| Exam Board | CAIE |
|---|---|
| Module | P3 (Pure Mathematics 3) |
| Year | 2018 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Total over time period |
| Difficulty | Moderate -0.8 This is a straightforward application of geometric progression formulas with clear context. Part (i) requires direct substitution into the nth term formula (a·r^(n-1) with a=8000, r=1.02, n=12), and part (ii) uses the standard GP sum formula. Both are routine calculations with no conceptual challenges or problem-solving required—easier than average A-level questions. |
| Spec | 1.04i Geometric sequences: nth term and finite series sum1.04k Modelling with sequences: compound interest, growth/decay |
| Answer | Marks | Guidance |
|---|---|---|
| 3(i) | Fully justify the given statement | B1 |
| Answer | Marks |
|---|---|
| 3(ii) | Separate variables and attempt integration of at least one side |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | B1 B1 | Must be working from∫1dy= ∫kdx |
| Answer | Marks | Guidance |
|---|---|---|
| with terms a ln y and bx, where ab ≠ 0 | M1 | |
| Obtain correct solution in any form | A1 | lny= 1x+ln3−2 |
| Answer | Marks | Guidance |
|---|---|---|
| Obtain answer y=3e2 , or equivalent | A1 | 1 x+ln3−2 x−1 .80 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 3:
--- 3(i) ---
3(i) | Fully justify the given statement | B1 | Some indication of use of gradient of curve = gradient of tangent
(PT) and no errors seen /no incorrect statements
1
--- 3(ii) ---
3(ii) | Separate variables and attempt integration of at least one side
1
Obtain terms ln y and x
2 | B1 B1 | Must be working from∫1dy= ∫kdx
y
B marks are not available for fortuitously correct answers
Use x = 4, y = 3 to evaluate a constant or as limits in a solution
with terms a ln y and bx, where ab ≠ 0 | M1
Obtain correct solution in any form | A1 | lny= 1x+ln3−2
2
1
x−2
Obtain answer y=3e2 , or equivalent | A1 | 1 x+ln3−2 x−1 .80
Accept y=e 2 , y=e 2 , y=3 ex−4
y =... scores A0
5
Question | Answer | Marks | GuidanceA company producing salt from sea water changed to a new process. The amount of salt obtained each week increased by 2% of the amount obtained in the preceding week. It is given that in the first week after the change the company obtained 8000 kg of salt.
\begin{enumerate}[label=(\roman*)]
\item Find the amount of salt obtained in the 12th week after the change. [3]
\item Find the total amount of salt obtained in the first 12 weeks after the change. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE P3 2018 Q3 [5]}}