OCR FP1 2015 June — Question 2 4 marks

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2015
SessionJune
Marks4
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 splitting the sum, applying Σr² = n(n+1)(2n+1)/6, and factorising the result. While it's Further Maths content, it's a routine textbook exercise with no problem-solving or insight required, making it easier than average overall.
Spec4.06a Summation formulae: sum of r, r^2, r^3
2 Find \(\sum _ { r = 1 } ^ { n } \left( 3 r ^ { 2 } - 5 \right)\), expressing your answer in a fully factorised form.
Question 2:
AnswerMarks Guidance
AnswerMarks Guidance
M1*Express as difference using standard result for \(\sum r^2\)
\(\frac{1}{2}n(n+1)(2n+1) - 5n\)A1 Correct unsimplified expression
DM1Obtain at least factor of \(n\)
\(\frac{1}{2}n(2n-3)(n+3)\) or \(n(n-\frac{3}{2})(n+3)\)A1 Obtain correct answer, only these versions
[4] 
## Question 2:

| Answer | Marks | Guidance |
|--------|-------|----------|
| | M1* | Express as difference using standard result for $\sum r^2$ |
| $\frac{1}{2}n(n+1)(2n+1) - 5n$ | A1 | Correct unsimplified expression |
| | DM1 | Obtain at least factor of $n$ |
| $\frac{1}{2}n(2n-3)(n+3)$ or $n(n-\frac{3}{2})(n+3)$ | A1 | Obtain correct answer, only these versions |
| **[4]** | | |

---
2 Find $\sum _ { r = 1 } ^ { n } \left( 3 r ^ { 2 } - 5 \right)$, expressing your answer in a fully factorised form.

\hfill \mbox{\textit{OCR FP1 2015 Q2 [4]}}
This paper (10 questions)
View full paper
Q1 3 Q2 4 Q3 5 Q4 5 Q5 8 Q6 7 Q7 10 Q8 10 Q9 10 Q10 10