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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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14 questions

SA-9709-P3-DE4-0031 markL1 FoundationCalculatorInterpreting models
The temperature of a cooling liquid is θ=20+80e−0.14t\theta=20+80e^{-0.14t}. State the value that θ\theta approaches as tt becomes large.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-DE4-0091 markL1 FoundationCalculatorInterpreting models
A population is modelled by dNdt=kN\dfrac{dN}{dt}=kN with k>0k>0. Which is a limitation of this model?
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-DE4-G013 marksL1 FoundationCalculatorIn context
A colony of bacteria grows according to dNdt=0.1N\dfrac{dN}{dt}=0.1N, with N=50N=50 when t=0t=0 (tt in hours). Find the exact value of NN when t=10t=10.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-DE4-Q011 markL1 FoundationCalculatorInterpreting models
In the cooling model θ=20+80e−kt\theta=20+80e^{-kt}, the 2020 represents
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-DE-0074 marksL2 StandardCalculatorIn context
A population NN grows according to dNdt=0.02N\dfrac{dN}{dt}=0.02N, with N=500N=500 when t=0t=0. Find the time taken for the population to double, correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-DE4-0013 marksL2 StandardCalculatorIn context
A radioactive substance decays according to dmdt=−km\dfrac{dm}{dt}=-km. Its half-life is 88 days. Find the exact value of kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-DE4-0051 markL2 StandardCalculatorInterpreting models
A population satisfies dNdt=0.02N(100−N)\dfrac{dN}{dt}=0.02N(100-N), starting at N=20N=20. State the value that NN approaches as tt becomes large.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-DE-0055 marksL3 ExamCalculatorIn context
A liquid cools so that its temperature is θ=20+60e−kt\theta=20+60e^{-kt} after tt minutes. After 1010 minutes the temperature is 50∘50^\circC. Find the exact value of kk, and the temperature after 2020 minutes.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-DE4-0026 marksL3 ExamCalculatorIn context
A liquid at 100∘100^\circC is placed in a room at 20∘20^\circC and cools according to dθdt=−k(θ−20)\dfrac{d\theta}{dt}=-k(\theta-20), with tt in minutes. After 55 minutes it is at 60∘60^\circC. Find the time at which it reaches 30∘30^\circC.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-DE4-0065 marksL3 ExamCalculatorIn context
The depth hh cm of water in a tank satisfies dhdt=−kh\dfrac{dh}{dt}=-k\sqrt h, with tt in minutes. When t=0t=0, h=36h=36; when t=10t=10, h=16h=16. Find kk and the time at which the tank is empty.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-DE4-0075 marksL3 ExamCalculatorIn context
A tank is filled at 2020 cm3^3 s−1^{-1} and leaks at 0.1V0.1V cm3^3 s−1^{-1}, so dVdt=20−0.1V\dfrac{dV}{dt}=20-0.1V. The tank is empty at t=0t=0. Find the time at which V=100V=100, correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-DE-0086 marksL4 ChallengingCalculatorIn context
The depth hh cm of water in a tank satisfies dhdt=−kh\dfrac{dh}{dt}=-k\sqrt h, where tt is in minutes. Initially h=16h=16, and after 55 minutes h=9h=9. Find kk, and the time at which the tank becomes empty.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-DE4-0047 marksL4 ChallengingCalculatorIn context
A population satisfies dNdt=0.02N(100−N)\dfrac{dN}{dt}=0.02N(100-N), with N=20N=20 when t=0t=0. Find the exact time at which N=50N=50.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-DE4-0088 marksL5 ExtensionCalculatorIn context
A population satisfies dNdt=0.02N(100−N)\dfrac{dN}{dt}=0.02N(100-N), with N=20N=20 when t=0t=0. Show that N=1001+4e−2tN=\dfrac{100}{1+4e^{-2t}}, and find the exact time at which the population reaches 9090.

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Salam Academy Original Practice · Proposed mark scheme