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IGCSE (9–1) Maths - practice paper 5 mark schemeResults Plus data on 90 of the 100 marks:Paper 5Edexcel averages:YearPaperQu. noNew qu. no.Mean scoreMax scoreMean %ALLA*ABCDE17013HRQ01Q011.08254.01.081.621.140.550.310.160.2417013HRQ07Q023.49487.33.493.963.973.532.981.340.3217013HRQ08Q033.90578.03.904.804.263.512.561.661.0017063HRQ08Q042.09369.72.092.782.451.971.380.670.2117013HRQ09Q053.05476.33.053.643.342.772.171.431.0017013HRQ10Q062.73468.32.733.833.102.280.870.150.0017014HRQ08Q072.14371.32.142.882.531.770.900.180.1217014HRQ10Q082.19454.82.193.332.171.340.650.140.0817014HRQ11Q091.23261.51.231.851.370.670.310.130.0017013HRQ11a-bQ104.39587.84.394.964.754.503.712.190.9617014HRQ12Q115.14773.45.146.705.704.002.861.630.6917014HRQ13Q122.74468.52.743.692.892.331.470.550.00Spec pprs2HQ14Q13517014HRQ14Q144.82768.94.816.685.413.791.980.390.0017014HRQ15Q155.43777.65.436.766.264.953.351.560.4317014HRQ16Q161.62354.01.622.541.500.870.440.160.1517014HRQ17Q172.55463.82.553.712.731.890.830.130.0017014HRQ18Q182.04540.82.043.681.470.640.130.040.0017014HRQ19Q193.10562.03.104.553.412.160.900.070.0017014HRQ20Q203.26654.33.265.403.001.250.560.280.0017014HRQ21Q213.47657.83.475.563.501.890.330.130.04SAMs1HQ23Q225????60.469067.2?60.4582.9264.9546.6628.6912.995.24Problem-solving questions:6, 7, 11, 19, 21, 22Reasoning questions:8, 10, 13, 16, 21QWorkingAnswerMarkNotes11002 or 10 000 M1e.g. 12 × 100?120 0002A1Total 2 marks2x?2?101234y1086420?2y = 6 – 2x drawn from x = ?2 tox = 44B4For a correct line between x = ?2 and x = 4B3For a correct straight line segment through at least 3 of (?2, 10) (?1, 8) (0, 6) (1, 4) (2, 2) (3, 0) (4,?2)OR for all of (?2, 10) (?1, 8) (0, 6) (1, 4) (2, 2) (3, 0) (4, ?2)plotted but not joinedB2For at least 2 correct points plotted B1For at least 2 correct points stated (may be in a table) ORfor a line drawn with a negative gradient through (0, 6) OR a line with gradient ?2Total 4 marks3a224 ÷ 8 oe2M128A1b523 – 411 (=112) or or (=127.3...) 3M1 or 100ד1.273” – 100 or “127.3” – 100M1dep27.3A127.25 – 27.3Total 5 marks4aCorrect triangle(?1, ?2) (?1, 0) (2, ?2)2B2(B1 for a rotation of 90o clockwise about a different centrei.e. a triangle in the same orientation as the correct triangle orrotation by 90o anticlockwise about (0, 2))bCorrect trapezium(1, ?1) (1, ?2) (3, 1) (3, ?2)1B1Total 3 marks5a100 < w ≤ 1101B1b85 × 3 + 95 × 5 + 105 × 7 + 115 × 4 + 125255 + 475 + 735 + 460 + 1253M2for frequency × mid-interval for at least 4 products multiplied consistently and summingIf not M2 then award M1 for multiplying consistently by value within intervals for at least 4 products (eg. end of interval) and summing products or mid-intervals used but not summed.2050A1SC : B2 for an answer of 102.5 Total 4 marks6182 – (14÷2)2 (=275)4M1or M1 for cosx = or siny =or or or or 16.5… or 16.6M1or M1 for x = cos -1 or x = 67.1…or y = or y = 22.8…or z = or z = 45.77...0.5 × 14 × “16.5…” or 35M1or M1 for 0.5×14×18×sin(“67.1…”) or0.5×18×18×sin(2×”22.8…”) or 0.5×18×18×sin(“45.77...”)116A1116 – 116.1 NB Allow use of Hero’s formulaTotal 4 marksAlternative scheme25(25 – 18)(25 – 18)(25 – 14)(= 13475)oe4M2√13475 oeM1116A1Total 4 marks7160 – 3x + 7x – 20 = 180 or2(160 – 3x) + 2(7x – 20) = 360 oe3M1For a correct equatione.g. 4x = 180 – 140 or – 3x + 7x = 180 + 20 – 160 or 4x =40 or 14x – 6x = 360 – 320 + 40 oeM1For isolating the terms in x in a correct equation10A1 Dep on at least M1Total 3 marks8(a)2M1For with a = 4 or b = 3 111375A1Accept oe(b)2M1For or (and no 11) or n × 33 × 5? where n ≠ 112025A1Accept oeTotal 4 marks9y = –2x + 12M1A1 For y = –2x + c (c ≠ 1) ory = mx + 1or for a correct method to find the gradientor m = ?2 and c = 1 statedor ?2x + 1 or L = –2x + 1oeTotal 2 marks10ae.g.12x = 36 or 24y = ?603M1for addition of given equations or a complete method to eliminate y or x (condone one arithmetic error)e.g. 7 ”3”+ 2y = 16 or7x + 2 ×?2.5 = 16M1 (dep) for method to find second variablex = 3 oe, y = ?2.5A1 dep on M1 for both values correct. NB. Candidates showing no working score zerobk2 + 9k – 5k ? 