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Year 7 progress test in mathematics Ma YEAR 7 LEVELS 2005 3–4 2005 Mark scheme for Paper 1, Paper 2 and Mental mathematics Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme Introduction Introduction The test papers will be marked by external markers. The markers will apply the mark schemes in this 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 named 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 11 (Paper 1) and page 21 (Paper 2) of this booklet. The two columns on 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. 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. The U number can be any whole number from 1 to the number of marks in the question. 2 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 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 schemes state 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, algebra, coordinates or negative numbers. Unless otherwise specified in the mark schemes, markers should apply the following guidelines in all cases. 3 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 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 column. 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 digit from the larger in calculations such as 45 m 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 schemes, 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 2005 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 schemes, 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 schemes state otherwise. Mark, according to the mark schemes, 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 schemes. 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 schemes specifically state otherwise. 5 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 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 ✓ 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 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 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 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 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 6 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme General guidance Responses involving the use of algebra For example: 2p n n p 2 2n n n2 2 Accept ✓ ✓ Unambiguous use of a different case or variable eg N used for n x used for n Take care ! Do not accept ! Unconventional notation eg n t 2 or 2 t n or n2 or n p n for 2n n t n for n2 n d 2 for n or 1 n 2 2 2 p 1n for 2 p n 2 p 0n for 2 Within a question that demands simplification, do not accept as part of a final answer involving algebra Accept within a method when awarding partial credit, or within an explanation or general working Embedded values given when solving equations eg in solving 3x p 2 e 32, 3 t 10 p 2 e 32 for x e 10 To avoid penalising the two types of error below more than once within each question, do not award the mark for the first occurrence of each type within each question. Where a question part carries more than one mark, only the final mark should be withheld ✓ Words used to precede or follow equations or expressions eg t 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 ! Words or units used within equations or expressions eg n tiles p 2 n cm p 2 Do not accept on their own Ignore if accompanying an acceptable response Ambiguous letters used to indicate expressions eg n e n p 2 for n p 2 7 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme General guidance Responses involving coordinates For example: ( 5, 7 ) Accept ✓ Do not accept ✓ Unconventional notation eg ( 05, 07 ) ( five, seven ) Incorrect or ambiguous notation eg ( 7, 5 ) y x ( 7, 5 ) ( 5x, 7y ) ( 5x, 7y ) ( x m 5, y m 7 ) x y ( 5, 7 ) ( x = 5, y=7 ) Responses involving negative numbers For example: m2 Accept ✓ Do not accept To avoid penalising the error below more than once within each question, do not award the mark for the first occurrence of the error within each question. Where a question part carries more than one mark, only the final mark should be withheld Incorrect notation eg 2m 8 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 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 20 June 2005. QCA will also send a copy to each school by 1 July 2005. 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. 