OCR Further Pure Core 2 2021 November — Question 4 3 marks

Exam BoardOCR
ModuleFurther Pure Core 2 (Further Pure Core 2)
Year2021
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSequences and series, recurrence and convergence
TypeStandard summation formulae application
DifficultyModerate -0.8 This is a straightforward application of standard summation formulae requiring expansion of (2r+3)² into 4r² + 12r + 9, then applying the formulae for Σr², Σr, and Σ1. While it involves algebraic manipulation and multiple steps, it's a routine textbook exercise with no problem-solving insight required, making it easier than average for Further Maths.
Spec4.06a Summation formulae: sum of r, r^2, r^3
4 In this question you must show detailed reasoning.
Determine the value of \(\sum _ { r = 1 } ^ { 100 } ( 2 r + 3 ) ^ { 2 }\).
Question 4:
AnswerMarks
4DR
100 100 100 100
∑(2r+3)2 =4∑r2 +12∑r+9∑1
r=1 r=1 r=1 r=1
100 1
∑r2 = ×100(100+1)(2×100+1)
6
r=1
AnswerMarks
4×338350 + 12×½×100×101 + 900 = 1414900B1
M1
A1
AnswerMarks
[3]3.1a
1.1a
AnswerMarks
1.1Expanding and separating
100
Use of formula for ∑r2
r=1
Question 4:
4 | DR
100 100 100 100
∑(2r+3)2 =4∑r2 +12∑r+9∑1
r=1 r=1 r=1 r=1
100 1
∑r2 = ×100(100+1)(2×100+1)
6
r=1
4×338350 + 12×½×100×101 + 900 = 1414900 | B1
M1
A1
[3] | 3.1a
1.1a
1.1 | Expanding and separating
100
Use of formula for ∑r2
r=1
4 In this question you must show detailed reasoning.\\
Determine the value of $\sum _ { r = 1 } ^ { 100 } ( 2 r + 3 ) ^ { 2 }$.

\hfill \mbox{\textit{OCR Further Pure Core 2 2021 Q4 [3]}}
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