IGCSEMaths: ExtendedCIEExam Questions2. Algebra & Graphs2.10 Functions

Syllabus Edition

First teaching 2021

Last exams 2024

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Functions (CIE IGCSE Maths: Extended)

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4 hours52 questions

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2.10 Functions

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2.10 Functions

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1
Sme Calculator4 marks

straight g open parentheses x close parentheses space equals space 2 x space plus space 7         straight h open parentheses x close parentheses space equals space 3 x space minus space 8

i)
Find gh left parenthesis x right parenthesis in its simplest form.
[2]
ii)
Find space straight g to the power of negative 1 end exponent open parentheses x close parentheses.

space straight g to the power of negative 1 end exponent open parentheses x close parentheses ................................................ [2]

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2
Sme Calculator2 marks

straight f left parenthesis x right parenthesis equals 3 x minus 5.
 
Find straight f to the power of negative 1 end exponent left parenthesis x right parenthesis.

 straight f to the power of negative 1 end exponent left parenthesis x right parenthesis equals.................................................... 

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3
Sme Calculator2 marks

straight f left parenthesis x right parenthesis equals 7 plus 3 x.
 
Find  straight f to the power of negative 1 end exponent left parenthesis x right parenthesis.
 

straight f to the power of negative 1 end exponent left parenthesis x right parenthesis =  ................................................ 

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4
Sme Calculator3 marks

straight f left parenthesis x right parenthesis equals x cubed space space space space space space space space space space straight g left parenthesis x right parenthesis equals 5 x plus 2

i)
Find  gf left parenthesis x right parenthesis.
 

[1]

ii)
Find  straight g to the power of negative 1 end exponent left parenthesis x right parenthesis.
 

 straight g to the power of negative 1 end exponent left parenthesis x right parenthesis = ............................................... [2]

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5a
Sme Calculator1 mark

straight f and straight g are functions such that

               straight f open parentheses x close parentheses space equals space 2 over x squared space space space space space space space space space space and space space space space space space straight g open parentheses x close parentheses space equals space 4 x cubed

Find straight f left parenthesis negative 5 right parenthesis

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5b
Sme Calculator2 marks

Find fg open parentheses 1 close parentheses.

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6a
Sme Calculator2 marks

      straight f open parentheses x close parentheses space equals space 3 x space minus space 2 straight g open parentheses x close parentheses space equals fraction numerator space 10 over denominator x plus 2 end fraction

Express the inverse function straight f to the power of negative 1 end exponent in the form straight f to the power of negative 1 end exponent open parentheses x close parentheses space equals space...

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6b
Sme Calculator2 marks

Find  gf open parentheses x close parentheses
Simplify your answer.

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1
Sme Calculator2 marks

straight f open parentheses x close parentheses space equals space 3 x squared space plus space a  where space a space is an integer.
straight f open parentheses negative 2 close parentheses space equals space 19

Find the value of a.

a space equals ................................................ 

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2a
Sme Calculator2 marks

straight f left parenthesis x right parenthesis space equals space 4 x plus 3 space space space space space space space space space space space space space straight g left parenthesis x right parenthesis space equals space 5 x minus 4

fg left parenthesis x right parenthesis space equals space 20 x plus p


Find the value of p.


space p space equals .................................................. 

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2b
Sme Calculator3 marks

straight h open parentheses x close parentheses equals fraction numerator 5 x minus 1 over denominator 3 end fraction


Find  straight h to the power of negative 1 end exponent open parentheses x close parentheses.


straight h to the power of negative 1 end exponent open parentheses x close parentheses equals .................................................. 

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3
Sme Calculator2 marks

f left parenthesis x right parenthesis equals 3 x minus 5      g left parenthesis x right parenthesis equals 2 to the power of x

Find f g left parenthesis 3 right parenthesis.

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4
Sme Calculator2 marks

text f end text left parenthesis x right parenthesis equals 2 x plus 3
 
Find text f end text left parenthesis 1 minus x right parenthesis in its simplest form.

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5
Sme Calculator2 marks

straight f left parenthesis x right parenthesis equals 7 plus 3 x space space space space space space space space space space space space space straight g left parenthesis x right parenthesis equals x to the power of 4
 

Find the value of x when  straight f left parenthesis x right parenthesis equals straight g left parenthesis 2 right parenthesis.
 

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

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6
Sme Calculator2 marks

straight h left parenthesis x right parenthesis equals a x squared plus 1


Find the value of a when straight h left parenthesis negative 2 right parenthesis equals 21.
 

a = ............................................... 

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7a
Sme Calculator2 marks

text f end text left parenthesis x right parenthesis equals 5 minus 2 x         straight g left parenthesis x right parenthesis equals x squared plus 8

Calculate ff left parenthesis negative 3 right parenthesis

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7b
Sme Calculator3 marks

Find 

i)
straight g left parenthesis 2 x right parenthesis,


[1]

ii)