GCSE MARKING SCHEME METHODS IN MATHEMATICS (LINKED PAIR PILOT)

Transcription

1 GCSE MARKING SCHEME METHODS IN MATHEMATICS (LINKED PAIR PILOT) JANUARY 01

2 INTRODUCTION The marking schemes which follow were those used by WJEC for the January 01 examination in GCSE METHODS IN MATHEMATICS (LINKED PAIR PILOT). They were finalised after detailed discussion at examiners' conferences by all the examiners involved in the assessment. The conferences were held shortly after the papers were taken so that reference could be made to the full range of candidates' responses, with photocopied scripts forming the basis of discussion. The aim of the conferences was to ensure that the marking schemes were interpreted and applied in the same way by all examiners. It is hoped that this information will be of assistance to centres but it is recognised at the same time that, without the benefit of participation in the examiners' conferences, teachers may have different views on certain matters of detail or interpretation. WJEC regrets that it cannot enter into any discussion or correspondence about these marking schemes. Page Unit 1 Foundation Tier 1 Unit 1 Higher Tier Unit Foundation Tier 10 Unit Higher Tier 1

3 METHODS - UNIT 1 FOUNDATION TIER Methods Unit 1 Foundation Tier January 01 Mark Comments 1. (a) (i) 0 (ii) ten million (b) (i) 11 (ii) 9 (iii) 8 (iv) 8 (c) (i) 10 (ii) 100. Number other than 1- Any three different numbers from 1 to. Head OR Tail Yellow (Dylan saves) (1/10 00 =)( ) 0 (No of weeks) 0/ 0. (He can afford the bike after) 7 (weeks) Look for: Clear workings and labelling Correct use of units eg, weeks QWC: Candidates will be expected to present relevant work clearly, with words explaining process or steps AND make few if any mistakes in spelling, punctuation and grammar QWC1: Candidates will be expected to present work clearly which is mostly relevant, with words explaining process or steps OR make few if any mistakes in spelling, punctuation and grammar and include units in their final answer 8 B QWC Eg, Odd (numbers) OR Even (numbers) OR any other correct answer e.g. 1,, or or a prime number. for any or correct entries for correct entries FT their 0 Any appropriate method eg 0 or 0 7 or 0 or 80 Any correct indication FT for equivalent level of difficulty QWC Presents relevant material in a coherent and logical manner, using acceptable mathematical form, and with few if any errors in spelling, punctuation and grammar. QWC1 Presents material in a coherent and logical manner but with some errors in use of mathematical form, spelling, punctuation or grammar OR evident weaknesses in organisation of material but using acceptable mathematical form, with few if any errors in spelling, punctuation and grammar. QWC0 Evident weaknesses in organisation of material, and errors in use of mathematical form, spelling, punctuation or grammar. 1

4 Methods Unit 1 Foundation Tier January 01 Mark Comments. (a) 9 (b) (i) -10 (ii) 1 0 or 0 1. Valid Reason 7 Valid Reason 10 Valid Reason / or (a) Correct diagram (b) 1, 18, (c) Number of seats = Number of tables(t) + (d) 0 (e) (8 )/ =0 9. (a) x + y (b) ( x ) =7 10. For correct in a form which allows comparison For all correct in a form which allows comparison /8, ½,,¾ 11. (a) x = y = 0 (b) a = 80 Noticing that b and b and 80 is 180 b= 0 B 8 for meeting any clues e.g., 1, 81, for meeting any two clues e.g. 1,,,, 7, 11, 1,... E marks dependent on B marks Eg 1=1 Eg 1 and itself goes into it. Only factors. Eg =100. Ten squared=100. Or seen in diagram. FT their 0 CAO Award for two correct entries Accept n for number of tables Award for + Do not accept add four FT for equivalent level of difficulty FT for equivalent level of difficulty Or equivalent method Must be an expression, as shown. Award for either of the terms correct within an expression or both terms correct but not in an expression. CAO Answer only gets. CAO FT their 80

5 Methods Unit 1 Foundation Tier January 01 Mark Comments 1. (a) 1 Head H1 H H H H H Tail T1 T T T T T (b) 1/1 (c) /1 1. (a) x 0 + x 11x - (b) x ( - y) 1(a) (= ) x indicated as ( =) 8( ) Two appropriate stages of explanation given, e.g. angles on a straight line 180 AND angles in a triangle 180, or corresponding angles or equivalent, or interior angles, or equivalent (b) Sight of 0( ) Showing or stating OR = 180 WITH straight line sum 180 stated Use of, or statement that, angles at a point add to 0( ) 1(a) All correct entries Fraction Decimal Recurring or terminating? /0 Terminating 0.( ) Recurring for at least correct entries Across parts (b) and (c), penalise incorrect notation, e.g. 1 in 1, once only. ISW FT for consistent incorrect denominator for x( - y) or x( -.) or correct partially factorised 1st step of appropriate working OR an appropriate ( ) indicated on the diagram. Allow even if then incorrectly assuming an isosceles trapezium FT their (=180 1) evaluated correctly May be on diagram, do not accept contradiction in answers for x in working space and on diagram Accept reference to C and F angles Allow FT for isosceles trapezium provided both stages explained, i.e. parallel fact and sum 0 If no marks: SC for x = 1 from an isosceles triangle with explanation of triangle sum 180 AND a parallel line fact, OR SC1 for x = 1 from an isosceles triangle Alternative method 1 8 = 8( ) Explanation: exterior angle of a triangle is the sum of the two other angles AND corresponding angle May be shown on a diagram, showing angles at a point, or a diagram showing they do tessellate FT their OR angle sum of the tile is 0( ). For award of 0( ) at a point MUST be stated, not simply implied If no marks then allow for the statement all quadrilaterals tessellate, then possible for an explanation, e.g. angle sum at a point is 0( ) /0. Do not accept 1/ Do not accept 0. unless 0. seen in working Terminating and recurring in the correct cells. CAO

6 Methods Unit 1 Foundation Tier January 01 Mark Comments 1(a) No AND a reason, e.g. y coordinate is not times the x coordinate, or a=- then a=-1 (b) All points plotted fit rule (a, a), with no incorrect plots Any counter example ((-, -1) or (-/, -)) must be relevant and correct with NO stated for at least correct plots and no more than incorrect plots, OR for sets of possible coordinates listed, which may be outside the grid 17(a) All 9 numbers placed correctly B for any 7 or 8 numbers placed correctly, the other numbers omitted or incorrectly placed, OR for any or numbers placed correctly, the other numbers omitted or incorrectly placed. Any ambiguous duplicates are marked as an incorrect placement for that number (b) Venn diagram AND full reason, e.g. multiples of are a subset of multiples of and there is a multiple of which is a multiple of, or set B is a subset of set A, and set A intersects with set C, or A & B share some of the numbers, but C only shares numbers with A, or C & B have nothing in common, and B shares everything with A E OR selects Venn diagram and explains why the other Venn diagrams are not selected for choice of Venn diagram AND a partial reason, i.e. only mentions 1 aspect or attempts an explanation e.g. times table is within times table, or shows which of A are within times table, or is in A but not in C, or no multiples of in C OR for selection of Venn diagram and explains why 1 of the other Venn diagrams are not selected Accept informal words such as within for subset, overlap for intersection

7 METHODS UNIT 1 HIGHER TIER Methods Unit 1 Higher Tier January 01 Mark Comment 1(a) (1 + 10)/(9 + ) (b) -18x y (c) (x + 7) (a) (= ) = x indicated as ( =) 8( ) Two appropriate stages of explanation given, e.g. angles on a straight line 180 AND angles in a triangle 180, or corresponding angles or equivalent, or interior angles, or equivalent Look for: Clear identification of any angles referred to on the diagram Use of degree symbol Appropriate use of = Use of correct terminology for angles, not C or F angles QWC: Candidates will be expected to present work clearly, with words explaining process or steps AND make few if any mistakes in mathematical form, spelling, punctuation and grammar and include units in their final answer QWC1: Candidates will be expected to OR (b) Sight of 0( ) present work clearly, with words explaining process or steps make few if any mistakes in mathematical form, spelling, punctuation and grammar and include units in their final answer Showing or stating OR = 180 WITH straight line sum 180 stated Use of, or statement that, angles at a point add to 0( ) QWC 8 Allow 1 error with a sign or 1 slip CAO Must be an expression as shown for either of the terms Do not ignore further work if then -1 ISW 1st step of appropriate working OR an appropriate ( ) indicated on the diagram. Allow even if then incorrectly assuming an isosceles trapezium FT their (=180 1) evaluated correctly May be on diagram, do not accept contradiction in answers for x in working space and on diagram Accept reference to C and F angles Allow FT for isosceles trapezium provided both stages explained, i.e. parallel fact and sum 0 If no marks: SC for x = 1 from an isosceles triangle with explanation of triangle sum 180 AND a parallel line fact, OR SC1 for x = 1 from an isosceles triangle Alternative method 1 8 = 8( ) Explanation: exterior angle of a triangle is the sum of the two other angles AND corresponding angle QWC Presents relevant material in a coherent and logical manner, using acceptable mathematical form, and with few if any errors in spelling, punctuation and grammar. QWC1 Presents relevant material in a coherent and logical manner but with some errors in use of mathematical form, spelling, punctuation or grammar OR evident weaknesses in organisation of material but using acceptable mathematical form, with few if any errors in spelling, punctuation and grammar. QWC0 Evident weaknesses in organisation of material, and errors in use of mathematical form, spelling, punctuation or grammar. May be shown on a diagram, showing angles at a point, or a diagram showing they do tessellate FT their OR angle sum of the tile is 0( ). For award of 0( ) at a point MUST be stated, not simply implied If no marks then allow for the statement all quadrilaterals tessellate, then possible for an explanation, e.g. angle sum at a point is 0( )

8 Methods Unit 1 Higher Tier January 01 Mark Comment (a) All correct entries Fraction Decimal Recurring or terminating? /0 Terminating 0.( ) Recurring (b) OR OR OR. OR 0.7 OR / (a) No AND a reason, e.g. y coordinate is not times the x coordinate, or a=- then a=-1 (b) All points plotted fit rule (a, a), with no incorrect plots (c) y = x (a) All 9 numbers placed correctly m1 B /0. Do not accept 1/ Do not accept 0. unless 0. seen in working Terminating and recurring in the correct cells. CAO OR any appropriate correct first calculation Place value must be correct for OR appropriate correct second calculation CAO. Allow sight of / Must be from correct working, watch for compensating errors. If no working then / allow m1 Any counter example ((-, -1) or (-/, -)) must be relevant and correct with NO stated for at least correct plots and no more than incorrect plots, OR for sets of possible coordinates listed, which may be outside the grid FT their points provided they fall on a straight line for attempt to find the gradient as /1, or y = a, or equivalent for any 7 or 8 numbers placed correctly, the other numbers omitted or incorrectly placed, OR for any or numbers placed correctly, the other numbers omitted or incorrectly placed. Any ambiguous duplicates are marked as an incorrect placement for that number (b) Venn diagram AND full reason, e.g. multiples of are a subset of multiples of and there is a multiple of which is a multiple of, or set B is a subset of set A, and set A intersects with set C, or A & B share some of the numbers, but C only shares numbers with A, or C & B have nothing in common, and B shares everything with A (c) /9 (=1/) 7/9 1/9 E 8 OR selects Venn diagram and explains why the other Venn diagrams are not selected for choice of Venn diagram AND a partial reason, i.e. only mentions 1 aspect or attempts an explanation e.g. times table is within times table, or shows which of A are within times table, or is in A but not in C, or no multiples of in C OR for selection of Venn diagram and explains why 1 of the other Venn diagrams are not selected Accept informal words such as within for subset, overlap for intersection FT their Venn diagram. FT a slip in the denominator used consistently FT a slip in the denominator used consistently

