| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2012 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Express in form with given base |
| Difficulty | Easy -1.3 This is a straightforward C1 indices question testing basic index law recall and manipulation. All three parts involve direct application of standard rules (fractional indices, negative indices, and combining powers) with no problem-solving or conceptual challenge beyond recognizing that 49 = 7^2. This is easier than average A-level content, being foundational Core 1 material. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\sqrt[4]{7} = 7^{\frac{1}{4}}\) | B1 [1] | Allow \(7^{0.25}\), \(k = 0.25\) etc. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\frac{1}{7\sqrt{7}} = 7^{-\frac{3}{2}}\) | M1 | Clear evidence of correct use of \(7^a \times 7^b = 7^{a+b}\) or a single term \(\frac{1}{7^d} = 7^{-d}\). Allow \(\frac{1}{7^d 7^e} = (7^d 7^e)^{-1}\) [not \(= 7^d 7^{-e}\)] |
| A1 [2] | Allow \(-1.5\), \(k = -1.5\) etc. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(7^4 \times 7^{20}\) | M1 | \(7^{20}\) or \(49^2\) seen (or \(49^{12}\)). \((7^2)^{10}\) is not good enough for M1 |
| \(= 7^{24}\) | A1 [2] | Allow \(k = 24\) |
## Question 2(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\sqrt[4]{7} = 7^{\frac{1}{4}}$ | B1 [1] | Allow $7^{0.25}$, $k = 0.25$ etc. |
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## Question 2(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{1}{7\sqrt{7}} = 7^{-\frac{3}{2}}$ | M1 | Clear evidence of correct use of $7^a \times 7^b = 7^{a+b}$ or a single term $\frac{1}{7^d} = 7^{-d}$. Allow $\frac{1}{7^d 7^e} = (7^d 7^e)^{-1}$ [not $= 7^d 7^{-e}$] |
| | A1 [2] | Allow $-1.5$, $k = -1.5$ etc. |
---
## Question 2(iii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $7^4 \times 7^{20}$ | M1 | $7^{20}$ or $49^2$ seen (or $49^{12}$). $(7^2)^{10}$ is **not** good enough for M1 |
| $= 7^{24}$ | A1 [2] | Allow $k = 24$ |
---2 Express each of the following in the form $7 ^ { k }$ :\\
(i) $\sqrt [ 4 ] { 7 }$,\\
(ii) $\frac { 1 } { 7 \sqrt { 7 } }$,\\
(iii) $7 ^ { 4 } \times 49 ^ { 10 }$.
\hfill \mbox{\textit{OCR C1 2012 Q2 [5]}}