IB Questionbank Test



1.8 1a. [1 mark] Markschemewn ? ?? (A1) (C1)??[1 mark]Examiners report [N/A] 1b. [1 mark] Markschemeun ? ?? (A1) (C1)?[1 mark]Examiners report [N/A] 1c. [2 marks] Markscheme10?(2)11?1? ? ? (M1)?Note: Award (M1) for correct substitutions into geometric sequence formula.?= 10?240? ? ? (A1)(ft) (C2)?Note: Exact answer only. Accuracy rules do not apply in this question part; do not accept the 3 sf answer of 10?200.?[2 marks]Examiners report [N/A] 1d. [2 marks] Markscheme? OR? ? ? ?(M1)?Note: Award (M1) for correct substitutions into arithmetic series formula.?= 2100? ? ??(A1)(ft) (C2)?[2 marks]Examiners report [N/A] 2a. [3 marks] Markscheme54?× (0.94)50? ? ?(M1)(A1)Note: Award (M1) for substitution into geometric sequence formula, (A1) for correct substitution.2.45 (cm) (2.44785… cm)? ? ? (A1) (C3)[3 marks]Examiners report [N/A] 2b. [3 marks] Markscheme (or equivalent)? ? ?(M1)(A1)(ft)Note: Award (M1) for substitution into geometric series formula, (A1)(ft) for correct substitution using their common ratio from part (a).= 862 (cm)? (861.650…(cm))? ? (A1)(ft) (C3)[3 marks]Examiners report [N/A] 3a. [3 marks] Markscheme60 + 10 × 10? ? ?(M1)(A1)Note: Award (M1) for substitution into the arithmetic sequence formula, (A1) for correct substitution.= ($) 160? ? ?(A1)(G3)[3 marks]Examiners report [N/A] 3b. [3 marks] Markscheme? ? ?(M1)(A1)(ft)Note: Award (M1) for substituting the arithmetic series formula, (A1)(ft) for correct substitution. Follow through from their first term and common difference in part (a).= ($) 1380? ? ?(A1)(ft)(G2)[3 marks]?Examiners report [N/A] 3c. [3 marks] Markscheme60 × 1.110? ? ?(M1)(A1)Note: Award (M1) for substituting the geometric progression nth term formula, (A1) for correct substitution.= ($) 156? (155.624…)? ? ?(A1)(G3)Note: Accept the answer if it rounds correctly to 3 sf, as per the accuracy instructions.[3 marks]?Examiners report [N/A] 3d. [3 marks] Markscheme? ? ?(M1)(A1)(ft)Note: Award (M1) for substituting the geometric series formula, (A1)(ft) for correct substitution. Follow through from part (c) for their first term and common ratio.= ($)1280? (1283.05…)? ? ?(A1)(ft)(G2)[3 marks]Examiners report [N/A] 3e. [4 marks] Markscheme? ? (M1)(M1)Note: Award (M1) for correctly substituted geometric and arithmetic series formula with n (accept other variable for “n”), (M1) for comparing their expressions consistent with their part (b) and part (d).OR? ? ?(M1)(M1)Note: Award (M1) for two curves with approximately correct shape drawn in the first quadrant, (M1) for one point of intersection with approximate correct position.Accept alternative correct sketches, such asAward (M1) for a curve with approximate correct shape drawn in the 1st (or 4th) quadrant and all above (or below) the x-axis, (M1) for one point of intersection with the x-axis with approximate correct position.17? ? ? (A2)(ft)(G3)Note: Follow through from parts (b) and (d).An answer of 16 is incorrect. Award at most (M1)(M1)(A0)(A0) with working seen. Award (G0) if final answer is 16 without working seen.[4 marks]Examiners report [N/A] 4a. [1 mark] Markscheme3800 m ? ? (A1)[1 mark]Examiners report [N/A] 4b. [2 marks] MarkschemeOR ? ? (M1)(A1)?Note: ? ? Award (M1) for substitution into arithmetic sequence formula, (A1) for correct substitution.?[2 marks]Examiners report [N/A] 4c. [2 marks] Markscheme ? ? (M1)?Notes: ? ? Award (M1) for their correct inequality. Accept .Accept OR . Award (M0) for .? ? ? (A1)(ft)(G2)?Note: ? ? Follow through from part (a)(ii), but only if is a positive integer.?[2 marks]Examiners report [N/A] 4d. [4 marks] Markscheme ? ? (M1)(A1)(ft)?Note: ? ? Award (M1) for substitution into sum of an arithmetic series formula, (A1)(ft) for correct substitution.? ? ? (A1)?Note: ? ? Award (A1) for their seen.? ? ? (A1)(ft)(G3)?Note: ? ? Award (A1)(ft) for correctly converting their answer in metres to km; this can be awarded independently from previous marks.?OR ? ? (M1)(A1)(ft)(A1)?Note: ? ? Award (M1) for substitution into sum of an arithmetic series formula, (A1)(ft) for correct substitution, (A1) for correctly converting 3000 m and 400 m into km.? ? ? (A1)(G3)[4 marks]Examiners report [N/A] 4e. [3 marks] Markscheme ? ? (M1)(A1)?Note: ? ? Award (M1) for substitution into geometric series formula, (A1) for correct substitutions.? ? ? (A1)(G3)OR ? ? (M1)(A1)?Note: ? ? Award (M1) for substitution into geometric series formula, (A1) for correct substitutions.? ? ? (A1)(G3)[3 marks]Examiners report [N/A] 4f. [3 marks] Markscheme ? ? (M1)(A1)?Notes: ? ? Award (M1) for substitution into sum of a geometric series formula, (A1) for correct substitutions. Follow through from their ratio () in part (d). If (distance does not increase) or the final answer is unrealistic (eg ), do not award the final (A1).? ? ? (A1)(G2)[3 marks]Examiners report [N/A] 5a. [2 marks] MarkschemeOR ? ? (M1)?Note: ? ? Award (M1) for dividing any by .? ? ? (A1) ? ? (C2)[2 marks]Examiners report [N/A] 5b. [2 marks] Markscheme ? ? (M1)?Note: ? ? Award (M1) for their correct substitution into geometric sequence formula.? ? ? (A1)(ft) ? ? (C2)?Note: ? ? Follow through from part (a).Award (A1)(A0) for or with or without working.?[2 marks]Examiners report [N/A] 5c. [2 marks] Markscheme ? ? (M1)?Note: ? ? Award (M1) for correct substitution into geometric series formula.? ? ? (A1)(ft) ? ? (C2)[2 marks]Examiners report [N/A] 6a. [1 mark] Markscheme ? ? (A1) ? ? (C1)[1 mark]Examiners report [N/A] 6b. [2 marks] Markscheme ? ? (M1)?Note: ? ? Award (M1) for their correct substitution into the geometric sequence formula. Accept a list of their five correct terms.? ? ? (A1)(ft) ? ? (C2)?Note: ? ? Follow through from their common ratio from part (a).?[2 marks]Examiners report [N/A] 6c. [3 marks] Markscheme ? ? (M1)(M1)?Notes: ? ? Award (M1) for their correct substitution into the geometric sequence formula with a variable in the exponent, (M1) for comparing their expression with .Accept an equation.? ? ? (A1)(ft) ? ? (C3)?Note: ? ? Follow through from their common ratio from part (a). “” must be a positive integer for the (A1) to be awarded.?[3 marks]Examiners report [N/A] 7a. [2 marks] Markscheme ? ?(M1)?Note: ? ? Award (M1) for correct substitution into geometric sequence formula.? ? ?(A1) ? ? (C2)[2 marks]Examiners report [N/A] 7b. [2 marks] Markscheme ? ?(M1)?Note: ? ? Award (M1) for correct substitution into geometric sequence formula or list of eight values using their . Follow through from part (a), only if answer is positive.??? ? (A1)(ft) ? ? (C2)?[2 marks]Examiners report [N/A] 7c. [2 marks] Markscheme ? ?(M1)?Note: ? ? Award (M1) for correct substitution into geometric series formula. Follow through from part (a), only if answer is positive.? ? ?