452M1for 3 terms correct or all 4 terms correct ignoring signs or y2 + 4k +….. or… + 4k ? 45k2 + 4k ? 45A1Total 5 marks11(a)Correct probabilities2B1B1For 0.4 on LH branchFor 0.3, 0.7 and 0.3 on RH branches(b)0.422M1A1For 0.6 × 0.7oe(c)0.6 × "0.3" × "0.8" + "0.4" × 0.7 × "0.8" + "0.4" × "0.3" × 0.2 (= 0.144 + 0.224 + 0.024) oe 3M2ftFor a complete methodM1ft for 0.6 × "0.3" × "0.8" or 0.144 or "0.4" × 0.7 × "0.8" or 0.224 or "0.4" × "0.3" × 0.2 or 0.024 0.392A1cao oeAlternative method1 – [(0.6 × 0.7 × 0.2) + (0.4 × 0.3 × 0.8) + (0.6 × 0.7 × 0.8) + (0.6 × 0.3 × 0.2) + (0.4 × 0.7 × 0.2)]M2ftFor complete methodM1ft for 1 – (at least 2 correct products).0.392A1caoTotal 7 marks12(a) 3M1Allow Pq? = k or Do not allow oe or k = 12.8 × 2? or k = 51.2M1For correct substitution in a correct equation. Implies first M1Award M2 if k = 51.2 stated unambiguously A1Award 3 marks if answer is but k is evaluated in (a) or (b)SCB2 for Pq? = 51.2 or (b)51.28? 0.81B1ftft equation in the form oe Total 4 marks13(a)2M1For selecting 10x = 3.2424.... and 1000x = 324.2424... oeshowA1 (b)e.g. 3M1M1A1For multiplying the numerator and denominator by (7 + )For a correct single fraction with brackets expanded in denominatordep on correct working seen Total 5 marks14(a)e.g. or 1.6 or or 0.625 or e.g. 4 × or 4 ÷ oe ore.g. or oe2M1For correct scale factor or correct expression for AZ orfor a correct equation involving AZoe6.4A1oe e.g. (b)Eg or or oe3.752M1A1 Correct expression for BCoe(c)3M2For a fully correct method or M1 for or 20.531.98A1Accept 32.0 or 32Total 7 marks15(a)(y – 8)(y + 6)2M1A1For (y ± 8)(y ± 6)cao(b)4 = 5(e – 3) or 4 = 5e – 15 or = e – 3M12A1345 or 3.8(c)or 3M1oe e.g. oeM1A1oe e.g. Total 7 marks16(a) or 40 2M1 Or bar of height 40 wrong widthCorrect barA1(b)51B1Total 3 marks17(a)0.5 × (360 – 260) or 0.5 × 100 50 2M1A1For a complete method(b)e.g. 360 – (“50” + 260 + 30) (= 20), 90 – "20"or 2M1ftFor a complete method.70A1Total 4 marks18(a)–3.42M1A1Line y = –5 drawn or clear attempt to take reading at y = –5Accept –3.35 to –3.45 inclusive(b)3M2y = – 5x drawn.M1 for x? – 0.2x? – 9x + 7 = –5x or y = –5x oe–2.5A1dep on at least M1 (?2.45 - ?2.55)Total 5 marks19(π × 5?) + π × 5 × l (25π) + 5πl5M1For a correct expression for total surface area(l =) 13A1For the correct slant height(h = ) M1For the correct method to find hft if first M1 scored(= 314 - 314.3)M1For the correct method to find Vft if first M1 scored100πA1Total 5 marks20(a)6c – 9 +2c – 3c or 3c – 9 +2c 3M1Accept cc or (c )2 instead of cc = 5k = 3A1B1(b) or 3M1M1A1gains M2 onlyTotal 6 marks21(a)3x – 13 – 501B1or 3x – 13 – 25 ? 25(b)x – 52 5B1or x – 2 – 25 × 225(3x – 63)(x – 52) (= 81900)M1For a correct expression for volume of boxeg 3x? – 156x – 63x + 3276 (= 3276)or 75x? – 3900x – 1575x +81900 (= 81900)M1For brackets correctly expandedeg 3x? – 219x = 0 or 3x(x – 73) = 0or 75x? – 5475x = 0M1For correctly reducing to 2 term quadratic equation (x = 0) or x = 7373A1For x = 73NB: A1 dependent on at least 2 method marksTotal 6 marksQuestionWorkingAnswerMarkAONotes22a + 3d = 17 or a + 9d = 35 orAO1M1M1 for 17 = 4p + q and 35 = 10p + q35 – 17 = 6dA1p = 3 and q = 5d = 3A1ft from d = 3u1 = 8 and u50 = 155a = 8M1 × 50(8 + 155) (2 × '8' + (50 ? 1) '3') oe40755A1 ................
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