GCSEFurther MathsAQATopic Questions2. Algebra & FunctionsIndices

Indices (AQA GCSE Further Maths)

Topic Questions

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1a
Sme Calculator1 mark

fraction numerator y to the power of 6 cross times space y over denominator y to the power of m end fraction space equals space y to the power of 4

Circle the value of m.

– 2 1.5 2 3

[1]

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1b
Sme Calculator1 mark

a to the power of n space cross times space a to the power of 5 space equals space a to the power of 5

Work out the value of n.

[1]

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1c
Sme Calculator2 marks

open parentheses c to the power of 5 close parentheses to the power of p space equals space open parentheses c squared close parentheses to the power of 6

Work out the value of p.

[2]

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2
Sme Calculator2 marks

Solve cube root of 7 x space minus space 13 end root space equals space 2

x = ........................[2]

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3
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Solve    x to the power of negative 2 over 3 end exponent space equals space 12 space 1 fourth

x = .................[3]

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4
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Solve   8 to the power of x equals fraction numerator 2 to the power of 56 minus 4 to the power of 26 over denominator 30 end fraction

[4]

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5
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Solve    cube root of 2 w minus 10 end root equals 18

w equals.......................[2]

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6a
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a is a value greater than 1

Work out the value of m for which   left parenthesis a to the power of m right parenthesis to the power of 4 space equals space left parenthesis a to the power of 5 right parenthesis to the power of 2 m end exponent

m equals..................[2]

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6b
Sme Calculator2 marks

w cubed x squared y to the power of 5 equals w to the power of 13 x to the power of 7
Write y in terms of w and x.
Give your answer in its simplest form.

y equals..................[2]

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7
Sme Calculator3 marks

Solve   cube root of open parentheses 2 square root of x minus 10 close parentheses end root equals 2

[3]

x = .......................

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8
Sme Calculator2 marks

Write fourth root of a cross times a to the power of negative 9 end exponent end root  as an integer power of a.

[2]

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9
Sme Calculator3 marks

Simplify fully   fraction numerator open parentheses 4 c d squared close parentheses cubed over denominator 2 c d to the power of 4 end fraction

[3]

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10
Sme Calculator3 marks

The curve space y space equals space 2 space square root of x minus a end root space plus space 5 spacepasses through the point (1, 8)

Work out the value of a.

[3]

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11
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Work out the value of open parentheses table row cell 3 to the power of 1 half end exponent plus end cell cell 3 to the power of 3 over 2 end exponent end cell end table close parentheses squared

You must show your working.

[3]

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12
Sme Calculator4 marks

Work out the value of p when

9 to the power of 0.5 p end exponent space cross times space 81 space equals space 27 to the power of 2 p – 1 end exponent

[4]

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13
Sme Calculator3 marks

Solve   open parentheses 3 minus square root of x close parentheses to the power of begin inline style 1 third end style end exponent equals negative 2

x equals...............[3]

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14
Sme Calculator4 marks

fourth root of x equals 2   and  y to the power of negative 2 end exponent equals 25

x greater than 0 and y less than 0

Work out the value of x over y

[4]

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15
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Simplify fully   open parentheses 2 over 3 x cubed y close parentheses cubed

[2]

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16a
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Solve   2 over 5 square root of x equals 1

x equals.................[2]

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16b
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Solve   x cubed equals 5 x squared

[2]

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