OCR MEI C1 — Question 1 5 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Marks5
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Mark schemeDownload PDF ↗
TopicIndices and Surds
TypeExpress in form with given base
DifficultyEasy -1.2 This is a straightforward C1 question testing basic index laws and rationalising denominators. Part (i) requires simple manipulation of powers of 3, while part (ii) is a standard rationalisation exercise. Both are routine techniques with no problem-solving required, making this easier than average but not trivial.
Spec1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators
  1. Express \(\frac{81}{\sqrt{3}}\) in the form \(3^k\). [2]
  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. [3]
Question 1:
AnswerMarks Guidance
1(i) 37/2 oe or k = 7/2 oe 2
M1 for or or 8131/2or 33 3
3 31/2
or 27 × 31/2 or better or for 81 = 34 or 3
1
= 31/2 or 31/2 or (following
3
correct rationalisation of denominator)
for 27 = 33
AnswerMarks
isw conversion of 7/2 oeM0 for just 81 = 3 × 3 × 3 × 3 oe – indices needed
allow an M mark for partially correct work still seen in
34
fraction form eg gets mark for 81 = 34
31/2
AnswerMarks
1145 3 2810 3
(ii) or www isw
AnswerMarks Guidance
11 223 M1 for multiplying num and denom by
5 + 3
and M1 for num or denom correct in
AnswerMarks
final answer (M0 if wrongly obtained)2nd M1 is not dependent on 1st M1 
Question 1:
1 | (i) 37/2 oe or k = 7/2 oe | 2 | 34 81
M1 for or or 8131/2or 33 3
3 31/2
or 27 × 31/2 or better or for 81 = 34 or 3
1
= 31/2 or 31/2 or (following
3
correct rationalisation of denominator)
for 27 = 33
isw conversion of 7/2 oe | M0 for just 81 = 3 × 3 × 3 × 3 oe – indices needed
allow an M mark for partially correct work still seen in
34
fraction form eg gets mark for 81 = 34
31/2
1 | 145 3 2810 3
(ii) or www isw
11 22 | 3 | M1 for multiplying num and denom by
5 + 3
and M1 for num or denom correct in
final answer (M0 if wrongly obtained) | 2nd M1 is not dependent on 1st M1
\begin{enumerate}[label=(\roman*)]
\item Express $\frac{81}{\sqrt{3}}$ in the form $3^k$. [2]

\item Express $\frac{5 + \sqrt{3}}{5 - \sqrt{3}}$ in the form $\frac{a + b\sqrt{3}}{c}$, where $a$, $b$ and $c$ are integers. [3]
\end{enumerate}

\hfill \mbox{\textit{OCR MEI C1  Q1 [5]}}
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