| Exam Board | Edexcel |
|---|---|
| Module | Paper 1 (Paper 1) |
| Year | 2020 |
| Session | October |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Find term or common difference |
| Difficulty | Moderate -0.8 This is a straightforward application of arithmetic and geometric sequence formulas with clear given values (first and sixth terms). Part (a) requires finding the common difference and calculating the third term; part (b) requires finding the common ratio and calculating the fifth term. Both are direct formula applications with no conceptual challenges or multi-step reasoning, making this easier than average. |
| 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 |
| Uses \(115 = 28 + 5d \Rightarrow d = (17.4)\) | M1 | Translates problem using \(n\)th term \(= a+(n-1)d\) and attempts to find \(d\). Note \(115=28+6d \Rightarrow d=\ldots\) is M0. |
| Uses \(28 + 2\times\text{"}{17.4}\text{"} = \ldots\) | M1 | Uses model to find fastest speed in 3rd gear using \(28+2"d"\) or equivalent. Can be awarded following incorrect \(d\). |
| \(= 62.8 \ (\text{km h}^{-1})\) | A1 | Lack of units condoned. Allow exact \(\frac{314}{5}\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Uses \(115 = 28r^5 \Rightarrow r = (1.3265)\) | M1 | Translates problem using \(n\)th term \(= ar^{n-1}\) and attempts to find \(r\). Must use 1st and 6th gear. Implied by stating or using \(r = \text{awrt } 1.33\) |
| Uses \(28\times\text{"}{1.3265}^4\text{"} = \ldots\) or \(\dfrac{115}{\text{"}{1.3265}\text{"}}\) | M1 | Uses model to find fastest speed in 5th gear. Can be awarded following incorrect \(r\). |
| \(= 86.7 \ (\text{km h}^{-1})\) | A1 | awrt 86.7 km/h. Lack of units condoned. Expressions must be evaluated. |
## Question 5:
### Part (a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Uses $115 = 28 + 5d \Rightarrow d = (17.4)$ | M1 | Translates problem using $n$th term $= a+(n-1)d$ and attempts to find $d$. Note $115=28+6d \Rightarrow d=\ldots$ is M0. |
| Uses $28 + 2\times\text{"}{17.4}\text{"} = \ldots$ | M1 | Uses model to find fastest speed in 3rd gear using $28+2"d"$ or equivalent. Can be awarded following incorrect $d$. |
| $= 62.8 \ (\text{km h}^{-1})$ | A1 | Lack of units condoned. Allow exact $\frac{314}{5}$ |
### Part (b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Uses $115 = 28r^5 \Rightarrow r = (1.3265)$ | M1 | Translates problem using $n$th term $= ar^{n-1}$ and attempts to find $r$. Must use 1st and 6th gear. Implied by stating or using $r = \text{awrt } 1.33$ |
| Uses $28\times\text{"}{1.3265}^4\text{"} = \ldots$ or $\dfrac{115}{\text{"}{1.3265}\text{"}}$ | M1 | Uses model to find fastest speed in 5th gear. Can be awarded following incorrect $r$. |
| $= 86.7 \ (\text{km h}^{-1})$ | A1 | awrt 86.7 km/h. Lack of units condoned. Expressions must be evaluated. |
---\begin{enumerate}
\item A car has six forward gears.
\end{enumerate}
The fastest speed of the car
\begin{itemize}
\item in $1 ^ { \text {st } }$ gear is $28 \mathrm {~km} \mathrm {~h} ^ { - 1 }$
\item in $6 ^ { \text {th } }$ gear is $115 \mathrm {~km} \mathrm {~h} ^ { - 1 }$
\end{itemize}
Given that the fastest speed of the car in successive gears is modelled by an arithmetic sequence,\\
(a) find the fastest speed of the car in $3 { } ^ { \text {rd } }$ gear.
Given that the fastest speed of the car in successive gears is modelled by a geometric sequence,\\
(b) find the fastest speed of the car in $5 ^ { \text {th } }$ gear.
\hfill \mbox{\textit{Edexcel Paper 1 2020 Q5 [6]}}