| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2013 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Solve power equations |
| Difficulty | Easy -1.3 This is a straightforward indices question testing basic recall of index laws. Part (i) requires knowing that any number to power 0 equals 1, part (ii) involves simple negative indices, and part (iii) requires applying fractional indices. All three parts are routine manipulations with no problem-solving required, making this easier than average for A-level. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks |
|---|---|
| B1 | Allow \(3^0\) |
| [1] |
| Answer | Marks | Guidance |
|---|---|---|
| M1 | or \(t^3 = \frac{1}{64}\) or \(64t^3 = 1\) or \(\left(\frac{1}{t}\right)^3 = 64\) | Allow embedded. \(4^3\) www alone implies M1 A0 |
| A1 | \(4^3\) is A0 if \(\pm\frac{1}{4}\) is A0 | |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| M1 | or \(8p^3 = 8^3\). Allow \(2p^3 = 8\) for M1 www | If not 512, evidence of \(8 \times 8 \times 8\) needed. SC Spotted B1 for 2, B1 for -2, B1 for justifying exactly 2 solutions. SC \(8p^3 = 8\), \(p = \pm 1\) B1 |
| A1 | www | |
| A1 | www | |
| [3] |
### (i)
$n = 0$
| B1 | Allow $3^0$ |
| [1] | |
### (ii)
$\frac{1}{t^3} = 64$ (or $4^3$), $t = \frac{1}{4}$
| M1 | or $t^3 = \frac{1}{64}$ or $64t^3 = 1$ or $\left(\frac{1}{t}\right)^3 = 64$ | Allow embedded. $4^3$ www alone implies M1 A0 |
| A1 | $4^3$ is A0 if $\pm\frac{1}{4}$ is A0 | |
| [2] | | |
### (iii)
$2p^3 = 8$, $p = 2$ or $p = -2$
| M1 | or $8p^3 = 8^3$. Allow $2p^3 = 8$ for M1 www | If not 512, evidence of $8 \times 8 \times 8$ needed. SC Spotted B1 for 2, B1 for -2, B1 for justifying exactly 2 solutions. SC $8p^3 = 8$, $p = \pm 1$ B1 |
| A1 | www | |
| A1 | www | |
| [3] | | |Solve the equations
\begin{enumerate}[label=(\roman*)]
\item $3^n = 1$, [1]
\item $t^{-3} = 64$, [2]
\item $(8p^6)^{\frac{1}{3}} = 8$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C1 2013 Q2 [6]}}