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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2730 questions · page 39 of 137 · choose a topic above to narrow them down

SA-9709-P5-DV-0082 marksL1 FoundationCalculatorGeometric

X\sim\text{Geo}(0.3)

. Find

P(X=4)

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-DV1-0012 marksL1 FoundationCalculatorDistributions

The random variable

X

has

P(X=x)=k(x+1)

for

x=0,1,2,3

. Find

k

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-DV1-0021 markL1 FoundationCalculatorDistributions

X

takes the values

1

2

and

3

with probabilities

0.2

0.5

and

p

. Find

p

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-DV1-0051 markL1 FoundationCalculatorDistributions

X

takes the values

0,1,2,3

with probabilities

0.1,\ 0.3,\ 0.4,\ 0.2

. Find

P(X\ge2)

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-DV2-0012 marksL1 FoundationCalculatorE(X) and Var(X)

X

takes the values

1,2,3

with probabilities

0.5,\ 0.3,\ 0.2

. Find

E(X)

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-DV2-0052 marksL1 FoundationCalculatorE(X) and Var(X)

A random variable has

E(X)=3

and

E(X^2)=13

. Find its standard deviation.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-DV2-0072 marksL1 FoundationCalculatorExpected value in context

Two fair coins are tossed and

X

is the number of heads. Find

E(X)

and

\text{Var}(X)

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-DV3-0012 marksL1 FoundationCalculatorBinomial

X\sim B(5,0.5)

. Find

P(X=2)

as a fraction.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-DV3-0021 markL1 FoundationCalculatorBinomial

X\sim B(12,0.25)

. Find

P(X=0)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-DV4-0011 markL1 FoundationCalculatorGeometric

X\sim\text{Geo}(0.2)

. Find

P(X=3)

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-DV-G014 marksL1 FoundationCalculatorE(X) and Var(X)

X

takes the values

1,2,3,4

with probabilities

0.1,0.3,0.4,0.2

respectively. Find

E(X)

and

\text{Var}(X)

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-ND-0012 marksL1 FoundationCalculatorStandardising

X\sim N(50,16)

. Find

P(X>45)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-ND-0131 markL1 FoundationCalculatorStandardising

Z\sim N(0,1)

. Find

P(Z<-0.5)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-ND1-0012 marksL1 FoundationCalculatorStandardising

X\sim N(20,25)

. Find

P(X<27)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-ND1-0022 marksL1 FoundationCalculatorStandardising

X\sim N(60,9)

. Find

P(X>55)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-ND2-0011 markL1 FoundationCalculatorInverse normal

Z\sim N(0,1)

. Find

z

such that

P(Z<z)=0.95

, correct to 3 decimal places.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-ND3-0012 marksL1 FoundationCalculatorApproximation

X\sim B(50,0.4)

is to be approximated by

Y\sim N(\mu,\sigma^2)

. Find

\mu

and

\sigma^2

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-ND-G012 marksL1 FoundationCalculatorStandardising

X\sim N(50,16)

. Find

P(X<56)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-PC-0012 marksL1 FoundationCalculatorRepeats

Find the number of different arrangements of the letters of the word BANANA.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P5-PC-0061 markL1 FoundationCalculatorSelections

A committee of

4

is to be chosen from

7

men and

5

women. How many different committees are possible?

Salam Academy Original Practice · Proposed mark scheme