| Exam Board | Edexcel |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2019 |
| Session | January |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Express in terms of substitution |
| Difficulty | Moderate -0.8 This is a straightforward indices manipulation question requiring only basic index laws (division rule, converting roots to fractional powers, and equating powers). It's simpler than average A-level questions as it involves a single equation with routine algebraic steps and no problem-solving insight needed. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.06c Logarithm definition: log_a(x) as inverse of a^x |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| Attempts both sides as powers of 3: \(\frac{3^x}{3^{4y}} = 3^3 \times 3^{0.5} \Rightarrow 3^{x-4y} = 3^{3.5}\) | M1 | Must attempt subtraction law LHS and addition law RHS; condone errors writing \(27\sqrt{3}\) as single power of 3 provided working shown |
| Sets powers equal and attempts to make \(y\) the subject: \(x - 4y = 3.5 \Rightarrow y = \ldots\) | dM1 | Dependent on M1; must have 3 terms; cannot lose one in rearrangement; do not award if making \(x\) subject |
| \(y = \frac{1}{4}x - \frac{7}{8}\) | A1 | Accept \(y = \frac{2x-7}{8}\), \(y = 0.25x - 0.875\); NOT \(y = \frac{x - \frac{7}{2}}{4}\) or \(y = \frac{x-3.5}{4}\) |
## Question 2:
$$\frac{3^x}{3^{4y}} = 27\sqrt{3}$$
| Working/Answer | Marks | Guidance |
|---|---|---|
| Attempts both sides as powers of 3: $\frac{3^x}{3^{4y}} = 3^3 \times 3^{0.5} \Rightarrow 3^{x-4y} = 3^{3.5}$ | M1 | Must attempt subtraction law LHS and addition law RHS; condone errors writing $27\sqrt{3}$ as single power of 3 provided working shown |
| Sets powers equal and attempts to make $y$ the subject: $x - 4y = 3.5 \Rightarrow y = \ldots$ | dM1 | Dependent on M1; must have 3 terms; cannot lose one in rearrangement; do not award if making $x$ subject |
| $y = \frac{1}{4}x - \frac{7}{8}$ | A1 | Accept $y = \frac{2x-7}{8}$, $y = 0.25x - 0.875$; NOT $y = \frac{x - \frac{7}{2}}{4}$ or $y = \frac{x-3.5}{4}$ |
---\begin{enumerate}
\item Given
\end{enumerate}
$$\frac { 3 ^ { x } } { 3 ^ { 4 y } } = 27 \sqrt { 3 }$$
find $y$ as a simplified function of $x$.\\
\hfill \mbox{\textit{Edexcel P1 2019 Q2 [3]}}