| Exam Board | AQA |
|---|---|
| Module | Further Paper 2 (Further Paper 2) |
| Year | 2024 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Standard summation formulae application |
| Difficulty | Standard +0.3 This is a straightforward series summation question requiring sigma notation and proof by standard methods (likely method of differences or standard summation formulas). Part (a) is trivial pattern recognition, and part (b) is a routine algebraic manipulation that appears frequently in A-level Further Maths curricula. The result is a standard formula that students typically practice multiple times. |
| Spec | 1.04g Sigma notation: for sums of series4.06b Method of differences: telescoping series |
| Answer | Marks |
|---|---|
| 5(a) | n |
| Answer | Marks | Guidance |
|---|---|---|
| r=1 | 2.5 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Subtotal | 1 | |
| Q | Marking Instructions | AO |
| Answer | Marks |
|---|---|
| 5(b) | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| required. | 2.1 | R1 |
| Subtotal | 2 | |
| Question total | 3 | |
| Q | Marking instructions | AO |
Question 5:
--- 5(a) ---
5(a) | n
∑
Obtains r(r+1) OE
r=1
ISW
n
Condone ∑ r2 +r
r=1 | 2.5 | B1 | n
∑
r(r+1)
r=1
Subtotal | 1
Q | Marking Instructions | AO | Marks | Typical Solution
--- 5(b) ---
5(b) | 1
Uses n(n+1)(2n+1)
6
1
and n(n+1)
2 | 1.1a | M1 | n 1 1
∑ (r2 +r)= n(n+1)(2n+1)+ n(n+1)
6 2
r=1
1
= n(n+1)(2n+1+3)
6
1
= n(n+1)(n+2)
3
Completes fully correct
working, with at least one
intermediate step, to
1
obtain n(n+1)(n+2) AG
3
LHS of typical solution not
required. | 2.1 | R1
Subtotal | 2
Question total | 3
Q | Marking instructions | AO | Marks | Typical solutionThe first four terms of the series $S$ can be written as
$$S = (1 \times 2) + (2 \times 3) + (3 \times 4) + (4 \times 5) + ...$$
\begin{enumerate}[label=(\alph*)]
\item Write an expression, using $\sum$ notation, for the sum of the first $n$ terms of $S$
[1 mark]
\item Show that the sum of the first $n$ terms of $S$ is equal to
$$\frac{1}{3}n(n + 1)(n + 2)$$
[2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Further Paper 2 2024 Q5 [3]}}