(A1)(ft) ? ? (C2)[2 marks]Examiners report [N/A] 8a. [3 marks] Markschemei) ? ?? ? ? ? (A1)?ii) ? ? ? ? ? (M1)Note: Award (M1) for ?OR? ? ? ??(A1)(G3)Examiners reportQuestion 5: Arithmetic and Geometric progressionMost candidates calculated the salaries in the second year correctly. The most common error was to calculate the salaries for the third instead of the second year. In part (b) the use of instead of was very common. For the geometric sequence often a ratio of 0.05 instead of 1.05 was used. Also many of the expressions given did not represent a geometric sequence. Candidates who used a list for part (c) did usually better than the ones that tried to solve an equation. In part (d) the sum of the arithmetic progression was done better than the geometric series. Many candidates calculated the 15th term of the progression and not the series. In general this question part was not answered well. 8b. [4 marks] Markschemei) ? ?? ? ? ? ?(M1)(A1)Note: Award (M1) for substitution in arithmetic sequence formula; (A1) for correct substitutions.?ii) ? ? ? ? ? ?(M1)(A1)Note: Award (M1) for substitution in arithmetic sequence formula; (A1) for correct substitutions.?Examiners reportQuestion 5: Arithmetic and Geometric progressionMost candidates calculated the salaries in the second year correctly. The most common error was to calculate the salaries for the third instead of the second year. In part (b) the use of instead of was very common. For the geometric sequence often a ratio of 0.05 instead of 1.05 was used. Also many of the expressions given did not represent a geometric sequence. Candidates who used a list for part (c) did usually better than the ones that tried to solve an equation. In part (d) the sum of the arithmetic progression was done better than the geometric series. Many candidates calculated the 15th term of the progression and not the series. In general this question part was not answered well. 8c. [2 marks] Markscheme ? ? ? ?(M1)Note: Award (M1) for setting a correct inequality using their expressions for (b)(i) and (b)(ii). Accept an equation.ORlist of at least 4 correct terms of each sequence ? ? ? ?(M1)Note: Award (M1) for correct lists corresponding to their answers for parts (b)(i) and (b)(ii). ? ? ? ?(A1)(ft)(G2)Note: Value must be an integer for the final (A1) to be awarded. Follow through from parts (b)(i) and (b)(ii). Award (G1) for a final answer of seen without working.Examiners reportQuestion 5: Arithmetic and Geometric progressionMost candidates calculated the salaries in the second year correctly. The most common error was to calculate the salaries for the third instead of the second year. In part (b) the use of instead of was very common. For the geometric sequence often a ratio of 0.05 instead of 1.05 was used. Also many of the expressions given did not represent a geometric sequence. Candidates who used a list for part (c) did usually better than the ones that tried to solve an equation. In part (d) the sum of the arithmetic progression was done better than the geometric series. Many candidates calculated the 15th term of the progression and not the series. In general this question part was not answered well. 8d. [7 marks] Markschemei) ? ?? ? ? ? ? (M1)(A1)(ft)Note: Award (M1) for substitution into geometric series formula and (A1) for correct substitution of and their from part (b)(ii). Follow through from part (b)(ii).OR ? ? ? ?(M1)(A1)(ft)Note: Follow through from part (b)(ii). ? ? ? ??(A1)(ft)(G2)?ii) ? ? ? ? ? ? (M1)(A1)(ft)Note: Award (M1) for substitution into arithmetic series formula and (A1) for correct substitution, using their first term and their last term from part (b)(i), or their ?and . Follow through from part (b)(i).OR ?? ? ? ??(M1)(A1)(ft)Note: Follow through from part (b)(i). ? ? ? ??(A1)(ft)(G2)Antonio does not earn more than Barbara(his total salary will be less than Barbara’s) ? ? ? ??(A1)(ft)Note: Award (A1)(ft) for a final answer that is consistent with their part (d)(i) and (d)(ii). Accept “Barbara earns more”. The final (A1) can only be awarded if two total salaries are seen.?Examiners reportQuestion 5: Arithmetic and Geometric progressionMost candidates calculated the salaries in the second year correctly. The most common error was to calculate the salaries for the third instead of the second year. In part (b) the use of instead of was very common. For the geometric sequence often a ratio of 0.05 instead of 1.05 was used. Also many of the expressions given did not represent a geometric sequence. Candidates who used a list for part (c) did usually better than the ones that tried to solve an equation. In part (d) the sum of the arithmetic progression was done better than the geometric series. Many candidates calculated the 15th term of the progression and not the series. In general this question part was not answered well. 9a. [2 marks] Markscheme(i) ? ? ? ? ? ? ?(A1)?(ii) ? ? ? ? ? ? ?(A1)(ft)Note: Follow through from part (a)(i).Examiners reportQuestion 2: Arithmetic and geometric sequences and seriesParts (a), (b), (c) and (e) were well done. Quite a few forgot to convert their answer to km in part (c). The main problem with part (d) was that candidates chose to equate the term formula to 1800 rather than the sum of the first n terms formula. Some of those who managed to write the correct equation were not always successful at solving it. Some candidates made use of the trial and error method to reach the correct answer. Part (e) was obvious to some, others put it into a formula with little understanding and a surprising number of candidates had place value issues (stating 10% of 17000 was 170). Many candidates used the compound interest formula in both parts (e) and (f). In part (f) many candidates did not realize that they needed to use the sum of a geometric series formula. They either used the sum of an arithmetic series or as previously mentioned, the compound interest formula. 9b. [2 marks] Markscheme ? ? ? ?(M1)Note: Award (M1) for correct substitution into arithmetic sequence formula. A list of their correct terms (excluding those given in question and the from part (a)(ii)) must be seen for the (M1) to be awarded. ? ? ? ??(A1)(ft)(G2)Note: Follow through from their value for .If a list is used, award (A1) for their term.Examiners reportQuestion 2: Arithmetic and geometric sequences and seriesParts (a), (b), (c) and (e) were well done. Quite a few forgot to convert their answer to km in part (c). The main problem with part (d) was that candidates chose to equate the term formula to 1800 rather than the sum of the first n terms formula. Some of those who managed to write the correct equation were not always successful at solving it. Some candidates made use of the trial and error method to reach the correct answer. Part (e) was obvious to some, others put it into a formula with little understanding and a surprising number of candidates had place value issues (stating 10% of 17000 was 170). Many candidates used the compound interest formula in both parts (e) and (f). In part (f) many candidates did not realize that they needed to use the sum of a geometric series formula. They either used the sum of an arithmetic series or as previously mentioned, the compound interest formula. 9c. [3 marks] Markscheme OR? ? ? ? ??(M1)Note: Award (M1) for correct substitution into arithmetic series formula. Follow through from their part (a)(i). Accept a list added together until the term. ? ? ? ? ?(A1)(ft)Note: Follow through from parts (a) and (b). ? ? ? ? ?(A1)(ft)(G2) ? ?Note: Award (A1)(ft) for correctly converting their metres to kilometres, irrespective of method used. To award the last (A1)(ft) in follow through, the candidate’s answer in metres must be seen.Examiners reportQuestion 2: Arithmetic and geometric sequences and seriesParts (a), (b), (c) and (e) were well done. Quite a few forgot to convert their answer to km in part (c). The main problem with part (d) was that candidates chose to equate the term formula to 1800 rather than the sum of the first n terms formula. Some of those who managed to write the correct equation were not always successful at solving it. Some candidates made use of the trial and error method to reach the correct answer. Part (e) was obvious to some, others put it into a formula with little understanding and a surprising number of candidates had place value issues (stating 10% of 17000 was 170). Many candidates used the compound interest formula in both parts (e) and (f). In part (f) many candidates did not realize that they needed to use the sum of a geometric series formula. They either used the sum of an arithmetic series or as previously mentioned, the compound interest formula. 9d. [3 marks] Markscheme ? ? ? ? ??(M1)Note: Award (M1) for correct substitution into arithmetic series formula equated to . Follow through from their part (a)(i). Accept a list of terms that shows clearly the second and ?second distances.Correct use of kinematics equations is a valid method. ? ? ? ??(A1)(ft) (seconds) ? ? ? ??(A1)(ft)(G2)Note: Award (A1)(ft)?for correct unrounded value for . The second (A1)(ft)?is awarded for the correct rounding off of their value for ?to the nearest second if their unrounded value is seen.Award (M1)(A2)(ft) for their ?if method is shown. Unrounded value for ?may not be seen. Follow through from their and ?only if workings are shown.OR ? ? ? ? ??(M1)Note: Award (M1) for adding the terms until reaching . ? ? ? ? ? ?(A2)(ft)Note: In this method, follow through from their ?from part (a) and their ?from part (c).Examiners reportQuestion 2: Arithmetic and geometric sequences and seriesParts (a), (b), (c) and (e) were well done. Quite a few forgot to convert their answer to km in part (c). The main problem with part (d) was that candidates chose to equate the term formula to 1800 rather than the sum of the first n terms formula. Some of those who managed to write the correct equation were not always successful at solving it. Some candidates made use of the trial and error method to reach the correct answer. Part (e) was obvious to some, others put it into a formula with little understanding and a surprising number of candidates had place value issues (stating 10% of 17000 was 170). Many candidates used the compound interest formula in both parts (e) and (f). In part (f) many candidates did not realize that they needed to use the sum of a geometric series formula. They either used the sum of an arithmetic series or as previously mentioned, the compound interest formula. 9e. [2 marks] Markscheme?(or equivalent) ? ? ? ? ?(M1)Note: Award (M1) for multiplying by or equivalent. ? ? ? ? ? ? ? ? ??(A1)(G2)Examiners reportQuestion 2: Arithmetic and geometric sequences and seriesParts (a), (b), (c) and (e) were well done. Quite a few forgot to convert their answer to km in part (c). The main problem with part (d) was that candidates chose to equate the term formula to 1800 rather than the sum of the first n terms formula. Some of those who managed to write the correct equation were not always successful at solving it. Some candidates made use of the trial and error method to reach the correct answer. Part (e) was obvious to some, others put it into a formula with little understanding and a surprising number of candidates had place value issues (stating 10% of 17000 was 170). Many candidates used the compound interest formula in both parts (e) and (f). In part (f) many candidates did not realize that they needed to use the sum of a geometric series formula. They either used the sum of an arithmetic series or as previously mentioned, the compound interest formula. 9f. [3 marks] Markscheme ? ? ? ? ? (M1)(A1)(ft)Note: Award (M1) for substitution into the geometric series formula, (A1)(ft) for correct substitution. Award (A1)(ft)?for a list of their correct ?terms, (M1) for adding their ?terms. ? ? ? ? ? (A1)(ft)(G2)Note: Follow through from their in part (e).Examiners reportQuestion 2: Arithmetic and geometric sequences and seriesParts (a), (b), (c) and (e) were well done. Quite a few forgot to convert their answer to km in part (c). The main problem with part (d) was that candidates chose to equate the term formula to 1800 rather than the sum of the first n terms formula. Some of those who managed to write the correct equation were not always successful at solving it. Some candidates made use of the trial and error method to reach the correct answer. Part (e) was obvious to some, others put it into a formula with little understanding and a surprising number of candidates had place value issues (stating 10% of 17000 was 170). Many candidates used the compound interest formula in both parts (e) and (f). In part (f) many candidates did not realize that they needed to use the sum of a geometric series formula. They either used the sum of an arithmetic series or as previously mentioned, the compound interest formula. 10a. [3 marks] Markscheme(i) ? ? (or equivalent) ? ? (M1)Note: Award (M1) for one correct equation. Accept a list of at least 5 correct terms.? ? ? (A1)?(ii) ? ? ? ? (A1)(ft) ? ? (C3)Note: Follow through from (a)(i), irrespective of working shown if ORExaminers reportPart (a) was answered correctly by many candidates, but working using equations was rarely seen. A “trial and error” method, based upon a list of terms was the most seen method. 10b. [3 marks] MarkschemeOR?? ? (M1)(A1)(ft)Note: Award (M1) for substituted geometric sequence formula,?(A1)(ft) for their correct substitutions.?OR ? ? (M1)(A1)(ft)Note:?Award (M1) for a list of at least 5 consecutive terms of a geometric sequence, (A1)(ft) for terms corresponding to their answers in part (a).? ? ? (A1)(ft) ? ? (C3)Note: Follow through from part (a).Examiners reportIn part (b) many found the correct answer, but many others did not. Some gave the seventh term of the arithmetic sequence, some gave a term of an incorrect order and some a completely incorrect answer. Finding the correct ratio was the most common problem. Often repeated multiplication was used to find the answer, but also the formula for the nth term of a geometric sequence was used. Several did not use the correct three terms from the question. 11a. [2 marks] Markscheme(i) ? ? OR ? ? (A1) ? ? (C1)(ii) ? ? OR ? ? (A1) ? ? (C1)Examiners report [N/A] 11b. [1 mark] MarkschemeOR ? ? (A1) ? ? (C1)Note: Accept ‘divide by 2’ for (A1).Examiners report [N/A] 11c. [3 marks] Markscheme ? ? (M1)(A1)(ft)Notes: Award (M1) for substitution in the GP term formula,?(A1)(ft) for their correct substitution.Follow through from their common ratio in part (b)(i).?OR ? ? (M1)(A1)(ft)Notes:?Award (M1) for terms 5 and 6 correct (using their ratio).Award (A1)(ft) for terms 7, 8 and 9 correct (using their ratio).? ? ? (A1)(ft) ? ? (C3)Examiners report [N/A] 12a. [3 marks] Markscheme ? ? (M1)(A1)?Note:?Award (M1) for substituted arithmetic sequence formula, (A1) for correct substitutions. If a list is used, award (M1) for at least 6 correct terms seen, award (A1) for at least 20 correct terms seen.? ? ? (A1)(G3)[3 marks]Examiners report [N/A] 12b. [3 marks] Markscheme ? ? (M1)(A1)?Note:?Award (M1) for substituted arithmetic series formula, (A1) for their correct substitutions. Follow through from part (a). For consistent use of geometric series formula in part (b) with the geometric sequence formula in part (a) award a maximum of (M1)(A1)(A0) since their final answer cannot be an integer.?OR ? ? (M1) ? ? (M1)?Note:?Award (M1) for their correctly substituted arithmetic sequence formula, (M1) for their correctly substituted arithmetic series formula. Follow through from part (a) and within part (b).?Note:?If a list is used, award (M1) for at least 10 correct terms seen, award (A1) for these terms being added.? ? (accept ) ? ? (A1)(ft)(G2)[3 marks]Examiners report [N/A] 12c. [3 marks] Markscheme ? ? (M1)(A1)?Note:?Award (M1) for substituted geometric sequence formula, (A1) for correct substitutions. If a list is used, award (M1) for at least 6 correct terms seen, award (A1) for at least 8 correct terms seen.? ? ? (A1)(G3)?Note:?Exact answer only. If both exact and rounded answer seen, award the final (A1).?[3 marks]Examiners report [N/A] 12d. [3 marks] Markscheme ? ? (M1)(A1)(ft)?Note:?Award (M1) for substituted geometric series formula, (A1) for their correct substitutions. Follow through from part (c). If a list is used, award (M1) for at least 8 correct terms seen, award (A1) for these 8 correct terms being added. For consistent use of arithmetic series formula in part (d) with the arithmetic sequence formula in part (c) award a maximum of (M1)(A1)(A1).? ? ? (A1)(ft)(G2)[3 marks]Examiners report [N/A] 12e. [3 marks] Markscheme ? ? (M1)?Note:?Award (M1) for their correct inequality; allow equation.?Follow through from parts (a) and (c). Accept sketches of the two functions as a valid method.? ? (may be implied) ? ? (A1)(ft)?Note:?Award (A1) for seen. The GDC gives answers of and to the inequality; award (M1)(A1) if these are seen with working shown.?OR ? ? ? ? (M1) ? ? ? ? (M1)?Note:?Award (M1) for and both seen, (M1) for and both seen.? ? ? (A1)(ft)(G2)?Note:?Award (G1) for and seen as final answer without working. Accept use of .?[3 marks]Examiners report [N/A] 13a. [2 marks] MarkschemeThe first time an answer is not given to the nearest dollar in parts (a) to (e), the final (A1) in that part is not awarded. ? ? (M1)?Note:?Award (M1) for correct product.? ? ? (A1)(G2)[2 marks]Examiners report [N/A] 13b. [5 marks] MarkschemeThe first time an answer is not given to the nearest dollar in parts (a) to (e), the final (A1) in that part is not awarded.(i) ? ? ? ? (M1)(A1)?Note:?Award (M1) for substituted arithmetic sequence formula, (A1) for correct substitution.? ? ? (A1)(G2)(ii) ? ? ? ? (M1)OR ? ? (M1)?Note:?Award (M1) for correct substitution in arithmetic series formula.? ? ? (A1)(ft)(G1)?Note: Follow through from part (b)(i).?[5 marks]Examiners report [N/A] 13c. [5 marks] MarkschemeThe first time an answer is not given to the nearest dollar in parts (a) to (e), the final (A1) in that part is not awarded.(i) ? ? ? ? (M1)(A1)?Note:?Award (M1) for substituted geometric sequence formula, (A1) for correct substitutions.? ? ? (A1)(G2)?Note:?Award (M1)(A1)(A0) for .? ? ?Award (G1) for if workings are not shown.?(ii) ? ? ? ? (M1)?Note:?Award (M1) for correct substitution in geometric series formula.? ? ? (A1)(ft)(G1)?Note: Follow through from part (c)(i).?[5 marks]Examiners report [N/A] 13d. [3 marks] Markscheme?The first time an answer is not given to the nearest dollar in parts (a) to (e), the final (A1) in that part is not awarded. ? ? (M1)(A1)?Note:?Award (M1) for substituted compound interest formula, (A1) for correct substitutions.?OR ? ? (A1)(M1)?Note:?Award (A1) for seen, (M1) for other correct entries.?OR ? ? (A1)(M1)?Note:?Award (A1) for seen, (M1) for other correct entries.? ? ? (A1)(G2)[3 marks]?Examiners report [N/A] 13e. [1 mark] MarkschemeThe first time an answer is not given to the nearest dollar in parts (a) to (e), the final (A1) in that part is not awarded.Option D ? ? (A1)(ft)?Note:?Follow through from their parts (a), (b), (c) and (d). Award (A1)(ft) only if values for the four options are seen and only if their answer is consistent with their parts (a), (b), (c) and (d).?[1 mark]Examiners report [N/A] 13f. [3 marks] Markscheme ? ? (M1)(A1)Note:?Award (M1) for substituted compound interest formula equated to , (A1) for correct substitutions into formula.?OR ? ? (A1)(M1)?Note:?Award (A1) for seen, (M1) for other correct entries.? ? ? (A1)(G2)[3 marks]Examiners report [N/A] 14a. [3 marks] Markscheme ? ? (M1)(A1)?Note:?Award (M1) for substituted geometric progression formula, (A1) for correct substitution.?? ? If a list is used, award (M1) for a list of at least six terms, beginning with and (A1) for first six terms correct.? ? ??(A1) ? ? (C3)[3 marks]Examiners reportThe first part of this question was answered quite well, especially by candidates who used a list. Part (b) was poorly answered. Common errors in part (b) were to find the number of rounds rather than the total number of matches played or to take the first term as 512 rather than 256. 14b. [3 marks] Markscheme ? OR ? ? ? (M1)(A1)?Note:?Award (M1) for substituted sum of a GP formula, (A1) for correct substitution.?? ? If a list is used, award (A1) for at least 9 correct terms, including , and (M1) for their 9 terms, including , added together.? ? ??