41 C3 2 C1 for each correct explanation of the impact on the H F(x) = a(b)x i population as varies b < 1 the population decreases. b ii = 1 the population stays the same. b iii > 1 the population increases. b 3 42 a Epidemic started by a single carrier so M1 2 M1 for correct interpretation of , and use of, the H + 1 = xn Rtx0 = 1. iterative formula x0 = R10 x10 Considering infection after 10 days so A1 A1 for cao = 10. t b C1 C1 for relevant , informative headline Newspaper headline to engage readers with the story of this epidemic e.g. how long before people are infected. 3 x 43 0.43 bar M1 2 M1 for correct use of formula H A1 A1 cao 2 44 a as workings. M1 3 M1 for algebraic manipulation H Show that… = 1 + x C1 C1 for clarity of justification 3) = 3 + 11 x(x – x – 3x = + 8 x2 – x 4x 8 0 = x2 – – M1 M1 for correct use of iteration if = 5 x1 b B1 B1 for substitutions = 1 + = 1 + = 6.5 x2 = 1 + = 4.14286 x3 … A1 A1 for one root found (no credit if both roots are found) = to 2 dp x –1.46 Using = 5 as the first iteration, after 19 iterations you x arrive at = to 2 dp x –1.46 Likewise, if the first trial is 11 iterations lead to the –1, solution = to 2 dp. 5 x –1.46
41 i ii iii F(x) = a(b)x b < 1 the population decreases. b = 1 the population stays the same. b > 1 the population increases. C3 2 C1 for each correct explanation of the impact on the population as b varies H 3 42 a b Epidemic started by a single carrier so x0 = 1. Considering infection after 10 days so t = 10. xn + 1 = Rtx0 x10 = R10 Newspaper headline to engage readers with the story of this epidemic e.g. how long before x people are infected. M1 A1 C1 2 M1 for correct interpretation of , and use of, the iterative formula A1 for cao C1 for relevant , informative headline H 3 43 0.43 bar M1 A1 2 M1 for correct use of formula A1 cao H 2 44 a b x = 1 + x(x – 3) = x – 3 + 11 x2 – 3x = x + 8 x2 – 4x – 8 = 0 if x1 = 5 x2 = 1 + = 1 + = 6.5 x3 = 1 + = 4.14286 … Show that… as workings. x = –1.46 to 2 dp M1 C1 M1 B1 A1 3 M1 for algebraic manipulation C1 for clarity of justification M1 for correct use of iteration B1 for substitutions A1 for one root found (no credit if both roots are found) Using x = 5 as the first iteration, after 19 iterations you arrive at x = –1.46 to 2 dp Likewise, if the first trial is –1, 11 iterations lead to the solution x = –1.46 to 2 dp. H 5
Higher_Skills_Ratio_MarkScheme_Edexcel.docx