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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-9709-P6-LC3-0013 marksL1 FoundationCalculatorNormal combinations
X∼N(30,4)X\sim N(30,4) and Y∼N(20,5)Y\sim N(20,5) are independent. Find P(X+Y<53)P(X+Y<53), correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC3-0052 marksL1 FoundationCalculatorPoisson sums
X∼Po(1.5)X\sim\text{Po}(1.5) and Y∼Po(2.5)Y\sim\text{Po}(2.5) are independent. Find P(X+Y=0)P(X+Y=0), correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC-Q031 markL1 FoundationCalculatorNormal combinations
If XX and YY are independent normal variables, 2X−3Y2X-3Y is
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC-0023 marksL2 StandardCalculatorNormal combinations
X∼N(50,9)X\sim N(50,9) and Y∼N(30,16)Y\sim N(30,16) are independent. Find P(X+Y>85)P(X+Y>85), correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC3-0023 marksL2 StandardCalculatorNormal combinations
X∼N(12,1)X\sim N(12,1) and Y∼N(10,8)Y\sim N(10,8) are independent. Find P(X>Y)P(X>Y), correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC3-0033 marksL2 StandardCalculatorNormal combinations
Jar masses are N(350,16)N(350,16) g and lid masses are N(20,1)N(20,1) g, independently. Find the probability that a jar with its lid weighs more than 375375 g, correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC3-0062 marksL2 StandardCalculatorPoisson sums
X∼Po(2)X\sim\text{Po}(2) and Y∼Po(3)Y\sim\text{Po}(3) are independent. Find P(X+Y=2)P(X+Y=2), correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC3-0071 markL2 StandardCalculatorPoisson sums
X∼Po(3)X\sim\text{Po}(3). Find Var(2X)\text{Var}(2X). (Comparing it with E(2X)=6E(2X)=6 shows why 2X2X is not Poisson.)

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC-0044 marksL3 ExamCalculatorNormal combinations
X∼N(50,9)X\sim N(50,9) and Y∼N(45,16)Y\sim N(45,16) are independent. Find P(X>Y)P(X>Y), correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC3-0044 marksL3 ExamCalculatorNormal combinations
X∼N(5,1)X\sim N(5,1) and Y∼N(9,4)Y\sim N(9,4) are independent. Find P(2X>Y)P(2X>Y), correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC-0065 marksL4 ChallengingCalculatorNormal combinations
Lengths A∼N(12,0.52)A\sim N(12,0.5^2) and B∼N(8,0.42)B\sim N(8,0.4^2) are independent. Find P(A>1.4B)P(A>1.4B), correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC3-0085 marksL4 ChallengingCalculatorNormal combinations
The heights of two children are A∼N(150,36)A\sim N(150,36) cm and B∼N(148,28)B\sim N(148,28) cm, independently. Find the probability that their heights differ by less than 55 cm, correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme