Mark Scheme Sample Assessment Material GCSE GCSE in Mathematics Specification A Higher Tier Paper 2: (Calculator) Edexcel Limited. Registered in England and Wales No. 4496750 Registered Office: One90 High Holborn, London WC1V 7BH General Marking Guidance x All candidates must receive the same treatment. Examiners must mark the first candidate in exactly the same way as they mark the last. x Mark schemes should be applied positively. Candidates must be rewarded for what they have shown they can do rather than penalised for omissions. x All the marks on the mark scheme are designed to be awarded. Examiners should always award full marks if deserved, i.e. if the answer matches the mark scheme. Examiners should also be prepared to award zero marks if the candidate’s response is not worthy of credit according to the mark scheme. x Where some judgement is required, mark schemes will provide the principles by which marks will be awarded and exemplification may be limited. x Crossed out work should be marked UNLESS the candidate has replaced it with an alternative response. x Mark schemes will indicate within the table where, and which strands of QWC, are being assessed. The strands are as follows: i) ensure that text is legible and that spelling, punctuation and grammar are accurate so that meaning is clear Comprehension and meaning is clear by using correct notation and labelling conventions. ii) select and use a form and style of writing appropriate to purpose and to complex subject matter Reasoning, explanation or argument is correct and appropriately structured to convey mathematical reasoning. iii) organise information clearly and coherently, using specialist vocabulary when appropriate. The mathematical methods and processes used are coherently and clearly organised and the appropriate mathematical vocabulary used. Guidance on the use of codes within this mark scheme M1 – method mark A1 – accuracy mark B1 – working mark C1 – communication mark QWC – quality of written communication oe – or equivalent cao – correct answer only ft – follow through sc - special case Edexcel GCSE in Mathematics A Sample Assessment Materials © Edexcel Limited 2009 155 156 Edexcel GCSE in Mathematics A Sample Assessment Materials © Edexcel Limited 2009 Edexcel GCSE in Mathematics A Sample Assessment Materials © Edexcel Limited 2009 157 5. (c) (b) (a) 1MA0/2H Question Old median = 22 New median = 22 + 5 Key 4 I 6 means 46 minutes 0: 8 1: 023578 2: 0122233 3: 1345 4: 456 Working The same + reason 27 minutes Correct stem and leaf Answer 1 2 3 Mark Total for Question: 6 marks C1 All the values have increased by 5 minutes so when you subtract the 5 minutes will cancel out. M1 finds median correctly for original data and adds 5 A1 cao OR M1 Redoes table (ft) with each value increased by 5 and attempts to find median A1 cao B3 Fully correct (B2 All entries correct, no key) (B1 correct entries unordered, key or no key) OR (B2 Three rows correct, key or no key) (B1 Two rows correct, key or no key) Additional Guidance 158 Edexcel GCSE in Mathematics A Sample Assessment Materials © Edexcel Limited 2009 7. 