Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2010 | June | Q#2

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Question

a.   Express  in the form  , where m and n are integers.

b.   Hence express  in the form  , where p and q are integers.

Solution

a.
 

We have algebraic formula;

For the given case;

b.
 

We are given the expression;

We have found in (a) that;

Therefore;

If we need a rational number in the denominator of a fraction, we need to follow procedure of  “denominator rationalization” as given below.

ü If the denominator is of the form  then multiply both numerator and denominator by

ü If the denominator is of the form  then multiply both numerator and denominator by  .

ü If the denominator is of the form  then multiply both numerator and denominator by  .

Hence;

We have algebraic formula;

Since 

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