A.P - G.P WS [90 marks] 1a. Markscheme valid approach (M1) eg 11-5,11=5+d d = 6 A1 N2 [2 marks] [2 marks] 1b. Markscheme [2 marks] valid approach (M1) eg u2-d, 5-6, u1+(3-1)(6) = 11 U1 =- 1 A1 N2 [2 marks] 1c. Markscheme [2 marks] correct substitution into sum formula eg 2(2(-1)+19(6)), 20(-1+113) (A1) A1 N2 S20 = 1120 [2 marks]
2a [2 marks] Markscheme valid approach (M1) eg "1, 2.226, 2.226 = 2.1r r = 1.06 (exact) A1 N2 [2 marks] 2b. Markscheme [2 marks] correct substitution (A1) eg 2.1 ×1.069 3.54790 A1 N2 U10 = 3.55 [2 marks] 2c. [3 marks] Markscheme correct substitution into S formula (A1) 2.1(1.06"-1) 1.06-1 1.06-1 eg 2.1(1.06"-1) > 5543, 2.1 (1.06" - 1) = 332.58, sketch of Sn and y = 5543 correct inequality for n or crossover values A1 eg n> 87.0316, S87 = 5532.73 and S88 = 5866.79 n = 88 A1 N2 [3 marks]
[2 marks] 3. Markscheme recognition that 225 terms of wn consists of 113 non-zero terms (M1) 113 112 ?? eg 1, 0, 113 1 1 m = 112 (accept k=0 124 X pk; r may be incorrect) A1 N2 [2 marks] 4a Markscheme [3 marks] * This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure. 1.042 × 880 × 1.25 OR (880 + 0.042 × 880) x 1.25 (M1)(M1) Note: Award (M1) for multiplying 880 by 1.042 and (M1) for multiplying 880 by 1.25. 1150 (CAD) (1146.20 (CAD)) (A1) (G2) Note: Accept 1146.2 (CAD) [3 marks] 4b [3 marks] Markscheme 704 880 OR 704 (M1) 563.20 Note: Award (M1) for correctly dividing sequential terms to find the common ratio, or 0.8 seen. 880(0.8)5-1 (M1) Note: Award (M1) for correct substitution into geometric sequence formula. 360.45 (USD) (A1)(G3) Note: Do not award the final (A1) if the answer is not correct to 2 decimal places. Award at most (M0)(M1)(A0) if r = 1.25 . [3 marks]