| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2016 |
| 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 C1 indices question requiring only direct application of index laws (division rule, power of a power, and recognizing 4 and 16 as powers of 2). Part (i) is mechanical calculation, while part (ii) requires the additional step of converting 4 and 16 to base 2, but both are standard textbook exercises with no problem-solving element. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((2^{-2})^3\) or \(2^{15} \div 2^{21}\) | B1 | Valid attempt to simplify; correct use of either index law; \(\left(\frac{1}{2}\right)^6\) oe is B1 |
| \(2^{-6}\) | B1 | Correct answer. Accept \(p = -6\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(5\times(2^2)^{\frac{2}{3}} + 3\times(2^4)^{\frac{1}{3}}\) | M1 | Attempts to express both terms or combined term as a power of 2; e.g. both \(4=2^2\) and \(16=2^4\) soi |
| \(= 5\times 2^{\frac{4}{3}} + 3\times 2^{\frac{4}{3}}\) or \(10\times 2^{\frac{1}{3}} + 6\times 2^{\frac{1}{3}}\) | B1 | Correctly obtains \(2^{\frac{4}{3}}\) or \(2^{\frac{1}{3}}\) for either term. If M0: SC B1 for \(8\times16^{\frac{1}{3}}\) or \(8\times4^{\frac{2}{3}}\) |
| \(= 8\times 2^{\frac{4}{3}} = 2^{\frac{13}{3}}\) | A1 | Correct final answer |
## Question 5:
### Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(2^{-2})^3$ or $2^{15} \div 2^{21}$ | B1 | Valid attempt to simplify; correct use of either index law; $\left(\frac{1}{2}\right)^6$ oe is B1 |
| $2^{-6}$ | B1 | Correct answer. Accept $p = -6$ |
### Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $5\times(2^2)^{\frac{2}{3}} + 3\times(2^4)^{\frac{1}{3}}$ | M1 | Attempts to express both terms or combined term as a power of 2; e.g. both $4=2^2$ and $16=2^4$ soi |
| $= 5\times 2^{\frac{4}{3}} + 3\times 2^{\frac{4}{3}}$ or $10\times 2^{\frac{1}{3}} + 6\times 2^{\frac{1}{3}}$ | B1 | Correctly obtains $2^{\frac{4}{3}}$ or $2^{\frac{1}{3}}$ for **either** term. If M0: SC B1 for $8\times16^{\frac{1}{3}}$ or $8\times4^{\frac{2}{3}}$ |
| $= 8\times 2^{\frac{4}{3}} = 2^{\frac{13}{3}}$ | A1 | Correct final answer |
---5 Express the following in the form $2 ^ { p }$.\\
(i) $\left( 2 ^ { 5 } \div 2 ^ { 7 } \right) ^ { 3 }$\\
(ii) $5 \times 4 ^ { \frac { 2 } { 3 } } + 3 \times 16 ^ { \frac { 1 } { 3 } }$
\hfill \mbox{\textit{OCR C1 2016 Q5 [5]}}