| Exam Board | AQA |
|---|---|
| Module | Paper 1 (Paper 1) |
| Year | 2021 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Two related arithmetic progressions |
| Difficulty | Standard +0.3 This is a straightforward two-part arithmetic sequence problem requiring standard formula application. Part (a) involves solving simultaneous equations using aā=3 and Sāā=42 with familiar formulas. Part (b) requires equating two sum formulas and solving a quadratic equation. All techniques are routine for AS-level with no novel insight needed, making it slightly easier than average. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(a + 8d = 3\) | B1 (1.1b) | OE |
| \(\frac{21}{2}(2a + 20d) = 42\) | B1 (1.1b) | OE |
| Solve simultaneously: \(a + 10d = 2\), \(a = 7\), \(d = -0.5\) | M1 (3.1a) | Elimination of one variable or better; condone slips \(a+9d=3\) or \(\frac{21}{2}(2a+20d)=21\) |
| Correct \(a\) and \(d\) | A1 (1.1b) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\frac{n}{2}(14 - 0.5(n-1)) = \frac{n}{2}(-36 + 0.75(n-1))\) giving \(n = 0\) or \(41\) | B1F (1.1b) | At least one correct unsimplified expression for \(S_n\) or \(T_n\); FT non-zero values of \(a\) and \(d\); PI by simplified correct equation |
| Equates \(S_n\) and \(T_n\) expressions | M1 (3.1a) | FT non-zero \(a\), \(d\); finds non-zero value of \(n\); PI by \(n = 41\) |
| \(n = 41\) | R1 (2.2a) | Deduces correct value |
## Question 6(a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $a + 8d = 3$ | B1 (1.1b) | OE |
| $\frac{21}{2}(2a + 20d) = 42$ | B1 (1.1b) | OE |
| Solve simultaneously: $a + 10d = 2$, $a = 7$, $d = -0.5$ | M1 (3.1a) | Elimination of one variable or better; condone slips $a+9d=3$ or $\frac{21}{2}(2a+20d)=21$ |
| Correct $a$ and $d$ | A1 (1.1b) | |
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## Question 6(b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{n}{2}(14 - 0.5(n-1)) = \frac{n}{2}(-36 + 0.75(n-1))$ giving $n = 0$ or $41$ | B1F (1.1b) | At least one correct unsimplified expression for $S_n$ or $T_n$; FT non-zero values of $a$ and $d$; PI by simplified correct equation |
| Equates $S_n$ and $T_n$ expressions | M1 (3.1a) | FT non-zero $a$, $d$; finds non-zero value of $n$; PI by $n = 41$ |
| $n = 41$ | R1 (2.2a) | Deduces correct value |
---6
\begin{enumerate}[label=(\alph*)]
\item The ninth term of an arithmetic series is 3
The sum of the first $n$ terms of the series is $S _ { n }$ and $S _ { 21 } = 42$\\
Find the first term and common difference of the series.\\[0pt]
[4 marks]\\
6
\item A second arithmetic series has first term - 18 and common difference $\frac { 3 } { 4 }$\\
The sum of the first $n$ terms of this series is $T _ { n }$\\
Find the value of $n$ such that $T _ { n } = S _ { n }$\\[0pt]
[3 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 1 2021 Q6 [7]}}