9 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk BLANK PAGE Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 1 Mark scheme for Paper 1 Making models Question 1 Correct response 1m Additional guidance 12 Working out Question 2 Correct response 1m 27 1m Additional guidance 26 11 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 1 Same values? Question 3 a Correct response 1m Additional guidance Indicates Yes and gives a correct explanation The most common correct explanations: Complete the calculations eg ■ 17 p 15 e 32 and 2 t 16 e 32 ■ They are both 32 ■ 10 p 10 e 20, 7 p 5 e 12 and 2 t 10 e 20, 2 t 6 e 12 ✓ Minimally acceptable explanation eg ◆ ◆ 32 seen, with no evidence of incorrect working 20 p 12 and 20 p 12 Incomplete explanation eg ◆ 17 p 15 e 2 t 16 ◆ Same answer ◆ I did the calculations Use knowledge of near doubles eg ■ Subtract 1 from 17 and add it to the 15 and you have 16 p 16 which is the same as 16 t 2 ■ Double 15 e 30 then add 2 and it’s the same as double 16 b 1m 1m 3 eg ◆ ◆ 16 p 1 p 16 – 1 e 2 t 16 17 p 15 e 16 + 16 Incomplete explanation eg ◆ 17 p 15 e 2 t 16 17 c ✓ Minimally acceptable explanation ! Answer of 3 t 1 Condone 12 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 1 Coins Question 4 Correct response 2m 57 p or 1m Additional guidance Shows the digits 57 or Shows the digits 105 and 48 or Shows the digits 1(00) and 43 with no evidence of an incorrect method or incorrect units or Shows a complete correct method with not more than one error eg ■ 100 m 48 p 5 ■ £1.05 m 38p (error) e 67 ! For 1m, units incorrect or inconsistent Condone provided no ambiguity between pounds and pence is caused eg, for 1m accept ◆ 1 m 48 e 42 (error) [attempt is 100 m 48] 42 p 5 e 47 eg, for 1m do not accept ◆ 1 m 48 e 47 (error) [attempt is 48 m 1] 47 p 5 e 52 Beanbag Question 5 a Correct response 1m Additional guidance ! Other beanbags indicated Indicates only the correct beanbag, ie Ignore marks made on any beanbags inside the 100cm circle as these may have been used for part (b) Do not accept any other beanbags indicated 100cm 200cm b 1m 8 c 1m 6 U1 13 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 1 Decimals Question 6 Correct response a 1m b 1m Additional guidance Gives any pair of decimal numbers that add to 1 other than those given eg ■ 0.1 0.9 ■ 0.5 0.5 ■ 0.75 0.25 ■ 1.2 –0.2 Whole numbers or fractions eg ◆ 1.0 0.0 0.15 or equivalent decimal Equivalent fractions ◆ 1 4 3 4 Given pair in reverse order eg ◆ 0.7 0.3 One line Question 7 Correct response 1m Indicates one more square so the first shape has one line of symmetry, ie indicates one of the four black squares shown below Additional guidance ! Square not shaded Accept provided the indication is unambiguous ! Line(s) of symmetry drawn Ignore, even if incorrect 1m Indicates one more square so the second shape has one line of symmetry, ie 14 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 1 Cost of pens Question 8 Correct response 2m or 1m £ 1.30, with no evidence of incorrect working Additional guidance Incorrect working eg ◆ 5 m 1.10 e 4.90 4.90 d 3 e 1.30 Shows the value 1.3 or 130, with no evidence of incorrect working or Shows the digits 39(0) or Shows a complete correct method with not more than one computational error, provided their value is rounded or truncated to the nearest penny eg ■ 5 m 1.10 e 4.90 4.90 d 3 e 1.63 Conceptual error eg ◆ 5 m 1.10 e 4.10 4.10 d 3 e 1.37 U1 Completing calculations Question 9 Correct response 1m 1m Gives any three numbers that combine as shown to give 60 eg ■ 100 p 20 m 60 ■ 60 p 1 m 1 ■ 60 p 60 m 60 Additional guidance ✓ Fractions, decimals or negatives ✓ Zero(s) used Gives any three numbers that combine as shown to give 0.6 eg ■ 0.5 p 0.5 m 0.4 ■ 2 p 1 m 2.4 ■ 0.6 p 1 m 1 U1 15 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 1 Using rules Question 10 Correct response a 1m Gives both correct numbers in the correct positions, ie 3 and 35 b 2m Additional guidance Gives both correct numbers in the correct positions, ie 5 and 95 or 1m Gives one correct number in the correct position How many? Question 11 a Correct response 1m 10 Additional guidance ✓ Throughout the question, responses embedded eg, for part (a) ◆ 10 t 4 b 1m 5 ! Follow through For part (b), accept follow through as their (a) d 2 c 1m 80 ! Follow through For part (c), accept follow through as either their (a) t 8 or their (b) t 16 16 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 1 Youth club Question 12 Correct response a 1m 10 b 1m 6 c 2m Additional guidance Completes the dot plot correctly, ie ! Symbols not shaded, accurate or grouped in a straight line