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IGCSE (9–1) Maths - practice paper 2 mark schemeResults Plus data on 92 of the 100 marks:Paper 2Edexcel averages:YearPaperQu. noNew qu. no.Mean scoreMax scoreMean %ALLA*ABCDE17064HRQ02Q013.09477.33.093.783.312.842.201.320.4917014HQ02Q024.51590.24.514.974.884.724.443.892.4517013HQ05c, eQ03a-b2.53463.32.533.683.112.591.830.930.4816063HQ7bQ03c1.85292.51.851.981.951.861.510.950.3617013HQ09Q041.73357.71.732.682.281.721.130.400.1717013HQ10Q051.77359.01.772.882.391.630.990.370.0917064HQ08Q062.09369.72.092.922.351.410.580.230.1217064HQ09Q073.37484.33.373.863.623.232.391.040.2817064HQ10Q08a,b,d,e4.86681.04.865.745.034.313.502.541.3917064HRQ05gQ08c0.91191.00.910.990.940.880.810.710.4917064HQ11Q093.09561.83.094.663.391.780.530.140.1817064HQ12Q101.42347.31.421.961.421.050.660.420.2217064HQ13Q112.56551.22.564.132.551.180.470.280.1917064HQ14Q122.76469.02.763.402.872.341.721.140.6117063HRQ13Q131.46348.71.462.621.670.820.330.070.0217064HQ15Q143.27654.53.275.273.361.490.530.180.0417064HQ16Q154.17583.44.174.904.623.822.501.400.6417064HQ17Q163.38656.33.385.443.311.700.710.320.1117064HQ18Q171.53351.01.532.251.630.960.390.110.0317064HQ19Q181.79359.71.792.651.951.090.380.210.0717064HQ20Q191.50437.51.502.651.370.530.130.050.01Spec pprs1HQ20Q20417064HQ21Q212.30638.32.304.531.780.430.050.010.01SAMs2HQ24Q22417064HQ23Q230.95423.80.952.180.370.060.020.020.01????56.899261.8?56.8980.1260.1542.4427.8016.738.46Problem-solving questions:1, 7, 9, 16, 18, 21, 23Reasoning questions:2, 12, 13, 14, 17, 20, 22QWorkingAnswerMarkNotes1(a) (i)5, 151B1 (ii)5, 7, 9, 10, 11, 13, 151B1(b)4, 6, 8, 10, 12, 142B2B2 for all correct and none incorrect.If not B2 then B1 for 4 or more correct and no more than 1 incorrect.Total 4 marks2(a) or 0.33M1 or M1dep0.15A1(b)2M180A1Note: Award M1A1 for 80 out of 200Award M1A0 for 80/200 Total 5 marks3(a)7 × (?2)? + 5 or 7 × 4 + 5 or7 (?2)? + 5 2M1for correct substitution or 7 × 4 or 2833A1(b)?7t ≥ 31 – 3 or 7t ≤ 3 – 31 oe2M1 ?7t ≥ 31 – 3 or 7t ≤ 3 – 31 or ? 4 or t ≥ ?4accept an equation or the wrong inequality sign in the workingt ≤ ?4A1or for ?4 ≥ t3(c)M1for 3 correct terms or 4 correct terms ignoring signs orx2 ? 7x + a for any non-zero value of a or... ? 7x ? 18x2 ? 7x ? 182A1Total 6 marks44x? + 6x + 6x + 9 or 4x? + 12x + 93M1for at least 3 terms correct in expansion of first pair of brackets2x? ? 10x + 3x – 15 or 2x2 – 7x – 15 M1for at least 3 terms correct in expansion of second pair of brackets orall 4 terms correct ignoring signsallow –2x2 – 7x – 152x? + 19x + 24A1Alternative method(2x + 3)[(2x + 3) – (x – 5)]M1(2x + 3)(x + 8)M12x? + 19x + 24A1Total 3 marks50.82x = 25.83 or 82% = 25.833M1or for use of 0.82 in a calculation25.830.82 or 25.8382 × 100M131.5(0)A1Total 3 marks6180 – 156 (=24) or 180(n – 2) = 156n oeor 90(2n – 4) = 156n oeM1360 ÷ “24” or (180 × 2) ÷ (180 – 156) or M1complete method153A1Total 3 marks7420 ÷ (4 + 5 + 3) (=35) [or Manu = 140 or Liam = 175]M1M2 for “35” × 3 (=105)M1or Ned = 105 oe oeM1434A142.85 – 43 Total 4 marks8(a)e151B1(b)M1for ng8 or 4gm or 4g82A1(condone g8)(c)e151B1(d)11B1(e) (3x2)2 or 9(x?)