OCR MEI Further Pure Core AS 2021 November — Question 1 3 marks

Exam BoardOCR MEI
ModuleFurther Pure Core AS (Further Pure Core AS)
Year2021
SessionNovember
Marks3
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Mark schemeDownload PDF ↗
TopicSequences and Series
TypeSum of Powers Using Standard Formulae
DifficultyModerate -0.8 This is a straightforward application of standard summation formulae (sum of r² and sum of r) with basic algebraic manipulation. It requires only direct substitution into known formulae and factorisation, making it easier than average but not trivial since it involves two formulae and algebraic simplification.
Spec4.06a Summation formulae: sum of r, r^2, r^3
1 Using standard summation formulae, find \(\sum _ { r = 1 } ^ { n } \left( r ^ { 2 } - 3 r \right)\), giving your answer in fully factorised form.
Question 1:
AnswerMarks
1n n n
∑(r2−3r)=∑r2−3∑r
r=1 r=1 r=1
= 1n(n+1)(2n+1)−3n(n+1)
6 2
=1n(n+1)(n−4)
AnswerMarks
3M1
A1
A1
AnswerMarks
[3]1.1a
1.1
1.1
Question 1:
1 | n n n
∑(r2−3r)=∑r2−3∑r
r=1 r=1 r=1
= 1n(n+1)(2n+1)−3n(n+1)
6 2
=1n(n+1)(n−4)
3 | M1
A1
A1
[3] | 1.1a
1.1
1.1
1 Using standard summation formulae, find $\sum _ { r = 1 } ^ { n } \left( r ^ { 2 } - 3 r \right)$, giving your answer in fully factorised form.

\hfill \mbox{\textit{OCR MEI Further Pure Core AS 2021 Q1 [3]}}
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Q1 3 Q2 3 Q3 7 Q4 5 Q5 5 Q6 12 Q7 9 Q8 7 Q9 9