9 Methods Unit 1 Higher Tier January 01 Mark Comment (a) (10) (7/10) 1/0 0/0 /0 8/0 (0.7) or 0.7 Not 0. (b) Relative frequencies plotted accurately (c) Conclusion, no, as there is still a variation in relative frequencies, no, the results are not settled, results are still going down 7. Total of interior angles 180( ) = 900( ) 900 sum of angles given (9 ) (=0) (Each of the angles is) 10( ) 8(a) 18 (b) (1 9) = 1 (c) Two of the prime factors are and Other factor is either or 7 Missing number is 70 9(a) Correct sketch (b) Correct sketch (c) Correct sketch 10(a) with 0 evaluated as 8000 = 7879 (b) n + or equivalent m1 M 7 B Cumulative numbers 7, 1, 0,, 8 Fractions, FT their cumulative numbers Decimals, FT their cumulative numbers as quotients over cumulative denominators, correctly evaluated Ignore if points joined or not FT their relative frequencies provided no more than 1 is outside the range 0. to 0.8. for plots accurate. Do not accept FT answers of yes. Allow no, needs more to get a more accurate answer. Ignore further foolish comments. Do not accept no, need to throw more times Or equivalent full method FT their 900 provided >9 Unique division by, no further operations Alternative: Corresponding exterior angles are ( ), 0( ), 0( ) and 10( ) Remaining exterior angles = 0 sum of exterior angles found (1 ) (= ) m1 (Each of the remaining exterior angles =) 78( ) (Each of the remaining interior angles =) 10( ) FT provided,, m1, 180 their 78 for sight of each of 1 or 9 FT from provided simplified using surd notation if necessary An answer of 7 gets,, A0 Award all marks for sight of unsupported 70. An answer of 70 from incorrect working is not awarded all marks Example: An answer of 0 is,, A0 (as it meets, for factors and, with ) If no marks, allow SC1 for prime numbers which sum to 70 AND clues to are met, e.g Alternative: Considering multiples of a number which would include 10 Considering multiples of 10 which would include 10, i.e. multiples of 0 or 70 m1 Answer 70 FT reflection in x-axis of their (a) Accept full description in words or given in a fully labelled diagram for B, or as appropriate for 1n + (not for 1n ), OR for 1n or for sight of the nd difference 7

10 Methods Unit 1 Higher Tier January 01 Mark Comment 11(a) Correct entries 0.7 and 0. Other entries 0.8, 0. with 0.8 Labels correct for no cereal, no toast, toast and no toast (b) (a) (x + )(x -1) (b) dw = m m = dw/ m = (+) (dw/) = 0.0 (=/100) (c) ab bc = e b(a c) = e b = e a-c 1. Strategy, e.g. suitable outline of a suitable tree diagram Sight of P(man red) = 1/ or P(woman red) = /10 1/ /10 = /0 Conclusion greater than stated or implied, with reason, e.g. /100>/100 1(a) x + 1xy -1xy y (+ xy) = x y (b) 7x(x ) + (x + ) as a numerator (x + )(x ) as a denominator 1x -1x + x + 1x -10x + (x + )(x ) 1. Selecting y = x AND y = -x Showing that m 1 = ¼ and m = - ¼ - = -1 or equivalent 1(a) P indicated correctly, where XY touches the circle (b) WXY is a tangent meeting the circle radius at 90 Corresponding angles equal (angles at X and W) OR Supplementary angles OR shows or states both angles are 90 (c) <HBG=10 or <ABW= 80 or equivalent Reason, e.g. angle at the centre is twice the angle at the circumference 100 Reason, e.g. sum of angles in a quadrilateral is 0 (and right angle where tangent meets the radius) or allied (interior) angles m1 8 S1 7 7 In this order if no labels, otherwise as their label order Not a FT need to match probabilities. If labels incorrect B0, however allow previous for order 0.8, 0., 0.8 FT from their probability tree for only CAO. Allow for sight of an unsupported 0. for (x± )(x± ) Square root must clearly be over dw/ entirely If no marks SC1 for (w/d) from 1 initial error Collect FT until nd error Factorise Divide Listing WM, MW, MM, WW is not a suitable strategy The award of also implies S1 FT provided at least 1 other mark has been awarded. Accept if compared with %, i.e. same format for % and their answer for any of the expansion terms correct FT from. Mark final answer. Allow x + y Mark final answer. If the denominator is expanded it must be correct. FT from 1 error in numerator expansion, provided it is a trinomial Accept description in words Accept description in words 8

11 Methods Unit 1 Higher Tier January 01 Mark Comment 17(a) a = x + 8x + 1 (-11) OR alternative method to find b b = -11 (b) (x + ) 11 = 0 (x + ) = 11 x + = (+) 11 x = Accept embedded answers Accept embedded answers Use of completing the square from (a), FT from their (a) provided equivalent format Must show + Use of formula leading to (-8+ 11)/ gets, (-8+ )/ gets B0 9

