Surds (Edexcel IGCSE Maths A: Higher): Exam Questions

Show that can be written as 

Show that

Show that 

Martin did this question.

Here is how he answered the question.

Martin's answer is wrong.

Find Martin's mistake.

Sian did this question.

Here is how she answered the question.

Sian's answer is wrong.

Find Sian's mistake.

Simplify fully 

You must show your working.

Show that  can be written in the form  and state the value of . You must show your full working.

Show that    simplifies to  .

Show that can be rewritten as 

Show that

Rationalise the denominator of 

Show each stage of your working.

Give your answer in the form  where  and  are fractions in their simplest forms.

Given that  is a prime number,

express  in the form  where ,  and are integers.

Without using a calculator, rationalise the denominator of 

Simplify your answer.
You must show each stage of your working.

Show that  can be written in the form  , where  is an integer.

Show your working clearly.

Express  in the form 

where and are integers.
Show your working clearly.

Show that    simplifies to an integer.

Rationalise the denominator of

Show each stage of your working.

Give your answer in the form where and are fractions in their simplest forms.

Express in the form where is an integer.
Show your working clearly.

Show that  stating the value of 

Show that    can be written in the form  where and  are integers.

Show that  can be written as 

can be written in the form 

Find the value of
Show your working clearly.

Rationalise the denominator of  where  is an integer and is a prime number.

Simplify your answer.

Show that  can be written in the form 

where and are integers.
Show your working clearly.

Express  in the form  where a and b are integers.

Show each stage of your working clearly.

The area of a rectangle is

The length of the rectangle is .

Without using a calculator and showing each stage of your working, find the width of the rectangle.

Give your answer in the form where , and are integers.

.....................

Show that can be written in the form , where  and  are integers.

Show each stage of your working clearly and give the value of a and the value of .

 Show that  can be simplified to 

The diagram shows a cuboid with a square cross section.

The volume of the cuboid is cm³

Without using a calculator, find the value of
Give your answer in the form where and are integers.
Show your working clearly