Date | November Example question | Marks available | 2 | Reference code | EXN.1.AHL.TZ0.13 |
Level | Additional Higher Level | Paper | Paper 1 | Time zone | Time zone 0 |
Command term | Write down | Question number | 13 | Adapted from | N/A |
Question
Consider the second order differential equation
¨x+4(˙x)2-2t=0
where x is the displacement of a particle for t≥0.
Write the differential equation as a system of coupled first order differential equations.
When t=0, x=˙x=0
Use Euler’s method with a step length of 0.1 to find an estimate for the value of the displacement and velocity of the particle when t=1.
Markscheme
* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.
˙x=y M1
˙y=2t-4y2 A1
[2 marks]
tn+1=tn+0.1
xn+1=xn+0.1yn
yn+1=yn+0.1(2tn-4y2n) (M1)(A1)
Note: Award M1 for a correct attempt to substitute the functions in part (a) into the formula for Euler’s method for coupled systems.
When t=1
x=0.202 (0.20201…) A1
˙x=0.598 (0.59822…) A1
Note: Accept y=0.598.
[4 marks]