Practise

Question bank

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

TopicSkillDifficulty

2730 questions · page 93 of 137 · choose a topic above to narrow them down

SA-9709-P6-PO1-0022 marksL2 StandardCalculatorProbabilities

X\sim\text{Po}(4.5)

. Find

P(X<3)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-PO2-0023 marksL2 StandardCalculatorScaling λ

Breakdowns of a machine occur at random at an average rate of

0.8

per day. Find the probability of at most

3

breakdowns in a

7

-day week, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-PO2-0052 marksL2 StandardCalculatorScaling λ

X\sim\text{Po}(\lambda)

and

P(X=0)=0.2

. Find

\lambda

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-PO3-0072 marksL2 StandardCalculatorPoisson for binomial

1.5\%

of components are defective, independently. Use a Poisson approximation to find the probability that a box of

200

contains no defective components, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-SE-0013 marksL2 StandardCalculatorUnbiased estimates

A sample of

50

values gives

\Sigma(x-20)=35

and

\Sigma(x-20)^2=1250

. Find unbiased estimates of the population mean and variance (variance to 3 s.f.).

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-SE-0023 marksL2 StandardCalculatorNormal sample means

X\sim N(100,15^2)

. A random sample of

25

is taken. Find

P(\bar X>104)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-SE-0044 marksL2 StandardCalculatorCI for a mean

A random sample of

40

has mean

72.4

. The population standard deviation is

6

. Find a

95\%

confidence interval for the population mean, with limits to 2 decimal places.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-SE-0054 marksL2 StandardCalculatorCI for a proportion

In a random sample of

200

people,

48

are left-handed. Find a

90\%

confidence interval for the proportion of left-handed people, with limits to 3 decimal places.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-SE-0112 marksL2 StandardCalculatorCLT

X

has standard deviation

12

. Find the standard deviation of the mean of a random sample of

36

values.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-SE1-0053 marksL2 StandardCalculatorUnbiased estimates

A random sample of

5

values is

3,\ 5,\ 6,\ 8,\ 8

. Find unbiased estimates of the population mean and variance.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-SE2-0043 marksL2 StandardCalculatorNormal sample means

X\sim N(200,25^2)

. A random sample of

16

is taken. Find

P(195<\bar X<205)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-SE3-0023 marksL2 StandardCalculatorCI for a mean

A random sample of

36

from a population with standard deviation

15

has mean

120

. Find a

90\%

confidence interval for the population mean, with limits to 2 decimal places.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-SE3-0034 marksL2 StandardCalculatorCI for a proportion

In a random sample of

150

people,

60

prefer brand A. Find an approximate

95\%

confidence interval for the proportion of people who prefer brand A, with limits to 3 decimal places.

Salam Academy Original Practice · Proposed mark scheme

SA-AB-AR-0032 marksL2 StandardCalculatorRQ

Calculate the RQ for tripalmitin:

\mathrm{2C_{51}H_{98}O_6+145O_2\rightarrow102CO_2+98H_2O}

Salam Academy Original Practice · Proposed mark scheme

SA-AB-AR-0041 markL2 StandardCalculatorRQ

An RQ of 1.0 indicates the substrate is

Salam Academy Original Practice · Proposed mark scheme

SA-AB-AR-0051 markL2 StandardCalculatorGlycolysis

In mammals, anaerobic respiration converts pyruvate to

Salam Academy Original Practice · Proposed mark scheme

SA-AB-BD-0012 marksL2 StandardCalculatorMeasuring

Counts of four species: 10, 20, 30, 40 (N = 100). Calculate Simpson's index D.

Salam Academy Original Practice · Proposed mark scheme

SA-AB-BD-0022 marksL2 StandardCalculatorMeasuring

50 snails are marked and released. Later, 40 are caught, of which 10 are marked. Estimate the population.

Salam Academy Original Practice · Proposed mark scheme

SA-AB-BD-0041 markL2 StandardCalculatorClassification

The correct order from largest to smallest group is

Salam Academy Original Practice · Proposed mark scheme

SA-AB-BD-0051 markL2 StandardCalculatorMeasuring

A belt transect is best for studying

Salam Academy Original Practice · Proposed mark scheme