| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2012 |
| Session | January |
| Marks | 5 |
| 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 and surd simplification with no problem-solving required. Each part is a single-step calculation using standard rules (negative indices, fractional indices, surd division), making it significantly easier than average A-level questions which typically require multi-step reasoning. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\frac{1}{9}\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\left(\sqrt[4]{16}\right)^3\) | M1 | Interprets the power \(\frac{3}{4}\) correctly. Allow \((\sqrt[4]{16})^3\) or \((\sqrt[4]{16^3})\) or \(\left(16^{\frac{1}{4}}\right)^3\) or \(\left(16^3\right)^{\frac{1}{4}}\) |
| \(= 8\) | A1 | \(\pm 8\) is A0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(5\sqrt{8} \div \sqrt{8}\) | M1 | \(\sqrt{100}\,\sqrt{2}\div\sqrt{4}\,\sqrt{2}\) or \(\sqrt{\frac{200}{8}}\) or \(\sqrt{25}\,\sqrt{8}\div\sqrt{8}\) or \(\sqrt{1600}\div 8\) soi |
| \(= 5\) | A1 | Condone \(\pm 5\) |
## Question 4(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{1}{9}$ | B1 | |
---
## Question 4(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\left(\sqrt[4]{16}\right)^3$ | M1 | Interprets the power $\frac{3}{4}$ correctly. Allow $(\sqrt[4]{16})^3$ or $(\sqrt[4]{16^3})$ or $\left(16^{\frac{1}{4}}\right)^3$ or $\left(16^3\right)^{\frac{1}{4}}$ |
| $= 8$ | A1 | $\pm 8$ is **A0** |
---
## Question 4(iii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $5\sqrt{8} \div \sqrt{8}$ | M1 | $\sqrt{100}\,\sqrt{2}\div\sqrt{4}\,\sqrt{2}$ or $\sqrt{\frac{200}{8}}$ or $\sqrt{25}\,\sqrt{8}\div\sqrt{8}$ or $\sqrt{1600}\div 8$ soi |
| $= 5$ | A1 | Condone $\pm 5$ |
---4 Evaluate\\
(i) $3 ^ { - 2 }$,\\
(ii) $16 ^ { \frac { 3 } { 4 } }$,\\
(iii) $\frac { \sqrt { 200 } } { \sqrt { 8 } }$.
\hfill \mbox{\textit{OCR C1 2012 Q4 [5]}}