OCR FP1 2016 June — Question 1 5 marks

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2016
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSequences and series, recurrence and convergence
TypeStandard summation formulae application
DifficultyModerate -0.5 This is a straightforward application of standard summation formulae requiring expansion to quadratic and linear terms, then direct substitution of known results. While it's Further Maths content, it's a routine first question requiring only algebraic manipulation and formula recall with no problem-solving insight needed.
Spec4.06a Summation formulae: sum of r, r^2, r^3

1 Find \(\sum _ { r = 1 } ^ { n } ( 3 r + 1 ) ( r - 1 )\), giving your answer in a fully factorised form.

Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
\(\frac{1}{2}n(n+1)(2n+1) - n(n+1) - n\)M1* Expand and attempt to use standard series, at least one used correctly
Any two terms correct, may be unsimplifiedA1 Any two terms correct
All terms correctA1 All terms correct
\(\frac{1}{2}n(2n+3)(n-1)\) or \(n(n+\frac{3}{2})(n-1)\)DM1 Attempt to find 3 factors
Obtain correct answerA1 Obtain correct answer
[5]
## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{1}{2}n(n+1)(2n+1) - n(n+1) - n$ | M1* | Expand and attempt to use standard series, at least one used correctly |
| Any two terms correct, may be unsimplified | A1 | Any two terms correct |
| All terms correct | A1 | All terms correct |
| $\frac{1}{2}n(2n+3)(n-1)$ or $n(n+\frac{3}{2})(n-1)$ | DM1 | Attempt to find 3 factors |
| Obtain correct answer | A1 | Obtain correct answer |
| **[5]** | | |

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1 Find $\sum _ { r = 1 } ^ { n } ( 3 r + 1 ) ( r - 1 )$, giving your answer in a fully factorised form.

\hfill \mbox{\textit{OCR FP1 2016 Q1 [5]}}