BASIC APPLIED MATHEMATICS
INSTRUCTIONS:-
This paper consists of 10 questions.
Attempt all questions showing clearly all the necessary steps.
Non-programmable calculators and mathematical tables may be used.
1. By using non-programmable calculator, evaluate
(a)
1/ 4
2 / 3 1/ 2
2.074
0.823 1.754
(b)
1.41
1.76
0.25 0.25
0.25 0.25
log10
2.946 In 5
e
e e
e e
(c)
1/5 22
log 31.42 In31.42
(d)
1/ 2
1 8.22
0.001182
12 tan 3.42 e
2. (a) Given
x for x
x for x
x for x
f x
2 1
0 1
0
2
(i) sketch the graph of
f .
(ii) determine the domain and range of
f .
(b) (i) Solve the equation
5 36 0
4 2
x x
(ii) Solve simultaneously in terms of r
y x r
x y r
2 10
25 2 2 2
3. (a) In an A.P the 3rd term is 8 and the 7th term is 20. Find the sum of the first 50 terms.
(b) In a G.P the sixth term is 8 times the third term, and the sum of the seventh and eighth
terms is 192.
Determine the sum of the fifth to eleventh terms.
4. (a) If
,
2
y x x
then find
dx
dy
by definition.
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(b) Find
dx
dy
when
1
1
2
2
x
x
y
(c) Determine the turning points on the curve
3
5
6
3 2
3 2
x
x x
y
and state their nature.
5. (a) Define the following terms:
(i) Vertical asymptote
(ii) Horizontal asymptote
(b) Sketch the graph of
2 4
3 2
( )
x
x
f x
and state its domain and range.
(c) Find the inverse of
4
4 8
x
x
f x
6. (a) Evaluate .....
2
1
.....
8
1
4
1
2
1
1 1
n
(b) The third term of a convergent G.P is the arithmetic mean of the 1st and 2nd terms. Find the
common
ratio and, if the first term is 1, find the sum to infinity.
(c) Use the concept of sum to infinity to change
. .
0.45
into fraction.
7. (a) If
x :3:5 8: y :9,
find the value of
x
and
y.
(b) If
z
varies directly as the square root of
x
and inversely as the square root of
y,z 4
when
x 4
and
y 2. Find the value of
z
when
9
1
x
and
3
1
y
8. (a) the curve is given parametrically by the equations
3 4
2
x t and
2
y 4t t
. Find the
slope of this
curve when t = 1.
(b) Find
dx
dy
given that
2 3 2 7
2 2
x y xy y x
(c) The daily profit, p, of an oil refinery is given by
8 0.02 ,
2
p x x
where
x
is the number of
barrels of
oil refined. How many barrels will give maximum profit and what is the maximum profit?
9. (a) Divide
( ) 8
3
p x x
by
Qx x 2
(b) If
R 1,4, 2,3, 1,1, 3,2, 4,1
(i) Find R-1
(ii) Draw a pictorial representation of R-1
.
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10. (a) Determine the turning points of the curve:
3
5
6
3 2
3 2
x
x x
y
and distinguish between
them.
(b) Find the range of values of
x
for which the series
1 1 1 1 .....
2 3
x x x
converges.
(c) Prove that
0 1
1
1
k
k k
x
x
for
x 1
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ADVANCE MATHEMATICS
INSTRUCTION:
Answer All Questions
1. (a) Use non-programmable calculator to calculate
4.120
2 2
0.0001980
3.1416[(9.483) (5.075)
Correct to 5 decimal places.
(03 marks)
(b) Solve that quadric equation by inspection method; 4x 18x 23x 3x 6 0
4 3 2
.
(04 marks)
2. (a) Simplify (A’B) [An(B )]
(03 marks)
(b) In a class of 34 students all taking at least one of the subjects A, B and C has n(AB’C’) = 2n(A’
C’ B), n(A B)= 7, n(B C A’) and students taking exactly two subjects among these
three are of the same number, find:-
(i) n(A B C)
(ii) n(A)
(iii) the number of students taking either A or B but not C.
(06 marks)
3. (a) If “Np denotes p “ and “Apq denotes p˄ q” using only A and N, write (p ↔ q) ˄ r
(03 marks)
(b) Is this valid? [(p → r) ˅ (q → r)] →r
(03 marks)
(c) Draw the electrical network of [(p ˄q) ↔ p]˄ r
(03 marks)
4. (a) Find the sum to n terms of ....
4 5 6
7
3 4 5
5
2 3 4
3
1 2 3
1
(05 marks)
(b) Given that
1
0
n
i
i
x
, find
(i) the sum of the first n terms
(ii) the sum to infinity of the series.
(05 marks)
5. (a) For what values of p will the equation
p 1
p 1
ax c
x bx 2
has roots equal in magnitude but
opposite in sign.
(04 marks)
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(b) Find the coefficient of x15 in the expansion of
12
2 3
x
x
(04 marks)
(c) The products of the first three terms of a Geometric progression is 1000.
If we add 6 to its second term and 7 to the third term the resulting three
terms form Arithmetic progression. Find the terms of the G.P.
(04 marks)
6. (a) A quadratic equation has positive roots
and
such that
2
and
15.
Determine
its equation, and hence obtain the quadratic equation, whose roots are
and
.