(A1) ? ? (C3)[3 marks]Examiners reportThe first part of this question was answered quite well, especially by candidates who used a list. Part (b) was poorly answered. Common errors in part (b) were to find the number of rounds rather than the total number of matches played or to take the first term as 512 rather than 256. 15a. [2 marks] Markscheme ??? (M1) ? ? (A1)???? (C2)Examiners reportThe weakest candidates erroneously used an arithmetic sequence rather than a geometric sequence as specified in the question. 15b. [2 marks] Markscheme ??? (M1)OR???? (M1)OR(by list) ? ? (M1)Notes: Award (M1) for their correct substitution in geometric sequence formula, or stating explicitly and . ? ? (A1)(ft)???? (C2)Note: Follow through from their answer to part (a).Examiners reportThe weakest candidates erroneously used an arithmetic sequence rather than a geometric sequence as specified in the question. 15c. [2 marks] Markscheme???? (M1)Notes: Award (M1) for their correct substitution in geometric series formula. ??? Accept a list of all their ten geometric terms.= 1210 (1207.918...) ? ? (A1)(ft) ? ? (C2)Note: Follow through from their parts (a) and (b).Examiners reportThe weakest candidates erroneously used an arithmetic sequence rather than a geometric sequence as specified in the question. 16a. [3 marks] Markscheme ? ? (M1)(A1)Notes: Award (M1) for substituted AP formula, (A1) for correct substitutions. Accept a list of 4 correct terms.= 160???? (A1)(G3)Examiners report [N/A] 16b. [3 marks] Markscheme ? ? (M1)(M1)Notes: Award (M1) for correctly substituted AP formula, (M1) for equating to 260. Accept a list of correct terms showing at least the 14th and 15th terms.= 15 ? ? (A1)(G2)Examiners report [N/A] 16c. [4 marks] Markscheme or ???? (M1)(A1)(ft)Notes: Award (M1) for substituted AP sum formula, (A1)(ft) for correct substitutions. Accept a sum of a list of 15 correct terms. Follow through from their answer to part (b).2850 seconds ? ? (A1)(ft)(G2)Note: Award (G2) for 2850 seen with no working shown.47.5 minutes???? (A1)(ft)(G3)Notes: A final (A1)(ft) can be awarded for correct conversion from seconds into minutes of their incorrect answer. Follow through from their answer to part (b).Examiners report [N/A] 16d. [3 marks] Markscheme???? (M1)(A1)Notes: Award (M1) for substituted GP formula, (A1) for correct substitutions. Accept a list of 3 correct terms.= 135 (134.832) ? ? (A1)(G2)Examiners report [N/A] 16e. [3 marks] Markscheme???? (M1)(A1)Notes: Award (M1) for substituted GP sum formula, (A1) for correct substitutions. Accept a sum of a list of 4 correct terms.= 525 (524.953...) ? ? (A1)(G2)Examiners report [N/A] 16f. [3 marks] Markscheme ??? (M1)(M1)Notes: Award (M1) for correct left hand side, (M1) for correct right hand side. Accept an equation. Follow through from their expressions given in parts (a) and (d).ORList of at least 2 terms for both sequences (120, 130, … and 120, 127.2, …) ? ? (M1)List of correct 12th and 13th terms for both sequences (..., 230, 240 and …, 227.8, 241.5) ? ? (M1)ORA sketch with a line and an exponential curve, ? ? (M1)An indication of the correct intersection point???? (M1)13th lap ? ? (A1)(ft)(G2)Note: Do not award the final (A1)(ft) if final answer is not a positive integer.Examiners report [N/A] 17a. [2 marks] Markscheme2r2 = 2.205???? (M1)Note: Award (M1) for correct substitution in geometric sequence formula.?r = 1.05 ? ? (A1) ? ? (C2)[2 marks]Examiners reportIn part (a), 1.1025 proved to be a popular, but erroneous, answer. Similarly to question 4, such candidates failed to find a square root. Whilst this accuracy mark was lost for such candidates, much good work was seen in this question reflecting how well drilled the majority of candidates were in both arithmetic and geometric sequence techniques. 17b. [2 marks] Markscheme2(1.05)10???? (M1)Note: Award (M1) for the correct substitution, using their answer to part (a), in geometric sequence formula.?= 3.26 ? ? (3.25778…) ? ? (A1)(ft)???? (C2)Note: Follow through from their part (a).[2 marks]Examiners reportIn part (a), 1.1025 proved to be a popular, but erroneous, answer. Similarly to question 4, such candidates failed to find a square root. Whilst this accuracy mark was lost for such candidates, much good work was seen in this question reflecting how well drilled the majority of candidates were in both arithmetic and geometric sequence techniques. 17c. [2 marks] Markscheme ??? (M1)Note: Award (M1) for their correct substitution in geometric sum formula.?= 82.9 ? ? (82.8609…)???? (A1)(ft) ? ? (C2)Notes: Accept an answer of 3.97221...if r = ?1.05 is found in part (a) and used again in part (c). Follow through from their part (a).[2 marks]Examiners reportIn part (a), 1.1025 proved to be a popular, but erroneous, answer. Similarly to question 4, such candidates failed to find a square root. Whilst this accuracy mark was lost for such candidates, much good work was seen in this question reflecting how well drilled the majority of candidates were in both arithmetic and geometric sequence techniques. 18a. [1 mark] Markscheme1.65 (km) or 1650 (m)???? (A1) ? ? (C1)[1 mark]Examiners reportMost candidates could answer the first part of this question, although a number found it difficult to find the total distance run after 7 days. Many gave the correct answer of 1.65 km or 1650 m for part (a). 18b. [2 marks] Markscheme???? (M1)Notes: Award (M1) for correct substitution of candidate’s 10 % into the correct formula. Accept a list.14.2 (km)???? (A1)(ft)???? (C2)[2 marks]Examiners reportIn part (b), stronger candidates answered correctly, however many used a list or the incorrect arithmetic formula. 18c. [3 marks] Markscheme???? (M1)Note: Award (M1) for setting up their inequality/equation. Accept a list.n = 21.371... ? ? (A1)(ft)n = 22 ? ? (A1)(ft) ? ? (C3)Notes: Follow through from their values of 1.1 and 1.5 in part (b). The final (A1)(ft) is for rounding up their answer for n to a whole number of days.[3 marks]Examiners reportIn part (c), the most common mistake was to use the arithmetic formula. Many candidates rounded their answer down rather than up. 19a. [2 marks] Markscheme(i) u1 + 5d = 100???? (A1)?(ii) u1 + 9d = 124???? (A1) ?[2 marks]Examiners reportPart A: ArithmeticThe contextual nature of this question posed problems for many, though there were many fine attempts. Failure to discriminate between the sequence and series formulas was the cause of the most errors. The final part saw many able to substitute into the formula for the series, but then unable to continue. The use of the GDC in such situations is encouraged; either by graphing each side of the equation and drawing the resultant sketch or by the solver function. 