| Exam Board | AQA |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2021 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Compound growth applications |
| Difficulty | Moderate -0.8 This is a straightforward geometric progression question with standard applications. Parts (a)-(d) involve routine GP calculations (finding terms, sum of finite/infinite series) with clear scaffolding. Part (e) requires basic real-world reasoning. The context is accessible and the mathematical techniques are core A-level content with no novel problem-solving required. |
| Spec | 1.04e Sequences: nth term and recurrence relations1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
| Answer | Marks |
|---|---|
| 7(a) | Obtains the correct volume |
| Answer | Marks | Guidance |
|---|---|---|
| units | 1.1b | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Subtotal | 1 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 7(b) | States A = 30 |
| Answer | Marks | Guidance |
|---|---|---|
| n | 1.1b | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| to three terms | 3.3 | E1 |
| Subtotal | 2 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 7(c) | Uses geometric model with their |
| Answer | Marks | Guidance |
|---|---|---|
| 15 | 3.4 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Condone unrounded answers | 1.1b | A1F |
| Subtotal | 2 | |
| Q | Marking instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 7(d) | Uses sum to infinity formula with | |
| their value of A substituted | 3.4 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| sum to infinity | 1.1b | A1F |
| Answer | Marks | Guidance |
|---|---|---|
| millilitres | 3.2a | A1 |
| Subtotal | 3 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 7(e) | Explains that the model used |
| Answer | Marks | Guidance |
|---|---|---|
| indefinitely which is unrealistic | 3.5b | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| water consumed by animals | 3.5a | E1 |
| Subtotal | 2 | |
| Question Total | 10 | |
| Q | Marking instructions | AO |
Question 7:
--- 7(a) ---
7(a) | Obtains the correct volume
AWRT 29
Condone incorrect or missing
units | 1.1b | B1 | W = 29.4
2
Subtotal | 1
Q | Marking instructions | AO | Mark | Typical solution
--- 7(b) ---
7(b) | States A = 30
PI by building up of a sequence
to three terms or
W =30×0.98n−1 seen
n | 1.1b | B1 | W is the nth term of a geometric
n
sequence, a 2% reduction gives a
common ratio of 0.98
A = 30
Explains W is (the nth term of)
n
a geometric sequence
explaining that a 2% reduction
gives a common ratio of 0.98
PI by building up of a sequence
to three terms | 3.3 | E1
Subtotal | 2
Q | Marking instructions | AO | Mark | Typical solution
--- 7(c) ---
7(c) | Uses geometric model with their
value of A substituted to find S
15 | 3.4 | M1 | ( )
30 1−0.9815
S =
15 1−0.98
=392
Obtains their correct value of
S
15
FT their value of A
Condone unrounded answers | 1.1b | A1F
Subtotal | 2
Q | Marking instructions | AO | Mark | Typical solution
--- 7(d) ---
7(d) | Uses sum to infinity formula with
their value of A substituted | 3.4 | M1 | 30
S =
∞ 1−0.98
=1500
1.5 + 4 = 5.5 litres
Obtains their correct value of
sum to infinity | 1.1b | A1F
Obtains 5.5 litres
CAO
Accept answer in litres or
millilitres | 3.2a | A1
Subtotal | 3
Q | Marking instructions | AO | Mark | Typical solution
--- 7(e) ---
7(e) | Explains that the model used
assumes the drips continue
indefinitely which is unrealistic | 3.5b | E1 | The sum to infinity was used but
this assumes there are infinite
drips, but they have stopped
Water will evaporate over several
hours
States a relevant environmental
factor
eg water has evaporated or
wind affected water level or
water consumed by animals | 3.5a | E1
Subtotal | 2
Question Total | 10
Q | Marking instructions | AO | Mark | Typical solutionA building has a leaking roof and, while it is raining, water drips into a 12 litre bucket.
When the rain stops, the bucket is one third full.
Water continues to drip into the bucket from a puddle on the roof.
In the first minute after the rain stops, 30 millilitres of water drips into the bucket.
In each subsequent minute, the amount of water that drips into the bucket reduces by 2%.
During the $n$th minute after the rain stops, the volume of water that drips into the bucket is $W_n$ millilitres.
\begin{enumerate}[label=(\alph*)]
\item Find $W_2$
[1 mark]
\item Explain why
$$W_n = A \times 0.98^{n-1}$$
and state the value of $A$.
[2 marks]
\item Find the increase in the water in the bucket 15 minutes after the rain stops.
Give your answer to the nearest millilitre.
[2 marks]
\item Assuming it does not start to rain again, find the maximum amount of water in the bucket.
[3 marks]
\item After several hours the water has stopped dripping.
Give two reasons why the amount of water in the bucket is not as much as the answer found in part (d).
[2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 3 2021 Q7 [10]}}