Mathematics tests. Mark scheme KEY STAGE 3. for Paper 12 Tiers 3 5, 4 6, 5 7 and 6 8 ALL TIERS. National curriculum assessments. PrimaryTools.co.

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1 Ma KEY STAGE 3 ALL TIERS Mathematics tests Mark scheme f Paper 12 Tiers 3 5, 4 6, 5 7 and National curriculum assessments

2 2009 KS3 Mathematics test mark scheme: Paper 2 Introduction Introduction This booklet contains the mark scheme f paper 2 at all tiers. The paper 1 mark scheme is printed in a separate booklet. Questions have been given names so that each one has a unique identifier irrespective of tier. The structure of the mark schemes The marking infmation f each question is set out in the fm 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 f that question part. The Crect response column usually includes two types of infmation: a statement of the requirements f the award of each mark, with an indication of whether credit can be given f crect wking, and whether the marks are independent cumulative examples of some different types of crect response, including the most common. The Additional guidance column indicates alternative acceptable responses, and provides details of specific types of response that are unacceptable. Other guidance, such as when follow-through is allowed, is provided as necessary. Questions with a Using and applying mathematics (UAM) element are identified in the mark scheme by the symbol U1. The number 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. F graphical and diagrammatic responses, including those in which judgements on accuracy are required, marking overlays have been provided as the centre pages of this booklet. The 2009 key stage 3 mathematics tests and mark schemes were developed by the Test Development Team at Pearson Research and Assessment. 2

3 2009 KS3 Mathematics test mark scheme: Paper 2 General guidance General guidance Using the mark schemes Answers that are numerically equivalent algebraically equivalent are acceptable unless the mark scheme states otherwise. In der to ensure consistency of marking, the most frequent procedural queries are listed on the following two pages with the prescribed crect action. This is followed by further guidance relating specifically to the marking of questions that involve money, native numbers, time, measures, codinates, probability algebra. Unless otherwise specified in the mark scheme, markers should apply the following guidelines in all cases. Recding marks awarded on the test paper All questions, even those not attempted by the pupil, should be marked, with a 1 a 0 entered in each marking space. Where can be split into gained and lost, with no explicit der, then this will be recded by the marker as 1 0 The total marks awarded f a double page should be written in the box at the bottom of the right-hand page, and the total number of marks obtained on the paper should be recded on the front of the test paper. A total of 120 marks is available in each of tiers 3 5, 4 6, 5 7 and 6 8. Awarding levels The sum of the marks gained on paper 1, paper 2 and the mental mathematics paper determines the level awarded. Level threshold tables, which show the mark ranges f the award of different levels, will be available on the NAA website from April

4 2009 KS3 Mathematics test mark scheme: Paper 2 General guidance What if Marking procedure The pupil s response is numerically algebraically equivalent to the answer in the mark scheme. The pupil s response does not match closely any of the examples given. The pupil has responded in a non-standard way. There appears to be a misreading affecting the wking. No answer is given in the expected place, but the crect answer is given elsewhere. The final answer is wrong, but the crect answer is shown in the wking. Markers should award the mark unless the mark scheme states otherwise. Markers should use their judgement in deciding whether the response cresponds with the statement of the requirements given in the Crect response column. Refer also to the Additional guidance. Calculations, fmulae and written responses do not have to be set out in any particular fmat. Pupils may provide evidence in any fm as long as its meaning can be understood. Diagrams, symbols wds are acceptable f explanations f indicating a response. Any crect method of setting out wking, however idiosyncratic, should be accepted. Provided there is no ambiguity, condone the continental practice of using a comma f a decimal point. This is when the pupil misreads the infmation given in the question and uses different infmation without altering the iginal intention difficulty level of the question. F each misread that occurs, deduct one mark only. Where a pupil has shown understanding of the question, the mark(s) should be given. In particular, where a wd number response is expected, a pupil may meet the requirement by annotating a graph labelling a diagram elsewhere in the question. 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 increct answer is due to a transcription err If so, award the mark. in questions not testing accuracy, the crect If so, award the mark. answer has been given but then rounded truncated the pupil has continued to give redundant extra If so, award the mark. wking which does not contradict wk already done the pupil has continued, in the same part of the If so, do not award question, to give redundant extra wking which the mark. Where a does contradict wk already done. question part carries me than one mark, only the final mark should be withheld. The pupil s answer is crect but the wrong wking is shown. A crect response should always be marked as crect unless the mark scheme states otherwise. 4