For 2m or 1m, condone provided the number of symbols is unambiguous for each age 9 10 11 12 13 14 9 10 11 12 13 14 or or 1m Completes a dot plot that satisfies at least four of the following six conditions, even if there are other errors 1. There is a total of 14 dots 2. Age 11 has 3 dots 3. Only age 9 and age 14 have no dots 4. Age 13 has the greatest number of dots 5. Age 12 has more dots than age 11 6. Age 10 has at least one dot or Shows or implies either set of correct values for the ages, even if the dot plot is incorrect or omitted eg ■ (0), 2, 3, 4, 5, (0) ■ (0), 1, 3, 4, 6, (0) ■ 9 10 11 12 13 14 U2 17 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 1 Keys Question 13 Correct response Additional guidance a 1m 5.3 ✓ Equivalent fractions or decimals b 1m 8.1 ! Follow through Accept follow through as their (a) p 2.8, provided this requires ‘bridging the units’ eg, from their (a) as 6.4 accept ◆ 9.2 U1 Angles in a square Question 14 a Correct response 1m 90 Additional guidance ! Throughout the question, incorrect units inserted Ignore b 1m 45 ! Follow through Accept follow through as their (a) d 2 provided 0 < their (a) < 90 Incomplete processing eg 1 ◆ of 90 2 18 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 1 Multiplication Question 15 Correct response 1m 150 2m 400 Additional guidance ! For 2m or 1m, follow through For 2m, accept a correct evaluation of (250 p their answer to 6 t 25) For 1m, accept a correct method eg, for 1m accept ◆ 10 t 25 p their answer to 6 t 25 ◆ 250 p their answer to 6 t 25 or 1m Shows a complete correct method with not more than one computational error eg ■ 6 t 25 e 150 10 t 25 e 250 16 t 25 e 150 p 250 ■ 16 t 20 e 320 16 t 5 e 80, 320 p 80 ■ 16 t 100 e 1600 1600 d 2 e 800 800 d 2 ■ 10 6 ■ 20 200 120 5 50 25 (error) 200 p 120 p 50 p 25 = 395 16 25 320 80 300 (error) For 1m, conceptual error eg ◆ 16 25 32 80 112 ! Method is repeated addition For 1m, at least some multiplication must be shown or implied eg, for 1m do not accept ◆ 16 p 16 p …… p 16 [shown 25 times] Areas Question 16 Correct response a 1m 4 b 1m 2 Additional guidance ✓ Follow through as their (a) d 2 19 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 1 Pairs of values Question 17 a Correct response 1m Gives two correct pairs of values for x and y that add to 30 eg ■ x = 10, y = 20 x = 15, y = 15 ■ x = 1, y = 29 x = 30, y = 0 Additional guidance ✓ Fractions, decimals or negatives ! Same values repeated, but order reversed As this still gives different values for x and y, condone eg ◆ x = 10, y = 20 x = 20, y = 10 U1 b 1m 10 Incomplete processing eg ◆ 40 m 30 Answer of m10 20 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 2 Mark scheme for Paper 2 Number lines Question 1 Correct response a 1m Additional guidance ! Inaccurate indication Indicates the value 26, ie Accept provided the pupil’s intention is clear ✓ Unambiguous indication eg ◆ 20 30 20 b 1m 26 30 105 Shopping Question 2 Correct response 1m Additional guidance £ 5.36 21 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 2 Times Question 3 Correct response a 1m 1m b 1m Additional guidance Completes the missing time correctly eg ■ 06:45 ■ 6:45 am ! For the first mark, indication of am Completes the missing time correctly eg ■ 19:15 ■ 7:15 pm ! For the second mark, indication of pm Completes the missing time correctly eg ■ 9pm ■ Nine o’clock at night ! Indication of pm unconventional or omitted unconventional or omitted Condone, but do not accept incorrect times eg, accept ◆ 6:45 morning ◆ 6:45 eg, do not accept ◆ 6:45 pm ◆ 18:45 unconventional or omitted Do not accept any indications other than the 24 hour clock and/or pm eg, accept ◆ 19:15pm eg, do not accept ◆ 7:15 ◆ 7:15 in the evening Condone any unconventional indication eg, accept ◆ 9 o’clock afternoon Accept indication of pm omitted only if this error has already been penalised for the second mark in part (a) Time not interpreted eg ◆ 21pm ◆ Twenty-one hundred hours Titles Question 4 Correct response a 1m 10 b 1m 14 c 1m Additional guidance 3 22 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 2 Units Question 5 Correct response a 1m Indicates No and gives a correct explanation eg ■ 100cm is 1 metre ■ 1000mm is 1m, not 1000cm ■ 1000cm = 10 metres not 1 metre Additional guidance ✓ Minimally acceptable explanation eg ◆ ◆ ◆ 100 1000mm 10m ! Explanation uses known measurement(s) Accept provided there is a comparison eg, accept ◆ I would be less than 1 metre tall but I am 