CAIE P3 2018 June — Question 3 5 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2018
SessionJune
Marks5
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Mark schemeDownload PDF ↗
TopicGeometric Sequences and Series
TypeSum of first n terms
DifficultyStandard +0.3 This is a straightforward application of geometric series formulas requiring substitution of r=0.99 and n=100 into standard formulas, then calculating a percentage. The arithmetic is slightly tedious but the method is routine with no problem-solving insight needed, making it slightly easier than average.
Spec1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1
The common ratio of a geometric progression is 0.99. Express the sum of the first 100 terms as a percentage of the sum to infinity, giving your answer correct to 2 significant figures. [5]
Question 3:
AnswerMarks Guidance
3Integrate by parts and reach axsin3x+b∫sin3xdx M1*
1 `1
Obtain xsin3x− ∫sin3xdx, or equivalent
AnswerMarks
3 3A1
1 1
Complete the integration and obtain xsin3x+ cos3x, or equivalent
AnswerMarks
3 9A1
Substitute limits correctly having integrated twice and obtained ax sin 3x + b cos 3xM1(dep*)
1 ( )
Obtain answer π−2 OE
AnswerMarks Guidance
18A1
Total:5
QuestionAnswer Marks 
Question 3:
3 | Integrate by parts and reach axsin3x+b∫sin3xdx | M1*
1 `1
Obtain xsin3x− ∫sin3xdx, or equivalent
3 3 | A1
1 1
Complete the integration and obtain xsin3x+ cos3x, or equivalent
3 9 | A1
Substitute limits correctly having integrated twice and obtained ax sin 3x + b cos 3x | M1(dep*)
1 ( )
Obtain answer π−2 OE
18 | A1
Total: | 5
Question | Answer | Marks
The common ratio of a geometric progression is 0.99. Express the sum of the first 100 terms as a percentage of the sum to infinity, giving your answer correct to 2 significant figures. [5]

\hfill \mbox{\textit{CAIE P3 2018 Q3 [5]}}
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Q1 3 Q2 3 Q3 5 Q4 6 Q5 5 Q6 7 Q7 9 Q8 8 Q9 9 Q10 9 Q11 11