12 METHODS UNIT FOUNDATION TIER Methods Unit Foundation Tier January 01 Mark Comments 1. (a) 19 (b) 91. % and /8. ( ) 0 x ( ) or p. (a) D and E B and H A for 1 correct and no more than 1 incorrect OR for correct and 1 incorrect Allow 0.0p for 0.0 or with wrong units or no units Accept triangle(s) Accept circle(s) (b) Diameter Tangent. (a)(i) 8 cm³ U1 Independent of all other marks. ii) (Yes and Volume = ) implied or drawn (b) 8 =10 ( cm³). (a) Correct diagram (b) 7. (a) 8 pancakes 1 pancakes 80 pancakes Flour 100g 00(g) 1000g B for straight lines correct or for correct curve for each correct entry Eggs 1 10 Milk 0(ml) 00(ml) 00ml Melted Butter 1 tablespoon tablespoons 10 tablespoons Raspberries 10g 00g 100(g) (b) 100 :10 or equivalent : ISW FT their flour for 1 pancakes or their raspberries for 80 pancakes Award SC1 for : 10

13 Methods Unit Foundation Tier January 01 Mark Comments 8. (a) /100 x =( ) 11.9 (b) /9 x = For correct in a form which allows comparison For all correct in a form which allows comparison 7%, ¾, (a) a=8 a=1 a= (b) Equation with answer x=10 Equation with answer t =- 11.(Width of rectangle=) / 9 = cm (Perimeter=) =8cm Look for: Area = length x width Explanation of perimeter Correct use of Units QWC: Candidates will be expected to present relevant work clearly, with words explaining process or steps AND make few if any mistakes in spelling, punctuation and grammar QWC1: Candidates will be expected to present work clearly which is mostly relevant, with words explaining process or steps OR make few if any mistakes in spelling, punctuation and grammar and include units in their final answer 1. (a) x= (b) y = 0 (c) a = a = (d) b = (e) d=8 (d=) 8/ 1.(0) QWC 8 FT their width QWC Presents relevant material in a coherent and logical manner, using acceptable mathematical form, and with few if any errors in spelling, punctuation and grammar. QWC1 Presents material in a coherent and logical manner but with some errors in use of mathematical form, spelling, punctuation or grammar OR evident weaknesses in organisation of material but using acceptable mathematical form, with few if any errors in spelling, punctuation and grammar. QWC0 Evident weaknesses in organisation of material, and errors in use of mathematical form, spelling, punctuation or grammar. Allow embedded answers in all parts FT from 1 error for equation in the form ma=n, m 1 OR realising drinks cost 8 11

14 Methods Unit Foundation Tier January 01 Mark Comments 1. Enlargement scale factor 1. (a) (b).7 (c) 10 (d) 0. (e) x>1 x> 1 (a) ½...9 (cm ) or.(cm ) (b) (hypotenuse =). +. h(ypotenuse) =. or hypotenuse =. h(ypotenuse =) (.1 cm) 1.(a) πr = π (cm) 8 for any two lines correct or points correct for 10.(199 ) for 0.7 rounded or truncated CAO Only accept (cm ) from correct working Allow FT from, A0 For equating, or r =, or r = If no marks allow SC1 for.9(9..cm) from calculation (b) (Perimeter) x + x + x x 8 = 1 x - = 1 or x = 18 x = (Height of the trapezium (x 8)cm =) 1 (cm) 17. Position Name 1 Catrin (...)% Debbie (.1 )% Beatrice 1% Abbie 7(.8 )% 7 B Algebraic notation not required for M, A and B marks FT their sum of terms, including x and number terms, equated to 1 FT their collection for equivalent difficulty FT for evaluation, not left as a fraction FT their x-8 provided M awarded Alternative: Trial and improvement Trial to sum the correct sides Clearly working towards 1, more than 1 trial and moving closer Clearly working towards 1, one below and one above (Height) 1(cm) FT their x-8provided M awarded Names in the correct order and all results appropriately and correctly compared (same form) for at least results correctly in a suitable format to compare and their comparisons appropriately sorted for at least results correctly in a suitable format to compare and their comparisons appropriately sorted, OR for at least results correctly in a suitable format to compare Remember: format of 1 of the result with others to compare counts as results If no other marks, then award SC1 for names in the correct order If fractions used for comparison they need to be common denominators or awareness of size, e.g. 1/ =9/7 compared with 9/8 same numerator Fractions: Catrin 8/8, Debbie 7/8 (=9/8), Beatrice /8, Abbie /8 Marks: Catrin 8, Debbie 7, Beatrice, Abbie 1

