| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2013 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Solve exponential equation using logarithms |
| Difficulty | Easy -1.2 This is a straightforward C1 question testing basic exponential equation solving. Part (a) requires simple recognition that 8 = 2³, while part (b) needs rewriting 4 as 2² and combining indices before solving—standard textbook exercises with minimal problem-solving demand, easier than average A-level questions. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(2^y = 8 \Rightarrow y = 3\) | B1 | cao (can be implied i.e. by \(2^3\)) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(8 = 2^3\) | M1 | Replaces 8 by \(2^3\) (may be implied) |
| \(4^{x+1} = (2^2)^{x+1}\) or \((2^{x+1})^2\) | M1 | Replaces 4 by \(2^2\) correctly |
| \(2^{3x+2} = 2^3 \Rightarrow 3x+2 = 3 \Rightarrow x = \frac{1}{3}\) | M1A1 | M1: Adds powers of 2 on lhs and puts equal to 3 leading to solution for \(x\). A1: \(x=\frac{1}{3}\) or \(x=0.\dot{3}\) or awrt 0.333 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(4^{x+1} = 4 \times 4^x\) | M1 | Obtains \(4^{x+1}\) in terms of \(4^x\) correctly |
| \(2^x \times 4^x = 8^x\) | M1 | Combines \(2^x\) and \(4^x\) correctly |
| \(4 \times 8^x = 8 \Rightarrow 8^x = 2 \Rightarrow x = \frac{1}{3}\) | M1A1 | M1: Solves \(8^x = k\) leading to solution for \(x\). A1: \(x=\frac{1}{3}\) or awrt 0.333 |
## Question 5(a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $2^y = 8 \Rightarrow y = 3$ | B1 | cao (can be implied i.e. by $2^3$) |
## Question 5(b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $8 = 2^3$ | M1 | Replaces 8 by $2^3$ (may be implied) |
| $4^{x+1} = (2^2)^{x+1}$ or $(2^{x+1})^2$ | M1 | Replaces 4 by $2^2$ **correctly** |
| $2^{3x+2} = 2^3 \Rightarrow 3x+2 = 3 \Rightarrow x = \frac{1}{3}$ | M1A1 | M1: Adds powers of 2 on lhs and puts equal to 3 leading to solution for $x$. A1: $x=\frac{1}{3}$ or $x=0.\dot{3}$ or awrt 0.333 |
**Way 2:**
| Answer/Working | Mark | Guidance |
|---|---|---|
| $4^{x+1} = 4 \times 4^x$ | M1 | Obtains $4^{x+1}$ in terms of $4^x$ **correctly** |
| $2^x \times 4^x = 8^x$ | M1 | Combines $2^x$ and $4^x$ **correctly** |
| $4 \times 8^x = 8 \Rightarrow 8^x = 2 \Rightarrow x = \frac{1}{3}$ | M1A1 | M1: Solves $8^x = k$ leading to solution for $x$. A1: $x=\frac{1}{3}$ or awrt 0.333 |
---5. Solve
\begin{enumerate}[label=(\alph*)]
\item $2 ^ { y } = 8$
\item $2 ^ { x } \times 4 ^ { x + 1 } = 8$
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2013 Q5 [5]}}