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GCSE Maths: Surds Practice

This document contains instructions and 20 practice questions for a GCSE exam on surds. Students are advised to use black ink, show all working, answer all questions in the spaces provided, and check answers at the end. The questions involve writing expressions in different forms involving integers and surds, expanding, simplifying, rationalizing denominators, and performing other algebraic operations with surd expressions. Marks for each question are shown in brackets.

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321 views8 pages

GCSE Maths: Surds Practice

This document contains instructions and 20 practice questions for a GCSE exam on surds. Students are advised to use black ink, show all working, answer all questions in the spaces provided, and check answers at the end. The questions involve writing expressions in different forms involving integers and surds, expanding, simplifying, rationalizing denominators, and performing other algebraic operations with surd expressions. Marks for each question are shown in brackets.

Uploaded by

5595m8752q
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Name: ___________________________

GCSE (1 – 9)

Surds

Instructions

• Use black ink or ball-point pen.


• Answer all questions.
• Answer the questions in the spaces provided
– there may be more space than you need.
• Diagrams are NOT accurately drawn, unless otherwise indicated.
• You must show all your working out.

Information

• The marks for each question are shown in brackets


– use this as a guide as to how much time to spend on each question.

Advice

• Read each question carefully before you start to answer it.


• Keep an eye on the time.
• Try to answer every question.
• Check your answers if you have time at the end

mathsgenie.co.uk
1 Write 48 in the form k 3 , where k is an integer.

…..........................
(Total for question 1 is 2 marks)

2 Write 50 in the form k 2 , where k is an integer.

…..........................
(Total for question 2 is 2 marks)

3 Write 5 27 in the form k 3 , where k is an integer.

…..........................
(Total for question 3 is 2 marks)

4 Write 7 20 in the form k 5 , where k is an integer.

…..........................
(Total for question 4 is 2 marks)
5 Expand and Simplify (2 + 3 )(2 – 3)

…..........................
(Total for question 5 is 2 marks)

6 Write (3 + 5 )2 in the form a + b 5 , where a and b are integers.

…..........................
(Total for question 6 is 2 marks)

7 Expand and Simplify (2 + 5 )(1 – 5)

…..........................
(Total for question 7 is 2 marks)

8 Write (3 – 2 )2 in the form a + b 2 , where a and b are integers.

…..........................
(Total for question 8 is 2 marks)
9 Expand and Simplify (2 + 3 )2 – (2 – 3 )2

…..........................
(Total for question 9 is 2 marks)

10 Rationalise the denominator 6


3

…..........................
(Total for question 10 is 2 marks)

11 Rationalise the denominator x


x

…..........................
(Total for question 11 is 2 marks)

12 Rationalise the denominator 1 + 5


2

…..........................
(Total for question 12 is 2 marks)
13 Simplify (3 + 6 )
3

(Total for question 13 is 3 marks)

14 Simplify fully (4 + 2 3 )(4 – 2 3 )


11

You must show all your working.

(Total for question 14 is 3 marks)


15 Show that 5 + 2 3 can be written as 4 – 3
2+ 3

(Total for question 15 is 3 marks)

3 3+3
16 Show that can be written as 3
3+ 3

(Total for question 16 is 3 marks)


1 2
17 Show that can be written as
1 3
+ 2
2

(Total for question 17 is 3 marks)

18 Show that 2 can be written as 3 – 3


1
+1
3

(Total for question 18 is 3 marks)


19 Simplify fully ( a + b )( a – b)

(Total for question 19 is 2 marks)

2
20 Simplify fully ( 2a + b )

(Total for question 20 is 2 marks)

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