| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Rationalize denominator simple |
| Difficulty | Moderate -0.8 Part (i) is straightforward index manipulation (125=5³, so answer is 5^{3.5}). Part (ii) requires rationalizing a denominator and collecting like terms, which is routine C1 content requiring multiple steps but no problem-solving insight. Slightly easier than average due to being standard textbook exercises. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| \(5^{3.5}\) or \(k = 7/2\) (oe) | 2 marks | M1 for \(125 = 5^3\) or \(\sqrt{5} = 5^{\frac{1}{2}}\) soi; M0 for just answer of \(5^3\) with no reference to 125 |
| Answer | Marks | Guidance |
|---|---|---|
| Attempting to multiply numerator and denominator of fraction by \(1 + 2\sqrt{5}\) | M1 | Some candidates incorporate \(10 + 7\sqrt{5}\) into the fraction; M1 available even if done wrongly or if \(10 + 7\sqrt{5}\) also multiplied by \(1 + 2\sqrt{5}\) |
| Denominator \(= -19\) soi | M1 | Must be obtained correctly but independent of first M1; eg M1 for denominator of 19 with minus sign in front of whole expression or with attempt to change signs in numerator |
| \(8 + 3\sqrt{5}\) | A1 |
## Question 4:
**(i)**
$5^{3.5}$ or $k = 7/2$ (oe) | 2 marks | M1 for $125 = 5^3$ or $\sqrt{5} = 5^{\frac{1}{2}}$ soi; M0 for just answer of $5^3$ with no reference to 125
**(ii)**
Attempting to multiply numerator and denominator of fraction by $1 + 2\sqrt{5}$ | M1 | Some candidates incorporate $10 + 7\sqrt{5}$ into the fraction; M1 available even if done wrongly or if $10 + 7\sqrt{5}$ also multiplied by $1 + 2\sqrt{5}$
Denominator $= -19$ soi | M1 | Must be obtained correctly but independent of first M1; eg M1 for denominator of 19 with minus sign in front of whole expression or with attempt to change signs in numerator
$8 + 3\sqrt{5}$ | A1 |
---4 (i) Express $125 \sqrt { 5 }$ in the form $5 ^ { k }$.\\
(ii) Simplify $10 + 7 \sqrt { 5 } + \frac { 38 } { 1 - 2 \sqrt { 5 } }$, giving your answer in the form $a + b \sqrt { 5 }$.
\hfill \mbox{\textit{OCR MEI C1 Q4 [5]}}