| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Solve power equations |
| Difficulty | Easy -1.2 This is a straightforward C1 question testing basic index laws. Part (i) requires converting to a common base and simplifying - a routine manipulation. Part (ii) is a simple one-step equation solved by raising both sides to the power of -3. Both parts are standard textbook exercises requiring only recall and direct application of index rules with no problem-solving insight needed. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{2^6}{8^{\frac{1}{2}} \times 2^{-\frac{1}{2}}}=\frac{2^6}{2^{7.5} \times 2^{-0.5}}=2^{6-7.5+0.5}=2^{-1}=\frac{1}{2}\) | M1 | Powers of 2 |
| B1 | Correct signs | |
| B1 |
| Answer | Marks |
|---|---|
| \(x^{-\frac{1}{3}}=8 \Rightarrow x^{\frac{1}{3}}=\frac{1}{8} \Rightarrow x=\left(\frac{1}{8}\right)^3=\frac{1}{512}\) | M1 |
| A1 |
## Question 9(i):
$\frac{2^6}{8^{\frac{1}{2}} \times 2^{-\frac{1}{2}}}=\frac{2^6}{2^{7.5} \times 2^{-0.5}}=2^{6-7.5+0.5}=2^{-1}=\frac{1}{2}$ | M1 | Powers of 2
| B1 | Correct signs
| B1 |
**Total: 3**
## Question 9(ii):
$x^{-\frac{1}{3}}=8 \Rightarrow x^{\frac{1}{3}}=\frac{1}{8} \Rightarrow x=\left(\frac{1}{8}\right)^3=\frac{1}{512}$ | M1 |
| A1 |
**Total: 2**
---9 (i) Simplify $\frac { 2 ^ { 6 } } { 8 ^ { 2 \frac { 1 } { 2 } } \times 2 ^ { - \frac { 1 } { 2 } } }$\\
(ii) Solve the equation $x ^ { - \frac { 1 } { 3 } } = 8$.
\hfill \mbox{\textit{OCR MEI C1 Q9 [5]}}