15 Methods Unit Foundation Tier January 01 Mark Comments 18.(a) /1 ISW (b) ( 00 ) 1. ( ) 0.7 or equivalent, in either order for sight of 1, e.g. /1 or ++8 for sight of either 1. or 1/100 OR for 0.7 or 7/100 If no marks SC1 for sight of 8.0 1

16 METHODS UNIT HIGHER TIER Methods Unit Higher Tier January 01 Mark Comment 1.(a) 0 (b) 1x 9 = OR x 1 = / 1x = 8 OR x = 8 x = 7 (c) x + = 1 x = (a) Kite 1 1 B Parallelogram 0 Rhombus FT until nd error Or x/1 = - /1 for 0.7 rounded or truncated for any or correct entries, for any or correct entries Allow 0 in top right hand cell (b) πr = π. (cm) Position Name 1 Catrin (...)% Debbie (.1 )% Beatrice 1% Abbie 7(.8 )%.(a) /1 ISW (b) ( 00 ) 1. ( ) 0.7 or equivalent, in either order (c)(i) / 1 ¼ or 1min per cm or cm in 1 min or 1cm in min ½ (hour) or 0 (minutes) (ii) 0/7 or min per 1cm or cm in 1 min or 1cm in min 0/7 or 0... or... or 0/ or (⅓ or)0...cm in 1 min or... cm in 10 min.7 (cm) B 9 For equating, or r =, or r = If no marks allow SC1 for.9(9..cm) from calculation Names in the correct order and all results appropriately and correctly compared (same form) for at least results correctly in a suitable format to compare and their comparisons appropriately sorted for at least results correctly in a suitable format to compare and their comparisons appropriately sorted, OR for at least results correctly in a suitable format to compare Remember: format of 1 of the result with others to compare counts as results If no other marks, then award SC1 for names in the correct order If fractions used for comparison they need to be common denominators or awareness of size, e.g. 1/ =9/7 compared with 9/8 same numerator Fractions: Catrin 8/8, Debbie 7/8 (=9/8), Beatrice /8, Abbie /8 Marks: Catrin 8, Debbie 7, Beatrice, Abbie for sight of 1, e.g. /1 or ++8 for sight of either 1. or 1/100 OR for 0.7 or 7/100 If no marks SC1 for sight of 8.0 Do not accept / 1.1, recording of time must be correct If units are given they must be correct FT from (c)(i) FT their depth corrected to significant figures 1

17 Methods Unit Higher Tier January 01 Mark Comment. (Perimeter) x + x + x x 8 = 1 x - = 1 or x = 18 x = (Height of the trapezium (x 8)cm =) 1 (cm) Look for the use of notation (watch for the use of = being appropriate) steps shown, not x = / labels given perimeter, height (in trial and improvement, the trials and choices need to be clearly explained) QWC: Candidates will be expected to present work clearly, with words explaining start, process or steps AND make few if any mistakes in mathematical form, spelling, punctuation and grammar in their answer QWC1: Candidates will be expected to OR present work clearly, with words explaining start, process or steps make few if any mistakes in mathematical form, spelling, punctuation and grammar in their answer 7.(a) b = c OR c = ½ b ISW (b) n + 7 < n < OR n < / n < 9 8.(a) Correct rotation (b) Correct enlargement (scale factor ) in lower left quadrant Correct position 9.(a) Semi C = ½ π (cm) to 1.9( cm) (b) Volume = π (...) to.( ) cm Q W C 7 m1 U1 Algebraic notation not required for M, A and B marks FT their sum of terms, including x and number terms, equated to 1 FT their collection for equivalent difficulty FT for evaluation, not left as a fraction FT their x-8 provided M awarded Alternative: Trial and improvement Trial to sum the correct sides Clearly working towards 1, more than 1 trial and moving closer Clearly working towards 1, one below and one above (Height) 1(cm) FT their x-8provided M awarded QWC Presents relevant material in a coherent and logical manner, using acceptable mathematical form, and with few if any errors in spelling, punctuation and grammar. QWC1 Presents relevant material in a coherent and logical manner but with some errors in use of mathematical form, spelling, punctuation or grammar OR evident weaknesses in organisation of material but using acceptable mathematical form, with few if any errors in spelling, punctuation and grammar. QWC0 Evident weaknesses in organisation of material, and errors in use of mathematical form, spelling, punctuation or grammar. Do not accept use of = in (b) FT from 1 error FT only for a whole number answer for a near miss or for 90 anticlockwise rotation appropriate FT to lower left quadrant Accept 1(cm) from correct working For answer of 9.7(...) allow and SC1 If no marks SC1 for sight 19.(7...) to 19.(8...) or.(7...) to.(8...) Independent mark 1

