Cambridge IGCSE Mathematics practice

exam practice - Comprehend and apply the concept of surds, which involves simplifying expressions such as √20 = 2√5 and √(200 - 32) = 6√2. Additionally, rationalize denominators in expressions like √10 = 2√5/5 and 1/(1 + √3) = (1 - √3)/(2 - 1). - Surds

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At a glance

Paper

Marks

Topic

Surds

Exam-style question

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Paper 2Core or Extended Mathematics6 marks

Rationalising Denominators

Description

Rationalise the denominators of the following expressions and simplify your answers.

Expression
\( \frac{1}{\sqrt{10}} \)
\( \frac{1}{1 + \sqrt{3}} \)

a
Calculate Rationalise the denominator of \( \frac{1}{\sqrt{10}} \).
Your answer
Aim for approximately 2 distinct marking points.
[2]
b
Calculate Rationalise the denominator of \( \frac{1}{1 + \sqrt{3}} \).
Your answer
Aim for approximately 4 distinct marking points.
[4]

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Maths method check

Topic focus: Surds.
Question style: structured_mathematics.
Reasoning demand: reasoning.
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Paper 2Core or Extended Mathematics5 marks

Description

Simplify the following surds and express your answers in simplest form.

Expression
\( \sqrt{20} \)
\( \sqrt{200 - 32} \)

a
Calculate Simplify \( \sqrt{20} \).
Your answer
Aim for approximately 2 distinct marking points.
[2]
b
Calculate Simplify \( \sqrt{200 - 32} \).
Your answer
Aim for approximately 3 distinct marking points.
[3]