5 2009 KS3 Mathematics test mark scheme: Paper 2 General guidance What if Marking procedure The pupil has made a conceptual err. In some questions, a method mark is available provided the pupil has made a computational, rather than conceptual, err. A computational err is a slip such as writing 4 6 = 18 in an otherwise crect long multiplication. A conceptual err is a me serious misunderstanding of the relevant mathematics; when such an err is seen, no method marks may be awarded. Examples of conceptual errs are: misunderstanding of place value, such as multiplying by 2 rather than 20 when calculating subtracting the smaller value from the larger in calculations such as to give the answer 21 increct signs when wking with native numbers. The crect response has been crossed rubbed out and not replaced. Me than one answer is given. The pupil s answer crectly follows through from earlier increct wk. The answer is crect but, in a later part of the question, the pupil has contradicted this response. The pupil s accuracy is marginal accding to the overlay provided. The pupil has drawn lines which do not meet at the crect point. Any lible crossed rubbed out wk that has not been replaced should be marked accding to the mark scheme. If the wk is replaced, then crossed rubbed out wk should not be considered. If all answers given are crect ( a range of answers is given, all of which are crect), the mark should be awarded unless prohibited by the mark scheme. If both crect and increct responses are given, no mark should be awarded. 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 crect response an acceptable follow-through response should be marked as crect. A mark given f one part should not be disallowed f wking answers given in a different part, unless the mark scheme specifically states otherwise. Overlays can never be 100% accurate. However, provided the answer is within touches the boundaries given, the mark(s) should be awarded. Markers should interpret the phrase lines not accurate to mean meeting within on a circle of radius m with centre at the crect point. within the circle accepted on the circle accepted outside the circle not accepted 5

6 2009 KS3 Mathematics test mark scheme: Paper 2 General guidance Responses involving money Accept Do not accept Where the sign is given f example: 3.20, 7 Where the p sign is given f example: 40p Where no sign is given f example: 3.20, 40p Any unambiguous indication of the crect amount, 3.20p 3 20 pence , :20 320p with sign crossed out 40p Any unambiguous indication of the crect amount, 0.40p.40p 0.40 with p sign crossed out p 40p 0.40 Any unambiguous indication of the crect amount in p as shown above At levels 3 and 4 only also accept omission of units, Increct placement of pounds pence, p Increct placement of decimal point, increct use omission of 0, Increct ambiguous use of pounds pence, 0.40p 40p Omission of final zero, Responses involving native numbers Accept Do not accept F example: 2 To avoid penalising the err below me than once within each question, do not award the mark f the first occurence of the err within each question. Where a question part carries me than one mark, only the final mark should be withheld. Increct notation, 2 6

7 2009 KS3 Mathematics test mark scheme: Paper 2 General guidance Responses involving time Accept Do not accept A time interval f example: 2 hours 30 minutes A specific time f example: 8:40am, 17:20 2 hours 30 minutes Any unambiguous, crect indication, hours 2.5 hours 2h 30 2h 30 min 2 30 Digital electronic time, ie 2:30 8:40am 8:40 twenty to nine Any unambiguous, crect indication, ,40 Unambiguous change to hour clock, 17:20 as 5:20pm 17:20pm Increct ambiguous time interval, 2.3 hours 2.3h 2h min , Increct time, 8.4am 8.40pm Increct placement of separats, spaces, etc increct use omission of 0, 840 8:4: Responses involving measures Accept Do not accept Where units are given ( kg, m, l) f example: 8.6kg 8.6kg Any unambiguous indication of the crect measurement, 8.60kg kg 8kg 600g Increct ambiguous use of units, 8600kg Note If a pupil leaves the answer box empty but writes the answer elsewhere on the page, then that answer must be consistent with the units given in the answer box and the conditions listed above. If a pupil changes the unit given in the answer box, then their answer must be equivalent to the crect answer, using the unit they have chosen, unless otherwise indicated in the mark scheme. 7

