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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-RR-0012 marksL1 FoundationNon-calculatorFirst order
un+1=3unu_{n+1}=3u_n, u0=2u_0=2. Find u4u_4.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RR-G011 markL1 FoundationNon-calculatorFirst order
un+1=2un+3u_{n+1}=2u_n+3, u1=1u_1=1. Find u3u_3.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RR-Q011 markL1 FoundationNon-calculatorSecond order
un+2−4un+1+4un=0u_{n+2}-4u_{n+1}+4u_n=0 has general solution
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RR-X011 markL1 FoundationNon-calculatorFirst order
un+1=2unu_{n+1}=2u_n, u0=5u_0=5. Find u3u_3.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RR-X021 markL1 FoundationNon-calculatorModelling
Find the constant (steady-state) solution of un+1=0.5un+10u_{n+1}=0.5u_n+10.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RR-0022 marksL2 StandardNon-calculatorFirst order
Find the constant solution un=ku_n=k of un+1=2un+3u_{n+1}=2u_n+3.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RR-0032 marksL2 StandardNon-calculatorSecond order
Find the roots of the auxiliary equation for un+2=5un+1−6unu_{n+2}=5u_{n+1}-6u_n.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RR-X032 marksL2 StandardNon-calculatorSecond order
Find the roots of the auxiliary equation of un+2=un+1+6unu_{n+2}=u_{n+1}+6u_n.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RR-X052 marksL2 StandardNon-calculatorModelling
A savings account follows un+1=1.1un−50u_{n+1}=1.1u_n-50 with u0=1000u_0=1000. Find u2u_2.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RR-0044 marksL3 ExamNon-calculatorSecond order
un+2=5un+1−6unu_{n+2}=5u_{n+1}-6u_n with u0=1u_0=1, u1=4u_1=4. Find u3u_3 using the closed form.

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RR-0052 marksL3 ExamCalculatorSecond order
Find the larger root of the auxiliary equation for un+2=un+1+unu_{n+2}=u_{n+1}+u_n (to 4 s.f.).

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Salam Academy Original Practice · Proposed mark scheme
SA-FP-RR-X043 marksL3 ExamNon-calculatorSecond order
un+2−6un+1+9un=0u_{n+2}-6u_{n+1}+9u_n=0 with u0=1u_0=1, u1=6u_1=6. Use the general solution (A+Bn)3n(A+Bn)3^n to find u2u_2.

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Salam Academy Original Practice · Proposed mark scheme