| Exam Board | Edexcel |
|---|---|
| Module | PMT Mocks (PMT Mocks) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Quadratic in exponential form |
| Difficulty | Standard +0.3 This is a straightforward quadratic-in-exponential problem requiring substitution of u=2^x, solving the resulting quadratic equation, then back-substituting. It's a standard technique taught in C2/C3 with no novel insight required, making it slightly easier than average. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks | Guidance |
|---|---|---|
| Find exact coordinates of point \(A\) where \(y = 21 - 2^x\) meets \(y = 2^{2x+1}\) | (4) | B1 Combines equations \(21 - 2^x = 2^{2x+1}\) to reach correct quadratic equation in \(2^x\); M1 Solves quadratic equation of form \(ay^2 + by \pm 21 = 0\) by factorisation or completion of square or correct use of formula; dM1 Uses logs correctly and proceeds to value for \(x\) from equation of form \(2^x = k\) where \(k > 1\) and attempts to find corresponding \(y\)-value; A1 Correct solution only \((\log_2 3, 18)\) |
Find exact coordinates of point $A$ where $y = 21 - 2^x$ meets $y = 2^{2x+1}$ | (4) | B1 Combines equations $21 - 2^x = 2^{2x+1}$ to reach correct quadratic equation in $2^x$; M1 Solves quadratic equation of form $ay^2 + by \pm 21 = 0$ by factorisation or completion of square or correct use of formula; dM1 Uses logs correctly and proceeds to value for $x$ from equation of form $2^x = k$ where $k > 1$ and attempts to find corresponding $y$-value; A1 Correct solution only $(\log_2 3, 18)$
---8.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{cb92f7b6-2ba5-4703-9595-9ba8570fc52b-14_976_1296_283_429}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
The curves with equation $y = 21 - 2 ^ { x }$ meet the curve with equation $y = 2 ^ { 2 x + 1 }$ at the point $A$ as shown in Figure 2.
Find the exact coordinates of point $A$.\\
\hfill \mbox{\textit{Edexcel PMT Mocks Q8 [4]}}