8 2009 KS3 Mathematics test mark scheme: Paper 2 General guidance Responses involving codinates Accept Do not accept F example: (5, 7) Unconventional notation, (05, 07) (five, seven) x y (5, 7) ( x = 5, y = 7 ) Increct ambiguous notation, (7, 5) y x (7, 5) (5x, 7y ) (5 x, 7 y ) (x 5, y 7) Responses involving probability Accept! Take care Do not accept A numerical probability should be expressed as a decimal, fraction percentage only. f example: % 10 Equivalent decimals, fractions and percentages, % The first four caties of err below should be igned if accompanied by an acceptable response, but should not be accepted on their own. However, to avoid penalising the first three types of err below me than once within each question, do not award the mark f the first occurrence of each type of err unaccompanied by an acceptable response. Where a question part carries me than one mark, only the final mark should be withheld. A probability crectly expressed in one acceptable fm which is then increctly converted, but is still less than 1 and greater than 0, = 18 25!! A probability that is increctly expressed, 7 in 10 7 over 10 7 out of 10 7 from 10 A probability expressed as a percentage without a percentage sign.! A fraction with other than inters in the numerat and/ denominat.! A probability expressed as a ratio, 7:10 7:3 7 to 10 A probability greater than 1 less than 0 8

9 2009 KS3 Mathematics test mark scheme: Paper 2 General guidance Responses involving the use of algebra Accept! Take care Do not accept F example: 2 + n n + 2 2n Unambiguous use of a different case variable, N used f n x used f n! Unconventional notation, n 2, 2 n, n2 n + n f 2n n n f n 2 n 2 f n n n 2 n n f 2 + n 2 + 0n f 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, within an explanation general wking. Embedded values given when solving equations, in solving 3x + 2 = 32, = 32 f x = 10 To avoid penalising the two types of err below me than once within each question, do not award the mark f the first occurrence of each type within each question. Where a question part carries me than one mark, only the final mark should be withheld. Wds used to precede follow equations expressions,! Wds units used within equations expressions, t = n + 2 tiles tiles = t = n + 2 f t = n + 2 n tiles + 2 n cm + 2 Do not accept on their own. Igne if accompanying an acceptable response. Unambiguous letters used to indicate expressions, Ambiguous letters used to indicate expressions, t = n + 2 f n + 2 n = n + 2 f n + 2 9

10 2009 KS3 Mathematics test mark scheme: Paper 2 Tier 3 5 only 1 Mark Crect response Additional guidance School shop a 19 b Friday Unambiguous indication, f part (b) c Ruler F, f part (c) U1 R 2 Mark Crect response Additional guidance Missing numbers Mark Crect response Additional guidance Parcels 6.10 Gives the answer 6.1 Shows the value 3.9(0) 390 Shows a complete crect method with not me than one computational err 1.3(0) 3 = 3.6(0) (err), (0) = 6.4(0) 10

11 2009 KS3 Mathematics test mark scheme: Paper 2 Tier 3 5 only 4 Mark Crect response Additional guidance Joining Draws all three different sized squares, in any der! Lines not ruled accurate Accept provided the pupil s intention is clear! Internal lines shown Only the outline of any shape drawn should be considered Vertices of square do not use the pins U1 Draws any two of the three different sized squares 11

