IGCSE Edexcel Maths 1 hour 31 questions
Exam Questions
Surds
Simplifying Surds / Rationalising Denominators
Medium (8 questions) /20 Scan here to return to the course
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Hard (13 questions) /37
Very Hard (10 questions) /32
Total Marks /89
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Medium Questions
12
1 (a) Show that can be rewritten as 4 3
3
(2 marks)
(b) Show that ( 2 + 8 ) 2 = 18
(2 marks)
2 Show that ( 12 − 3 ) 2 = 3
(2 marks)
10
3 Show that can be rewritten as 2 5
5
(2 marks)
12
4 Show that
3+2
can be written in the form a b where a is a simplified fraction and b is an integer.
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(2 marks)
5 Show that (6 + 2 12 ) 2 = 12(7 + 4 3 )
Show each stage of your working.
(3 marks)
20 + 80
6 Show that can be expressed in the form a where a is an integer.
3
Show your working clearly.
(3 marks)
7 Show that 45 + 20 = 5 5
Show your working clearly.
(2 marks)
8 Without using a calculator, show that 20 = 2 5 .
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(2 marks)
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Hard Questions
5 5 2
1 (a) Show that can be written as
2 2
(2 marks)
(b) Show that (2 + 3 ) 2 − (2 − 3 ) 2 = 8 3
(2 marks)
2 Show that (1 + 2 ) (3 − 2 ) = 1 + 2 2
(2 marks)
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3 (a) Martin did this question.
14
Rationalise the denominator of
2+ 3
Here is how he answered the question.
14 14 × (2 − 3)
=
2+ 3 (2 + 3 ) (2 − 3)
28 − 14 3
=
4 + 2 3 − 2 3 +3
28 − 14 3
=
7
= 4− 2 3
Martin's answer is wrong.
Find Martin's mistake.
(1 mark)
(b) Sian did this question.
5
Rationalise the denominator of
12
Here is how she answered the question.
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Sian's answer is wrong.
Find Sian's mistake.
(1 mark)
(6 − 5 ) (6 + 5 )
4 Simplify fully
31
You must show your working.
(3 marks)
5 Show that 5( 8 + 18 ) can be written in the form a 10 and state the value of a .
You must show your full working.
(3 marks)
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(4 − 3 ) (4 + 3 )
6 Show that simplifies to 13 .
13
(2 marks)
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7 (a) Show that 3+ 12 can be rewritten as 3 3
(2 marks)
⎛⎜ 1 ⎞⎟7 3
(b) Show that ⎜⎜ ⎟⎟ =
81
⎝ 3 ⎠
(3 marks)
4
8 Rationalise the denominator of
7− 5
Show each stage of your working.
Give your answer in the form a + b 5 where a and b are fractions in their simplest
forms.
(3 marks)
9 Given that y is a prime number,
3 a +b y
express in the form where a , b and c are integers.
2− y c−y
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(2 marks)
6
10 Without using a calculator, rationalise the denominator of
3− 7
Simplify your answer.
You must show each stage of your working.
(3 marks)
8
11 Show that can be written in the form n + n , where n is an integer.
8 −2
Show your working clearly.
(3 marks)
2
12 Express in the form p + q
3 −1
where p and q are integers.
Show your working clearly.
(2 marks)
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13 Show that (5 3 − 12 ) 2 simplifies to an integer.
(3 marks)
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