Question 1 - A-Level Maths

OCR MEI Paper 2 2023 June — Question 1 3 marks

Exam Board	OCR MEI
Module	Paper 2 (Paper 2)
Year	2023
Session	June
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Geometric Sequences and Series
Type	Find sum to infinity
Difficulty	Easy -1.2 This is a straightforward application of the sum to infinity formula for a geometric series. The common ratio r = -1/3 is immediately visible, \|r\| < 1 is satisfied, and students simply need to apply S∞ = a/(1-r) with a = 9. This requires only direct recall and substitution with no problem-solving or conceptual challenges.
Spec	1.04j Sum to infinity: convergent geometric series \|r\|<1

1 Determine the sum of the infinite geometric series \(9 - 3 + 1 - \frac { 1 } { 3 } + \frac { 1 } { 9 } + \ldots\)

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Question 1:

Answer	Marks	Guidance
Answer	Marks	Guidance
\(\frac{a}{1-r}\) used	M1	\(a\) and \(r\) are numerical values; \(a = 9\) and/or \(r = \pm\frac{1}{3}\)
\(\frac{9}{1\pm\frac{1}{3}}\) soi	M1
\(\frac{27}{4}\) or \(6\frac{3}{4}\) or \(6.75\) cao isw	A1	if unsupported allow SC2 for correct answer
[3]

## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{a}{1-r}$ used | M1 | $a$ and $r$ are numerical values; $a = 9$ and/or $r = \pm\frac{1}{3}$ |
| $\frac{9}{1\pm\frac{1}{3}}$ soi | M1 | |
| $\frac{27}{4}$ or $6\frac{3}{4}$ or $6.75$ cao isw | A1 | if unsupported allow **SC2** for correct answer |
| **[3]** | | |

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1 Determine the sum of the infinite geometric series $9 - 3 + 1 - \frac { 1 } { 3 } + \frac { 1 } { 9 } + \ldots$

\hfill \mbox{\textit{OCR MEI Paper 2 2023 Q1 [3]}}

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Q1 3 Q2 3 Q3 3 Q4 5 Q5 3 Q6 4 Q7 4 Q8 6 Q9 5 Q10 5 Q11 6 Q12 4 Q13 9 Q14 8 Q15 7 Q16 8 Q17 6 Q18 11