12 2009 KS3 Mathematics test mark scheme: Paper 2 Tier 3 5 only 5 Mark Crect response Additional guidance Spinner Makes all four crect decisions, ie True False Makes three crect decisions Unambiguous indication f True, f False 6 Mark Crect response Additional guidance Fractions a Indicates any three squares! Squares not shaded Accept any unambiguous indication b 3 5 equivalent Equivalent decimals! Part squares indicated Accept provided the pupil s intention is clear 12

13 2009 KS3 Mathematics test mark scheme: Paper 2 Tier 3 5 only 7 Mark Crect response Additional guidance Number of sides Matches all three shapes crectly, ie! Shape matched to me than one number F, do not accept as a crect match 2 3! Extra shapes added Igne extra shapes and any lines drawn from them Triangle 4 Hexagon 5 Octagon 6 Quadrilateral 7 8 Matches any two shapes crectly 8 Mark Crect response Additional guidance Grid Completes the grid crectly, ie U2 Completes both the middle column and the bottom row crectly 13

14 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 3 5, Mark Crect response Additional guidance Digital 10:45! Indication of am pm Condone either am pm shown implied, accept 10:45 am 22:45 Gives a crect description of the time in wds Five past ten! Wds and numbers used in description Condone, provided the time has been interpreted crectly, accept 5 past 10 Digital time described in wds Ten O five Description of time increct using numbers Ten five Mark Crect response Additional guidance Reflecting Reflects the shape crectly in the mirr line, ie!! Throughout the question, lines not ruled accurate Accept provided the pupil s intention is clear Throughout the question, extra lines drawn Accept provided the pupil s intention is clear Reflects the shape crectly in the mirr line, ie 14

15 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 3 5, Mark Crect response Additional guidance Test a a C b b 21 U Mark Crect response Additional guidance Rounding a a b b Gives a value greater than equal to 795 but less than Mark Crect response Additional guidance Castle 5(.00) Shows the value 22(.00) Shows implies a complete crect method with not me than one computational err (err) + 9 = Answer given as

16 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 3 5, Mark Crect response Additional guidance Baby a a 4 Any reference to extra days b b 9 Any reference to extra weeks days 15 6 Mark Crect response Additional guidance Count on a a 27 b b 1 Shows implies that the size of two steps is ? 5 Shows steps of unequal size U Shows implies that the size of one step is 2 The gaps are Second number is 1 Fourth number is 3 3 to 5 is 8,

17 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 3 5, Mark Crect response Additional guidance Shoe sizes a a 12 b b 3 c c Indicates Both the same and gives a crect explanation The most common crect explanations: Use given values Range of boys is 4, range of girls is is the same as to 9 = 4 to 8 Minimally acceptable explanation 4, 4 8 4, 9 5 Both 4! Ambiguous notation 4 8, 5 9 Condone Reason generally about spread Boys cover 5 sizes, girls cover 5 sizes Minimally acceptable explanation Both have the same number of sizes! Explanation implies references to the number of blank sizes Boys have one blank, girls have one blank Because the girls didn t have size 9 and the boys didn t have size 4 Condone U1 Ambiguous increct explanation 5 in each They both have a range of five sizes Girls: 4, 5, 6, 7, 8 Boys: 5, 6, 7, 8, 9 17

18 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 3 5, Mark Crect response Additional guidance Finding x and y Mark Crect response Additional guidance Seventy U1 Indicates No and gives a crect explanation that shows implies at least one odd fact Facts of 70 are 1, 2, 5, 7, 10, 14, 35 and 70, so some are odd and some are even There are four odd facts and four even facts of 70 It could be 1 (odd) 5 14 = = is even, but 1 is odd and goes into everything Minimally acceptable explanation 1, 2, 5, 7, 10, 14, 35 and 70 7! Incomplete list of facts given Condone, provided none is increct and at least one odd fact is shown, accept The facts of 70 are 1, 2, 5 and 7 Incomplete increct explanation 70 has some odd and some even facts 70 is a fact of 1 All facts of 70 are odd 18

