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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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13 questions

SA-9709-P6-CR-0012 marksL1 FoundationCalculatorPDFs
For f(x)=x29f(x)=\tfrac{x^2}9 on 0≤x≤30\le x\le3, find P(X<2)P(X<2).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR-0111 markL1 FoundationCalculatorSketching pdfs
For a continuous random variable XX, P(X=2)P(X=2) is
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR1-0012 marksL1 FoundationCalculatorPDFs
f(x)=kxf(x)=kx for 0≤x≤40\le x\le4, and 00 otherwise, is a probability density function. Find kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR1-0022 marksL1 FoundationCalculatorPDFs
f(x)=38x2f(x)=\tfrac38x^2 for 0≤x≤20\le x\le2, and 00 otherwise. Find P(X>1)P(X>1).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR1-0031 markL1 FoundationCalculatorSketching pdfs
f(x)=0.25f(x)=0.25 for 1≤x≤51\le x\le5, and 00 otherwise. Find P(2<X<3.5)P(2<X<3.5).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR1-0041 markL1 FoundationCalculatorSketching pdfs
Which of these cannot be a probability density function on the given interval?
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR-G012 marksL1 FoundationCalculatorPDFs
XX has probability density function f(x)=kx2f(x)=kx^2 for 0≤x≤30\le x\le3, and 00 otherwise. Find kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR-Q011 markL1 FoundationCalculatorPDFs
Which is a property of every probability density function?
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR-0044 marksL2 StandardCalculatorPDFs
f(x)=k(4−x)f(x)=k(4-x) for 0≤x≤40\le x\le4, and 00 otherwise. Find kk and P(X>1)P(X>1).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR-0073 marksL2 StandardCalculatorPDFs
f(x)=kx(4−x)f(x)=kx(4-x) for 0≤x≤40\le x\le4, and 00 otherwise. Find kk, and state E(X)E(X).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR1-0053 marksL2 StandardCalculatorPDFs
f(x)=k(x+1)f(x)=k(x+1) for 0≤x≤20\le x\le2, and 00 otherwise. Find kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR1-0062 marksL2 StandardCalculatorSketching pdfs
f(x)=332x(4−x)f(x)=\tfrac3{32}x(4-x) for 0≤x≤40\le x\le4, and 00 otherwise. Find the mode of XX.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR-0083 marksL3 ExamCalculatorPDFs
For f(x)=332x(4−x)f(x)=\tfrac3{32}x(4-x) on 0≤x≤40\le x\le4, find P(1<X<3)P(1<X<3).

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Salam Academy Original Practice · Proposed mark scheme