? or or or or M1or kx4 or 9xn (not just 9 or xn)9x42A1Total 7 marks9eg (d2 = ) 72 + 72 or r2 + r2 = 7? or cos 45 = or sin 45 = or cos 45 = or sin 45 = M1Start of method to find radius or diameter of circleeg (d=) (9.899..) or (r=)(=4.9...) or d = or d = or r2 = 24.5or r = 7cos 45 or r = 7sin 45M1complete method to find radius or diameter or r2(if method to find radius or diameter shown then allow use of radius = 5 for method marks only)eg. π × “4.9..”2 (=76.969...)M1For method to find area of circle or semi-circle or quarter circle – use of radius from correct workingeg. π × “4.9..”2 – 72M1for complete method285A127.9 – 28 Total 5 marks1010 12 15 16 17 19 19 23 24 27 27 or M1Ordered list – allow one error or omission15 and 24 identifiedM193A1Total 3 marks11(a)y = 3 – 1.5x or 2x – 1.5 = y orm = 2 (A) or m = ?1.5 (B) or m = 2 (C) or m = ?2 (D)M1If using gradients, must state m = or gradient = A and C2A1(allow correct equations listed)(b)y = x + c or y – y1 = M1c can be any value, e.g. 3 = × 1 + c or c = oe or y = x + ory – 3 = or 2(y – 3) = ?5(x – 1)M15x + 2y = 113A1oe eg. 10x + 4y = 22 or in a different but correct form but must have integer values, e.g. 2y = ?5x + 11Total 5 marks12(a) (i)52B1(a) (ii)angles in same segment or angles subtended by the same arc 2B1Dep on B1 in (ai)(b) (i)104B1accept 256 (b) (ii)angle at centre is twice angle at circumference2B1oeDep on B1 in (bi) or correct working Total 4 marks13M1for either y = 2x + 1 or x + y = 10 drawn correctlyM1for all lines drawn correctlyCorrect region3A1for all 3 lines correct and the region identifiedLines may be full lines or broken linesTotal 3 marks14(a) or (3x + 1)(x + 3) = 120 or(2x – 4)(x + 3) + ?(9 – x)(x + 3) or(x + 5)(x + 3) ? ?(9 – x)(x + 3)M1correct expression for area(trapezium)(rectangle + triangle)(rectangle – triangle) oeM1correct expansion of (all pairs) brackets in a correct equation3x? + 10x + 3 = 120 or1.5x? + 5x + 1.5 = 60shown3A1dep on fully correct working to get to 3x2 + 10x – 117 = 0(b) oroe or NB: denominator must be 2 × 3 or 6 and there must be evidence for correct order of operations in the numerator M2If not M2 then M1 for (may have just + rather than ±)Condone one sign error in substitution; allow partial evaluation4.803A1Award M2A1 for answers in range 4.796 – 4.8 (and no other answer) with sufficient correct working that would gain at least M1[Award M2A0 for working sufficient for M1 with both the –ve and +ve answers (?8.13 & 4.80)]Total 6 marks15(a)0.2, 0.65, 0.35, 0.4, 0.62B2oeB1 for any 2 correct probabilities (in correct position)(b)0.8 × “0.35”(=0.28) or “0.2” × “0.4”(=0.08)M1ft from (a)M2 ft from (a) for 1?