| Exam Board | AQA |
|---|---|
| Module | Paper 1 (Paper 1) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Sum of first n terms |
| Difficulty | Moderate -0.8 Both parts are straightforward applications of standard arithmetic sequence formulas. Part (a) requires only the sum formula S_n = n(a+l)/2 with given values. Part (b) involves setting up two simultaneous equations from the sum formula and the 6:1 ratio condition, then solving—a routine multi-step problem with no conceptual challenges beyond basic arithmetic sequence manipulation. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks |
|---|---|
| 10(a) | Substitutes n=300,a=−7 and |
| Answer | Marks | Guidance |
|---|---|---|
| d = AWRT 0.13 | 3.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Obtains 3750 | 1.1b | A1 |
| Subtotal | 2 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 10(b) | Forms an equation using |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | 3.4 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| highest term to the lowest term. | 3.4 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| values. | 3.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| CAO | 3.2a | A1 |
| Subtotal | 4 | |
| Question 10 Total | 6 | |
| Q | Marking instructions | AO |
Question 10:
--- 10(a) ---
10(a) | Substitutes n=300,a=−7 and
l =32
n
Into S = ( a + l )
n
2
Or
Substitutes n=300,a=−7
39 3
and d = = into
299 23
n
S = ( 2a+(n−1 )d )
n
2
Condone n = 299 or 301 and
d = AWRT 0.13 | 3.1a | M1 | 300
S = (−7+32 )
300 2
=3750
Obtains 3750 | 1.1b | A1
Subtotal | 2
Q | Marking instructions | AO | Marks | Typical solution
--- 10(b) ---
10(b) | Forms an equation using
S = 1 2 6 0
9
Might see
9
(2a+8d)=1260a+4d =140
2 | 3.4 | M1 | 9
( a + ) l = 1 2 6 0 a + l = 2 8 0
2
l = 6 a
7 a = 2 8 0
a = 4 0 , l = 2 4 0
Value of top prize = £240
Forms an equation using the
relationship between the highest
and least values.
eg a+8d =6a or l = 6 a
OE
1
Might see l = a which may
6
indicate the candidate is
correctly working from the
highest term to the lowest term. | 3.4 | M1
Obtains and solves an equation
in one variable having formed
one equation using S =1260
9
OR used the relationship
between the highest and least
values. | 3.1a | M1
Obtains £240
Must have correct units.
CAO | 3.2a | A1
Subtotal | 4
Question 10 Total | 6
Q | Marking instructions | AO | Marks | Typical solution\begin{enumerate}[label=(\alph*)]
\item An arithmetic sequence has 300 terms.
The first term of the sequence is $-7$ and the last term is 32
Find the sum of the 300 terms.
[2 marks]
\item A school holds a raffle at its summer fair.
There are nine prizes.
The total value of the prizes is £1260
The values of the prizes form an arithmetic sequence.
The top prize has the highest value, and the bottom prize has the least value.
The value of the top prize is six times the value of the bottom prize.
Find the value of the top prize.
[4 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 1 2024 Q10 [6]}}