25 correctly eg N N Altogether there are 100 pupils in year 9 100 pupils are in year 9 Incomplete response eg N How many pupils altogether in 4 classes? N It’s the number of classes in year 9 with the number of students N Four classes with 25 pupils in year 9 Response does not refer to the given context eg N 25 pupils each have 4 rulers. How many rulers do they have altogether? Response matches a different calculation eg N If there are 100 students in year 9 and only 4 teachers, how many pupils are in each class? http://www.SATs-Papers.co.uk 15 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tier & Question Throwing coins 3-5 4-6 5-7 6-8 9 4 a a Tiers 3–5, 4–6 Correct response 1m Indicates ‘True’ and gives a correct explanation that implies there are two outcomes, both of which are equally likely eg I There are two equally likely possibilities, heads or tails I A head is just as likely as a tail I Both sides are equally likely Additional guidance Minimally acceptable explanation eg, implicit reference to equally likely N There are 2 sides N It can land on H or T eg, implicit reference to two outcomes N It’s 50 – 50 N It’s an even chance N As it’s a fair coin Incomplete explanation eg N You don’t know what will come up next N Coins sometimes land on heads N It is equal N It’s a fair chance b b 1m Indicates ‘False’ and gives a correct explanation The most common correct explanations: State the outcome cannot be predicted with certainty eg I Each throw is random I You don’t know what you will get. It’s just chance I You don’t know until you’ve thrown I You never know which side the coin will land on Minimally acceptable explanation eg, for the first category N It’s random N It’s chance eg, for the second category N You might get something different N You don’t know that’s what you’ll get N Each one could land on any side ! Explanation refers to one throw of one coin Show there are alternative outcomes eg I You might get 4 heads I There are more possibilities like HHHH, HHHT, HHTH and so on I You could get just one tail Condone provided reference is made to both uncertainty and two outcomes eg N It can land on either side N It could land on H or T Incomplete explanation eg N It could be anything N You don’t know N It’s not certain Incorrect or ambiguous explanation eg N There are five different outcomes N You are as likely to get 3 heads and 1 tail N It’s 50 m 50 16 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 3–5, 4–6, 5–7 Tier & Question Folding 3-5 4-6 5-7 6-8 10 5 a a Correct response 2m Both correct, ie 12 by 4 (either order) and 6 by 8 (either order) or 1m b b Additional guidance One correct, the other incorrect or omitted 1m 3 Tier & Question Yards 3-5 4-6 5-7 6-8 11 6 1 Correct response Additional guidance a a a 1m 91.44 91 or 91.4 b b b 2m 109 or 109.(…) with no evidence of an incorrect method ! Answer of 110 or 1m Accept provided a more accurate value or a correct method is seen Correct answer from an incorrect method eg N 100 m 91.44 e 8.56, 100 p 8.56 is about 109 Shows the digits 109(…) but the decimal point is positioned incorrectly or omitted or ! Answers to parts (a) and (b) reversed Treat as a misread and deduct the first mark only Shows the correct inverse operations, in any order eg I t 100, d 2.54, d 36 or Shows d 91.44 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 17 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 3–5, 4–6, 5–7 Tier & Question Scales 3-5 4-6 5-7 6-8 12 7 2 Correct response Additional guidance a a 1m 14 to 14.2 inclusive b b 1m 220 to 230 inclusive Fractional value c 2m 35 to 36 inclusive ! Follow through from part (a) c Accept provided it is explicit in the working that the method incorporates this incorrect value or 1m Shows how to use the scale to find 1000g, even if the scale is read incorrectly eg I Work out what it is for 100g, then t 10 I 400g p 400g p 200g I 200g is 7, 5 t 7 I 100g is 4 (error) ounces, 4 t 10 I 500g is 17 (error), then double 17 I 250 is 9, 9 t 4 e 32 (error) Poor mathematical communication Do not infer incorrect reading of the scale eg N 3 t 10 (No indication of method through written working or