| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2006 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Solve power equations |
| Difficulty | Easy -1.8 This is a straightforward recall question testing basic index laws with no problem-solving required. Each part involves a single-step manipulation: (i) cube both sides, (ii) recognize that any number to power 0 equals 1, (iii) simplify the left side then take fourth roots. These are routine textbook exercises significantly easier than average A-level questions. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(\frac{1}{x^3} = 2\), \(x = 8\) | B1, I, 8 | Allow embedded values throughout question 1 |
| (ii) \(10^t = 1\), \(t = 0\) | B1, 1, 0 | |
| (iii) \((y^{-3})^2 = \frac{1}{81}\), \(y^{-4} = \frac{1}{81}\), \(y = \pm 3\) | B1, B1, 2 | \(y = 3\); \(y = -3\) |
**(i)** $\frac{1}{x^3} = 2$, $x = 8$ | B1, I, 8 | Allow embedded values throughout question 1
**(ii)** $10^t = 1$, $t = 0$ | B1, 1, 0 |
**(iii)** $(y^{-3})^2 = \frac{1}{81}$, $y^{-4} = \frac{1}{81}$, $y = \pm 3$ | B1, B1, 2 | $y = 3$; $y = -3$1 Solve the equations\\
(i) $x ^ { \frac { 1 } { 3 } } = 2$,\\
(ii) $10 ^ { \prime } = 1$,\\
(iii) $\left( y ^ { - 2 } \right) ^ { 2 } = \frac { 1 } { 81 }$.
\hfill \mbox{\textit{OCR C1 2006 Q1 [4]}}