Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

TopicSkillDifficulty

12 questions

SA-DM-DA-G012 marksL1 FoundationNon-calculatorEMV

A gamble pays £1000 with probability

0.6

and loses £200 with probability

0.4

. Find its EMV in pounds.

Salam Academy Original Practice · Proposed mark scheme

SA-DM-DA-Q011 markL1 FoundationNon-calculatorEMV

When rolling back a decision tree, at a decision node you

Salam Academy Original Practice · Proposed mark scheme

SA-DM-DA-X012 marksL1 FoundationNon-calculatorEMV

A venture gains £2000 with probability

0.3

and loses £500 with probability

0.7

. Find its EMV in pounds.

Salam Academy Original Practice · Proposed mark scheme

SA-DM-DA-X021 markL1 FoundationNon-calculatorEMV

Another option pays £400 or £100 with equal probability. Find its EMV in pounds.

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SA-DM-DA-X061 markL1 FoundationNon-calculatorEMV

In a decision tree, a chance node is usually drawn as a

Salam Academy Original Practice · Proposed mark scheme

SA-DM-DA-X071 markL1 FoundationNon-calculatorEMV

A chance node has branches with probabilities

0.2

0.5

and

q

. Find

q

Salam Academy Original Practice · Proposed mark scheme

SA-DM-DA-0022 marksL2 StandardCalculatorUtility

With

u(x)=\sqrt{x+200}

, find the expected utility of the gamble (3 s.f.).

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SA-DM-DA-X042 marksL2 StandardNon-calculatorUtility

With

u(x)=\sqrt{x+500}

, find the expected utility of the venture (gain £2000 with probability

0.3

, lose £500 with probability

0.7

Salam Academy Original Practice · Proposed mark scheme

SA-DM-DA-X051 markL2 StandardNon-calculatorEMV

A survey costs £120. The EMV with the survey (before paying for it) is £400. Find the net EMV.

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SA-DM-DA-0012 marksL3 ExamNon-calculatorEMV

For what probability

p

of winning £1000 (else losing £200) is the gamble's EMV equal to a certain £500?

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SA-DM-DA-0032 marksL3 ExamNon-calculatorEMV

A firm can pay £100 for a survey before deciding. Without it the best EMV is £520; with it the EMV (before paying) is £650. Find the net EMV of surveying.

Salam Academy Original Practice · Proposed mark scheme

SA-DM-DA-X032 marksL3 ExamNon-calculatorEMV

For the venture (gain £2000 with probability

p

, else lose £500), find

p

for which the EMV equals a certain £200.

Salam Academy Original Practice · Proposed mark scheme