| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2015 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Express in form with given base |
| Difficulty | Easy -1.3 This is a straightforward indices question requiring only direct application of index laws (powers of powers, negative indices, fractional indices). All parts involve simple manipulation to express numbers as powers of 5 with no problem-solving or multi-step reasoning required. Easier than average A-level content. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(5^8\) | B1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(5^{-\frac{1}{4}}\) | M1 | Fourth root \(\equiv \frac{1}{4}\) soi |
| A1 | cao www |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(5^{\frac{9}{2}}\) | M1 | \((5^2)^3\) or \(5^3 \times 5^{\frac{3}{2}}\) or other correct product of two simplified powers of 5 |
| A1 | oe cao www |
## Question 3:
### Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $5^8$ | B1 | **cao** |
### Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $5^{-\frac{1}{4}}$ | M1 | Fourth root $\equiv \frac{1}{4}$ soi |
| | A1 | **cao www** |
### Part (iii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $5^{\frac{9}{2}}$ | M1 | $(5^2)^3$ or $5^3 \times 5^{\frac{3}{2}}$ or other correct product of two simplified powers of 5 |
| | A1 | oe **cao www** |
---3 Express each of the following in the form $5 ^ { k }$.\\
(i) $25 ^ { 4 }$\\
(ii) $\frac { 1 } { \sqrt [ 4 ] { 5 } }$\\
(iii) $( 5 \sqrt { 5 } ) ^ { 3 }$
\hfill \mbox{\textit{OCR C1 2015 Q3 [5]}}