(0.8ב0.6’+‘0.2’ב0.6’)M1 for 1 – (0.8ב0.65’) or 1? (‘0.2’ב0.6’)0.8 × “0.35” + “0.2” × “0.4”M1ft from (a)0.36 oe3A1eg , 36%Total 5 marks16(a)24x2 – 6x – 25 2M1A1for 2 correct from 3 × 8x? , ?3×2x ,?25fully correct(b)24x2 – 6x – 25 = 5M1ft from (a)24x2 – 6x – 30 (= 0) or 4x2 – x – 5 (= 0)or 12x? ? 3x – 15 (= 0)M1ft from (a) for a 3 term quadraticwith no coefficients of zero(4x – 5)(6x + 6) (=0) or (4x – 5)(x + 1) (= 0)(4x – 5)(3x + 3) (= 0) or M1ft from (a) for a 3 term quadraticwith no coefficients of zero.If using quadratic formula some simplification may be seen.1.25 oe, ?14A1cao dep on M1[ignore attempts to work out y values]Total 6 marks1760 ÷ 30 (=2) or 270 ÷ 60 (=4.5) or 150 ÷ 30 (=5) or 156 ÷ 120 (=1.3) or 24 ÷ 60 (=0.4)M1for use of areaeg. any one correct fd or any 2 correct bars of different widthsfd : 2, 4.5, 5, 1.3, 0.4 M1for any 4 correct fd or barshistogram3A1for a correct histogram, including frequency density (FD) label and scale/correct keyTotal 3 marks180.5 × 6.4 × 9.7 × sin 110 (= 29.16…)M1M2 for 6.4 × 9.7 × sin 1102 × “29.16…”M158.33A1for 58.3 – 58.4alternativeAC = (=13.323...)DAC = orACD = M1For method to find AC and angle DAC or angle ACDArea = (sin ‘43.167..’ × 6.4 × 2 × ‘13.323..’) ÷ 2 Or area = (sin ’26.83..’ × 9.7 × 2 × ’13.323...’) ÷ 2 M1find DB and then area using half product of diagonals58.3A1for 58.3 – 58.4Total 3 marks1945.75 or 45.85 or 63.25 or 63.75B1Accept or 45.8499... or or 63.7499... (= 1.379)... or (=0.764)...M1Or for or where, × 60 oe e.g. M1× 60 oe, e.g. 82.84A1Or better (82.76990185) Total 4 marks20eg. 2n + 1, 2n + 3M1for algebraic representation of two consecutive odd numbers (2n + 3)2 – (2n + 1)2 =(4n2 + 6n + 6n + 9) – (4n2 + 2n + 2n + 1)M1for correct expansion of at least one bracket 8n + 8M1for simplified answer, may be factorisedproof4A1for completion of proofTotal 4 marks2115.62 + 4.32 – 2×15.6×4.3×cos72o (=220.39…)M1substitution into Cosine ruleLN = 14.8(4561…)A114.8(4561…) or orM1ft LN dep on 1st M1 or correct start to alternative method to find angle MLN or angle NLP or angle LNP[4.3?=14.8..?+15.6??2×14.8×15.6cosNLP](=51.49..) or (=15.99..) or(=87.99 or 92.00..) M1ft LN dep on 1st M1or complete alternative method to find angle MLN or angle NLP or angle LNPNB: LNP = 180 ?87.99 = 92.009... (=51.49..) and(=15.99..) or(=87.99 or 92.00..) M1ft LN dep on 1st M1or complete method to find angle MLN and angle NLP (or LNP acute or obtuse)67.56A1for 67.46 – 67.8Total 6 marksQuestionWorkingAnswerMarkAONotes22 AO1M1method to rationaliseM1correct expansion of brackets B1may be seen before expansionshown4A1answer from fully correct working with all steps seen23 or M1allow r = oeA1(allow 1.33... or better) M1dep on 1st M1 (need not include) or answer of (=4.96(44…)) 4A1 (accept 1.58(024…)Total 4 marks ................
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