62 x, P1 2 P1 for stating each term in algebraic form M Let the first number be then the next x x x x four are + 1, + 2, + 3 and + 4. M1 M1 for adding all 5 terms The sum of these is 5x + 1 + 2 + 3 + 4 which is 5x +10 = 5(x + 2), P1 P1 for showing they are multiple of 5 a multiple of 5. 3 63 2 M 10x = P1 P1 for expressing as subject a a Hence × 10x = b M1 M1 for substituting into other expression Substitute this into 10y = C1 C1 for showing the correct substitution to give 10y = Hence 10y = So 10y × 10x = 1 C1 C1 for showing the product of the two terms equal to 1 So 10(x + = 1 y) C1 C1 for showing combination of indices But 100 = 1 B1 B1 for 100 = 1 x y And so + = 0. P1 P1 for complete, clear proof with clear mathematical statements 7
62 Let the first number be x, then the next four are x + 1, x + 2, x + 3 and x + 4. The sum of these is 5x + 1 + 2 + 3 + 4 which is 5x +10 = 5(x + 2), a multiple of 5. P1 M1 P1 2 P1 for stating each term in algebraic form M1 for adding all 5 terms P1 for showing they are multiple of 5 M 3 63 10x = Hence b × 10x = a Substitute this into 10y = to give 10y = Hence 10y = So 10y × 10x = 1 So 10(x + y) = 1 But 100 = 1 And so x + y = 0. P1 M1 C1 C1 C1 B1 P1 2 P1 for expressing a as subject M1 for substituting into other expression C1 for showing the correct substitution C1 for showing the product of the two terms equal to 1 C1 for showing combination of indices B1 for 100 = 1 P1 for complete, clear proof with clear mathematical statements M 7
Higher_Skills_Algebra_MarkScheme_Edexcel.docx