19 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 3 5, 4 6, Mark Crect response Additional guidance Units Completes all five rows of the table crectly, ie L A V M cm l miles g m 2 oz Completes at least three rows of the table crectly Mark Crect response Additional guidance Rainfest a a a 27 b b b 175 to 185 inclusive c c c Indicates January, ie 19

20 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 3 5, 4 6, Mark Crect response Additional guidance Doughnuts Indicates shop A and gives a crect justification, based on crectly calculating a pair of comparable values At shop A: 2 5 = 10, at shop B: 3.5(0) 3 = 10.5(0) = = 0.6( ), = 0.7 F 1 you get doughnuts 13 7 doughnuts You pay 1.50 extra f 2 me doughnuts, but at shop A they re less than 75p each so shop A must be a better deal Shows a crect pair of comparable values but makes either an increct no decision Shows a complete crect method f finding a pair of comparable values with not me than one computational rounding err, and follows through to make their crect decision 5 2, , shop A indicated 2 3 = 0.75 (err), = 0.7, shop B indicated Makes a crect decision but the justification uses only the difference between a pair of comparable values A doughnut is 3.3( )p cheaper at shop A!! F, no decision F, crect decision and any pair of comparable values shown Note that common pairs (in pounds) are: 10 and 10.5(0) (per 15 doughnuts) 0.6( ) and 0.7(0) (per 1 doughnut) 2 and 2.1(0) (per 3 doughnuts) 3.3( ) and 3.5(0) (per 5 doughnuts) 1.5 and 1.4( ) (doughnuts per pound) F, comparison is per 3 doughnuts per 5 doughnuts but the given price is not restated Condone, f accept At shop B, 3 doughnuts would be 2.10 Additional increct wking Igne 20

21 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 3 5, 4 6, Mark Crect response Additional guidance Stopping distances a a a Draws a bar f the stopping distance f 40mph of length 9cm, ie! Bar increctly positioned Condone if bar is drawn crectly one line above below the position shown 20mph 40mph b b b 18! Follow-through Allow follow-through as 2 the length of their bar in (a), provided the result is greater than 12 Marking overlay available Mark Crect response Additional guidance Rotate 180 Draws the crect shape with all four vertices within the tolerances as shown on the overlay Shows at least three vertices within the tolerances as shown on the overlay Shows a crect shape in the crect ientation, with all four vertices within the tolerances as shown on the overlay, but in an increct position on the grid! Lines not ruled accurate Accept provided the pupil s intention is clear Mark Crect response Additional guidance Value 196 Incomplete processing

22 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 3 5, 4 6, Mark Crect response Additional guidance 12 cubes Draws a 1 by 1 by 12, a 1 by 3 by 4 a 2 by 2 by 3 cuboid, using the isometric grid 1 by 2 by 6 cuboid repeated F, internal lines omitted, f accept! F, hidden lines shown F, accept provided they are clearly indicated as hidden lines, f accept The only err is to omit some external lines to show some hidden lines!! Lines not ruled Accept provided the pupil s intention is clear Drawing not accurate Accept vertices within m of the dots of the grid Isometric grid not used crectly Crectly draws a possible 3-D shape made from 12 cubes that is not a cuboid, using the isometric grid! Other shapes drawn As these could be trials, igne 22

23 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 3 5, 4 6, Mark Crect response Additional guidance Cost of delivery a a a Gives both crect values crectly positioned, ie 7 then 20 Range given instead of Gives a crect value with the crect unit f that value 25p 25 pence 0.25 b b b

24 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 3 5, 4 6, Mark Crect response Additional guidance Shape area a a a Gives a shape with area a + 2b, ie 16 small triangles! Lines not ruled accurate Accept provided the pupil s intention is clear Internal lines shown, f part (a) Shape fmed with triangles and trapezium not joined side to side, f part (a)! Other shapes drawn As these could be trials, igne b b b Gives a shape with area a b, ie 4 small triangles U1 24

