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-DE3-G014 marksL1 FoundationCalculatorParticular solutions

Solve

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

for

x>0

, given that

y=3

when

x=1

. Give

y

in terms of

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE3-Q011 markL1 FoundationCalculatorHarder integrals

After separating

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

, the

x

integral is best done by

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE-Q031 markL1 FoundationCalculatorParticular solutions

A particular solution differs from the general solution because it

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE-0113 marksL2 StandardCalculatorParticular solutions

Given

\dfrac{dy}{dx}=3y

and

y=2

when

x=0

, find the exact value of

y

when

x=1

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE3-0034 marksL2 StandardCalculatorHarder integrals

Solve

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

for

-\tfrac\pi2<x<\tfrac\pi2

, given that

y=2

when

x=0

. Give

y

in terms of

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE3-0016 marksL3 ExamCalculatorHarder integrals

Solve

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

, given that

y=2

when

x=0

and

y>0

. Give

y

in terms of

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE3-0026 marksL3 ExamCalculatorHarder integrals

Solve

\dfrac{dy}{dx}=\dfrac{2y}{x(x+2)}

for

x>0

, given that

y=1

when

x=2

. Give

y

in terms of

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE3-0046 marksL3 ExamCalculatorHarder integrals

Solve

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

, given that

y=1

when

x=0

and

y>0

. Find the exact value of

y

when

x=\tfrac\pi2

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE3-0065 marksL3 ExamCalculatorParticular solutions

Solve

(1+x^2)\dfrac{dy}{dx}=xy

, given that

y=3

when

x=0

and

y>0

. Find the value of

y

when

x=\sqrt3

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE3-0056 marksL4 ChallengingCalculatorHarder integrals

Solve

\dfrac{dy}{dx}=e^{2y}\cos x

, given that

y=0

when

x=0

. Give

y

in terms of

x

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE-0097 marksL5 ExtensionCalculatorHarder integrals

Solve

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

for

x\ge0

, given that

y=1

when

x=0

. Give

y

in terms of

x

, and state the value that

y

approaches as

x

becomes large.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-DE3-0076 marksL5 ExtensionCalculatorHarder integrals

Solve

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

, given that

y=0

when

x=0

. Find

y

when

x=1

, correct to 3 significant figures, and the smallest positive value of

x

at which the solution stops existing.

Salam Academy Original Practice · Proposed mark scheme