through markings on the scale, and answer to the calculation is outside the acceptable range) or Shows a correct multiplication, or a correct addition, that would give an answer within the correct range, even if this is followed by incorrect processing eg I 3.6 t 10 I 5t7 I 14 p 14 p 7 18 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 3–5, 4–6, 5–7 Tier & Question Security lock 3-5 4-6 5-7 6-8 13 8 3 a a a Correct response 2m or 1m 24, with no incorrect working Additional guidance 24 obtained from listing that includes duplication Shows a correct method eg I 4t6 I There are 6 ways for the letter A and it is the same for each of the other letters or Lists in a systematic way for any one of the letters or any one of the numbers eg I C1, C2, C3, C4, C5, C6 I A / 6, 5, 4, 3, 2, 1 I A1, B1, C1, D1 b b b 1m 1 or equivalent probability 6 ! Decimal or percentage rounded or truncated Accept 0.17 or 0.167 or 0.166(…), or the equivalent % values. Do not accept 0.16 Tier & Question Screenwash 3-5 4-6 5-7 6-8 14 9 4 Correct response a a a 1m 600 b b b 1m 50 b b b 1m Additional guidance Indicates ‘No’ and gives a correct explanation The most common correct explanations: State that 25% implies a total of 4 parts but there are 5 eg I There are 5 parts not 4 I There are 4 parts of water not 3 Minimally acceptable explanation State what 25% would imply eg I 25% would be 1 part screenwash to 3 parts water I It would give a total of 125% Use of information from part (a) Refer to the correct percentage of 20% eg I It’s 20% I 1 out of 5 e 20 out of 100 Sourced from SATs-Papers.co.uk eg, for the first category N 1 : 4 means 5 parts altogether N It’s 1 out of 5 N There are 5 parts eg N 150ml t 5 = 750 not 600 Incomplete explanation eg N It’s less than a quarter screenwash N It’s more than 75% water N There are more than 4 parts N 1 part with 4 parts http://www.SATs-Papers.co.uk 19 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 3–5, 4–6, 5–7 Tier & Question 15 10 5 a a a Net Marking overlay available 3-5 4-6 5-7 6-8 Correct response 1m Additional guidance Indicates the correct shape, ie b b b 1m Lines correct ie uses a ruler to draw both straight lines from a common point, within the tolerance for length as implied by the overlay 1m Arc correct ie draws the arc within the tolerance as shown on the overlay. (Ignore continuation of the arc beyond the lines denoting the angle) shown on the overlay Angle correct ie draws or indicates the angle within the tolerance as shown on the overlay 1m Lines correct length but outside of the arcs Follow through from an incorrect angle ! Follow through from incorrect straight lines Accept, provided both lines are the same length and compasses have been used. Note the dashed lines on the overlay are a visual aid to help identify those who have not used compasses Arc shown as a series of points ! Extra information added to the net in an attempt to show a 3-D drawing Penalise one mark only, by withholding the final mark that would otherwise have been awarded 20 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 3–5, 4–6, 5–7 Tier & Question Piles of cards 3-5 4-6 5-7 6-8 16 11 6 Correct response a a a 1m Correct expression eg I 4n p 5 I 6n p 8 m (2n p 3) b b b 1m Correct expression eg I 3n p 4 I 6n p 8 2 I (6n p 8) d 2 c c c 2m Incorrect expression eg, for part (a) N 6n p 8 m 2n p 3 eg, for part (b) N 6n p 8 d 2 Correct expression repeated eg N 3n p 4 and 3n p 4 105 or 1m Additional guidance Shows the value 20 or Using an incorrect value of n, evaluates 5n p 5 correctly eg, from n e 26 I 5 t 26 p 5 e 135 eg, from n e 23 I 120 or ! Value for n if not stated Accept if embedded eg N 5 t 21 p 5 e 110 Do not accept if not specified and not embedded eg N 120 (neither n e 23, nor 5 t 23 p 5 shown) Using an incorrect value of n, evaluates 6n p 8 correctly and then subtracts 23 eg, from n e 24 I 6 t 24 p 8 e 152, 152 m 23 e 129 eg, from n = 23 I 6 t 23 p 8 e 146, 146 m 23 e 123 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 21 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 3–5, 4–6, 5–7 Tier & Question Cycling 3-5 4-6 5-7 6-8 17 12 7 Correct response 2m