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GCSEFurther MathsAQAExam Questions1. NumberSurds

Surds (AQA GCSE Further Maths): Exam Questions

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1
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Simplify   square root of 3 open parentheses square root of 75 plus square root of 48 close parentheses writing your answer as an integer.

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2
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Write left parenthesis 1 plus 2 square root of 5 right parenthesis left parenthesis 4 minus square root of 5 right parenthesis in the form a plus b square root of 5 where a and b are integers.

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3
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Rationalise the denominator and simplify fully   fraction numerator 6 over denominator square root of 7 plus 2 end fraction

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4
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Circle the value below that is equal to fraction numerator 14 over denominator square root of 7 end fraction

 

14 square root of 7 space space space space space space space space space space square root of 2 space space space space space space space space space space space 2 square root of 7 space space space space space space space space space space space 14

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5
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Write 3 square root of 5 in the form square root of k where k is an integer.

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1
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Rationalise and simplify fraction numerator square root of 3 minus 7 over denominator square root of 3 plus 1 end fraction

Give your answer in the form a plus b square root of 3 where a and b are integers.

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2
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Rationalise the denominator and simplify fully    fraction numerator 21 minus 11 square root of 5 over denominator 3 minus square root of 5 end fraction

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3
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Solve   square root of 125 plus square root of 20 equals square root of 80 plus square root of x

x equals........................

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4
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Solve

5 x equals x square root of 2 space plus 1

giving your answer in the form

fraction numerator a plus square root of 2 over denominator b end fraction

where a and b are integers to be found.

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5
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square root of 150 plus square root of 600 plus square root of k equals 18 square root of 6

Work out the value of k.

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1
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A B C is a triangle.

The perpendicular from A meets B C at D.

B C equals left parenthesis 6 plus 2 square root of 7 right parenthesis space cm

q21-paper1-nov2021-aqa-gcse-furthermaths

Area of triangle A B C space equals space left parenthesis 13 plus 3 square root of 7 right parenthesis space cm squared

Work out the length, in cm, of A D.

Give your answer in the form a plus b square root of c where a comma space b and c are integers.

........................cm

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2
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Rationalise the denominator and simplify fully fraction numerator 1 plus square root of 6 over denominator square root of 2 plus 2 square root of 3 end fraction

Give your answer in the form fraction numerator square root of p over denominator p end fraction where p is a prime number which you should find.

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3
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You are given that open parentheses 2 plus square root of a close parentheses cubed identical to 80 plus b square root of 3 where a and b are positive integers.

Find a and b.

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