6. FE QWC ii, iii (b) (a) 1MA0/2H Question 10 45 150 245 225 55 120 “908000” cm3 × 0.85 g/cm3 = 771800 g 224 > 200 1017.876 ÷ 4.54 = 224 gallons Vol of tank 602 u ʌ u 180 = 2035752.04..cm3 Half vol of tank = 1017876.02 cm3 = 1017.876…litres OR 908000< 1017876.02 1 gallon = 4.54 litres, 200 gallons = 908 litres = 908000 cm3 Vol of tank 602 u x ʌ u 180 = 2035752.04..cm3 Working 6.08 hours 771.8 No Answer 4 3 5 Mark Total for Question: 8 marks Total for Question: 4 marks M1 for mid interval values M1 for multiplying frequencies by mid-interval values M1 for adding (freq u mid-interval values) ÷ 120 A1 cao M1 “908000” × 0.85 M1(dep) 771800÷1000 A1 770 — 772 C1 Decision and reason QWC: Decision should be stated, with appropriate supporting statement M1 Using formulae to find volume of tank B1 Converts between litres and cubic centimetres M1 reads off graph for 1l, 2l , 4l, 5l or 10 litres within tolerance (4.4 — 4.6) A1 Answer in cm3, litres or gallons Calculations may be performed in different orders Response may convert into gallons, litres, or cm3 Additional Guidance Edexcel GCSE in Mathematics A Sample Assessment Materials © Edexcel Limited 2009 159 8. (b) (a) 1MA0/2H Question 170 x x 10 3 2 170 5 x 30 6 170 2 x 3 ( x 10 ) 6 x 210 5x = 1050 x x 10 3 2 2x + 3(x – 10) = 170 u 6 5x = 1050 x = 210 OR x x 10 3 2 Fred has 2 x left, so solving 3 for x using pays x 10 2 Malcolm gets £170 for Fred and Jim, so Malcolm gets x and Jim 3 Fred pays Working £140 Clear and coherent explanation Answer 4 1 Mark A1 cao Total for Question: 5 marks M1(dep) multiply through by 6 and collect terms M1 collects terms over 6 M1(dep) expand 3(x í 10) OR A1 cao M1 (dep)collect terms on each side correctly M1 multiply through by 6 and cancels fractions M1 (dep)expand 3(x í 10) C1 a clear and coherent explanation Additional Guidance 160 Edexcel GCSE in Mathematics A Sample Assessment Materials © Edexcel Limited 2009 FE 9. QWC i, iii 1MA0/2H Question Makes a comparison of the shape of the distribution by drawing Makes a comparison of the modal classes(31—40, 11—20) Makes a comparison of the class intervals that contain the medians.(31—40, 21—30) Works out an estimate of the total sales of each shop(2635, 3530) Working Correct comparisons Answer 4 Mark Total for Question: 4 marks C1 for comments on shape of the distributions QWC: Decisions should be stated, and all comments should be clear and follow through from any working or diagrams Plots frequency polygon or produces table compares modes compares medians compares total sales B1, B1, B1 for any 4 of the following done correctly Additional Guidance Edexcel GCSE in Mathematics A Sample Assessment Materials © Edexcel Limited 2009 161 162 Edexcel GCSE in Mathematics A Sample Assessment Materials © Edexcel Limited 2009 FE 12. QWC ii, iii FE 11. (c) sin 68 = AC 8.5 AC = 8.5 × sin 68o = 7.881 7.881 + 1 < 9 o 15% of 80 = 12 Reason supported by calculation Yes, with correct conclusion 26 68 – 42 (b) Answer 28 Working (a) 1MA0/2H Question 4 2 2 1 Mark 1 sq tolerance on each) 2 Total for Question: 5 marks AC Note AC sin 68 8.5 u sin 68 sin 90 Total for Question: 4 marks 8.5 does not get marks until in the form sin 90 C1 8.88(1… + conclusion QWC: Decision should be stated, supported by clearly laid out working M1 sin 68 = AC 8.5 M1 AC = 8.5 × sin 68o A1 7.88(1… o M1 looks up 68 or 40 min on cumulative frequency A1 correct conclusion A1 26 — 30 (need M1 68 — 42 B1 27 — 29 Additional Guidance Edexcel GCSE in Mathematics A Sample Assessment Materials © Edexcel Limited 2009 163 13. 