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 130 of 137 · choose a topic above to narrow them down

SA-ST-EX-G012 marksL2 StandardCalculatorProbabilities

Calls arrive at 3 per hour. Find the probability of waiting more than 30 minutes for the next call (3 s.f.).

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SA-ST-NP-0022 marksL2 StandardNon-calculatorWilcoxon

Differences:

3,-1,4,6,-2,5,7,8

. Find

T

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SA-ST-NP-0032 marksL2 StandardNon-calculatorWilcoxon

Values

|d|=2,5,5,7

are ranked. What rank does each

5

receive?

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SA-ST-NP-G012 marksL2 StandardCalculatorSign test

In a sign test with 10 non-zero differences, 2 are negative. Find

P(X\le2)

for

X\sim B(10,0.5)

(3 s.f.).

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SA-ST-PG-0022 marksL2 StandardNon-calculatorMoments

For

G(t)=\frac14(1+2t+t^2)

, find

E(X)

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SA-ST-SA-0022 marksL2 StandardNon-calculatorMethods

A company has 120 managers, 300 office staff and 780 factory workers. How many factory workers belong in a stratified sample of 80?

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SA-ST-TD-0013 marksL2 StandardCalculatorIntervals

n=10

\bar x=50

s=4

, and

t_9(97.5\%)=2.262

. Find the upper limit of the 95% confidence interval (3 s.f.).

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SA-ST-TD-0022 marksL2 StandardCalculatort-tests

With the same data, find the test statistic for

H_0:\mu=48

(3 s.f.).

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SA-ST-TD-0032 marksL2 StandardCalculatorIntervals

A sample of 5 has

\sum x=40

and

\sum x^2=330

. Find the unbiased estimate of the population variance.

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SA-VM-0062 marksL2 StandardCalculatorPosition

A ship's position at time

t

hours is

\mathbf r=[(-10+2t)\mathbf i+(5+3t)\mathbf j]

km. Find when it is due north of the origin.

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SA-VM1-0022 marksL2 StandardCalculatorMagnitude & direction

Find the angle between the vector

(2\mathbf i+5\mathbf j)

and

\mathbf i

, in degrees to 1 decimal place.

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SA-VM2-0032 marksL2 StandardNon-calculatorPosition

A boat's position at time

t

hours is

\mathbf r=[(6+3t)\mathbf i+(4t-8)\mathbf j]

km. Find the time when it is due east of the origin.

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SA-4024-AL6-0033 marksL3 ExamNon-calculatorFormulae

Make

x

the subject of

y=\dfrac{x+2}{x-1}

. Hence find

x

when

y=4

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SA-4024-PR-0083 marksL3 ExamNon-calculatorWithout replacement

From the same bag (

4

red,

6

blue), two balls are taken without replacement. Find the probability that they are different colours.

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SA-9702-DY2-0042 marksL3 ExamCalculatorElastic collisions

1.0

kg ball moving at

6.0

m s⁻¹ collides head-on and perfectly elastically with a stationary

2.0

kg ball. Calculate the final velocity of the

2.0

kg ball.

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SA-9702-DY2-0051 markL3 ExamCalculatorElastic collisions

In the same collision, calculate the final velocity of the

1.0

kg ball (positive in its original direction).

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SA-9709-P1-CG-0064 marksL3 ExamCalculatorEquation

Find the centre and radius of the circle

x^2+y^2+10x-8y+5=0

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SA-9709-P1-CG-0084 marksL3 ExamCalculatorTangents

The point

P(5,\,5)

lies on the circle

(x-2)^2+(y-1)^2=25

. Find the equation of the tangent to the circle at

P

, in the form

y=mx+c

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SA-9709-P1-CG-0095 marksL3 ExamCalculatorTangents

Find the coordinates of the points where the line

y=2x

meets the circle

(x-1)^2+(y-2)^2=5

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SA-9709-P1-CM-0084 marksL3 ExamCalculatorSegments

A chord

AB

of a circle with centre

O

and radius

6

cm subtends angle

AOB=\dfrac{\pi}{3}

. Find the exact area of the minor segment cut off by

AB

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