| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2011 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Simplify algebraic expressions with indices |
| Difficulty | Easy -1.3 This is a straightforward C1 indices question requiring only direct application of basic index laws (multiplication, division, and negative/fractional powers). Both parts are routine drill exercises with no problem-solving element—students simply apply memorized rules mechanically. Easier than average A-level content. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(\frac{16x^2 \times 2x^3}{x} = 32x^4\) | B1, B1, 2 | \(\frac{32}{x^4}\) or \(32x^{-4}\) |
| (ii) \(\frac{1}{6}x\) | M1, A1, B1 | \(6\) or \(\frac{1}{36^{\frac{1}{2}}}\) or \(\frac{1}{\sqrt{36}}\) seen |
| \(\frac{3}{5}x\) (Allow \(x^1\) in final answer) |
**(i)** $\frac{16x^2 \times 2x^3}{x} = 32x^4$ | B1, B1, 2 | $\frac{32}{x^4}$ or $32x^{-4}$
**(ii)** $\frac{1}{6}x$ | M1, A1, B1 | $6$ or $\frac{1}{36^{\frac{1}{2}}}$ or $\frac{1}{\sqrt{36}}$ seen | $\frac{1}{6}$ in final answer | $\frac{1}{\sqrt{36}}$ is M0 | $\pm\frac{1}{6}$ is A0
$\frac{3}{5}x$ (Allow $x^1$ in final answer) | |3 Simplify\\
(i) $\frac { ( 4 x ) ^ { 2 } \times 2 x ^ { 3 } } { x }$,\\
(ii) $\left( 36 x ^ { - 2 } \right) ^ { - \frac { 1 } { 2 } }$.
\hfill \mbox{\textit{OCR C1 2011 Q3 [5]}}