25 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 4 6, 5 7, Mark Crect response Additional guidance Midpoints Gives P as (30, 35) Gives Q as (42, 0)! Answers f P and Q transposed but otherwise completely crect If this is the only err, ie gives P as (42, 0) and gives Q as (30, 35), mark as 0, 1 U1 Gives R as (42, 35)! Follow-through f R as (their x codinate of Q, their y codinate of P) Allow follow-through provided their codinates f P, Q and R are different 25

26 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 4 6, 5 7, Mark Crect response Additional guidance Rainfall U1 Indicates place A and gives a crect justification = 160cm = 150cm ( ) 12 = 13.( )cm per month ( ) 12 = 12.5cm per month ( ) 2 = 80cm per 6 months ( ) 2 = 75cm per 6 months Gives a crect justification, even if the decision is increct omitted Shows a complete crect method with not me than one computational err, and follows through to make their crect decision = 120 (err) = 150, so place B F, minimally acceptable justification 160, 150 seen 80, 80 and 50, 100 seen > ( ), 12.5 seen Mark Crect response Additional guidance Thinking distances a a a 315 Shows the value 245 b b b 50 Shows a complete crect method, in which the squared has been crectly interpreted, with not me than one computational err = 4900, = 2450 (err), =

27 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 4 6, 5 7, Mark Crect response Additional guidance Two shapes 60 Shows the value 6 U1 Shows a complete crect method with not me than one computational err = 8 (err), 10 8 = Mark Crect response Additional guidance Recycling Shows the value Shows a complete crect method with not me than one err million = (err) =

28 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 4 6, 5 7, Mark Crect response Additional guidance Shapes on a grid a a a Gives a crect explanation The most common crect explanations: Refer to the sum of the angles in a triangle The angles are equal and add up to 180, so = 60 Angles in a triangle add up to 180, the three angles are equal so = 180 Minimally acceptable explanation = 180 The angles are the same and add up to 180 Incomplete explanation The three angles add up to 180 Angles in a triangle add up to 180 The three angles are equal 60 3 It s an equilateral triangle b b b U1 Refer to the sum of angles at a point You can see that six of the triangles fit together at a point, so = Total: 360 Gives all three crect angles, ie a = 60, b = 120 and c = 240 Gives two crect angles Minimally acceptable explanation = 360 Incomplete explanation Six of the angles add up to 360 Angles at a point add up to ! F, follow-through Provided their b is obtuse, accept c as 2 their b 360 their b 28

29 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 4 6, 5 7, Mark Crect response Additional guidance Five bags Matches all four bags to the crect probabilities, ie A 1 4! F, bag matched to me than one probability Do not accept as a crect match B 1 3 C 1 2 D 5 11 E 2 5 Matches two of the four bags to the crect probabilities Mark Crect response Additional guidance Bicycles U1 184 Shows implies a complete crect method with not me than one computational err = 22 (err), 22 8 = is 46, so 4 is 82 (err), 8 so total is 164 Digits 184 seen 29

30 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 5 7, Mark Crect response Additional guidance Eggs Indicates the grade is medium and shows implies a crect method f calculating the mass of the g that interprets the cubed crectly, even if a final value is not shown Value between 60 and inclusive seen π π Makes an increct no decision about the grade of the g, but shows implies a crect method f calculating the mass of the g that interprets the cubed crectly, even if a final value is not shown π Shows implies a crect method f calculating the mass of the g that interprets the cubed crectly, with not me than one computational rounding err, and makes their crect decision f the grade of the g (err) = 57.( ), so medium = 166 (premature rounding), = 59.9( ), so medium F, final value and decision not shown within a method containing a computational rounding err F, conceptual err = 16.5, 16.5 π = 5.9( ) 6, so small 30

