Edexcel A Level Further Maths
Topic questions Pure mathematics Differentiating inverse functions
9 questions · 67 marks · about 1.5 hours
Given that
The curve C has equation
Determine 
giving your answer in simplest form.
Hence determine the x coordinate of the point on C at which the gradient is 4
Given that
show that
f(x) = arcsin(ex) x ≤ 0
Prove that f(x) has no stationary points.
Given that
show that
f(x) = arcsin(ex)
x ≤ 0
Prove that f(x) has no stationary points.
f (x) = arcsinx−1 ≤ x 
1
Determine the first two non-zero terms, in ascending powers of x, of the Maclaurin series for f (x), giving each coefficient in its simplest form.
Substitute x = 
into the answer to part (a) and hence find an approximate value for π Give your answer in the form 
where p and q are integers to be determined.
f (x) = arcsinx−1 ≤ x 1
Determine the first two non-zero terms, in ascending powers of x, of the Maclaurin series for f (x), giving each coefficient in its simplest form.
Substitute x = into the answer to part (a) and hence find an approximate value for π Give your answer in the form where p and q are integers to be determined.
The curve C has equation
Show that C has no stationary points.
The normal to C, at the point where x = 1, crosses the x-axis at the point A and crosses the y-axis at the point B.
Given that O is the origin,
show that the area of the triangle OAB is 
p 
+ qπ + r 
2) where p, q and r are integers to be determined.
The curve C has equation
Show that C has no stationary points.
The normal to C, at the point where x = 1, crosses the x-axis at the point A and crosses the y-axis at the point B.
Given that O is the origin,
show that the area of the triangle OAB is 
p 
+ qπ + r 
2) where p, q and r are integers to be determined.
y= tan−1x
Assuming the derivative of tanx, prove that
Show that
where k is an arbitrary constant and A, B and C are constants to be determined.
y= tan−1x
Assuming the derivative of tanx, prove that
Show that
where k is an arbitrary constant and A, B and C are constants to be determined.
Memes
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