A1 for full simplification. B1 cao
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1 B1 for translation 1 Translation 3 by 4 B (a) Trend described C1 for percentage of people who use the shop decreases oe (bi) P1 for process to draw trend line on graph A1 for (bii) No + reason C1 for comment, eg no, because 2020 is beyond the time period covered by the given data 3 (a) 13y 1 M1 for expansion of one bracket A1 for full simplification (b) 35u 3 w 7 B1 for 2 of 35, u 3 and w 7 correct B1 cao P1 for process to find the exterior angle or interior angle of a hexagon or octagon P1 for process to find the both exterior angles or both interior angles A1 for 105 from correct working 145
2 5 (a)(i) 10, 12, 14, 15, 16, 18 B1 cao (ii) 12, 18 B1 cao (b) 7 10 M1 for 7 or indicating correct region or for 10, 14, 16, 11, 13, 17, 19 listed A1 for 7 10 oe 6 6 : 5 = 12 : 10 2 : 1 = 10 : 5 70 P1 P1 for strategy to start to solve the problem eg 12 : 10 and 10: 5 C : S : P = 12 : 10 : 5 P1 P1 for process to solve the problem eg A π 4.8² 6.58 B1 for use of formula for area of a circle region P1 for complete process to find area of shaded π 4.8² A1 for
3 8 (a) explanation C1 for incorrect expansion of brackets oe (b) explanation C1 for has not obtained both solutions oe 9 (a) 18 B1 cao (b) 5(x 1) M1 for method to find inverse function A1 for 5(x 1) or 5x 5 (c) 9x 48 shown M1 for method to find composite function A1 for working leading to 9x (a) (1.052) P1 for process to find population in 2016 P1 for complete process to find population in 2017 A1 for (b)(i) 2020 P1 for process to find when population will exceed A1 for 2020 (ii) C1 for correct comment on how assumption will affect the answer, eg if the percentage growth is higher the population may exceed earlier. 147
4 11 (a) 0.43 M1 for use of graph at 240 minutes A1 for oe (b) comparison B1 for at least one median ( or ) B1 for least one interquartile range (69 73 or 67-71) C1 for comment comparing average times eg females take longer than males oe C1 for comment comparing spreads of times from IQRs, eg the spread of times is about the same (NB at least one of the comments must be in context) 12 (a) P1 for process to find number of ways (b) P1 for process to find number of lists with boy then girl then boy or the number of lists with girl then boy then girl P1 for complete process to find the total number of lists 148
5 M1 for oe M1 for oe A1 accept explanation C1 for a correct evaluation, eg the value of D should be multiplied by 8, she has used 2 3 instead of 2³ 15 (a) M1 for finding gradient by drawing tangent M1 for method to calculate gradient A1 For (b) C1 for acceleration C1 for eg 4 second after the start of the race, when the speed is 7.6 m/s, in m/s 2 (c) limitation C1 for comment, eg dependent on accuracy of constructing a tangent 16 (i) 200 B1 cao (ii) 5.6 B1 For 5.6(2...) 149
6 ² 6.05² B1 for finding bounds of one measurement, , 6.05 or 6.15 P1 for process of choosing and using correct bounds P1 for process of Pythagoras rule with correct bounds A1 for 5.754(997 ) 18 ( aa + 2 bb)( aa 2 bb) a 4b M1 for expansion of brackets or 4b = 2 b aa aa 2 aa bb + 2 bb aa 2 bb 2 bb M1 for a or ( 4b) 19 (a) sketch B1 for correct shape for 0 x 360 B1 for fully correct sketch with labels (b)(i) sketch B1 cao (ii) sketch B1 cao 150
7 20 TSU = (=72) proof M1 for method to find interior or exterior angle of Exterior angles of a polygon regular pentagon add up to 360 o QRO = OTP = 90 The tangent to a circle is perpendicular (90 o )to the radius (diameter) ROT = (= 144) RUT = (= 72) The angle at the centre of a circle is twice the angle at the circumference Base angles of an isosceles triangle are equal M1 for using angle between tangent and radius M1 for method to find angle ROT C1 for method to find angle RUT with reason C1 for deduction that ST = UT with reasons 21 2xx 1 xx 4 = 16xx + 1 2xx , 5 P1 for process to write as an equation (2x 1)² = (16x + 1)( x 4) P1 for process to clear the fractions 12x² 59x 5 = 0 P1 for process to write equation in form ax² + bx + c = 0 (12x + 1)( x 5) = 0 P1 for process to solve the equation 151
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