Paper 1 June 2024, Question 14 7 marks
Solve the differential equation
given that y = 3 when x = ln2
Give your answer in an exact form.
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AQA A Level Further Maths
Topic questions Pure mathematics Differential equations
Differential equations
5 questions · 57 marks · about 1 hour
Differential equations questions
TopicDifferential equations▾
AQA 7367 Differential equations 5 questions
Paper 2 June 2024, Question 19 10 marks
Solve the differential equation
given that y = 
and 
= 0 when x = 0
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Paper 2 June 2023, Question 16 16 marks
A bungee jumper of mass m kg is attached to an elastic rope. The other end of the rope is attached to a fixed point.
The bungee jumper falls vertically from the fixed point.
At time t seconds after the rope first becomes taut, the extension of the rope is
(a)
A model for the motion while the rope remains taut assumes that the forces acting on the bungee jumper are
the weight of the bungee jumper
a tension in the rope of magnitude kx newtons
an air resistance force of magnitude Rv newtons
where k and R are constants such that 4km 
R2
(a)(i)
[6]
Show that this model gives the result
You do not need to find the value of A or the value of B
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(a)(ii)
[6]
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(b)
[4]
A second, simpler model assumes that the air resistance is zero.
The values of k, m and g remain the same.
Find an expression for x in terms of t according to this simpler model, giving the values of all constants to two significant figures.
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Paper 2 June 2022, Question 9 14 marks
(a)
[4]
A curve passes through the point (5, 12.3) and satisfies the differential equation
Use Euler’s step by step method once, and then the midpoint formula
once, each with a step length of 0.1, to estimate the value of y when x 
5
2
Give your answer to six significant figures.
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(b)(i)
[6]
Find the general solution of the differential equation
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(b)(ii)
[3]
Given that y satisfies the differential equation in part (b)(i) and that y 
12
3 when x 
5, find the value of y when x 52
Give your answer to six significant figures.
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(c)
[1]
Comment on the accuracy of your answer to part (a).
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Paper 1 November 2020, Question 10 10 marks
(a)
[8]
Find the general solution of the differential equation
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(b)
[2]
Find the particular solution for which y 0 when x 3
Give your answer in the form y f (x)
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