| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2020 |
| Session | March |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Real-world AP: find term or total |
| Difficulty | Moderate -0.8 This is a straightforward arithmetic sequence application with clear structure. Part (a) is trivial percentage calculation (600/30000). Part (b) requires finding the 24th term of an arithmetic sequence for the bonus and applying compound interest for salary, then calculating a percentage—all standard procedures with no conceptual challenges or problem-solving insight needed. |
| Spec | 1.04k Modelling with sequences: compound interest, growth/decay |
| Answer | Marks |
|---|---|
| \(2\%\) | B1 |
| Total: 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Bonus \(= 600 + 23\times100 = 2900\) | B1 | |
| Salary \(= 30000\times1.03^{23}\) | M1 | Allow \(30000\times1.03^{24}\) (60984) |
| \(= 59207.60\) | A1 | Allow answers of 3 significant figure accuracy or better |
| \(\frac{\text{their}\,2900}{\text{their}\,59200}\) | M1 | SOI |
| \(4.9(0)\%\) | A1 | |
| Total: 5 |
## Question 8(a):
| $2\%$ | B1 | |
|---|---|---|
| **Total: 1** | | |
---
## Question 8(b):
| Bonus $= 600 + 23\times100 = 2900$ | B1 | |
|---|---|---|
| Salary $= 30000\times1.03^{23}$ | M1 | Allow $30000\times1.03^{24}$ (60984) |
| $= 59207.60$ | A1 | Allow answers of 3 significant figure accuracy or better |
| $\frac{\text{their}\,2900}{\text{their}\,59200}$ | M1 | SOI |
| $4.9(0)\%$ | A1 | |
| **Total: 5** | | |
---8 A woman's basic salary for her first year with a particular company is $\$ 30000$ and at the end of the year she also gets a bonus of $\$ 600$.
\begin{enumerate}[label=(\alph*)]
\item For her first year, express her bonus as a percentage of her basic salary.\\
At the end of each complete year, the woman's basic salary will increase by $3 \%$ and her bonus will increase by $\$ 100$.
\item Express the bonus she will be paid at the end of her 24th year as a percentage of the basic salary paid during that year.
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2020 Q8 [6]}}