46 a P1 2 ar3 M P1 for equation showing at least up to and the 3 generalisation B P1 ar4 Sn a ar ar2 ar3 arn P1 for equation showing at least up to and the two = + + + + … generalisations rSn ar ar2 ar3 ar4 arn = + + + + + … arn + 1 c C2 C1 for top two rows shown correctly C1 for the bottom row shown correctly B1 B1 cao Therefore: Sn rSn a arn - = + 1 – B1 B1 cao d Sn(1 r) a(1 rn B1 = + 1) – – B1 cao e Sn = 7 47 C1 2 M Considering the area of an (x + 1) by C1 for explaining the sides of each square are (x + 1) (x + 1) square: C2 C1 for creating the square divided into the rectangles, x using the and the 1 The area of each rectangle created above is shown inside that rectangle, so C1 for areas of each rectangle indicated in the it can be seen that: rectangles x2 x x (x + 1)2 = + + + 1 x2 = + 2x + 1 as required C1 C1 for clear explanation of required result 4
46 a B c d e Sn = a + ar + ar2 + ar3 … + arn rSn = ar + ar2 + ar3 + ar4 … + arn + arn + 1 Therefore: Sn - rSn = a – arn + 1 Sn(1 – r) = a(1 – rn + 1) Sn = P1 P1 C2 B1 B1 B1 2 3 P1 for equation showing at least up to ar3 and the generalisation P1 for equation showing at least up to ar4 and the two generalisations C1 for top two rows shown correctly C1 for the bottom row shown correctly B1 cao B1 cao B1 cao M 7 47 Considering the area of an (x + 1) by (x + 1) square: The area of each rectangle created above is shown inside that rectangle, so it can be seen that: (x + 1)2 = x2 + x + x + 1 = x2 + 2x + 1 as required C1 C2 C1 2 C1 for explaining the sides of each square are (x + 1) C1 for creating the square divided into the rectangles, using the x and the 1 C1 for areas of each rectangle indicated in the rectangles C1 for clear explanation of required result M 4
Higher_Skills_Algebra_MarkScheme_Edexcel.docx