1.27 metres tall ◆ The door is 2m high, not 0.2m eg, do not accept ◆ I would be less than a metre tall ◆ The door is not 0.2m high ! Response contains an incorrect statement Ignore alongside a correct response eg, accept ◆ 100cm = 1m, so 1000cm = 1km eg, do not accept ◆ 1000cm = 1km Incomplete explanation eg ◆ 1000 ◆ 10 b 1m 10 Rounding Question 6 Correct response 1m Indicates that the amount was rounded to the nearest hundred pounds eg ■ Hundred ■ 100 Additional guidance ! Units repeated eg ◆ £100 Condone Ambiguous spelling eg ◆ Hundredth ◆ Hundreth 23 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 2 Shading fractions Question 7 Correct response Additional guidance a 1m Indicates only the correct shape, ie b 1m Indicates No and gives a correct explanation The most common correct explanations: Show or imply the correct evaluation of both calculations eg ■ eg ◆ ◆ 1 1 of 20 = 10 and of 40 = 10 2 4 ■ ✓ Minimally acceptable explanation They both equal 10 ■ ■ 10 10 10 ◆ 10, 10 seen Equal Same ◆ 10 10 10 1 1 of 20 = of 40 2 4 Incomplete explanation eg ◆ 10 seen ◆ ◆ Use ratio eg 1 1 20 doubled is 40 and half of is 2 4 1 of 20 is 10 2 1 of 40 is 10 4 ✓ Minimally acceptable explanation eg 1 1 d2e 2 4 ◆ 20 t 2 e 40, ◆ ■ 20 is half of 40 and 2 is half of 4 You have doubled the number and halved the fraction ◆ Incomplete explanation eg ◆ 1 1 is double 2 4 ◆ It’s just doubled U1 24 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 2 Number line again Question 8 Correct response 1m m2 1m Additional guidance 12 Place value Question 9 Correct response a 1m Indicates the correct number, ie 47 407 40007 b 1m Additional guidance 4007 400007 ! Unconventional grouping of digits 3 000 000 Accept any groupings provided the digits are correct Value given in words Turning direction Question 10 a Correct response 1m West Additional guidance ✓ Unambiguous indication eg, for part (a) ◆ W b 1m South c 1m 45 ✓ –45 ! Angle greater than 360 Accept any multiple of 360 p 45 eg ◆ 405 25 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 2 Moving on a grid Question 11 Correct response a 1m (5, 5) b 1m Gives a correct pair of coordinates for a point on the line shown [y e x p 2] eg ■ (0, 2) ■ (2, 4) ■ (3.5, 5.5) Additional guidance ✓ Response assumes the line continues as a straight line eg ◆ (8, 10) ◆ (m2, 0) ◆ (x, x p 2) Multiplying chain Question 12 Correct response 1m 1008 1m Additional guidance 24 26 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 2 Primary schools Question 13 Correct response 2m Additional guidance ✓ Unambiguous labelling Completes the pie chart correctly eg eg ◆ ■ Ash P Park A B P P B G Burgate Grange B G G B ! Lines not ruled or accurate Accept provided the pupil’s intention is clear or 1m Indicates all four sectors correctly but fails to label or labels incorrectly For sectors representing Grange and Park, line indicating 5% incorrect or omitted eg or Indicates and labels at least two of the sectors correctly ◆ G or A B G Indicates the size of all four sectors and labels them correctly, but the sectors are not continuous eg G B P ■ B P G B P B A P P B G B G P B 27 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 2 Thinking fractions Question 14 a Correct response 1m Additional guidance Indicates No and gives a correct explanation The most common correct explanations: ✓ Minimally acceptable explanation Show or imply the correct sum eg ■ eg 1 1 2 2 p e p 4 4 8 8 e ◆ ◆ ■ ■ 0.25 p 0.25 e 0.5 and 0.5 e 4 8 1 2 ◆ 1 1 1 2 1 p e , but e 4 4 2 8 4 2 4 ◆ 4 8 4 8 Half ■ p e Give a correct and comparable calculation that 2 gives 8 ✓ Minimally acceptable explanation eg ◆ eg ■ 1 2 p0e 4 8 ■ 1 2 1 e so you can’t add another 4 8 4 ■ 1 2 e 4 8 1 1 2 p e 8 8 8 Address the misconception eg ■ Sam has just added the top numbers together and the bottom numbers together and you can’t add fractions like that ■ You don’t need to change the bottom number, just add the top ones together ✓ Minimally acceptable explanation eg He added the top and bottom numbers together ◆ You only add the top numbers [denominator unchanged implied] ◆ You don’t add the bottom numbers [numerators added implied] ◆ Incomplete explanation eg ◆ You add the numerators ◆ You keep the denominator the same U1 28 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 2 Thinking fractions (cont) Question 14 b Correct response 1m Additional guidance ! Answer repeats fifths Indicates 5 Condone eg, accept ◆ 5 5 ◆ 1 1 1 1 1 p p p p 5 5 5 5 5 ! The stated 1 