| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Year | 2019 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Total over time period |
| Difficulty | Moderate -0.5 This is a straightforward geometric series application (part a) combined with arithmetic sequence calculations (parts b and c). Part (a) requires setting up and solving a GP sum equation, which is standard C2 content. Parts (b) and (c) are simple arithmetic sequence calculations requiring only direct formula application. The context is clear, all formulas are standard, and no novel problem-solving insight is required—just methodical application of learned techniques. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| Attempts \(S_N = \dfrac{25(1.1^N - 1)}{1.1 - 1} = 1000\) | M1 | Attempts correct sum formula \(S_N = \dfrac{a(r^N-1)}{r-1}\) with \(a=25, r=1.1, S_N=1000\) |
| \(\Rightarrow 1.1^N = 5\) | A1 | Proceeding to \(1.1^N = 5\) |
| \(\Rightarrow N = \dfrac{\log 5}{\log 1.1}\) | M1 | Uses logs correctly to solve equation of form \(a^N = b\) where both \(a\) and \(b\) are positive |
| \(\Rightarrow N = 17\) | A1 | \(N = 17\) from \(1.1^N = 5\) and correct work |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| Uses \(= 50 + 14 \times 20 = 330\) | M1 A1 | Uses \(a + (n-1)d\) with \(a=50, d=20, n=15\); 330 — this alone scores both marks |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| Attempts \(S_N = \dfrac{15}{2}\{2\times50 + 14\times20\}\) or \(S_N = \dfrac{15}{2}\{50+330\}\) | M1 | Attempts \(S_N = \dfrac{n}{2}\{2a+(n-1)d\}\) with \(a=50, n=15, d=20\) or \(a=250, n=15, d=100\) |
| Total \(= 2850 \times 5 = \text{(£)}14250\) or Total \(= \dfrac{15}{2}\{2\times250+14\times100\} = 14250\) | dM1 A1 | dM1: uses method to calculate total money raised (dependent on correct sum formula); A1: £14250 |
# Question 12:
## Part (a):
| Working | Mark | Guidance |
|---------|------|----------|
| Attempts $S_N = \dfrac{25(1.1^N - 1)}{1.1 - 1} = 1000$ | M1 | Attempts correct sum formula $S_N = \dfrac{a(r^N-1)}{r-1}$ with $a=25, r=1.1, S_N=1000$ |
| $\Rightarrow 1.1^N = 5$ | A1 | Proceeding to $1.1^N = 5$ |
| $\Rightarrow N = \dfrac{\log 5}{\log 1.1}$ | M1 | Uses logs correctly to solve equation of form $a^N = b$ where both $a$ and $b$ are positive |
| $\Rightarrow N = 17$ | A1 | $N = 17$ from $1.1^N = 5$ and correct work |
## Part (b):
| Working | Mark | Guidance |
|---------|------|----------|
| Uses $= 50 + 14 \times 20 = 330$ | M1 A1 | Uses $a + (n-1)d$ with $a=50, d=20, n=15$; 330 — this alone scores both marks |
## Part (c):
| Working | Mark | Guidance |
|---------|------|----------|
| Attempts $S_N = \dfrac{15}{2}\{2\times50 + 14\times20\}$ or $S_N = \dfrac{15}{2}\{50+330\}$ | M1 | Attempts $S_N = \dfrac{n}{2}\{2a+(n-1)d\}$ with $a=50, n=15, d=20$ or $a=250, n=15, d=100$ |
| Total $= 2850 \times 5 = \text{(£)}14250$ or Total $= \dfrac{15}{2}\{2\times250+14\times100\} = 14250$ | dM1 A1 | dM1: uses method to calculate total money raised (dependent on correct sum formula); A1: £14250 |
---12. Karen is going to raise money for a charity.
She aims to cycle a total distance of 1000 km over a number of days.\\
On day one she cycles 25 km .\\
She increases the distance that she cycles each day by $10 \%$ of the distance cycled on the previous day, until she reaches the total distance of 1000 km .
She reaches the total distance of 1000 km on day $N$, where $N$ is a positive integer.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $N$.
On day one, 50 people donated money to the charity. Each day, 20 more people donated to the charity than did so on the previous day, so that 70 people donated money on day two, 90 people donated money on day three, and so on.
\item Find the number of people who donated to the charity on day fifteen.
Each day, the donation given by each person was $\pounds 5$
\item Find the total amount of money donated by the end of day fifteen.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 2019 Q12 [9]}}