19b. [2 marks] Markscheme(i) 6???? (G1)(ft)?(ii) 70???? (G1)(ft)Notes: Follow through from their equations in parts (a) and (b) even if working not seen. Their answers must be integers. Award (M1)(A0) for an attempt to solve two equations analytically.?[2 marks]Examiners reportPart A: ArithmeticThe contextual nature of this question posed problems for many, though there were many fine attempts. Failure to discriminate between the sequence and series formulas was the cause of the most errors. The final part saw many able to substitute into the formula for the series, but then unable to continue. The use of the GDC in such situations is encouraged; either by graphing each side of the equation and drawing the resultant sketch or by the solver function. 19c. [3 marks] Markscheme???? (M1)(A1)(ft)Note: Award (M1) for substituted sum of AP formula, (A1)(ft) for their correct substituted values.= 2540???? (A1)(ft)(G2)Note: Follow through from their part (b).[3 marks]Examiners reportPart A: ArithmeticThe contextual nature of this question posed problems for many, though there were many fine attempts. Failure to discriminate between the sequence and series formulas was the cause of the most errors. The final part saw many able to substitute into the formula for the series, but then unable to continue. The use of the GDC in such situations is encouraged; either by graphing each side of the equation and drawing the resultant sketch or by the solver function. 19d. [4 marks] Markscheme???? (M1)(A1)Note: Award (M1) for substituted sum of AP formula, (A1) for their correct substituted values.4n2 +136n – 3200 = 0???? (M1)Note: Award (M1) for this equation (or other equivalent expanded quadratic) seen, may be implied if correct final answer seen.n = 16???? (A1)(G3)Note: Do not award the final (A1) for n = 16, – 50 given as final answer, award (G2) if n = 16, – 50 given as final answer without working.[4 marks]Examiners reportPart A: ArithmeticThe contextual nature of this question posed problems for many, though there were many fine attempts. Failure to discriminate between the sequence and series formulas was the cause of the most errors. The final part saw many able to substitute into the formula for the series, but then unable to continue. The use of the GDC in such situations is encouraged; either by graphing each side of the equation and drawing the resultant sketch or by the solver function. 19e. [1 mark] Markscheme9, 27???? (A1)[1 mark]Examiners reportPart B: GeometricThe early straightforward parts were accessible to the majority. The context caused the problems with many choosing the incorrect value of n when using the formulas. Weaker candidates were more successful via counting. The context again proved challenging in the final part, with the incorrect time being determined from the correct value of n. Here, as in Part A, the use of the GDC by graphing each side of the equation is encouraged; however, if teachers feel that such questions require the use (and teaching) of logarithms, such an approach is, of course, given full credit. 19f. [1 mark] Markscheme3???? (A1)[1 mark]Examiners reportPart B: GeometricThe early straightforward parts were accessible to the majority. The context caused the problems with many choosing the incorrect value of n when using the formulas. Weaker candidates were more successful via counting. The context again proved challenging in the final part, with the incorrect time being determined from the correct value of n. Here, as in Part A, the use of the GDC by graphing each side of the equation is encouraged; however, if teachers feel that such questions require the use (and teaching) of logarithms, such an approach is, of course, given full credit. 19g. [2 marks] Markscheme1 × 36???? (M1)= 729???? (A1)(ft)(G2)Note: Award (M1) for correctly substituted GP formula. Follow through from their answer to part (b).[2 marks]Examiners reportPart B: GeometricThe early straightforward parts were accessible to the majority. The context caused the problems with many choosing the incorrect value of n when using the formulas. Weaker candidates were more successful via counting. The context again proved challenging in the final part, with the incorrect time being determined from the correct value of n. Here, as in Part A, the use of the GDC by graphing each side of the equation is encouraged; however, if teachers feel that such questions require the use (and teaching) of logarithms, such an approach is, of course, given full credit. 19h. [2 marks] Markscheme???? (M1)Note: Award (M1) for correctly substituted GP formula. Accept sum 1+ 3 + 9 + 27 + ... + 729. If lists are used, award (M1) for correct list that includes 1093. (1, 4, 13, 40, 121, 364, 1093, 3280…)= 1093???? (A1)(ft)(G2) Note: Follow through from their answer to part (b). For consistent use of n = 6 from part (c) (243) to part (d) leadingto an answer of 364, treat as double penalty and award (M1)(A1)(ft) if working is shown.[2 marks]Examiners reportPart B: GeometricThe early straightforward parts were accessible to the majority. The context caused the problems with many choosing the incorrect value of n when using the formulas. Weaker candidates were more successful via counting. The context again proved challenging in the final part, with the incorrect time being determined from the correct value of n. Here, as in Part A, the use of the GDC by graphing each side of the equation is encouraged; however, if teachers feel that such questions require the use (and teaching) of logarithms, such an approach is, of course, given full credit. 19i. [3 marks] Markscheme???? (M1)Note: Award (M1) for correctly substituted GP formula. If lists are used, award (M1) for correct list that includes 29524. (1, 4, 13, 40, 121, 364, 1093, 3280, 9841, 29524, 88573...). Accept alternative methods, for example continuation of sum in part (d).n = 10 ? ? (A1)(ft)Note: Follow through from their answer to part (b).Exact time = 12:45???? (A1)(ft)(G2)[3 marks]Examiners reportPart B: GeometricThe early straightforward parts were accessible to the majority. The context caused the problems with many choosing the incorrect value of n when using the formulas. Weaker candidates were more successful via counting. The context again proved challenging in the final part, with the incorrect time being determined from the correct value of n. Here, as in Part A, the use of the GDC by graphing each side of the equation is encouraged; however, if teachers feel that such questions require the use (and teaching) of logarithms, such an approach is, of course, given full credit. 20a. [3 marks] Markscheme ?? ?