18 Methods Unit Higher Tier January 01 Mark Comment 10(a) ½...9 (cm ) or.(cm ) (b) (hypotenuse =). +. h(ypotenuse) =. or hypotenuse =. h(ypotenuse =) (.1 cm) 11.(a) x = = (b) y = = (a) PQ =..88 / 8. (b) BC =. (.88 / 8.) or equivalent or equivalent.9(cm).(cm) 1. Third angle 0( ) or 8( ) Statement that this implies similar Statement sides could be different clearly implies not necessarily congruent 1. Rearrange of equation(s) to format that could lead to a solution Method to find first variable, e.g. equal coefficients, equating a variable to give equation in 1 variable First variable Method to find second variable, e.g. substitution shown for first variable Second variable 1. - (x + 7y) + x + y = x y 1.(a) Statement C selected Reason, e.g. inverse implies the nature is opposite (b) f α 1/g OR f = k/g = k/ f = 100/g (c) g 1/ (+)100 f BC = 8./cos1 BC = 8.9(07.) Tan AĈB =.8/BC AĈB = tan (.11 ) A A m1 7 M Only accept (cm ) from correct working Allow FT from, A0 Intention to multiply for or or equivalent including to sig. figs. Intention to subtract in the correct order for or or (attempt standard form) or equivalent including to sig. figs. Or equivalent calculation that could lead to correct answer Accept.9(cm) FT premature approximation of the scale factor or equivalent premature approximation Or equivalent calculation that could lead to correct answer (Alternative: scale factors 0.7 or 10/7 may be used) Depends on the Accept Thomas is correct because sides may be different. Award this without previous and. e.g. x + y = 1 with x - y = -0, or making either x or y the subject FT from 1 error in rearrangement only Allow 1 error, but not in non equate variable FT their first variable x = - and y = 8 Allow for intention of using -OA + OB, e.g. -x+7y+x+y or x + 9y Accept 1x y Accept numerical examples Do not accept a repeat of the statement given FT non linear only Maybe implied in part (b) FT their non linear expression for each value for cos 1 = 8./BC FT their BC provided not 8. or.8 OR alternative using AC, following evaluation of AC using Pythagoras Theorem 1

19 Methods Unit Higher Tier January 01 Mark Comment 18. x = z or x = z x + y AC x + y z + BC AC = z(x + y) or x(z + BC) = z ( x + y) x BC = z(x + y) - z or xz + xbc = xz + yz x BC = xz +yz - z or x BC = yz x BC = yz/x 19. General cosine curve with appropriate orientation and position 1 and -1 indicated on y-axis, passes through (0, 1), (90,0), (-90,0) and approximately (-180,-1) and (180,-1) General tan curves with appropriate orientation and position Correct indication or use of asymptotes 0. Use of area = ½ absinc and cosine rule ½.9 x sin 9 =.8 x =.8/(½.9 sin 9 ) x = (cm) rounded or truncated (longest side y) y =.9 + x -.9 x cos9 y accept values between 1 and 1.1 y = 1.8 (cm) m1 S1 7 Or alternative correct first step Rearranged in form AC= FT BC = AC z provided AC in terms of x, y or z Or alternative correct stage of manipulation CAO If no marks then SC for BC=yz/x without working, OR SC1 for BC/y = z/x or BC/z=y/x or equivalent If no marks, SC1 for slight error in tends to infinity or idea of the shape of tanx Correct rearrangement FT their x, not.9 or spurious value Accept 1(cm) from correct working, not scale diagram Final depends on previous GCSE Methods in Mathematics MS January 01 17

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