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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-ST-EX-0011 markL1 FoundationNon-calculatorMean and memory
Find the variance of X∼Exp(4)X\sim\text{Exp}(4).

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-EX-Q011 markL1 FoundationNon-calculatorProbabilities
If events follow a Poisson process with rate λ\lambda, the time between events is
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-EX-X011 markL1 FoundationNon-calculatorMean and memory
Find the mean of X∼Exp(2)X\sim\text{Exp}(2).

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-EX-X021 markL1 FoundationNon-calculatorProbabilities
For X∼Exp(2)X\sim\text{Exp}(2), find P(X>1)P(X>1) exactly.

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-EX-X031 markL1 FoundationNon-calculatorProbabilities
For X∼Exp(2)X\sim\text{Exp}(2), find P(X<0.5)P(X<0.5) exactly.

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-EX-X041 markL1 FoundationNon-calculatorMean and memory
Find the standard deviation of X∼Exp(0.25)X\sim\text{Exp}(0.25).

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-EX-0022 marksL2 StandardCalculatorMean and memory
Find the median of Exp(3)\text{Exp}(3) (3 s.f.).

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-EX-0032 marksL2 StandardCalculatorProbabilities
X∼Exp(0.5)X\sim\text{Exp}(0.5). Find P(1<X<3)P(1<X<3) (3 s.f.).

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-EX-G012 marksL2 StandardCalculatorProbabilities
Calls arrive at 3 per hour. Find the probability of waiting more than 30 minutes for the next call (3 s.f.).

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-EX-X052 marksL2 StandardNon-calculatorMean and memory
Find the median of X∼Exp(0.5)X\sim\text{Exp}(0.5) exactly.

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-EX-X061 markL2 StandardNon-calculatorMean and memory
For X∼Exp(1)X\sim\text{Exp}(1), find P(X>5∣X>3)P(X>5\mid X>3) exactly.

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Salam Academy Original Practice · Proposed mark scheme
SA-ST-EX-0042 marksL3 ExamCalculatorMean and memory
A component's lifetime is Exp(0.1)\text{Exp}(0.1) years. Given it has lasted 5 years, find the probability it lasts at least 10 years in total (3 s.f.).

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Salam Academy Original Practice · Proposed mark scheme