Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

TopicSkillDifficulty

12 questions

SA-9709-P3-DE2-0033 marksL1 FoundationCalculatorGeneral solutions

Solve

\dfrac{dy}{dx}=6x^2y

, given that

y=4

when

x=0

. Give

y

in terms of

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE2-0041 markL1 FoundationCalculatorSeparating variables

\dfrac{dy}{dx}=e^{x+y}

separates as

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE-G014 marksL1 FoundationCalculatorSeparating variables

Solve the differential equation

\dfrac{dy}{dx}=2xy

, given that

y=3

when

x=0

. Give

y

in terms of

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE-Q011 markL1 FoundationCalculatorSeparating variables

Which differential equation can be solved by separating the variables?

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE-Q021 markL1 FoundationCalculatorGeneral solutions

The general solution of

\dfrac{dy}{dx}=ky

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE-0014 marksL2 StandardCalculatorSeparating variables

Solve

\dfrac{dy}{dx}=\dfrac xy

, given that

y=3

when

x=4

and

y>0

. Give

y

in terms of

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE-0034 marksL2 StandardCalculatorSeparating variables

Solve

\dfrac{dy}{dx}=y\cos x

, given that

y=2

when

x=0

. Give

y

in terms of

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE2-0014 marksL2 StandardCalculatorSeparating variables

Solve

\dfrac{dy}{dx}=y^2

, given that

y=1

when

x=0

. Give

y

in terms of

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE-0025 marksL3 ExamCalculatorSeparating variables

Solve

\dfrac{dy}{dx}=e^{x-y}

, given that

y=1

when

x=0

. Give

y

in terms of

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE-0124 marksL3 ExamCalculatorSeparating variables

Solve

\dfrac{dy}{dx}=xe^{-y}

, given that

y=0

when

x=0

. Give

y

in terms of

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE2-0024 marksL3 ExamCalculatorGeneral solutions

Solve

x\dfrac{dy}{dx}=1+y

for

x>0

, given that

y=1

when

x=1

. Give

y

in terms of

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE-0065 marksL4 ChallengingCalculatorSeparating variables

Solve

x\dfrac{dy}{dx}=1+y^2

for

x>0

, given that

y=1

when

x=1

. Give

y

in terms of

x

Salam Academy Original Practice · Proposed mark scheme