Additional guidance Gives a correct explanation The most common correct explanations: Show the mean is 39.9 which is less than 40 eg I 32.3 p 38.7 p 43.5 p 45.1 e 159.6, 159.6 d 4 e 39.9 which is 0.1 too small I 39.9 < 40 ! Response does not refer to 40 Show the total distance is 159.6 which is less than 160 eg I 40 t 4 e 160, 160 > 159.6 ! That 159.6 is less than 160 is not stated Compare and interpret the daily differences in distance from 40 eg I m 7.7 p m 1.3 p 3.5 p 5.1 e m 0.4 so it’s under 40 I 7.7 p 1.3 > 3.5 p 5.1 eg The mean is 39.9 Accept provided this is not accompanied by an incorrect statement eg, for 2m do not accept N 159.6 d 4 e 39.9 so she rode more than 40km a day N explicitly The values of 159.6 and 160 must be shown, but accept implicit comparison eg N It’s 159.6 not 160 As in the previous category, for 2m do not accept a correct response accompanied by an incorrect statement No interpretation eg N On Mon she did 7.7km less, Tues was 1.3km less, Wed was 3.5km more, Thurs was 5.1km more ! Values rounded eg 32 p 39 p 44 p 45 e 160 so the mean is 40 Mark as 1, 0 N or 1m Shows the value 159.6 or 160 or Shows a correct method to find the mean, or the difference between the mean and 40, with not more than one computational error eg I 32.3 p 38.7 p 43.5 p 45.1 e 158.6 (error) 158.6 d 4 e 39.65 I m 8.7 (error) m 1.3 p 3.5 p 5.1 e m 1.4 ! Median calculated correctly Accept for 1m, provided the word median is used and the statement is contradicted eg, accept for 1m N The median is 41.1 so she is correct eg, do not accept N The average is 41.1 so she is correct or Describes a complete correct method but does not completely evaluate eg I When you add them all up it doesn’t come to more than 4 t 40 22 Sourced from SATs-Papers.co.uk Incomplete method with no evaluation or interpretation eg N (32.3 p 38.7 p 43.5 p 45.1) d 4 http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 4–6, 5–7, 6–8 Tier & Question Same volume 3-5 4-6 5-7 6-8 13 8 1 Correct response a a a 1m Correct volume, ie 60 Additional guidance ! The value of 60 is shown to the power of 3 eg 3 60 3 60 cm Assume the power refers to units, ie mark as 1, 0 N N 1m b b b 1m Correct units eg 3 I cm I Centimetres cubed Informal but unambiguous language 6 ! Follow through as their part (a) d 10 eg N Cube centimetres Accept provided the value is exact and not rounded ! Incorrect units inserted Ignore Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 23 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 4–6, 5–7, 6–8 Tier & Question Angles again 3-5 4-6 5-7 6-8 14 9 2 Correct response 3m 10, with a correct and unambiguous method that clearly identifies the relevant angles being used by use of letters or, minimally, on the diagram Additional guidance ! Angles identified through a single letter Condone if otherwise unambiguous eg, for identification of ∠AKC accept N K The most common correct methods: Calculate ∠CAK and ∠AKC eg I ∠CAK e 25 (90 m 65) ∠AKC e 145 (180 m 35) 180 m 25 m 145 Minimally acceptable indication of method eg N N Use triangles ADC and KCB eg I ∠ACD e 25 (180 m 90 m 65) ∠KCB e 55 (180 m 90 m 35) 90 m 25 m 55 N Use alternate angles to find ∠ACB then subtract ∠KCB eg I ∠ACB e 65 (alternate angles) ∠KCB e 55 (180 m 90 m 35) 65 m 55 N N Use alternate angles to find ∠KCD then subtract ∠ACD eg I ∠KCD e 35 (alternate angles) ∠ACD e 25 (90 m 65) 35 m 25 ! Redundant angles identified Use alternate angles to find ∠ACB and ∠KCD, and recognise that the total of these is 90 p a eg I ∠ACB e 65 (angles in a Z) ∠KCD e 35 (angles in a Z) (65 p 35) m 90 24 Sourced from SATs-Papers.co.uk The mathematical communication should not allow ambiguity. Hence for 3m all of the identified angles must be correct. Note to markers: The correct angles are: http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 4–6, 5–7, 6–8 Tier & Question Angles again (cont) 3-5 4-6 5-7 6-8 14 9 2 Correct response or 2m Additional guidance Indicates a is 10, even if the relevant angles are not identified clearly or correctly or Shows a complete correct method with the relevant angles clearly identified and with not more than one computational