IGCSEMaths: ExtendedCIETopic QuestionsCoordinate Geometry & GraphsDifferentiation

Syllabus Edition

First teaching 2023

First exams 2025

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Differentiation (CIE IGCSE Maths: Extended)

Topic Questions

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1a
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straight f left parenthesis x right parenthesis space equals space x left parenthesis x space plus space 2 right parenthesis left parenthesis x space – space 3 right parenthesis space

On the diagram, sketch the graph of y space equals space straight f left parenthesis x right parenthesis space space space space space space for space – 3 space less-than or slanted equal to space x space less-than or slanted equal to space 4 .
Show the values of the intersections with the axes. 

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1b
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Expand and simplify.

x left parenthesis x space plus space 2 right parenthesis left parenthesis x space – space 3 right parenthesis

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1c
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A is the point space left parenthesis 1 comma space – 6 right parenthesis.
The tangent to the graph of y space equals space straight f left parenthesis x right parenthesis at  A meets the y-axis at B.

Find the coordinates of B.

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2
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space y equals x to the power of 4 minus 4 x cubed space

Find the two stationary points on the graph of space y equals x to the power of 4 minus 4 x cubed.
 

( ..................... , ..................... )
( ..................... , ..................... )

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3a
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A curve has equation y equals x cubed minus 3 x plus 4.

Work out the coordinates of the two stationary points.

( .................... , ....................)
( .................... , ....................)

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3b
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Determine whether each stationary point is a maximum or a minimum.
Give reasons for your answers.

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4a
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y space equals space x cubed space – space 6 x squared space – space 15 x.

Find fraction numerator straight d y over denominator straight d x end fraction.

fraction numerator straight d y over denominator straight d x end fraction space equals....................................

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4b
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The curve with equation y space equals space x cubed space – space 6 x squared space – space 15 x has two stationary points.

Work out the coordinates of these two stationary points.

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1a
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Differentiate space 6 space plus space 4 x space minus space x squared.

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1b
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Find the coordinates of the turning point of the graph of y space equals space 6 space plus space 4 x space minus space x squared.

( ...................... , ...................... )

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2a
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Use differentiation to find fraction numerator d y over denominator d x end fraction for the following:

y space equals space x to the power of 4

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2b
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y space equals space 2 x cubed

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2c
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y space equals space 4.

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3a
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For the curve with equation y space equals space 2 x squared space minus space 6 x space minus space 11 colon

find fraction numerator d y over denominator d x end fraction

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3b
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find the coordinates of the point on the curve where the gradient is 2.

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1
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cie-igcse-2020-oct-nov-p4-tz1-q10a

 The diagram shows a sketch of the curve  y space equals space x to the power of 2 space end exponent space plus space 3 x space minus space 4.

i)
Differentiate  y space equals space x to the power of 2 space end exponent space plus space 3 x space minus space 4
  
 [2]
ii)
Find the equation of the tangent to the curve at the point (2, 6). 
 
[3]

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2
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space y equals x to the power of p plus 2 x to the power of q space

fraction numerator d y over denominator d x end fraction equals 11 x to the power of 10 plus 10 x to the power of 4, where fraction numerator d y over denominator d x end fraction is the derived function.
 
Find the value of p and the value of q.
 

p equals................................................
q equals................................................

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3a
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A curve, C, has equation y space equals space 2 x squared space plus space 8 k squared x space minus space 3 where k is a constant.

Show that when k = 0, the turning point on C has coordinates (0, -3).

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3b
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Show that when k space not equal to space 0, the turning point on C must have a negative x-coordinate.

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3c
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When k space not equal to space 0 determine whether or not the y-coordinate of the turning point is negative.

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