| Exam Board | Edexcel |
|---|---|
| Module | Paper 1 (Paper 1) |
| Year | 2020 |
| Session | October |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Simple exponential equation solving |
| Difficulty | Easy -1.2 This is a straightforward application of logarithms to solve an exponential equation—a routine technique tested at AS/A-level. It requires only taking logs of both sides, applying log laws, and rearranging algebraically. The question explicitly tells students to use logarithms, removing any problem-solving element. This is easier than average as it's pure procedural recall with no conceptual challenge. |
| Spec | 1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(4^{3p-1} = 5^{210} \Rightarrow (3p-1)\log 4 = 210\log 5\) | M1 | Takes logs of both sides and uses power law on each side. Condone missing bracket on lhs and slips. Any base including ln but logs must be same base. |
| \(\Rightarrow 3p = \frac{210\log 5}{\log 4} + 1 \Rightarrow p = \ldots\) | dM1 | Full method leading to value for \(p\). Dependent on previous M. Must attempt to change subject in correct order. |
| \(p = \text{awrt } 81.6\) | A1 | awrt 81.6 following correct method. Bracketing errors can be recovered. Correct answer with no working scores 0. |
## Question 2:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $4^{3p-1} = 5^{210} \Rightarrow (3p-1)\log 4 = 210\log 5$ | M1 | Takes logs of both sides and uses power law on each side. Condone missing bracket on lhs and slips. Any base including ln but logs must be same base. |
| $\Rightarrow 3p = \frac{210\log 5}{\log 4} + 1 \Rightarrow p = \ldots$ | dM1 | Full method leading to value for $p$. Dependent on previous M. Must attempt to change subject in correct order. |
| $p = \text{awrt } 81.6$ | A1 | awrt 81.6 following correct method. Bracketing errors can be recovered. Correct answer with no working scores 0. |
---\begin{enumerate}
\item By taking logarithms of both sides, solve the equation
\end{enumerate}
$$4 ^ { 3 p - 1 } = 5 ^ { 210 }$$
giving the value of $p$ to one decimal place.
\hfill \mbox{\textit{Edexcel Paper 1 2020 Q2 [3]}}