Question 1 - A-Level Maths

CAIE Further Paper 2 2020 June — Question 1 6 marks

Exam Board	CAIE
Module	Further Paper 2 (Further Paper 2)
Year	2020
Session	June
Marks	6
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Second order differential equations
Type	Standard non-homogeneous with exponential RHS
Difficulty	Standard +0.3 This is a standard second-order linear differential equation with constant coefficients requiring the auxiliary equation method for the complementary function and particular integral by inspection or undetermined coefficients. While it's a Further Maths topic (inherently harder), the question is entirely procedural with no conceptual challenges—solve auxiliary equation m²-8m-9=0, find CF, then find PI of form Ae^(8t). Slightly above average difficulty only due to being Further Maths content.
Spec	4.10e Second order non-homogeneous: complementary + particular integral

Find the general solution of the differential equation $$\frac{d^2x}{dt^2} - 8\frac{dx}{dt} - 9x = 9e^{8t}.$$ [6]

Show mark scheme Show mark scheme source

Question 1:

Answer	Marks	Guidance
1	m2−8m−9=0m=−1,9	M1
x = Ae−t +Be9t	A1
x = ke8t  x =8ke8t  x= 64ke8t	B1
64ke8t −64ke8t −9ke8t = 9e8t  −9k = 9	M1
k = −1	A1
x = Ae−t + Be9t −e8t	A1

6

Answer	Marks	Guidance
Question	Answer	Marks

Question 1:
1 | m2−8m−9=0m=−1,9 | M1
x = Ae−t +Be9t | A1
x = ke8t  x =8ke8t  x= 64ke8t | B1
64ke8t −64ke8t −9ke8t = 9e8t  −9k = 9 | M1
k = −1 | A1
x = Ae−t + Be9t −e8t | A1
6
Question | Answer | Marks

Show LaTeX source

Find the general solution of the differential equation
$$\frac{d^2x}{dt^2} - 8\frac{dx}{dt} - 9x = 9e^{8t}.$$
[6]

\hfill \mbox{\textit{CAIE Further Paper 2 2020 Q1 [6]}}

This paper (8 questions)

View full paper

Q1 6 Q2 6 Q3 8 Q4 8 Q5 9 Q6 12 Q7 11 Q8 15