| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2009 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Real-world AP: find n satisfying a condition |
| Difficulty | Moderate -0.8 This is a straightforward multi-part question testing basic arithmetic and geometric series formulas with simple real-world context. Part (i) requires summing an arithmetic sequence and solving a quadratic equation, while part (ii) involves geometric series with powers of 2. All techniques are standard C2 content with no novel problem-solving required, making it easier than average but not trivial due to the multiple parts and calculations involved. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| iA \(10+20+30+40+50+60\) | B1 | or \(\frac{6}{2}(2\times10+5\times10)\) or \(\frac{6}{2}(10+60)\) |
| iB Correct use of AP formula with \(a=10\) and \(d=10\) | M1 | |
| \(n(5+5n)\) or \(5n(n+1)\) or \(5(n^2+n)\) or \((5n^2+5n)\) | A1 | |
| \(10n^2 + 10n - 20700 = 0\) | M1 | Or better |
| 45 c.a.o. | A1 | |
| iiA \(4\) | 1 | |
| iiB £2555 | 2 | M1 for \(5(1+2+...2^8)\) or \(5(2^9-1)\) o.e. |
| iiC Correct use of GP formula with \(a=5\), \(r=2\) | M1 | |
| \(5(2^n - 1)\) o.e. \(= 2621435\) | DM1 | "S" need not be simplified |
| \(2^n = 524288\) www | M1 | |
| 19 c.a.o. | A1 |
# Question 11:
| Answer/Working | Mark | Guidance |
|---|---|---|
| **iA** $10+20+30+40+50+60$ | B1 | or $\frac{6}{2}(2\times10+5\times10)$ or $\frac{6}{2}(10+60)$ | **[1]** |
| **iB** Correct use of AP formula with $a=10$ and $d=10$ | M1 | |
| $n(5+5n)$ or $5n(n+1)$ or $5(n^2+n)$ or $(5n^2+5n)$ | A1 | |
| $10n^2 + 10n - 20700 = 0$ | M1 | Or better |
| 45 c.a.o. | A1 | | **[4]** |
| **iiA** $4$ | 1 | | **[1]** |
| **iiB** £2555 | 2 | M1 for $5(1+2+...2^8)$ or $5(2^9-1)$ o.e. | **[2]** |
| **iiC** Correct use of GP formula with $a=5$, $r=2$ | M1 | |
| $5(2^n - 1)$ o.e. $= 2621435$ | DM1 | "S" need not be simplified |
| $2^n = 524288$ www | M1 | |
| 19 c.a.o. | A1 | | **[4]** |
---11
\begin{enumerate}[label=(\roman*)]
\item In a 'Make Ten' quiz game, contestants get $\pounds 10$ for answering the first question correctly, then a further $\pounds 20$ for the second question, then a further $\pounds 30$ for the third, and so on, until they get a question wrong and are out of the game.\\
(A) Haroon answers six questions correctly. Show that he receives a total of $\pounds 210$.\\
(B) State, in a simple form, a formula for the total amount received by a contestant who answers $n$ questions correctly.
Hence find the value of $n$ for a contestant who receives $\pounds 10350$ from this game.
\item In a 'Double Your Money' quiz game, contestants get $\pounds 5$ for answering the first question correctly, then a further $\pounds 10$ for the second question, then a further $\pounds 20$ for the third, and so on doubling the amount for each question until they get a question wrong and are out of the game.\\
(A) Gary received $\pounds 75$ from the game. How many questions did he get right?\\
(B) Bethan answered 9 questions correctly. How much did she receive from the game?\\
(C) State a formula for the total amount received by a contestant who answers $n$ questions correctly.
Hence find the value of $n$ for a contestant in this game who receives $\pounds 2621435$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 2009 Q11 [12]}}