| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2007 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Evaluate numerical powers |
| Difficulty | Easy -1.8 This is a straightforward recall question testing basic index laws (zero power, negative power, fractional power). Part (i) is trivial (any number to power 0 equals 1), and part (ii) requires recognizing 32 as 2^5 then applying index laws mechanically. No problem-solving or insight needed, just direct application of rules. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(1\) | B1 [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\frac{1}{2} \times 2^4\) | M1 | \(2^{-1}=\frac{1}{2}\) or \(32^{\frac{1}{5}}=2\) or \(2^5=32\) soi |
| M1 | \(32^{\frac{4}{5}}=2^4\) or \(16\) seen or implied | |
| \(= 8\) | A1 [3+1=4] | \(8\) |
## Question 2:
### Part (i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $1$ | B1 [1] | |
### Part (ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{1}{2} \times 2^4$ | M1 | $2^{-1}=\frac{1}{2}$ **or** $32^{\frac{1}{5}}=2$ **or** $2^5=32$ soi |
| | M1 | $32^{\frac{4}{5}}=2^4$ or $16$ seen or implied |
| $= 8$ | A1 [3+1=4] | $8$ |
---2 Evaluate\\
(i) $6 ^ { 0 }$,\\
(ii) $2 ^ { - 1 } \times 32 ^ { \frac { 4 } { 5 } }$.
\hfill \mbox{\textit{OCR C1 2007 Q2 [4]}}