31 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 5 7, Mark Crect response Additional guidance Ring size a a ( ) 57.2 b b Indicates size 6 and gives a crect justification 51 π = 16.2( ) = 16.2( ) 16.5 π = 51.8( ) π = 49.( ) 16.5 π = 51.8( ) and 15.7 π < 51 Shows a crect justification but makes an increct no decision Indicates size 6 and gives an incomplete justification 51 π ( ) ( ) 15.7 π < 51 F, minimally acceptable justification 16.2( ) 49.( ) and 51.8( ) 52 seen F, incomplete justification 51 π π = 51.8( ) F, increct no justification alongside a crect decision 51 3 = 17, so size 6 Because the circumference of a size 6 is 51 31

32 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 5 7, Mark Crect response Additional guidance Missing power Shows crect wking and gives the value of x as = = = 243, 10 2 = = 49, 49 7 = 7 343! Value embedded Accept provided there is no ambiguity and crect wking is shown, f accept 7 3 shown in crect wking, f do not accept 7 3 on the answer line, even with crect wking = Gives the value of x as 3, even if wking is incomplete omitted Shows the value 343 Shows the values 243 and

33 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 5 7, Mark Crect response Additional guidance School size U1 Shows that the average number of pupils in a secondary school is about four times as many as the average number in a primary school Primary school: = 230.( ) ( 231) Secondary school: = 979.( ) ( 980) = 4.2( ) = 5.2( ) = 1.2( ) 5.2( ) 1.2( ) = 4.2( ) 4.3 recurring Shows the values 230.( ) ( 231) and 979.( ) ( 980) Shows the intention to divide the total number of pupils by the number of schools f both caties using any reasonably rounded values , , , F, minimally acceptable justification 979.( ) 230.( ) ( ) 980, = , = Mark Crect response Additional guidance Container 15 Shows implies a complete crect method with not me than one err (40 20) Shows the digits 15 33

34 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 5 7, Mark Crect response Additional guidance nth term expressions 3m Completes all three rows of the table crectly, ie Expression nth term expression? 4th term 5n No n + 11 No 11n 6 Yes 38 n 2 (6 n) Yes 32 Completes two rows of the table crectly Completes either the row f the expression 11n 6 the row f the expression n 2 (6 n) crectly Completes the middle column of the table crectly, even if the right-hand column is increct omitted Unambiguous indication of Yes No Space f 4th term left blank f the expression n

35 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 5 7, Mark Crect response Additional guidance Exam 90 F, reference to 100 marks 90 out of Shows implies a complete crect method Total mark on 6 units must be 80 6 = 480 Total so far = 78 5 = = 2, 2 5 = 10, Shows the value Shows implies a complete crect method with not me than one computational err Total mark on 6 units must be 80 6 = 420 (err) = = 2, 2 5 = 10,

36 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 5 7, Mark Crect response Additional guidance Equations a a Indicates both crect equations, ie b b Gives two pairs of codinates f which y = x + 1 and gives a crect equation (3, 4) and (0, 1) y = x + 1 (1, 2) and (2, 3) x = y 1 ( 2, 1) and 1 2, 11 2 y x = 1! Unconventional notation, f y = x + 1 y1 = 1 x + 1 Condone Mark Crect response Additional guidance House sales a a b b ! Value rounded Accept 33 better c

37 2009 KS3 Mathematics test mark scheme: Paper 2 Tier 6 8 only 18 Mark Crect response Additional guidance Standard fm Indicates and , in either der Unambiguous indication, f part (a) and Mark Crect response Additional guidance Greater a d, by 7 b f, by 1 20 Mark Crect response Additional guidance Three years old thousand Shows the value ( ) Shows a complete crect method with not me than one computational rounding err, even if their value is not rounded to the nearest thousand (premature rounding) 0.98 = F, conceptual err =

