| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2011 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Express in form with given base |
| Difficulty | Easy -1.8 This is a straightforward indices question requiring only basic recall of index laws and the ability to express numbers as powers of 8. All three parts are routine manipulations: (i) √8 = 8^(1/2), (ii) 1/64 = 1/8² = 8^(-2), (iii) 2^8 = (2³)^(8/3) = 8^(8/3). No problem-solving or conceptual insight needed, just mechanical application of rules. Significantly easier than average A-level questions. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(8^{\frac{1}{2}}\) | B1 | 1 mark; Allow \(8^{0.5}\); Condone \(p = \frac{1}{2}\), just "\(\frac{1}{2}\)" seen as answer www |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(8^{-2}\) | B1 | 1 mark; Condone \(p = -2\), just "\(-2\)" seen as answer www; \(\frac{1}{8^2}\) only not enough |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(2^8 = \left(8^{\frac{1}{3}}\right)^8\) | M1 | \(2^8\) or \(2^6 = 8^2\) soi; Condone \(p = \frac{8}{3}\), just "\(\frac{8}{3}\)" seen as answer www |
| \(2 = 8^{\frac{1}{3}}\) soi | M1 | \(2^3 = 8\) not enough for second M mark |
| \(= 8^{\frac{8}{3}}\) | A1 | 3 marks (total 5); o.e. |
# Question 3:
## Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| $8^{\frac{1}{2}}$ | B1 | **1 mark**; Allow $8^{0.5}$; Condone $p = \frac{1}{2}$, just "$\frac{1}{2}$" seen as answer **www** |
## Part (ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| $8^{-2}$ | B1 | **1 mark**; Condone $p = -2$, just "$-2$" seen as answer **www**; $\frac{1}{8^2}$ only not enough |
## Part (iii)
| Answer | Mark | Guidance |
|--------|------|----------|
| $2^8 = \left(8^{\frac{1}{3}}\right)^8$ | M1 | $2^8$ or $2^6 = 8^2$ soi; Condone $p = \frac{8}{3}$, just "$\frac{8}{3}$" seen as answer **www** |
| $2 = 8^{\frac{1}{3}}$ soi | M1 | $2^3 = 8$ not enough for second M mark |
| $= 8^{\frac{8}{3}}$ | A1 | **3 marks** (total **5**); o.e. |
---3 Express each of the following in the form $8 ^ { p }$ :\\
(i) $\sqrt { 8 }$,\\
(ii) $\frac { 1 } { 64 }$,\\
(iii) $2 ^ { 6 } \times 2 ^ { 2 }$.
\hfill \mbox{\textit{OCR C1 2011 Q3 [5]}}