error, and follows through correctly to find their ∠ACK Minimally acceptable indication of method eg N or Identifies clearly any two of the six correct angles as shown previously, even if others are incorrect or 1m Shows a complete correct method with not more than one computational error, and follows through correctly to find their ∠ACK, but their angles are not clearly identified or Identifies clearly any one of the six correct angles as shown previously, even if others are incorrect Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 25 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 4–6, 5–7, 6–8 Tier & Question Photos 3-5 4-6 5-7 6-8 15 10 3 Correct response 4m or 3m Gives a correct conclusion eg I Film size 24, by £ 5.30 Shows £ 56.1(0) and £ 61.4(0) (the correct total cost for both film sizes) or Concludes film size 24, by £ 8.30 (only error is to omit the cost of postage or assume the total postage is the same) Additional guidance ! Method used is price per photo This correct method will lead to a correct answer provided the values are not rounded or truncated If the values are rounded or truncated, mark as 1, 1, 0, 0 eg N 24 size is 16p per photo, 36 is 17p per photo so 24 is cheaper by 1p per photo N £3.74 d 24 e 15p, £6.14 d 36 e 17p 2 t 360 so £7.20 cheaper for 24 size or Shows £ 56.1(0) or £ 61.4(0), and at least two of the values shown in the table below for the other film size, then follows through to their final conclusion Note there must not be more than one error throughout 24 film (56.10) £ 32.25 £ 14.85 £ 9 £ 23.85 or 2m 36 film (61.40) £ 26.5(0) £ 28.9(0) £ 6 £ 34.9(0) (buying film) (printing film) (postage) (printing & postage) Shows £ 56.1(0) or £ 61.4(0) or Shows all values correct from two rows of the table above or Shows £ 47.1(0) and £ 55.4(0) (error is to omit cost of postage) ! Both numbers of films incorrect For 2m, provided the numbers of films are different, allow follow through to their final conclusion. Note the final answer must be the difference between (£6.14 t their 10) and (£3.74 t their 15) For 1m, allow correct evaluation of either total cost, ie £6.14 t their 10, or £3.74 t their 15, even if their numbers of films are the same or Concludes film size 24, by £ 11.05 (only error is to omit cost of buying film) or Concludes film size 36, by £ 8.75 (only error is to omit cost of printing film) or 1m Shows all values correct from one row of the table above or Shows 15 and 10 (the correct number of films needed for both film sizes) 26 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 4–6, 5–7, 6–8 Tier & Question Equating 3-5 4-6 5-7 6-8 16 11 4 Correct response a a a 1m Additional guidance Values substituted into the given equations 8 Ignore 1m b b b 1m m3 Incomplete processing Writes a correct expression eg I 3a p 6b m (2c m d) I 3a p 6b m 2c p d I 3a p 6b m 3 I 7(2c m d) I 14c m 7d I 2c m d p 18 Incorrect expression eg N 3a p 6b m 2c m d N 7 t 2c m d N 2c m d t 7 I 7 (3a p 6b) 8 Sourced from SATs-Papers.co.uk Expression uses only one of a or b, or only one of c or d Note these are not possible without substitution of specific values and such expressions must therefore be incorrect http://www.SATs-Papers.co.uk 27 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 4–6, 5–7, 6–8 Tier & Question Same areas 3-5 4-6 5-7 6-8 17 12 5 a a a 1m Correct response Additional guidance Correct explanation that states the area of the rectangle is 6 and justifies why the area of the triangle is also 6 ! Units given Ignore ! Areas not evaluated The most common correct justifications for the triangle: Show, or imply by correct substitution, the relevant formula eg 1 I bth 2 I I I bthd2 3t4d2 1.5 t 4 Divide the triangle into two parts as shown, then justify why the area of the smaller triangle is 1.5 eg I Accept if unambiguous and equated eg N 3t2=3t4d2 Incomplete explanation eg N You add up the halves N Count the squares, join halves then join little bits to make 6 Spurious explanation eg N One of the sloping sides marked as 4 and used as the height of the triangle N Triangle incorrectly grouped to show 6 Area of A e 4.5 Area of rest of shape would be 2 but half is not shaded, so it’s 4.5 p 2 m 0.5 Show the area of the triangle is half that of the enclosing square, less 2 eg I 2 Area = 4 d 2 m 2 Note to markers: Correct responses based on grouping must include the following pairings: Show correct groupings eg I Area of triangle is 5 as shown and the bits shaded black makes 6 Use dissection eg I 28 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tier & Question Same areas (cont) 3-5 4-6 5-7 6-8 17 12 5 b b b 1m Tiers 4–6, 5–7, 6–8 Correct response Draws a parallelogram, with no right angles, that has an area of 6 eg, base 3 perpendicular height 2, or vice-versa Additional guidance ! Not accurate and/or lines not ruled Accept provided the pupil’s intention is clear I eg, base 6 perpendicular height 1, or vice-versa I eg, a parallelogram consisting of two triangles each of base 3 and height 2, or vice-versa I Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 29 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 4–6, 5–7, 6–8 Tier & Question Libraries 3-5 4-6 5-7 6-8 18 13 6 a a a 1m Correct response Indicates ‘False’ and gives a correct justification The most common correct justifications: Additional guidance ! Values read from the graph or calculated Accept 725 ± 10 and 362.5 ± 10 and qualified approximations such as ‘about 700’ but do not accept incorrect calculations eg N 725 d 2 e 312.5 (error) < 500 Interpret the significance of 362.5 (± 10) eg I Half of 725 is 362.5 but it only fell to 500 I 363 < 500 I It fell to 500 but it should have dropped to about 360 I The drop is about 225 but it would need to be 362.5 Minimally acceptable justification State or imply that half of 725 < 500 eg I 500 is more than half of 725 Minimally acceptable justification eg N N Half of 725 is 362.5 not 500 The graph doesn’t fall as low as 360 The significance of 362.5 (± 10) is not interpreted eg N Half of 725 is 362.5 eg N N N It only dropped from 725 to 500 725 halved isn’t 500 500 is not half of 725 Numbers stated without interpretation eg N It dropped from 725 to 500 State or imply that 500 t 2 > 725 eg I If you double the value for 1998 you would get 1000 libraries but there were far fewer than that open in 1988 ! Ambiguous reference to ‘more than half’ or ‘less than half’ As the reference could be to the fall or the number of libraries open, condone Explanation interprets the misconception prompted by the graph eg N Because the scale doesn’t start at zero, it looks as if it has dropped much more than it has in reality 30 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 4–6, 5–7, 6–8 Tier & Question Libraries (cont) 3-5 4-6 5-7 6-8 18 13 6 b b b 1m Correct response Indicates ‘Cannot be certain’ and gives a correct justification that you cannot predict beyond the data set eg I No data is given for those years I The diagram doesn’t show 2004 so there is not enough information I The trend might change I Although the graph shows the number is decreasing, we cannot know for certain that it will continue Additional guidance Minimally acceptable justification eg N N N N N N N N N The diagram doesn’t show 2004 It only goes to 1998 You can’t predict the future Who can tell what will happen? Anything might happen They might decide they’ve closed enough There could be an increase or a decrease More libraries could open There is not enough information given ! Justification describes the graph Ignore if accompanying a correct response, otherwise do not accept eg, accept N The graph is not falling at a steady rate and anything might happen eg, do not accept N It is not falling at a steady rate N The chart doesn’t go in a steady pattern N It is levelling out so there will probably be about 475 Incomplete justification eg N Some libraries could close down N It is uncertain Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 31 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 4–6, 5–7, 6–8 Tier & Question Equations Marking overlay available 3-5 4-6 5-7 6-8 19 14 7 Correct response a a 1m Draws a straight line within the tolerance, and at least of length, as specified by the overlay Additional guidance ! Points not plotted Ignore Points not joined b b 2m or 1m Draws a curve within the tolerance as specified by the overlay between (1, 12) and (12, 1), even if the curve is incorrect or omitted elsewhere The curve is within tolerance between (2, 6) and (6, 2), even if incorrect or omitted elsewhere or Plots 6 points correctly Tier & Question Walk 3-5 4-6 5-7 6-8 20 15 8 Correct response 1m Additional guidance Indicates ‘steady speed’, ie 32 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 5–7, 6–8 Tier & Question Swimming clubs 3-5 4-6 5-7 6-8 16 9 Correct response a a 1m Additional guidance Years and months omitted Both correct, ie eg Mean as 25 years 3 months N 4, 8 Range as 4 years 8 months b b 1m 25, 3 Indicates ‘less than 1 year’, ie 1m Indicates ‘not possible to tell’, ie Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 33 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 4–6, 5–7, 6–8 Tier & Question Arrow Marking overlay available 3-5 4-6 5-7 6-8 21 17 10 Correct response a a 2m or 1m Correct enlargement within the tolerance as shown on the overlay, with vertices joined Additional guidance ! Lines not ruled Accept provided the pupil’s intention is clear ! Construction lines shown At least 5 vertices correct Ignore or The only error is to use an incorrect centre of enlargement, ie the enlargement is the correct size as shown by the overlay, with vertices joined, but is in the incorrect place b b 1m For 1m, scale factor – 2 Arrow head length as 4 1m Angle as 40 1m Vertical height as 12 Tier & Question Questions 3-5 4-6 5-7 6-8 18 11 Correct response a a 1m 0.15 or equivalent probability 1m Additional guidance 0.65 or equivalent probability b b 1m 14 40 used within the answer Accept eg N 14 out of 40 N 34 Sourced from SATs-Papers.co.uk 14 40 http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 5–7, 6–8 Tier & Question Circling 3-5 4-6 5-7 6-8 19 12 Correct response 3m 25π or 78.5(...) or 79 Additional guidance For 3m, percentage truncated to 78 ! Incorrect units seen within working Ignore or 2m Shows or implies a correct method, even if values have been rounded or truncated eg 9π I t 100 36 I I I I I I The following values are commonly seen Markers may find them useful 2 πt3 28, 28.2(...), 28.3 2 (π t 3) 88 to 89 inclusive 2 π t 3 29 to 30 inclusive 9π d 36 ! π32 not evaluated or otherwise interpreted π 2 4 2 28.2(...) d 6 9π e 28 (rounded), 28 d 36 e 0.778 36 m 28.2 (truncated) e 7.8, 7.8 d 36 e 22 (rounded), 100 m 22 78 As a common error is to evaluate π3 as 2 (π3) , do not accept as evidence of a correct method or The only error is to give the percentage that is not shaded, ie 21.5 or 21.4(...) or 21 or 1m Shows or implies a correct method for the area of the circle, even if the value has been rounded or truncated eg I 9π I 3t3tπ I 28.27(...) I 28 or Divides their area, even if incorrect, by 36 eg 2 I π3 = 88.8, 88.8 d 36 Sourced from SATs-Papers.co.uk Their area represents the unshaded part of the diagram http://www.SATs-Papers.co.uk 35 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 5–7, 6–8 Tier & Question Blackbirds 3-5 4-6 5-7 6-8 20 13 Correct response a 1m Indicates ‘True’ and gives a correct explanation eg I There are no males that are 121 m 125 I Males start at 126 m 130, females start at 121 m 125 I Some females are in the smallest category I The smallest female wing length is not on the male chart Additional guidance Minimally acceptable explanation eg N The grey bar does not appear on the male chart End points of categories taken as exact eg N N No male is smaller than 126 The smallest female might be 125 but the smallest a male could be is 126 ! Explanation refers to a bird being at the end point of a category For both marks, accept reference to the possibility of such an occurrence but do not accept a definitive statement eg, for the first mark accept N The smallest female could be 121, but the smallest a male could be is 126 eg, for the first mark do not accept N The smallest female is 121, but the smallest male is 126 Incomplete explanation eg N 121 is less than 126 1m Indicates ‘Not enough information’ and gives a correct explanation eg I They are both within the