(M1)(A1)Notes: Award (M1) for substituted geometric sequence formula, (A1) for correct substitution.?ORIf a list is used, award (M1) for a list of 9 terms, (A1) for all 9 terms correct.???? (M1)(A1) () ? ? (A1)???? (C3)Note: Award (A1) for exact answer only.[3 marks]Examiners reportThe upper quartile of candidates scored well on this question with the vast majority scoring more than 4 marks. However, the lower quartile did very badly with the majority scoring less than 2 marks. A fundamental error in part (a) resulted in many less able candidates using a common ratio of instead of . Where lists were used in either part of the question, they were either invariably incomplete or contained numerical errors. Indeed, using lists seem to be as problematic in this question as they were in Q6 on arithmetic sequences. Correctly quoted and substituted formula in a correct inequality (= sign was allowed) did earn many candidates two marks here. The required answer of however did not always follow. 20b. [3 marks] Markscheme ??? (M1)(A1)(ft)Notes: Award (M1) for setting substituted geometric sum formula (A1)(ft) for correct substitution into geometric sum formula. Follow through from their common ratio.?ORIf list is used, award (M1) for S(6) and S(7) seen, values don’t have to be correct.(A1) for correct S(6) and S(7). (S(6) and S(7) ).???? (M1)(A1) ??? (A1)(ft) ? ? (C3)Notes: Follow through from their common ratio. Do not award the final (A1)(ft) if is less than or if is not an integer.[3 marks]Examiners reportThe upper quartile of candidates scored well on this question with the vast majority scoring more than 4 marks. However, the lower quartile did very badly with the majority scoring less than 2 marks. A fundamental error in part (a) resulted in many less able candidates using a common ratio of instead of . Where lists were used in either part of the question, they were either invariably incomplete or contained numerical errors. Indeed, using lists seem to be as problematic in this question as they were in Q6 on arithmetic sequences. Correctly quoted and substituted formula in a correct inequality (= sign was allowed) did earn many candidates two marks here. The required answer of however did not always follow. 21a. [1 mark] Markscheme???? (A1) ? ? (C1)Note: Accept .[1 mark]Examiners reportIn part a, many candidates gave the common ratio as 3. 21b. [2 marks] Markscheme ??? (M1)Note: Award (M1) for correct substitution in formula for nth term of a GP. Accept equivalent forms.? ? ? (A1)(ft) ? ? (C2)Notes: Accept . Follow through from their common ratio found in part (a). If used from part (a) award (M1)(A1)(ft) for an answer of or irrespective of whether working is shown.[2 marks]Examiners reportIn part a, many candidates gave the common ratio as 3. While they could set up the equation for part c, relatively few succeeded in solving it. Those who arrived at an answer did not always realize that the answer must be an integer. 21c. [3 marks] Markscheme???? (M1)(M1)Notes: Award (M1) for correct substitution in the sum of a GP formula, (M1) for equating their sum to . Follow through from parts (a) and (b).ORSketch of the function ???? (M1)Indication of point where ? ? (M1)OR ??? (M1)(M1)Note: Award (M1) for a list of at least 8 correct terms, (M1) for the sum of the terms equated to .? ? ? (A1)(ft)???? (C3)Notes: Follow through from parts (a) and (b). If k is not an integer, do not award final (A1). Accept alternative methods. If and used award (M1)(M1)(A1)(ft) for . If and used award (M1)(M1)(A0).[3 marks]Examiners reportIn part a, many candidates gave the common ratio as 3. While they could set up the equation for part c, relatively few succeeded in solving it. Those who arrived at an answer did not always realize that the answer must be an integer. 22a. [2 marks] Markscheme ? ? (M1) or ???? (M1)???? (AG)Notes: Award at most (M1)(M0) if last line not seen. Award (M1)(M0) if is found by repeated multiplication (division) of by .[2 marks]Examiners reportPart A: Geometric sequences/seriesThe majority of the candidates were not able to offer a satisfactory justification in a) and only scored 1 mark. 22b. [2 marks] Markscheme ??? (M1)Notes: Award (M1) for correct substitution into correct formula. Accept an equivalent method.?1???? (A1)(G2)[2 marks]Examiners reportPart A: Geometric sequences/seriesParts b) and c) were mostly well answered. 22c. [3 marks] Markscheme???? (M1)(A1)Note: Award (M1) for substitution into the correct formula, (A1) for correct substitution.?OR(A1) for complete and correct list of eight terms???? (A1)(M1) for their eight terms added???? (M1)???? (A1)(G2)[3 marks]Examiners reportPart A: Geometric sequences/seriesParts b) and c) were mostly well answered. 22d. [3 marks] Markscheme ??? (M1)(M1)(ft)Notes: Award (M1) for correct substitution into the correct formula for the sum, (M1) for comparing to . Accept equation. Follow through from their expression for the sum used in part (c).?ORIf a list is used: ??? (M1) ??? (M1) ??? (A1)(ft)(G2)Note: Follow through from their expression for the sum used in part (c).[3 marks]Examiners reportPart A: Geometric sequences/series The responses to part d) were often weak. Those candidates who set up the equation scored two marks but very few of them were able to reach the correct final answer. 22e. [2 marks] Markscheme (may be implied)???? (A1) ??? (A1)(G2)[2 marks]Examiners reportPart B: Arithmetic sequences/seriesParts a), and b)(i) were mostly answered correctly. 22f. [6 marks] Markscheme(i)???? ??? OR???? ??? (M1)???????? ??? (A1)(G2)?(ii)???? (a)???? ??? OR???? ??? (M1)?????????????????? ??? (M1)?????????????????? ? ? (AG)Notes: Award second (M1) for correct removal of denominator or brackets and no further incorrect working seen. Award at most(M1)(M0) if last line not seen.???????? (b)???? ??? (G2)Note: If both solutions to the quadratic equation are seen and the correct value is not identified as the required answer, award (G1)(G0).?[6 marks]Examiners reportPart B: Arithmetic sequences/seriesParts a), and b)(i) were mostly answered correctly. Parts b)(ii)a) and b)(ii)b) were poorly answered. Many candidates did not know how to approach the “show that” question. A few were able to solve the quadratic equation using the GDC. Those who attempted to solve it without the GDC generally failed to find the correct answer. 23a. [8 marks] MarkschemeOption 1:???? Amount???????? (M1)(A1)= ???? (A1)(G2)Note: Award (M1) for substitution in compound interest formula, (A1) for correct substitution. Give full credit for use of lists.Option 2: ? ? Amount???? ??? (M1)= ???? (A1)(G2)Note: Award (M1) for correct substitution in the compound interest formula. Give full credit for use of lists.?