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GCSEFurther MathsAQAExam Questions2. Algebra & FunctionsIndices

Indices (AQA GCSE Further Maths)

Exam Questions

54 mins17 questions
Medium
Hard
Very Hard
1a
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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.

negative 2 space space space space space space space space space space space space 1.5 space space space space space space space space space space space space 2 space space space space space space space space space space space space 3

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1b
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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.

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1c
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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.

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

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

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3
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Solve    cube root of 2 w minus 10 end root equals 18

w equals.......................

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4
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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

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5
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Simplify fully   open parentheses 2 over 3 x cubed y close parentheses cubed

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6a
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Solve   2 over 5 square root of x equals 1

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

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6b
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Solve   x cubed equals 5 x squared

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

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

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2a
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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..................

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2b
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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..................

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3
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Solve   cube root of open parentheses 2 square root of x minus 10 close parentheses end root equals 2

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

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4
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Write fourth root of a cross times a to the power of negative 9 end exponent end root  as an integer power of a.

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5
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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.

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6
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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.

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7
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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...............

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8
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

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1
Sme Calculator4 marks

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

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2
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

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3
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Solve square root of x minus fraction numerator 12 over denominator square root of x end fraction equals 1 where x greater than 0

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