| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2017 |
| Session | June |
| Marks | 7 |
| 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 sequences requiring only basic formula substitution. Part (a) uses the nth term formula with all values given, and part (b) combines the sum formula for weeks 1-12 with simple multiplication for weeks 13-52. No problem-solving insight needed, just routine calculation. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(206 = 140 + (12-1) \times d \Rightarrow d = ...\) | M1 | Uses \(206 = 140 + (12-1) \times d\) and proceeds as far as \(d = ...\) |
| \((d =)\ 6\) | A1 | Correct answer only can score both marks |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(S_{12} = \frac{12}{2}(140 + 206)\) or \(S_{12} = \frac{12}{2}(2 \times 140 + (12-1) \times "6")\) or \(S_{11} = \frac{11}{2}(140 + 206 - "6")\) or \(S_{11} = \frac{11}{2}(2 \times 140 + (11-1) \times "6")\) | M1 | Attempts \(S_n = \frac{n}{2}(a+l)\) or \(S_n = \frac{n}{2}(2a+(n-1)d)\) with \(n=12\), \(a=140\), \(l=206\), \(d=\)'6' WAY 1, or with \(n=11\), \(a=140\), \(l=206-\)'6', \(d=\)'6' WAY 2. If using \(S_n = \frac{n}{2}(2a+(n-1)d)\), the \(n\) must be used consistently |
| \(S = 2076\) WAY 1 or \(S = 1870\) WAY 2 | A1 | Correct sum (may be implied) |
| \((52-12) \times 206 = ...\) or \((52-11) \times 206 = ...\) | M1 | Attempts to find \((52-12) \times 206\) or \((52-11) \times 206\). Does not have to be consistent with their \(n\) used for first Method mark |
| Total \(=\) "2076" \(+\) "8240" \(= ...\) (WAY 1) or Total \(=\) "1870" \(+\) "8446" \(= ...\) (WAY 2) | ddM1 | Attempts to find the total by adding the sum to 12 terms with \((52-12)\) lots of 206, or sum to 11 terms with \((52-11)\) lots of 206. Consistency now required. Dependent on both previous method marks |
| \(10316\) | A1 | cao |
## Question 4:
### Part (a):
| Answer | Mark | Guidance |
|--------|------|----------|
| $206 = 140 + (12-1) \times d \Rightarrow d = ...$ | M1 | Uses $206 = 140 + (12-1) \times d$ and proceeds as far as $d = ...$ |
| $(d =)\ 6$ | A1 | Correct answer only can score both marks |
### Part (b):
| Answer | Mark | Guidance |
|--------|------|----------|
| $S_{12} = \frac{12}{2}(140 + 206)$ or $S_{12} = \frac{12}{2}(2 \times 140 + (12-1) \times "6")$ or $S_{11} = \frac{11}{2}(140 + 206 - "6")$ or $S_{11} = \frac{11}{2}(2 \times 140 + (11-1) \times "6")$ | M1 | Attempts $S_n = \frac{n}{2}(a+l)$ or $S_n = \frac{n}{2}(2a+(n-1)d)$ with $n=12$, $a=140$, $l=206$, $d=$'6' **WAY 1**, or with $n=11$, $a=140$, $l=206-$'6', $d=$'6' **WAY 2**. If using $S_n = \frac{n}{2}(2a+(n-1)d)$, the $n$ must be used consistently |
| $S = 2076$ **WAY 1** or $S = 1870$ **WAY 2** | A1 | Correct sum (may be implied) |
| $(52-12) \times 206 = ...$ or $(52-11) \times 206 = ...$ | M1 | Attempts to find $(52-12) \times 206$ or $(52-11) \times 206$. Does **not** have to be consistent with their $n$ used for first Method mark |
| Total $=$ "2076" $+$ "8240" $= ...$ **(WAY 1)** or Total $=$ "1870" $+$ "8446" $= ...$ **(WAY 2)** | ddM1 | Attempts to find the total by adding the sum to 12 terms with $(52-12)$ lots of 206, or sum to 11 terms with $(52-11)$ lots of 206. Consistency now required. **Dependent on both previous method marks** |
| $10316$ | A1 | cao |
---4. A company, which is making 140 bicycles each week, plans to increase its production. The number of bicycles produced is to be increased by $d$ each week, starting from 140 in week 1 , to $140 + d$ in week 2 , to $140 + 2 d$ in week 3 and so on, until the company is producing 206 in week 12.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $d$.
After week 12 the company plans to continue making 206 bicycles each week.
\item Find the total number of bicycles that would be made in the first 52 weeks starting from and including week 1.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2017 Q4 [7]}}