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Practise

Question bank

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

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12 questions

SA-FP-DE2-G012 marksL1 FoundationNon-calculatorComplementary function
Find the roots of the auxiliary equation for y′′−5y′+6y=0y''-5y'+6y=0.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE2-Q011 markL1 FoundationNon-calculatorComplementary function
If the auxiliary equation has roots p±qip\pm qi, the complementary function is
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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE2-X012 marksL1 FoundationNon-calculatorComplementary function
Find the roots of the auxiliary equation for y′′−5y′+6y=0y''-5y'+6y=0.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE2-X031 markL1 FoundationNon-calculatorComplementary function
The general solution of y′′+2y′+y=0y''+2y'+y=0 is
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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE2-X041 markL1 FoundationNon-calculatorParticular integral
Find the constant particular integral of y′′−5y′+6y=12y''-5y'+6y=12.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE2-0012 marksL2 StandardNon-calculatorComplementary function
The general solution of y′′+4y=0y''+4y=0 is Acos⁡ωx+Bsin⁡ωxA\cos\omega x+B\sin\omega x. Find ω\omega.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE2-0021 markL2 StandardNon-calculatorComplementary function
Find the repeated root of the auxiliary equation for y′′+2y′+y=0y''+2y'+y=0.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE2-0032 marksL2 StandardNon-calculatorParticular integral
Find the constant particular integral of y′′−3y′+2y=4y''-3y'+2y=4.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE2-X022 marksL2 StandardNon-calculatorComplementary function
Every solution of y′′+4y=0y''+4y=0 is periodic. Find the period.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE2-0043 marksL3 ExamNon-calculatorParticular integral
Find a particular integral of y′′+y=3xy''+y=3x, in terms of xx.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE2-X053 marksL3 ExamNon-calculatorParticular solutions
y′′+4y=0y''+4y=0, y(0)=1y(0)=1, y′(0)=4y'(0)=4. Find y(π4)y\left(\frac\pi4\right).

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-DE2-0055 marksL4 ChallengingNon-calculatorParticular solutions
y′′−y=0y''-y=0, y(0)=2y(0)=2, y′(0)=0y'(0)=0. Find the exact value of yy when x=ln⁡2x=\ln2.

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Salam Academy Original Practice · Proposed mark scheme