not included 5 Accept provided it is clear that it is not included eg, accept ◆ 4 more ◆ An extra 4 5 eg, do not accept ◆ 4 Net Question 15 Correct response 1m Additional guidance Indicates the correct name, ie Cube Prism Triangular-based pyramid ✓ Square-based pyramid Cuboid 29 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 2 Three odds Question 16 Correct response 1m Additional guidance Indicates No and gives a correct explanation The most common correct explanations: Give a counter example eg ■ 1 p 3 p 5 e 9, which is odd not even ✓ Minimally acceptable explanation eg ◆ ◆ 1p3p5e9 1 p 3 p 5 e odd ! Odd numbers taken to be the same Accept, even if the odd number repeated is 3 eg, accept ◆ 3 p 3 p 3 e 9 ◆ 3 t 3 e 9 ! Calculations or statements given that do not relate to the given statement or are incorrect Ignore alongside a correct counter example ! Incomplete explanation eg ◆ Make a general statement eg ■ An odd p another odd e an even Then even p the third odd e odd So the answer will always be odd ■ Odd numbers are just even numbers plus 1, and even p even p even e even and even p 3 e odd 1p3p5 ✓ Minimally acceptable explanation eg ◆ ◆ Odd p odd e even, even p odd e odd Even p even p even p 3 e odd ! Odd numbers taken to be the same Condone eg, accept ◆ 3 t odd is odd t odd which always gives odd Incomplete or incorrect explanation eg ◆ Adding three odd numbers does not make an even number ◆ Odd t odd e odd ◆ When you add all odd numbers it will always come to an odd number U1 30 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 2 Calculators Question 17 Correct response a 1m 28 b 1m 24 Additional guidance ! Parts (a) and (b) transposed but otherwise correct Mark as 0, 1 158 Question 18 Correct response 1m Additional guidance 632 U1 Block of three Question 19 Correct response 2m or 1m Additional guidance 40 Shows or implies correct dimensions for the large rectangle, even if there is further incorrect working eg ■ 12cm by 8cm ✓ For 1m, minimally acceptable implication eg ◆ 4 ■ 4 8 8 12 ◆ ■ ■ ■ 4p4p8p4p8p4p8 20 t 2 12 t 8 (e 96) 4 Four 4s and three 8s seen, with the intention to add also shown U1 31 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 2 Boxes of counters Question 20 a Correct response 1m Additional guidance Indicates box A and gives a correct explanation The most common correct explanations: State or imply that there are the same number of white counters in each, but different numbers of black counters or different totals eg ■ There are the same number of white in each box, but in box B there are more black, so you are less likely to get white from box B ■ Both boxes have three white but B has one extra black so there is more chance of picking a black from B ■ There’s the same number of whites in both, but in A it’s out of a smaller total ✓ Minimally acceptable explanation eg ◆ ◆ ◆ ◆ ◆ Same white, fewer black 3 white, but only one black 3 white, but more black in B Same number of white but fewer counters 3 is out of fewer counters Response details the number of white and black counters with no comparison shown or implied eg ◆ A has 3 white and 1 black B has 3 white and 2 black Incomplete explanation eg ◆ There is the same number of white counters in each box ◆ It’s only got one black counter ◆ Fewer black counters in A ◆ There are more black in B ◆ It is out of more counters in B Show the probabilities of getting a white counter or a black counter eg 3 ■ The probability of getting a white counter is 4 3 for box A but for box B 5 ■ For black it’s 25% for A and 40% for B ! Numerical probability unconventionally or incorrectly expressed As this is a level 4 mark, condone even if the comparison is not explicit, provided the correct box is ticked eg, accept ◆ A is 3 in 4, B is 3 in 5 ◆ 3 W to 1 B, 3 W to 2 B ◆ For black it’s 1 out of 4 and 2 out of 5 Incomplete explanation eg ◆ There’s a greater probability of choosing a white counter from box A ◆ B is the best box for getting a black counter U1 32 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 2005 Year 7 progress mathematics test mark scheme: Paper 2 Boxes of counters (cont) Question 20 b Correct response 1m Indicates equal numbers of black and white counters Additional guidance ✓ Unambiguous indication eg ◆ Filled circle for black, unfilled circle for white ! Number of black and white counters is zero Accept only if at least one counter clearly labelled with another colour is given Do not accept no counters given ! Counters clearly labelled with other colours alongside black and white counters Ignore Flats Question 21 Correct response a 1m Gives the values 37, 38, 39, 40 in any order b 1m Additional guidance 15 U1 33 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Sourced from SATs-Papers.co.uk Double seventeen. How many sides does a hexagon have? What is fifty per cent of sixty? What is four hundred divided by one hundred? 