6002q2.specimen

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General Certificate of Education Advanced Level

ADDITIONAL MATHEMATICS 6006/2

PAPER 2
SPECIMEN PAPER 3 hours
Additional materials:
Answer paper
Graph paper
List of Formulae
Scientific calculator

TIME 3 hours
INSTRUCTIONS TO CANDIDATES

Write your name, Centre number and candidate number in the spaces provided on the answer
paper/answer booklet.

Answer all questions
If a numerical answer cannot be given exactly, and the accuracy required is not specified in the

question, then in the case of an angle it should be given to the nearest degree, and in other cases it
should be given correct to 2 significant figures.

If a numerical value for g is necessary, take g = 9.81 ms~’.

INFORMATION FOR CANDIDATES

The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 120.

The use of a scientific calculator is expected, where appropriate.

Y ou are reminded of the need for clear presentation in your answers.

This question paper consists of 6 printed pages and 2 blank pages.

Copyright: Zimbabwe School Examinations Council, Specimen Paper.
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2m kg

The diagram shows a particle of mass 2m kg attached to one end of a light
inextensible string of length 1.3 metres. The other end of the string is attached
to a fixed point A. The particle moves at a constant speed in a horizontal circle
with the string inclined at an angle of 35° to the vertical.

Calculate the angular speed of the particle. [6]

A uniform rectangular lamina ABCD has a mass of 10 kg. AD =BC =2a and
AB =DC =a. The lamina rests in a fixed vertical plane with A on a rough
horizontal table. Side AD is inclined at 30° to the horizontal. A force, P, acting
along the side DC maintains equilibrium.

Find
@ P correct to 2 decimal places, [4]
(ii) the normal reaction at A. [5]

A small particle, P, of mass 1 kg is threaded on to a smooth circular wire which
is fixed in a vertical plane. The radius of the circle with centre O is 0.5m. The
particle is slightly disturbed from rest at the highest point A of the wire.

Find in terms of g, the

() speed of P when AOPis 90°, [3]
(ii) speed of P when it reached the lowest point, [3]

(iii) reaction, R, between the wire and the particle at the lowest point. [3]

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as

o
<5>< 5 >< = net

2kg

The diagram shows a particle of mass 2 kg which is suspended from a

spring of modulus of elasticity, / . The end of the spring is attached to a fixed
point O and the natural length of the spring is 1 metre. The particle remains at
rest when the stretch is 0.1 m. The spring is stretched a further x metres.

@ Find the modulus of elasticity, /, in terms of g. [3]
(ii) Hence show that x = —-10gx. [4]
(iii) Find the period of the motion. [3]

A smooth sphere, A, of mass 2 kg moving in a straight line, with a speed of

4 ms“, onasmooth horizontal plane, collides with a stationary smooth sphere,
B, of mass 3 kg. B then collides with a vertical wall which is perpendicular

to the direction of motion of the sphere. After rebounding from the wall, B

collides with A and coalesce. The coefficient of restitution is : at all impacts.

Find the

@ speed of the spheres after the first impact, [5]
(ii) impulse the wall exerts on sphere B, [4]
(iii) speed of the spheres when they coalesce. [3]

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A particle moves in a straight line with an initial velocity of 5/6 ms‘. The
particle moves against a resistive force that produces a retardation. The
retardation increases at a rate directly proportional to the distance moved.

Itis also given that the retardation increases from 2 ms*” to 6 ms”? to covera
distance of 10 metres.

The particle has a velocity, vms"', when it has moved a distance of x metres.
(a) Show that >” = 4119 423), [5]
de 5

(b) Hence or otherwise, find the
(1) distance moved by the particle in coming to rest,

(ii) time taken in coming to rest.

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Section (B): Statistics [60]
At Chizo Secondary School, the average pass rate in mathematics at ‘A’ level
was 40 %. The school hired an experienced mathematics teacher and 4 out of 9
students passed.
Test at 5 % level of significance whether there is evidence of an improvement
in the results. [7]
The distance travelled by a commuter driver in a day is assumed to be normally

distributed with a mean 360 km and a standard deviation 60 km.

(a) Find the probability that the average distance travelled per day will be
more than 370 km. [4]

(b) A random sample of 30 days travelled gave a mean distance of 350 km.

Calculate the 98 % confidence interval of the mean distance travelled
correct to 1 decimal place. [3]

Motor vehicles pass through a toll-gate independently and at random. Heavy
vehicles pass at an average rate of 2 in any 30-minute period and light vehicles
at a mean rate of 6 in any 30-minute period.

Calculate the probability that in any

(1) 30-minute period, there will be exactly 4 vehicles passing through
the toll gate, [3]

(i) 5 minute period, there will be more than 2 vehicles passing through
the toll gate. [4]

Some dogs whose mean mass was 6.5 kg, were given a special diet and were to
undergo a routine inspection of their masses. After a certain period, five dogs
were chosen at random and their masses in kgs, were

6.2; 5.8; 7.0; 8.7; 9.1.

(a) State two conditions that are necessary for the valid use of a t-test to test
a hypothesis about the mean mass of the dogs. [2]

(b) Use a5 % level of significance, to find out whether the special diet
increases the masses of the dogs. [7]

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12

13

6

In a hospital maternity unit, the weights of newly born babies were recorded.

The mean weight of female babies was 2 200 g with a standard deviation of 60 g.

The mean weight of male babies was 3 000 g with a stand

ard deviation of 50 g.

Two newly born babies, a male and a female, were chosen at random and their

weights observed .

(a) Find the probability that 3 times the weight of the female baby is less

than 2 times the weight of the male baby.

(b) __Itis found that 2 % of the babies develop some respiratory problems

immediately after birth.

Find using a suitable approximation, the probabili

ty that out of 100

randomly chosen babies, more than 2 develop respiratory problems.

The table shows values of two variables x and y, x being tl

he mass of a

child immediately after birth and y being the mass of the mother’s

placenta.

x(kg)} 2.2 ) 24 | 26 |] 28 | 3.0 | 3.2

y(kg) | 0.37} 0.42 | 0.43 | 0.45) 0.5 | 0.54

(a) Explain what is meant by the term correlation.

(b) @ Calculate the product moment correlation coefficient between
the mass of baby x, and the mass of the mother’s placenta y and

comment on the value.

(ii) ‘Find the equation of the regression line y 0

MX.

(iii) Find the mass of the mother’s placenta when the mass of the

baby is 2.3 kg.

A manufacturing company has to make 5 deliveries of a p
day to retail outlets. The probability that a delivery is acc

articular product per
epted is 0.3. During

90 days the number of deliveries accepted in each day were recorded as shown:

number of deliveries 0 1 2 3 4 5

frequency 5 10 15 30 20 10

Test at 5 % level of significance whether a Binomial distribution is an adequate

model for testing this data.

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[5]

[4]

[1]

[9]

[11]

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