1MA0/2H Question k A 4 A 4 60 A1 for 30.98… or 31.0 Total for Question: 4 marks Additional Guidance 60 oe 100 60 oe 100 40 u T = 40 M1 for T M2 for OR A1 for 30.98… or 31(.0) 4 A A1 T M1 T T T 4 Mark M1 40 = k 100 31.0 Answer T k A ; 40 = k 100 k=4 Working 164 Edexcel GCSE in Mathematics A Sample Assessment Materials © Edexcel Limited 2009 Edexcel GCSE in Mathematics A Sample Assessment Materials © Edexcel Limited 2009 165 17. 16. (b) (a) 1MA0/2H Question 220 sin 47 sin 75 = 166.57.. 220 AB ( ) sin 75 sin 58 = 15538 1 u 220u'166.57 'u sin 58 Area= 2 AC = AC sin 47 Angle BAC = 180º — 47º — 58º = 75º (4) r (4)2 4u 2u(51) 2u 2 4 r 424 x 4 x Vol = x u ( x 2 ) u 2 = 51 Vol = 2 x 2 4 x – 51 =0 Working 15500 m 5 3 6.15, -4.15 both to 3sf 2 4 Mark Derives given answer and condition Answer 4r 4 424 1 × 220 × “166.57” × sin58 2 A1 15500 m2 M1 AC 220 AB ( ) sin 58 M1 sin 47 sin 75 220 sin 47 M1 AC = sin 75 B1 for 75º A1 6.14(7…, î 4.14(7…) M1 x Total for Question: 5 marks Total for Question: 7 marks M1 correct substitution (allow sign errors in a, b and c) into quadratic formula M1 Vol = x u ( x 2 ) u 2 M1 expands bracket correctly A1 (E1) sets equal to 51 B1 x ! 2 as the lengths of the cuboid have to be positive. Additional Guidance 166 Edexcel GCSE in Mathematics A Sample Assessment Materials © Edexcel Limited 2009 18. 1MA0/2H Question sin 72 Using right-angled trigonometry; h = 5tan54º = 6.8819… Area of isosceles triangle = 1 u 10 u h 2 = 34.40954801… area of pentagon = 5 u 34.40954801 = 172.0477401 area of dodecahedron = 12 u 172.0477401 OR = 34.40954801.. area of pentagon = 5 u 34.40954801 = 172.0477401 area of dodecahedron = 12 u 172.0477401 1 2 x sin 72 2 area of isosceles triangle = 8.506508084… sin 54 Pentagon = 5 equal isos triangles 360 =72º 5 Base angles = (180 – 72) y 2 = 54º for finding equal sides of isosceles triangle; x 10 = Working 2065 cm 2 Answer 9 Mark x sin 54 2 10 sin 72 A1 for 34.40954801…(ft) B1 for area of pentagon = 5 u (ft) = 172.0477401…(ft) B1 for area of dodecahedron = 12 u (ft) = 2064.572881… cm2 A1 for 2065 cm2 (oe) M1 for using right-angled trigonometry; h = 5 tan54º A1 for 6.8819… M1 for finding area of isosceles triangle = 1 u 10 u h B1 for 360 = 72º 5 B1 (180 – 72) y 2 = 54 º OR A1 for 34.40954801…(ft) B1 for area of pentagon = 5 u (ft) = 172.0477401…(ft) B1 for area of dodecahedron = 12 u (ft)= 2064.572881… cm2 A1 for 2065 cm2 (oe) M1 for finding area of isosceles triangle = 1 x 2 sin 72 2 A1 for x = 8.506508084… M1 for finding equal sides of isosceles triangle; x = B1 for 360 = 72º 5 B1 (180 – 72) y 2 = 54º Additional Guidance Edexcel GCSE in Mathematics A Sample Assessment Materials © Edexcel Limited 2009 167 60 CDs sold 50 40 30 20 10 0 10 20 30 40 50 60 Frequency 9. 168 Edexcel GCSE in Mathematics A Sample Assessment Materials © Edexcel Limited 2009 x 4 2 0 2 4 6 8 y 14. Edexcel GCSE in Mathematics A Sample Assessment Materials © Edexcel Limited 2009 169 October 2009 For more information on Edexcel and BTEC qualifications please visit our website: www.edexcel.org.uk Edexcel Limited. Registered in England and Wales No. 4496750 Registered Office: One90 High Holborn, London WC1V 7BH. VAT Reg No 780 0898 07