AQA GCSE Maths

Topic Questions

Surds

1a
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2 marks

Rationalise the denominator of fraction numerator 5 over denominator square root of 2 end fraction.

1b
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2 marks

Expand and simplify open parentheses 2 space plus square root of 3 close parentheses squared minus open parentheses 2 minus square root of 3 close parentheses squared.

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2
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2 marks

Expand   open parentheses 1 plus square root of 2 close parentheses open parentheses 3 minus square root of 2 close parentheses
Give your answer in the form a space plus space b square root of 2 where a and b are integers.

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3
Sme Calculator
3 marks

Simplify fully  fraction numerator open parentheses 6 minus square root of 5 close parentheses open parentheses 6 plus square root of 5 close parentheses over denominator square root of 31 end fraction

You must show your working.

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4
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3 marks

square root of 5 open parentheses square root of 8 space plus square root of 18 close parentheses    can be written in the form  a square root of 10 where a is an integer.

Find the value of a.

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5
Sme Calculator
2 marks

Show that    fraction numerator open parentheses 4 minus square root of 3 close parentheses open parentheses 4 plus square root of 3 close parentheses over denominator square root of 13 end fraction simplifies to  square root of 13.

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6a
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2 marks

Express  square root of 3 plus square root of 12 in the form a square root of 3 where a is an integer.

6b
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3 marks

Express open parentheses fraction numerator 1 over denominator square root of 3 end fraction close parentheses to the power of 7 in the form fraction numerator square root of b over denominator c end fraction where b and c are integers.

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7
Sme Calculator
3 marks

Show that  open parentheses 5 square root of 3 minus square root of 12 close parentheses squared  simplifies to an integer.

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8
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3 marks

Show that fraction numerator square root of 150 minus square root of 6 over denominator square root of 2 cross times square root of 3 end fraction simplifies to an integer.

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1a
Sme Calculator
2 marks

Rationalise the denominator of fraction numerator 12 over denominator square root of 3 end fraction .

1b
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2 marks

Work out the value of  open parentheses square root of 2 space plus space square root of 8 close parentheses squared.

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2
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2 marks

Work out the value of        open parentheses square root of 12 space minus square root of 3 close parentheses squared.

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3
Sme Calculator
2 marks

Rationalise the denominator of    fraction numerator 10 over denominator square root of 5 end fraction.
Give your answer in its simplest form.

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4
Sme Calculator
3 marks

Work out       2 square root of 10 cross times square root of 80 cross times square root of 18

Give your answer as an integer.

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5
Sme Calculator
2 marks

Rationalise the denominator and simplify fraction numerator 10 over denominator 3 square root of 5 end fraction

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6
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1 mark

8300 space equals space 100 space cross times space 83

Circle the number that is closest in value to square root of 8300

19 90 830 900

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7
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2 marks

 Show that fraction numerator 14 over denominator square root of 7 end fraction  can be written in the form a square root of b where a and b are integers.

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8
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2 marks

Show that fraction numerator square root of 12 over denominator square root of 3 plus 2 end root end fraction

can be written in the form space a space square root of b space end rootwhere a is a simplified fraction and b is an integer.

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9
Sme Calculator
3 marks

Show that open parentheses 6 space plus 2 root index blank of 12 close parentheses squared space equals space 12 open parentheses 7 space plus space 4 square root of 3 close parentheses

Show each stage of your working.

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10
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3 marks

Show that fraction numerator square root of 20 space plus space square root of 80 over denominator square root of 3 end fraction can be expressed in the form square root of a where a is an integer.

Show your working clearly.

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11
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2 marks

Show that square root of 45 plus square root of 20 equals 5 square root of 5
Show your working clearly.

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12
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2 marks

Rationalise the denominator of fraction numerator 10 over denominator square root of 6 end fraction

Give your answer in its simplest form.

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13
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2 marks

Without using a calculator, show that square root of 20 equals 2 square root of 5.

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14
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3 marks

Write  open parentheses 1 space plus space square root of 3 close parentheses squared   in the form  a space plus space b square root of 3.

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15
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2 marks

Simplify square root of 6 cross times square root of 3.

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16
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3 marks

Simplify fully by rationalising the denominator.

fraction numerator 20 over denominator square root of 5 end fraction

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17
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2 marks

Simplify fully.

            square root of 200

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18
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3 marks

Write square root of 12 space plus space square root of 75 in the form k square root of 3.

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19
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2 marks

Simplify fully.

square root of 50 plus square root of 2.

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1
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4 marks

a space equals space square root of 8 plus 2
b space equals space square root of 8 minus 2
T space equals space a squared space minus space b squared

Work out the value of T.
Give your answer in the form c square root of 2 where c is an integer.

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2
Sme Calculator
3 marks

Simplify square root of 80 space plus space square root of 2 2 over 9 end root

Give your answer in the form  fraction numerator a square root of 5 over denominator b end fraction    where a and b are integers.

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3
Sme Calculator
4 marks

Work out    square root of 18 minus fraction numerator 28 over denominator square root of 50 end fraction

Give your answer in the form  fraction numerator square root of a over denominator b end fraction where a and b are integers.

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4
Sme Calculator
3 marks

Show that fraction numerator 2 square root of 6 over denominator square root of 5 end fraction space minus space fraction numerator square root of 3 over denominator square root of 10 end fraction can be written in the form fraction numerator c square root of d over denominator 10 end fraction

where space c spaceand d are integers.

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5
Sme Calculator
3 marks

table row a equals cell square root of 8 plus 4 end cell row b equals cell square root of 8 minus 4 end cell end table

left parenthesis a space – space b right parenthesis left parenthesis a space plus space b right parenthesis can be written in the form y space square root of 4 y end root

Find the value of y
Show your working clearly.

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6
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4 marks

In the following equation, n is an integer greater than 1.

open parentheses square root of 2 close parentheses to the power of n space equals space k square root of 2

i)
Find space k space when n = 7.

k = ...................... [2]

ii)
Find n when k = 64.

n = ..................... [2]

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7a
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1 mark

Here is a sequence.

      5   5 square root of 3     15   15 square root of 3

Work out the next term.

7b
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3 marks

Find the nth term.

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