38 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 6 8 only 21 Mark Crect response Additional guidance Height ( ) Method used is accurate scale drawing Shows implies a crect trigonometric ratio 17 sin 25 h = sin cos 65! F, answer of 7 Do not accept unless a crect method a me accurate value is seen! Units given Igne 22 Mark Crect response Additional guidance Fewest men 115 Shows the digits 114( ) 115 Shows a complete crect method with not me than one computational rounding err = 1.1 (premature rounding), = Mark Crect response Additional guidance Daisies a 32 b 7 c 25 38

39 2009 KS3 Mathematics test mark scheme: Paper 2 Tier 6 8 only 24 Mark Crect response Additional guidance Using Pythagas U1 20.8( )! Value of Do not accept unless a crect method a me accurate value is seen Shows implies a crect method, using Pythagas theem, f calculating the length of the missing side of the right-angled triangle with a hypotenuse of 22cm x 2 = x = 84 ( ) ! F, value rounded truncated Accept 9.1( ) 9.2 Do not accept 9 unless a crect method a me accurate value is seen 39

40 2009 KS3 Mathematics test mark scheme: Paper 2 Tiers 6 8 only 25 Mark Crect response Additional guidance Booklet 3m 60 Shows a crect value f the mass of the booklet Shows implies a crect method with not me than one err omission, and follows through to give their value crect to 2 significant figures, provided some rounding is required = , = , so [failure to convert to m 2 ] (err) = , = , so [increct conversion to m 2 ] = 10 [failure to find mass of 6 pages] Shows implies a crect method with not me than one err omission, even if their value is not given crect to 2 significant figures = , (err) = = 9.9( )! F, value rounded truncated Accept 59, 59.8( )

41 2009 KS3 Mathematics test mark scheme: Paper 2 Tier 6 8 only 26 Mark Crect response Additional guidance Hemisphere Completes the table crectly with two fully simplified expressions, ie Radius Volume Surface area r 2 3 πr3 3πr 2 Gives one crect and fully simplified expression Gives both crect, unsimplified expressions Radius Volume Surface area r 4 3 πr3 2 2πr 2 + πr 2 Radius Volume Surface area r 4 6 πr3 3πr r 41

42 2009 KS3 Mathematics test mark scheme: Paper 2 Index Index to mark schemes Tier Question Page 1 School shop 10 2 Missing numbers 10 3 Parcels 10 4 Joining 11 5 Spinner 12 6 Fractions 12 7 Number of sides 13 8 Grid 13 9 Digital Reflecting Test Rounding Castle Baby Count on Shoe sizes Finding x and y Seventy Units Rainfest Doughnuts Stopping distances Rotate Value cubes Cost of delivery Shape area 24 42

43 2009 KS3 Mathematics test mark scheme: Paper 2 Index Tier Question Page Midpoints Rainfall Thinking distances Two shapes Recycling Shapes on a grid Five bags Bicycles Eggs Ring size Missing power School size Container nth term expressions Exam Equations House sales Standard fm Greater Three years old Height Fewest men Daisies Using Pythagas Booklet Hemisphere 41 43

44 QCA wishes to make its publications widely accessible. Please contact us if you have any specific accessibility requirements. 29 Bolton Street London W1J 8BT Telephone: Minicom: Fax: Website: First published 2009 Qualifications and Curriculum Authity 2009 ISBN Reproduction, stage, adaptation translation, in any fm by any means, of this publication is prohibited without pri written permission of the publisher, unless within the terms of licences issued by the Copyright Licensing Agency. Excerpts may be reproduced f the purpose of research, private study, criticism review, by educational institutions solely f educational purposes, without permission, providing full acknowledgement is given. Printed in Great Britain by the Qualifications and Curriculum Authity under the authity and superintendence of the Controller of Her Majesty s Stationery Office and Queen s Printer of Acts of Parliament. The Qualifications and Curriculum Authity is an exempt charity under Schedule 2 of the Charities Act Qualifications and Curriculum Authity 83 Piccadilly London W1J 8QA F me copies: QCA Orderline, PO Box 29, Nwich NR3 1GN derline@qca.g.uk Tel: Fax: QCA/09/