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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-LC-0051 markL1 FoundationCalculatorMultiples vs sums
XX has variance σ2\sigma^2. X1X_1 and X2X_2 are independent observations of XX. Which is true?
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC2-0012 marksL1 FoundationCalculatorMultiples vs sums
Var(X)=5\text{Var}(X)=5. Find Var(4X)\text{Var}(4X) and Var(X1+X2+X3+X4)\text{Var}(X_1+X_2+X_3+X_4), where the XiX_i are independent observations of XX.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC2-0022 marksL1 FoundationCalculatorTotals
Egg masses are N(60,9)N(60,9) grams. Six eggs are chosen at random. Find the mean and variance of their total mass.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC2-0061 markL1 FoundationCalculatorMultiples vs sums
Why is Var(X1+X2)\text{Var}(X_1+X_2) smaller than Var(2X)\text{Var}(2X)?
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC-0102 marksL2 StandardCalculatorMultiples vs sums
X∼N(10,4)X\sim N(10,4). Find Var(3X)\text{Var}(3X) and Var(X1+X2+X3)\text{Var}(X_1+X_2+X_3), where the XiX_i are independent observations of XX.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC2-0034 marksL2 StandardCalculatorTotals
Apple masses are N(150,100)N(150,100) grams. A box holds 1212 randomly chosen apples. Find the probability that the total mass exceeds 18501850 g, correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC2-0043 marksL2 StandardCalculatorMultiples vs sums
X∼N(20,4)X\sim N(20,4). Find P(3X>65)P(3X>65), correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC2-0053 marksL2 StandardCalculatorTotals
X∼N(40,25)X\sim N(40,25). The mean Xˉ\bar X of 55 independent observations is found. Find P(Xˉ>42)P(\bar X>42), correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC2-0082 marksL2 StandardCalculatorMultiples vs sums
X∼N(10,4)X\sim N(10,4) and X1X_1, X2X_2, X3X_3 are independent observations of XX. Find E(X1+X2−2X3)E(X_1+X_2-2X_3) and Var(X1+X2−2X3)\text{Var}(X_1+X_2-2X_3).

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC-0034 marksL3 ExamCalculatorTotals
The masses of bags of rice are N(200,25)N(200,25) grams. Find the probability that the total mass of 44 randomly chosen bags is less than 790790 g, correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC-0094 marksL3 ExamCalculatorTotals
The masses of men are N(80,100)N(80,100) kg. A lift has a safe load of 700700 kg. Find the probability that 88 randomly chosen men exceed the safe load, correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-LC2-0074 marksL3 ExamCalculatorTotals
Adult masses are N(75,144)N(75,144) kg. A lift has a maximum load of 10001000 kg. Find the probability that 1313 randomly chosen adults exceed the maximum load, correct to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme