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Ma YEAR 7 LEVELS Mark schemes for Paper 1, Paper 2 and Mental mathematics 2003 3–4 2003 Year 7 progress test in mathematics Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme Introduction Introduction The test papers will be marked by external markers. The markers will follow the mark scheme in the booklet, which is provided here to inform teachers. This booklet contains the mark schemes for Paper 1, Paper 2 and the Mental mathematics test. Questions have been given names so that each one has a unique identifier. The structure of the mark schemes The marking information for questions in the written tests is set out in the form of tables, which start on page 9 (Paper 1) and 20 (Paper 2) of this booklet. The two columns of the left-hand side of each table provide a quick reference to the 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. For diagrammatic responses, in which judgements on accuracy are required, a marking overlay has been provided as the centre page of this booklet. 2 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme 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 or algebra. Unless otherwise specified in the mark scheme, markers should apply the following guidelines in all cases. Questions with a Using and applying mathematics element are identified in the mark scheme by an encircled U with a number that indicates the significance of using and applying mathematics in answering the question. 3 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme 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 = 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. This is when the pupil misreads the information given in the question and uses different information. If the original intention or difficulty level of the question is not reduced, deduct one mark only. If the original intention or difficulty level is reduced, do not award any marks for the question part. The correct answer is in the wrong place. Where a pupil has shown understanding of the question, the mark(s) should be given. In particular, where a word or number response is expected, a pupil may meet the requirement by annotating a graph or labelling a diagram elsewhere in the question. 4 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme 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; 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. 5 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme General guidance Marking specific types of question Responses involving money For example: £ 3.20 £7 Accept ✓ Do not accept 8 ✓ 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 ✓ 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 8 Incorrect or ambiguous use of pounds or pence eg £320, £320p or £700p, or 3.20 or 3.20p not in the answer space. 8 Incorrect placement of decimal points, spaces, etc or incorrect use or omission of 0 eg £3.2, £3 200, £32 0, £3-2-0, £7.0 Responses involving time A time interval For example: 2 hours 30 mins Accept ✓ Take care ! ✓ Any unambiguous indication eg 2.5 (hours), 2h 30 Do not accept 8 8 Incorrect or ambiguous time interval eg 2.3(h), 2.30, 2-30, 2h 3, 2.30min ✓ Digital electronic time ie 2:30 ! 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: 8.40 am 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 17:20 Do not accept 8 8 Incorrect time eg 8.4am, 8.40pm 8 Incorrect placement of separators, spaces, etc or incorrect use or omission of 0 eg 840, 8:4:0, 084, 84 6 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme General guidance Responses involving coordinates For example: (5, 7) Do not accept 8 Accept ✓ ✓ Unambiguous but unconventional notation eg ( 05, 07 ) ( five, seven ) x y ( 5, 7 ) ( x = 5, 8 Incorrect or ambiguous notation eg ( 7, 5 ) ( 5x, 7y ) ( x5, y7 ) ( 5x, 7y ) y=7 ) Responses involving the use of algebra For example: 2p n n p 2 2n Take care ! Do not accept 8 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 ! 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 8 Change of variable eg x used for 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 n 8 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. 8 Embedded values that are then contradicted eg for 3x + 2 = 32, 3 t 10 + 2 = 32, x=5 7 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme 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 100 marks is available (40 from Paper 1, 40 from Paper 2 and 20 from the mental mathematics test). Awarding levels The sum of the marks gained on Paper 1, Paper 2 and the mental mathematics paper determines the level awarded. Level threshold tables, which show the mark ranges for the award of different levels, will be available on the QCA website (www.qca.org.uk) from Monday 1 September 2003. QCA will also send a copy to each school during the autumn term. 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 2003 year 7 progress mathematics tests and mark schemes were developed by the Mathematics Test Development Team at QCA. 8 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 1 Mark scheme for Paper 1 Olympic Games Question 1 Correct response 2m Completes the bar chart correctly for 1996, showing 3 non-overlapping bars of heights 1, 8 and 6 in the correct order eg ■ or 1m Additional guidance ! Bars not shaded, or not of correct width, or not ruled or accurate Accept provided the pupil’s intention is clear and that the ‘Gold’ bar is nearer to 1 than 0 or 2 Shows correct heights for any two bars or Shows correct heights for all three bars but in an incorrect order 9 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 1 What number? Question 2 Correct response 1m 64 1m 49 1m 20 1m Additional guidance 4 Morning Question 3 a Correct response 1m (0)6:25 Additional guidance ✓ Responses in words eg ◆ Twenty-five past six ! Use of am or pm, or 24 hour clock Ignore eg, accept ◆ 6:25 am ◆ 6:25 pm ◆ 18:25 b 1m 20 10 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 1 Euro Question 4 a b Correct response 1m 1m Shows a correct combination of four banknotes whose values sum to 800 eg ■ 50, 50, 200, 500 ■ 100, 100, 100, 500 ■ 200, 200, 200, 200 Shows a correct combination of four banknotes whose values sum to 800, other than one credited in part (a) Additional guidance ! Units incorrect Ignore ! 800 consistently misread as 80 eg 20, 20, 20, 20 for part (a) 50, 10, 10, 10 for part (b) If both answers are correct for 80, mark as 0; 1 provided banknotes other than those given are not used ◆ 8 Banknotes other than those given eg ◆ 200, 200, 300, 100 U1 Using grids Question 5 Correct response a 1m Indicates numbers on the grid that sum to 460 eg ■ 400 and 60 ■ 300, 20, 50, 80, 6 and 4 b 1m Additional guidance Indicates numbers on the grid that sum to 46 eg ■ 40 and 6 11 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 1 Calculations Question 6 Correct response 1m 906 1m 159 1m Additional guidance 92 Drawing lines Question 7 a Correct response 1m Draws one vertical straight line on the rectangle to make one square and one rectangle that is not a square eg Additional guidance ! Line not ruled or accurate Accept provided the pupil’s intention is clear ■ b 1m Draws one straight line on the rectangle, from a vertex to a side, to make one triangle and one quadrilateral eg ■ ✓ Line not ruled ! Line not accurate If the line meets a side of the rectangle within 2mm of a vertex, assume that the pupil’s intention was for the line to go through the vertex eg, do not accept ◆ 12 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 1 Saving Question 8 a b Correct response 1m 1m Additional guidance ! Units of 50p or 20p given 15 Accept only if unambiguous eg, for part (a) accept ◆ 15 50p coins ◆ 15 50p However, if in parts (a) and (b) the only error is that the inclusion of 50 or 20 creates ambiguity, mark as 0; 1 eg ◆ 15 50, 11 20 ◆ 1550, 1120 11 ! Other units given eg, for part (a) ◆ 15p Penalise only the first occurrence U1 Using decimals Question 9 a b Correct response 1m 1m 5.6 or equivalent 6.3 or equivalent Additional guidance ! Change of units Complete correct use of the new units must be shown eg, for part (a) accept ◆ 5m 60cm ◆ 560cm However, if the only error is to consistently omit ‘cm’, mark as 0; 1 eg ◆ 5m 60, 6m 30 ◆ 560, 630 13 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 1 Number line Question 10 Correct response a 1m 5.2 or equivalent Additional guidance ! Units shown Ignore b 1m Indicates 5.8 on the number line ! Indication not accurate Accept if nearer to 5.8 than to 5.7 or 5.9 ! Arrow labelled Ignore, even if incorrect ! Own number line drawn Accept provided each 0.1 is marked and is equally spaced, and both 5 and 6, or both 6 and 7, are labelled c 1m 5.9 or equivalent 8 Correct answer shown in working but their final answer given as 59 8 Their answer shown as negative eg ◆ m5.9 Calendar Question 11 Correct response a 1m 40 b 1m Friday Additional guidance ✓ Unambiguous indication eg ◆ ◆ c 1m May 3rd F ‘Fri’ ringed at the top of the calendar ! Date given in different form Accept only if unambiguous eg, accept ◆ 3/5 ◆ 5/3/30 (US notation) ! Year/day given Ignore 8 Incomplete response eg ◆ ◆ 3rd May U1 14 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 1 Percentages Question 12 Correct response 1m Completes the first two diagrams correctly eg ■ Additional guidance ! Shading omitted Condone if their response shows the ratio 20 : 80 eg, for the first two diagrams accept ◆ ■ 1m Completes the third diagram correctly eg ■ ! Follow through Allow consistent follow through from the first two diagrams, provided the percentage shaded is not 0, 50 or 100 eg, for the second mark only, accept ◆ 40% shaded in all three diagrams Otherwise do not accept eg ◆ 40% shaded in only the second and third diagrams How many pupils? Question 13 a Correct response 1m Mon(day) and Thurs(day) Additional guidance ✓ Unambiguous indication eg ◆ M and Th 8 Ambiguous indication eg ◆ b 1m 8 M and T 8 Incorrect units eg ◆ 8% U1 15 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 1 Track Question 14 Correct response a 1m 60 b 1m Additional guidance 32 Spinner Question 15 Correct response 1m Writes at least two green but no blue Additional guidance ! The non-green section left blank Condone 16 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 1 Multiplication Question 16 Correct response 2m or 1m Additional guidance Shows a complete correct method with not more than one computational error eg ■ 32 21 620 (error but must be a multiple of 10) 32 652 Note: Markers may find the following useful: 672 eg 2 32 21 64 32 96 ◆ 20 600 40 1 30 21 t 32 630 42 672 8 Conceptual error ■ 30 32 t 21 640 32 672 2 600 p 40 p 30 p 2 ◆ 3 2 0 3 6 0 4 2 0 ■ 3 0 2 1 2 0 6 0 4 2 0 3 0 3 1 Answer 673 Answer 276 (error) ! Method is repeated addition ■ 210 p 210 p 210 p 21 p 21 For 1m, at least some multiplication must be shown or implied eg, for 1m do not accept ◆ 21 p 21 p ….. p 21 [shown 32 times] Metric Question 17 Correct response a 1m 500 b 1m 90 c 1m Additional guidance 8 17 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 1 Five tiles Question 18 Correct response 1m Shades a total of 5 squares to make a shape that has exactly one line of symmetry eg Additional guidance ! Squares not shaded or internal lines not drawn Accept provided there is no ambiguity ■ ✓ Shape has a ‘hole’ or has corner-to-corner joins eg ◆ ■ ◆ ■ ! Grid lines not used ■ eg ◆ Accept provided the pupil’s intention is clear 8 Shape has more than one line of symmetry eg ◆ ! Other shapes drawn If their five squares has exactly one line of symmetry, ignore further reflections eg, accept ◆ Do not accept their five squares reflected with the only line of symmetry the mirror line used for the reflection eg ◆ U1 18 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk The attached overlay should be removed and used to mark question 6 on Paper 2. Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 2 Mark scheme for Paper 2 Right or left-handed Question 1 Correct response a 1m 4 b 1m Completes the table correctly, ie Additional guidance right left boys 11 2 girls 9 3 U1 Some values left blank eg ◆ boys girls right 9 left 2 Mirror line Question 2 Correct response 2m Draws in and shades three triangles correctly, ie Additional guidance ! Lines not ruled or accurate Accept provided the pupil’s intention is clear or 1m Draws in three triangles correctly but the shading is omitted or incorrect or Any two of the triangles are drawn in and shaded correctly, even if the third triangle is incorrect or omitted 20 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 2 Theatre Question 3 Correct response 2m Additional guidance ! Answer rounded or truncated £ 272.35 For 2m, accept 272 provided there is no evidence of an incorrect method For 2m, do not accept 273 unless a more accurate value or a correct method is seen or 1m Shows at least one of the values 20.95, 239.85 or 32.5(0) or Shows or implies a complete correct method eg ■ (18.45 p 2.5) t 13 ■ 18.45 p 2.5(0) e 21 (error) 21 t 13 e (273) ■ Digits 27235 seen ■ Answer 273 ! Necessary brackets omitted Condone eg, accept for 1m ◆ 18.45 p 2.5(0) t 13 ◆ 50.95 ◆ 2.5(0) p 18.45 t 13 ◆ 242.35 Names Question 4 Correct response 2m Places all five names correctly, ie Additional guidance ! Incorrect spelling Condone, provided there is no ambiguity 1st 2nd William 3rd George 4th James 5th or 1m John Thomas Places at least three names correctly U2 21 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 2 Temperature Question 5 Correct response a 1m Additional guidance ! Indication not accurate Indicates –8 on the thermometer Accept, provided it is closer to m8 than to m9 or m7 b 1m 5 c 1m Orders correctly, ie ✓ Unambiguous indication eg –9°C –3°C 0°C 6°C ◆ 4th, 1st, 2nd, 3rd ! Units omitted or incorrect Ignore Question 6 a Climbing Marking overlay available Correct response 1m 1m Additional guidance 1 2 ✓ Value between 0.4 and 0.6 inclusive, even if 3 4 ✓ Value between 0.65 and 0.85 inclusive, even Indicates or equivalent fraction Indicates or equivalent fraction given as a decimal or percentage if given as a decimal or percentage eg ◆ b 1m Indicates the position of the climber within the tolerance as shown by the overlay 2 3 ✓ Any unambiguous indication ! Accuracy difficult to judge eg Climber drawn, but no line Line not horizontal In drawings of the climber with no line, take as their indication the mid-point of the climber’s feet. Otherwise, do not accept if their indication extends beyond the tolerance as shown by the overlay ◆ ◆ 22 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 2 Estimates Question 7 Correct response 1m Indicates 0.3 litres, ie 1m Additional guidance Indicates 100 grams, ie ✓ ✓ Measure Question 8 Correct response a 1m Gives a value from 7.4 to 7.6 inclusive, or equivalent b 1m Gives a value from 17.9 to 18.1 inclusive, or equivalent Additional guidance ✓ Follow through as 10.5 p their (a) 23 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 2 Safari Question 9 Correct response a 1m 30 b 1m Additional guidance 15 Printing Question 10 Correct response a 1m 25 b 2m 5, with no evidence of an incorrect method or 1m Additional guidance Shows the value 300 Correct answer from an incorrect method eg ◆ 20 m 15 e 5 or Shows or implies that 3 photos take 1 minute or Shows or implies a complete correct method eg ■ 15 t 20 d 60 ■ 15 t 20 e 320 (error), so 5 minutes 20 seconds or The only error is to assume that there are 100 seconds in 1 minute eg ■ Gives the answer 3 24 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 2 Squares Question 11 Correct response 1m Completes the sentence by stating that the sides must be equal in length eg ■ ... the same length ■ ... equal ■ ... one quarter of the perimeter Additional guidance ✓ Minimally acceptable statement eg ◆ ◆ … the same … 3cm ✓ Unambiguous statement eg ◆ ◆ … equilateral … equivalent Incomplete or incorrect statement eg ◆ … four ◆ … straight ◆ … the same length, half the perimeter 1m Completes the sentence by stating that the angles must be equal in size eg ■ ... 90° ■ ... right angles ■ ... the same angles ■ ... equal ✓ Minimally acceptable statement eg ◆ ◆ ◆ … the same … 90 … right ! Incorrect units Ignore Incomplete or incorrect statement eg ◆ … four ◆ … corners ◆ … 360° Area Question 12 Correct response 1m Gives a value between 18 1 1 and 20 inclusive 2 2 Additional guidance ✓ Equivalent fractions or decimals 25 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 2 Four cubes Question 13 Correct response 2m Draws an L-shape, with the correct dimensions, in any orientation eg ■ Additional guidance ! Lines not ruled Accept provided the pupil’s intention is clear ! Drawing not accurate Accept vertices within 2mm of the dots. If the drawing is less accurate, but the pupil’s intention is clear, deduct one mark ■ ✓ Some or all internal lines omitted eg ◆ ■ ! L-shape enlarged For 2m or 1m, accept provided a consistent scale factor has been used for all lengths or 1m For 2m, external lines omitted or some or all hidden lines shown eg Draws a correct view, using the isometric grid maintaining three dimensions, but omits one or more external lines, or some or all hidden lines are shown or ◆ ◆ Draws a view of a prism with an L-shaped crosssection, using the isometric grid and with all external lines shown and no hidden lines shown, but with one incorrect dimension eg ■ ■ 26 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 2 Counters Question 14 a Correct response 1m Indicates only the correct probability, ie 1 4 b 1m Additional guidance 1 3 1 2 1 1 10 Square grid Question 15 a b Correct response 1m 1m 7 or equivalent fraction 9 Indicates the correct squares, ie Additional guidance ! Answer given as a decimal If a correct fraction is seen, ignore subsequent conversion to a decimal even if incorrect If only a decimal is given, accept 0.78 or 0.77(…) Do not accept 0.8 unless a more accurate value is seen Incorrect shading eg ◆ 27 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 2 Nursery school Question 16 Correct response a 1m Additional guidance ! Incorrect units 20 eg, for part (a) ◆ 20% Penalise only the first occurrence ! Answers to both parts otherwise correct, but given as percentages or decimals eg ◆ 25% in part (a), 37.5% (or 37 or 38) in part (b) Withhold only the mark in part (a) Answers consistently given as fractions b 1m ! Follow through from part (a) 30 Accept 1.5 t their (a), or 1 (80 – their (a)) 2 eg, from their (a) as 10, accept ◆ 15 ◆ 35 What numbers? Question 17 Correct response a 1m 3 b 1m Additional guidance Incorrect statement eg, for part (a) ◆ n e 3 p 5 10 28 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 2 Measuring jugs Question 18 Correct response 2m Indicates A and gives the answer 75 or 1m Additional guidance Shows or implies that jug A contains 400 or Shows or implies that jug B contains 325 U1 Square number Question 19 Correct response 1m 25 Additional guidance Incomplete processing eg ◆ 5 t 5 29 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2003 Year 7 Progress Mathematics Test Mark Scheme: Paper 2 Consecutive Question 20 Correct response 1m Additional guidance Indicates No and gives a correct explanation The most common correct explanations: Give a counter example eg ■ 2 p 3 e 5 which is odd ■ 5, 6 gives 11 ■ 3 p 4 is not even Show why the result must be odd eg ■ You will always add an odd to an even and that gives you an odd number ■ Even p odd e odd ✓ Minimally acceptable explanation eg ◆ ◆ ◆ You will always add an odd to an even Even p odd The result is always odd ■ There will always be one left over so it will be odd Incomplete explanation that does not infer addition eg ◆ It goes odd, even, odd, even … Incorrect statement accompanying a correct statement eg ◆ You will always add an odd to an even and sometimes that gives you an odd number and sometimes it is even U1 30 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk This page may be used for your own notes Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Year 7 progress test in mathematics 2003 Time: 10 seconds Mental mathematics 6 Accept lines not drawn accurately, provided the pupil’s intention is clear Mark scheme 7 32 8 5 packs 9 Time: 5 seconds 1 10 Ignore reference to the number of cans that are left, eg, accept 5 r2 Any two numbers with a difference of 3 6 ( :00) pm Accept unambiguous time, eg 18:00 Do not accept incorrect time, eg 6(:00) am 90 11 12 75 % Do not accept equivalent fractions or decimals 13 4 Ignore other numbers shown, eg, accept 6 r4, 36 r4 14 18 28 4 9( .0) 5 32 Do not accept responses given in words 2 < answer < 3 2 3 1995 7 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Time: 15 seconds 15 19 games 19 20 16 Any square or rectangle with area 4 27, 81 Accept in either order Ignore subsequent terms given Accept inaccurate arrows, provided the pupil’s intention is clear Accept only the correct point on the circumference marked 17 8 cm 18 £ 0.70 or 70p Sourced from SATs-Papers.co.uk Do not accept with units incorrect or omitted http://www.SATs-Papers.co.uk 33 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk EARLY YEARS NATIONAL CURRICULUM 5–16 GCSE GNVQ GCE A LEVEL NVQ First published in 2003 © Qualifications and Curriculum Authority 2003 Reproduction, storage, adaptation or translation, in any form or by any means, of this publication is prohibited without prior written permission of the publisher, OTHER VOCATIONAL QUALIFICATIONS 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 by contacting: QCA Publications, PO Box 99, Sudbury, Suffolk CO10 2SN (tel: 01787 884444; fax: 01787 312950) Order ref: QCA/03/1025 Sourced from SATs-Papers.co.uk 255008 © Qualifications and Curriculum Authority 2003 QCA, Years 7 and 8 Team, 83 Piccadilly, London W1J 8QA http://www.SATs-Papers.co.uk