2 3 4 5 What is a quarter of twenty-four? Look at the scale on your answer sheet. What value is the arrow pointing to? Estimate the length of the line on your answer sheet in centimetres. The line graph shows the temperature during one afternoon. At what time was the highest temperature? 7 8 9 10 ‘Now turn over your answer sheet.’ Look at the calendar for the month of April. Alice was born on the twenty-second of the month. On what day was Alice born? 6 ‘For the next group of questions you will have 10 seconds to work out each answer and write it down.’ Look at the numbers on your answer sheet. Add them. 1 For the first group of questions you will have 5 seconds to work out each answer and write it down.’ ‘Now we are ready to start the test. 5 4 3 2 1 Time: 5 seconds Practice question School Last name First name Mental mathematics test Year 7 mathematics 2005 17 60 13 400 50% 19 95 Total marks 5 4 3 2 1 10 9 8 7 6 10 1 Temp (˚C) 0g Mon Tue Wed Thu Fri Sat Sun 2 11 12 13 14 15 16 17 25 26 27 28 29 30 cm pm 6 g 100g 24 18 19 20 21 22 23 24 3 4 5 Time (pm) 4 5 6 7 1 8 2 9 3 10 April Time: 10 seconds 10 9 8 7 6 2005 Year 7 progress mathematics test mark scheme: mental mathematics 34 http://www.SATs-Papers.co.uk Look at your answer sheet. It shows the temperature on Monday. On Tuesday, it was ten degrees higher. What was the temperature on Tuesday? What is the next square number after thirty-six? 13 14 Sourced from SATs-Papers.co.uk The table shows the cost of a pen and a pencil. I buy two pens and two pencils. How much does that cost altogether? Look at the sequence of numbers going down in steps of four. Write down the next two numbers in the sequence. The pie chart shows how some pupils travel to school. About what percentage of the pupils cycle to school? Look at the shaded shape drawn on a centimetre square grid. What is its area? 17 18 19 20 ‘Put your pens down. The test is finished.’ The bar chart shows pupils’ favourite colours. Altogether, how many pupils are there? 16 ‘For the next group of questions you will have 15 seconds to work out each answer and write it down.’ Four y equals forty-four. What is the value of y? There is one litre of water in a jug. Tom pours out two hundred and fifty millilitres of the water. How much water is left in the jug? 12 15 Work out the answer to the calculation on your answer sheet. 11 1 t °C 16 0 2 Green Blue Red 4 Time: 15 seconds 15 14 13 12 6 10 pupils 8 4 y = 44 36 – 8 °C ml 250 ml 16 15 14 13 12 20 19 18 25p 30p Walk Bus Car % cm2 Cycle 33, 29, 25, 21, …, … £ Pencil Pen 17 6 × 5 – 7 11 11 Time: 15 seconds continued Time: 10 seconds continued 20 20 19 18 17 2005 Year 7 progress mathematics test mark scheme: mental mathematics http://www.SATs-Papers.co.uk 35 Year 7 progress test in mathematics 2005 Mental mathematics Time: 10 seconds 6 Friday 7 6 8 25 g Accept any unambiguous indication, eg Fri or F Mark scheme 9 3.5 cm answer 4.5 cm Time: 5 seconds 1 32 10 2 34 3 6 4 30 5 3 pm 4 Do not accept incorrect % signs 36 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Time: 10 seconds continued Time: 15 seconds continued 23 12 17 £ 1.10 18 11 17 and 13 750 ml 13 2 °C 14 49 15 11 Accept pair in either order 19 23 % 20 answer 27 % 12 cm2 Accept embedded responses, eg 4 t 11 = 44 Time: 15 seconds 16 22 pupils 37 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk BLANK PAGE Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk BLANK PAGE Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk EARLY YEARS NATIONAL CURRICULUM 5–16 GCSE GNVQ GCE A LEVEL First published in 2005 NVQ © Qualifications and Curriculum Authority 2005 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. OTHER VOCATIONAL QUALIFICATIONS 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 Orderline, PO Box 29, Norwich NR3 1GN tel: 08700 606015; fax: 08700 606017 email: orderline@qca.org.uk 265498 Sourced from SATs-Papers.co.uk © Qualifications and Curriculum Authority 2005 QCA, Years 7 and 8 Team, 83 Piccadilly, London W1J 8QA Order ref: QCA/05/1483 (teacher pack) http://www.SATs-Papers.co.uk