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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-IAL-S1-DR-0052 marksL1 FoundationCalculatorDiscrete uniform
XX is the score on a fair six-sided die. Find (i) E(X)E(X) and (ii) Var(X)\text{Var}(X).

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-S1-DR2-0011 markL1 FoundationNon-calculatorE and Var
XX takes the values 0,1,20,1,2 with probabilities 0.250.25, 0.50.5, 0.250.25. Find E(X)E(X).

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-S1-DR2-0021 markL1 FoundationNon-calculatorE and Var
For the same distribution (0,1,20,1,2 with probabilities 0.250.25, 0.50.5, 0.250.25), find E(X2)E(X^2).

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-S1-DR2-0031 markL1 FoundationNon-calculatorE and Var
Using E(X)=1E(X)=1 and E(X2)=1.5E(X^2)=1.5, find Var(X)\text{Var}(X).

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-S1-DR2-0041 markL1 FoundationNon-calculatorDiscrete uniform
XX has a discrete uniform distribution on 1,2,…,101,2,\ldots,10. Find E(X)E(X).

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-S1-DR2-0051 markL1 FoundationNon-calculatorE and Var
E(X)=3E(X)=3. Find E(5−2X)E(5-2X).

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-S1-DR-Q021 markL1 FoundationCalculatorE and Var
Var(X+10)=\text{Var}(X+10)=
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-S1-DR-0014 marksL2 StandardCalculatorE and Var
XX takes the values 11, 22, 33 with probabilities 0.20.2, 0.50.5, 0.30.3. Find (i) E(X)E(X) and (ii) Var(X)\text{Var}(X).

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-S1-DR-0023 marksL2 StandardCalculatorE and Var
E(X)=2.1E(X)=2.1 and Var(X)=0.49\text{Var}(X)=0.49. Find (i) E(3X−2)E(3X-2) and (ii) Var(3X−2)\text{Var}(3X-2).

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-S1-DR-0062 marksL2 StandardCalculatorDiscrete uniform
XX has a discrete uniform distribution on 1,2,…,n1,2,\dots,n, and Var(X)=10\text{Var}(X)=10. Find nn.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-S1-DR-0083 marksL2 StandardCalculatorE and Var
E(X)=3E(X)=3 and E(X2)=11E(X^2)=11. Find (i) Var(X)\text{Var}(X) and (ii) Var(2X+5)\text{Var}(2X+5).

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-S1-DR-0096 marksL4 ChallengingCalculatorE and Var
XX takes the values 11, 22, 33 with probabilities aa, bb, 0.30.3, and E(X)=2.1E(X)=2.1. Find (i) aa and bb, (ii) Var(4−2X)\text{Var}(4-2X).

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Salam Academy Original Practice · Proposed mark scheme