same category so we need actual values I Both could be 140, we don’t know I The exact lengths could be anything from 136 m 140 I Both have birds in 136 m 140 I All the males might be 136 but there might be a female that is 140 Minimally acceptable explanation eg N N N The charts don’t show the sizes of individual birds You need the actual values It shows percentages not values Explanation interprets the misconception prompted by the graph eg N Just because for 136 m 140 there is a bigger percentage of males than females, it doesn’t mean the males must be bigger Incomplete explanation eg N The range is not given 36 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tier & Question Tiers 6–8 only Blackbirds (cont) 3-5 4-6 5-7 6-8 13 Correct response b 3m or 2m or 1m Gives a value that is greater than 132 but smaller than or equal to 133, and shows a complete correct method that encompasses the stages described below 1. The correct mid-points of 128, 133 and 138 are identified 2. The percentages used are within range and sum to 100 3. The intention to multiply mid-points by percentages is shown or implied 4. The answer is calculated correctly from the sum of their multiplications Additional guidance ! Range of percentages Accept within the following values: 21 to 24 inclusive, 59 to 62 inclusive, 16 to 19 inclusive ! Stage 3 not shown and their mean is given to the nearest integer As spurious methods lead to seemingly correct values, do not accept as evidence of the intention to multiply Within an otherwise correct method, only one of stages 1, 2 and 4 is incorrect, or stage 4 is omitted eg, stage 1 incorrect I 21 t 128.5 p 60 t 133.5 p 19 t 138.5 = 13340 so mean is 133.4 eg, stage 2 incorrect I 128 22 2816 133 62 8246 138 18 2484 (% sum to 102) 13546 d 100 (or 102), mean is 135 (or 133) eg, stage 4 omitted I 128 t 22 = 2816 133 t 61 = 8113 138 t 17 = 2346 Within an otherwise correct method, two of the stages are incorrect eg, stages 1 and 2 incorrect I 128.5 20 133 60 138.5 20 13320 d 100 = 133.2 (stage 3 not shown but implied both by the correct total and the corresponding mean) Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 37 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tiers 5–7, 6–8 Tier & Question Percentage change 3-5 4-6 5-7 6-8 21 14 Correct response a a 1m 1m Indicates 70 t 1.09 Gives a correct numerical interpretation for one of the calculations, even if it is not in question form eg, for 70 t 0.9 I What is 70 decreased by 10%? I Find 90% of 70 I What is 70% of 90? I What is 9 of 70? 10 eg, for 70 t 1.9 I It increases 70 by 90% I 190% of 70 eg, for 70 t 0.09 I What is 9% of 70? I 70 decreased by 91% 1m b b 1m Additional guidance ! Units or context given Ignore ! Two or more steps used eg, for 70 t 1.9 N Finds 90% of 70 then adds it on to 70 Penalise only the first occurrence ! Multiplication sign not interpreted eg, for 70 t 1.9 N 70 t 190% Penalise only the first occurrence Incorrect response eg, for 70 t 1.9 N Increase 70 by 190% Gives a correct interpretation for a different calculation 70 t 1.09 not chosen for the first mark, but interpreted later 0.86 Two-step process Incorrect % sign eg N 0.86% c 2m 21 or 1m Shows the value 121 or Shows a correct method, working only with the percentage increases eg 2 I 1.1 I 110 t 1.1 I 110 p 11 or Shows a complete correct method with not more than one computational error eg I 70 p 10% e 77 77 p 10% e 84.7 84.7 m 70 t 100 70 I 38 10 increased by 10% is 11 11 increased by 10% is 12.1 2.1 t 10 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tier 6–8 only Tier & Question Star 3-5 4-6 5-7 6-8 15 Correct response a 1m Correct interpretation eg I Number of hours it would take the spaceship to travel from Earth to the star I How many hours the journey would take Additional guidance Minimally acceptable explanation eg N N N Number of hours to travel How many hours it takes Time taken to travel at 40 000 km per hour Incomplete interpretation that does not refer to both the journey and the units of time eg N Number of hours N How long it takes N Time taken to travel No interpretation eg N Distance times light-years divided