| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2011 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Solve exponential equation by substitution |
| Difficulty | Moderate -0.8 This is a straightforward C2 exponential equation requiring standard substitution (let u = 7^x) to form a quadratic, then solve and back-substitute. Part (a) is basic graph sketching. Both parts are routine textbook exercises with no problem-solving insight required, making this easier than average. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06g Equations with exponentials: solve a^x = b |
Question 8(b)
Method of trial and improvement
M1: For a full method of trial and improvement by trialing $f(\text{value between } 0.1 \text{ and } 0.5645) = \text{value}$ and $f(\text{value between } 0.5645 \text{ and } 1) = \text{value}$
A1: Any one of these values correct to 1 sf or truncated 1 sf
A1: Both of these values correct to 1 sf or truncated 1 sf
M1: A method to confirm root to 2 dp by finding by trialing $f(\text{value between } 0.56 \text{ and } 0.5645) = \text{value}$ and $f(\text{value between } 0.5645 \text{ and } 0.565) = \text{value}$
A1: Both values correct to 1 sf or truncated 1 sf
B1: Confirmation that the root is $x = 0.56$ (only)
(6 marks)
Note: If a candidate goes from $7^x = 3$ with no working to $x = 0.5645\ldots$ then give M1A1 implied.\begin{enumerate}
\item (a) Sketch the graph of $y = 7 ^ { x } , x \in \mathbb { R }$, showing the coordinates of any points at which the graph crosses the axes.\\
(b) Solve the equation
\end{enumerate}
$$7 ^ { 2 x } - 4 \left( 7 ^ { x } \right) + 3 = 0$$
giving your answers to 2 decimal places where appropriate.\\
\hfill \mbox{\textit{Edexcel C2 2011 Q8 [8]}}