OCR MEI C1 2011 January — Question 7 5 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Year2011
SessionJanuary
Marks5
PaperDownload PDF ↗
TopicIndices and Surds
TypeExpress in form with given base
DifficultyEasy -1.2 Part (i) is straightforward index manipulation (81 = 3^4, √3 = 3^{1/2}, subtract exponents). Part (ii) is routine rationalizing the denominator by multiplying by the conjugate. Both are standard C1 techniques requiring only procedural recall with minimal problem-solving, making this easier than average.
Spec1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators

7
  1. Express \(\frac { 81 } { \sqrt { 3 } }\) in the form \(3 ^ { k }\).
  2. Express \(\frac { 5 + \sqrt { 3 } } { 5 - \sqrt { 3 } }\) in the form \(\frac { a + b \sqrt { 3 } } { c }\), where \(a , b\) and \(c\) are integers.

7 (i) Express $\frac { 81 } { \sqrt { 3 } }$ in the form $3 ^ { k }$.\\
(ii) Express $\frac { 5 + \sqrt { 3 } } { 5 - \sqrt { 3 } }$ in the form $\frac { a + b \sqrt { 3 } } { c }$, where $a , b$ and $c$ are integers.

\hfill \mbox{\textit{OCR MEI C1 2011 Q7 [5]}}