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

Try the question first, then check the answer and practise the same topic again.

At a glance

Paper

Marks

Topic

Surds

Exam-style question

Try this first

Paper 2Core or Extended Mathematics5 marks

Simplifying Surds

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]

0 of 2 parts answered

Answer every part before opening the mark scheme.

Maths method check

Topic focus: Surds.
Question style: structured_mathematics.
Reasoning demand: reasoning.
Check the operation, notation, units, and final answer form against the question before moving on.

Common mistake

No common mistake is linked to this question yet.

Flashcard 1 of 6

Press Space to flip, arrows to move

Paper 2Core or Extended Mathematics6 marks

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]