[8 marks]Examiners reportFor many, this question came as a welcome relief following the previous two questions. For those with a sound grasp of the topic, there were many very successful attempts.A common error was to make all the comparisons using interest alone; though much credit was given for doing this, candidates should be aware of what is being asked for in the question.Many did not understand the notion of monthly compounding periods. 23b. [1 mark] MarkschemeOption 1 is the best investment option. ? ? (A1)(ft)[1 mark]Examiners reportFor many, this question came as a welcome relief following the previous two questions. For those with a sound grasp of the topic, there were many very successful attempts.A common error was to make all the comparisons using interest alone; though much credit was given for doing this, candidates should be aware of what is being asked for in the question.Many did not understand the notion of monthly compounding periods. 23c. [2 marks] Markschemeu1 = 135 + 7(1)???? (M1)= 142 ? ? (A1)(G2)[2 marks]Examiners reportFor many, this question came as a welcome relief following the previous two questions. For those with a sound grasp of the topic, there were many very successful attempts.A common weakness was seen in the “show that” parts of the question where, despite a lenient approach to method, many were unable to communicate their thoughts on paper.For many, finding an expression for Sn in (c) was problematical.The final part was challenging to the great majority, with a large number not attempting it at all; only the highly competent reached the correct answer. 23d. [2 marks] Markschemeu2 = 135 + 7(2) = 149???? (M1)d = 149?– 142 ? ? OR alternatives ? ? (M1)(ft)d = 7???? (AG)[2 marks]Examiners reportFor many, this question came as a welcome relief following the previous two questions. For those with a sound grasp of the topic, there were many very successful attempts.A common weakness was seen in the “show that” parts of the question where, despite a lenient approach to method, many were unable to communicate their thoughts on paper.For many, finding an expression for Sn in (c) was problematical.The final part was challenging to the great majority, with a large number not attempting it at all; only the highly competent reached the correct answer. 23e. [3 marks] Markscheme???? (M1)(ft)?Note: Award (M1) for correct substitution in correct formula.? ??? OR equivalent???? (A1) ??? (= 3.5n2 + 138.5n)???? (A1)(G3)[3 marks]Examiners reportFor many, this question came as a welcome relief following the previous two questions. For those with a sound grasp of the topic, there were many very successful attempts.A common weakness was seen in the “show that” parts of the question where, despite a lenient approach to method, many were unable to communicate their thoughts on paper.For many, finding an expression for Sn in (c) was problematical.The final part was challenging to the great majority, with a large number not attempting it at all; only the highly competent reached the correct answer. 23f. [2 marks] Markscheme20r3?= 67.5 ? ? (M1)r3 = 3.375???? OR ? ? (A1)r = 1.5???? (AG)[2 marks]Examiners reportFor many, this question came as a welcome relief following the previous two questions. For those with a sound grasp of the topic, there were many very successful attempts.A common weakness was seen in the “show that” parts of the question where, despite a lenient approach to method, many were unable to communicate their thoughts on paper.For many, finding an expression for Sn in (c) was problematical.The final part was challenging to the great majority, with a large number not attempting it at all; only the highly competent reached the correct answer. 23g. [2 marks] Markscheme???? (M1)Note: Award (M1) for correct substitution in correct formula.= 643 (accept 643.4375) ? ? (A1)(G2)[2 marks]Examiners reportFor many, this question came as a welcome relief following the previous two questions. For those with a sound grasp of the topic, there were many very successful attempts.A common weakness was seen in the “show that” parts of the question where, despite a lenient approach to method, many were unable to communicate their thoughts on paper.For many, finding an expression for Sn in (c) was problematical.The final part was challenging to the great majority, with a large number not attempting it at all; only the highly competent reached the correct answer. 23h. [2 marks] Markscheme???? (M1)Note: Award (M1) for an attempt using lists or for relevant graph.n = 10 ? ? (A1)(ft)(G2) ?Note: Follow through from their (c).?[2 marks]Examiners reportFor many, this question came as a welcome relief following the previous two questions. For those with a sound grasp of the topic, there were many very successful attempts.A common weakness was seen in the “show that” parts of the question where, despite a lenient approach to method, many were unable to communicate their thoughts on paper.For many, finding an expression for Sn in (c) was problematical.The final part was challenging to the great majority, with a large number not attempting it at all; only the highly competent reached the correct answer. 24a. [2 marks] Markscheme (or equivalent)???? (M1)Note: Award (M1) for dividing correct terms.r = 1.04? ?? (A1)???? (C2)Notes: In (b) and (c) (ft) from candidate’s r. Allow lists, graphs etc. as working in (b) and (c).?[2 marks]Examiners reportMany marks were lost through incorrect rounding or premature rounding (if a year by year approach was used).This part was well attempted, errors being the use of 4% as the common ratio. 24b. [2 marks] MarkschemeFinancial penalty (FP) applies in this part?Fees = 8000 (1.04)6???? (M1)Note: Award (M1) for correct substitution into correct formula.(FP)???? Fees = 10122.55 USD (USD not required) ? ? (A1)(ft) ? ? (C2)Note: Special exception to the note above.Award maximum of (M1)(A0) if 5 is used as the power.[2 marks]Examiners reportMany marks were lost through incorrect rounding or premature rounding (if a year by year approach was used).The common error here was the use of the incorrect index in the formula. 24c. [2 marks] MarkschemeFinancial penalty (FP) applies in this part????? (M1)Notes: Award (M1) for correct substitution into correct formula.?Give full credit for solution by lists.(FP) ? ? Total = 73713.81 USD (USD not required) ? ? (A1)(ft) ? ? (C2)[2 marks]Examiners reportMany marks were lost through incorrect rounding or premature rounding (if a year by year approach was used).Attempts at calculation without use of the formula were largely unsuccessful.Printed for International School of Europe ? International Baccalaureate Organization 2019 International Baccalaureate? - Baccalauréat International? - Bachillerato Internacional? ................
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