by speed 1m Correct interpretation eg I Number of years it would take the spaceship to travel from Earth to the nearest star I Number of years from E to PC Minimally acceptable explanation eg N N Number of years to travel How many years to get there Incomplete interpretation that does not refer to the journey eg N Number of years Incomplete interpretation that does not refer to the units of time eg N Time taken to travel Incorrect interpretation eg N Time taken to travel in years and in days b 1m 114 000 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 39 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tier 6–8 only Tier & Question Trigonometry 3-5 4-6 5-7 6-8 16 Correct response a 2m Additional guidance ! Answer 8 8.4(...) Accept provided a correct method or a more accurate value is seen or 1m Shows a correct method eg I 14 t sin 37 Change of variable ! Incomplete notation that omits the angle eg or N Shows a correct trigonometric ratio eg I b 2m sin 37 = y 14 sin = y 14 Do not accept unless evaluation or other indication shows that the relevance of the angle has been understood ! Answer 65 64.6(...) Accept provided a correct method or a more accurate value is seen or 1m Uses 6 and 14 to form a correct trigonometric ratio using cosine, even if rounded or truncated eg –1 6 14 I cos I 6 cos m = 14 I I Change of variable Incomplete but unambiguous notation eg N cos = 6 14 cos m = 0.42857... cos m = 0.43 or Gives the answer 64 or 64.5(...) or Shows a complete correct method eg I 40 90 m sin Sourced from SATs-Papers.co.uk –1 6 14 http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tier 6–8 only Tier & Question Satellite 3-5 4-6 5-7 6-8 17 Correct response 3m Additional guidance ! Answer rounded to 30000 27143.(...) or 8640π Accept provided a correct method or a more accurate value is seen ! Answer 27000 or 27100 or 27140 Accept provided no incorrect method is seen or 2m Shows a complete correct method even if values are rounded or truncated eg I C = 2πr = 14400π, so speed is 14400π d 100 t 60 3 5 I (12800 + 1600) t π t I (14400 t 3.14) t 60 d 100 or Shows a correct value in km/min eg I 144π I 452.(...) or The only error is to omit to add one of the values of 800 eg I 8160π I 25635.(...) or or 1m Shows or implies the correct length of one orbit eg I 14400π I 7200 t 2π I (12800 + 2 t 800) t π I 45238.9(...) or Shows or implies both d 100 and t 60 eg I I I I I I I 3 t 5 t 0.6 d 1.66666(...) d (100 d 60) 7680π (no values of 800 added) 24127.(...) (no values of 800 added) 8640 (π omitted throughout) Sourced from SATs-Papers.co.uk For this mark, d 100 t 60 converted to a decimal which is rounded or truncated eg N N 1.7 1.66 http://www.SATs-Papers.co.uk 41 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Tier 6–8 only Tier & Question Simplify 3-5 4-6 5-7 6-8 18 Correct response a 1m Correct explanation eg a2 m b2 (a m b)(a p b) I amb amb = Additional guidance Minimally acceptable explanation eg N a2 m b2 = (a m b)(a p b) ! Numerical substitution Ignore if accompanying a correct algebraic explanation, otherwise do not accept a1 or a1 b0 b 1m a c amb 2m or 1m Shows a correct partial simplification eg a2b m ab2 I (dividing through by ab) ab a3 m a2b 2 I (dividing through by b ) a2 I 42 am Incorrect simplification eg a m a2b3 N a2b2 a2b3 (partial fractions, first term a2b2 simplified) Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2002 KS3 Mathematics Test Mark Scheme: Paper 2 Index Index to mark schemes Tier Question 3–5 4–6 5–7 6–8 Page 1 Game 10 2 Travelling to school 10 3 Holiday 11 4 Describing shapes 12 5 School trip 13 6 1 Place names 13 7 2 Dinner time 14 8 3 Which calculation? 15 9 4 Throwing coins 16 10 5 Folding 17 11 6 1 Yards 17 12 7 2 Scales 18 13 8 3 Security lock 19 14 9 4 Screenwash 19 15 10 5 Net 20 16 11 6 Piles of cards 21 17 12 7 Cycling 22 13 8 1 Same volume 23 14 9 2 Angles again 24 15 10 3 Photos 26 16 11 4 Equating 27 17 12 5 Same areas 28 18 13 6 Libraries 30 19 14 7 Equations 32 20 15 8 Walk 32 16 9 Swimming clubs 33 17 10 Arrow 34 18 11 Questions 34 19 12 Circling 35 20 13 Blackbirds 36 21 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 43