(05 marks)
(b) Find the value of a for the system below to be inconsistent. Then solve by using inverse matrix
method
0 2 a
1 2a 1
3 1 3
z
y
x
=
5
2
1 5
2
1 3
When a = 2
(06 marks)
(c) Find the value of k for the system below to
(i) have no solution
(ii) have many solutions
2x 3y 3z 2
kx y 2z 1
3x 4y z 2
(05 marks)
7. (a) Given
4
r 1
4
r 1
2
r 3r
, find
4
1
2
2
r
r
(04 marks)
(b) Prove by mathematical induction that 102n-1 + 1 is divisible by 11 for all positive integral values n.
(04 marks)
8. (a) Given
f(x) 2 3x 6
, sketch the graph of f(x) and obtain its domain and range.
(05 marks)
(b) Given
f x x 6x
2
, find
gx
such that
fog x 14x 40 4 2
(04 marks)
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9. (a) In the following diagram,
(i) Show that Q = Q1 – Q2 hence find the acute angle between the lines above.
(03 marks)
(ii) Show that
1 2
1 2
1 tanQ tanQ
tanQ tanQ tanQ
and hence find the acute angle between the lines
above.
(b) Find the equation of the circle through the intersection of the circles
x y 8 2y 7 0
2 2
and
4 10 8 0
2 2
x y x y
and having its centre on the y-axis.
(04 marks)
10. Azam company has a flour-store in Pugu district with 120 tons of flour and in Mbagala district having
40 tons of flour. Shoppers Plaza has ordered 80 tons, and Nakumatt 50 tons. Shoppers Plaza is 20 km
from Pugu and 40 km from Mbagala. Nakumatt is 15 km from Pugu district and 30 km from Mbagala
district. Delivery costs are proportional to the distance traveled. How should he supply his
customers to minimize the total transport costs? What is the minimal transport cost?
y
x
h
h
Q2 Q1
2,0
(4,4)
Q
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HISTORY
INSTRUCTIONS:-
1. This paper consists of eight (08) questions in total.
2. A candidate has to choose and answer four (05) questions ONLY.
3. Each question carries twenty (20) marks.
4. Be direct to the point.
5. Good handwriting will be appreciated.
1. Describe how slave trade contributed to the widening gap in development
between Africa and Europe. Provide six (06) points.
2. Inspite of its weaknesses pre-colonial education had several positive
elements. Verify it with the support of six (06) points.
3. Identify the six (06) differences in development of political systems
between Africa and Europe in the 15th century.
4. “Despite their differences, pre-colonial social formations in Africa were
homogeneous” Justify it with six (06) supportive evidences.
5. Explain the three (03) successes and three (03) problems of Back to Africa
movement.
6. Examine the contention that the struggles for civil right movement as
advocated by Martin Luther King Junior was spearheaded by economic
problems.
7. Explain why colonialism and imperialism never intended to develop
Africa. Provide six (06) points.
8. With eight (08) points discuss the violent nature of the colonial, state as
remarked by Frantz Fanon.
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KISWAHILI
MAELEKEZO
1. Jibu maswali matano (5).
2. Chagua swali moja toka kila sehemu.
3. Muda: Masaa matatu.
A: NADHARIA YA FASIHI 20%
1. Jadili nadharia kuhusu uhusiano wa fani na maudhui.
2. Jadili wataalamu watano wanaoelezea neno fasihi na fafanua dhima za mwanafasihi kwa
mifano halisi.
B: FASIHI SIMULIZI 20%
3. (a) Fafanua aina za sanaa.
(b) Jadili sifa za sanaa.
(c) Fafanua tofauiti tatu za kifani kati ya methali na vitendawili.
4. (i) Kwa kutoa hoja tano nzit, fafanua aina za wahusika wanyama.
(ii) Fafanua makundi matatu ya wahusika wa fasihi simulizi.
5. (a) Fafanua aina za riwaya pendwa.
(b) Fafanua sifa za riwaya pendwa.
(c) Nini maana ya hadithi fupi.
6. (a) Fafanua vijenzi vya tamthiliya.
(b) Fafanua tofauti tano kati ya tamthilia na riwaya.
D: TAMTHILIA (NGUZO MAMA) 20%
7. Jadili vipengele vya matumizi ya lugha kwa kutumia “NGUZO MAMA”.
8. Uongozi mbaya, kutowajibika na usaliti umechangia matatizo mengi katika jamii. Jadili
matatizo nane kutokana na “NGUZO MAMA”.
E: SARUFI
9. (a) Jadili aina tano za vitenzi vishirikishi vipungufu na matumizi yake.
(b) Fafanua kwa mifano kuhusu Kitenzi kishirikishi kikamilifu.
10. (a) Fafanua aina tano za Vivumishi vya pekee.
(b) Fafanua ain atano za Vivumishi vimilikishi.
Page 10 of 28
GEOGRAPHY
INSTRUCTIONS:-
1. This paper consists of two sections A and B.
2. Attempt five (5) questions in all. Two (2) questions from section A and three (3) questions from
section B.
3. Questions ONE (1) is compulsory.
4. Use of relevant sketch maps may add you more marks.
SECTION A
MAPWORK AND PRACTICAL GEOGRAPHY
Attempt two (2) questions from this section. Question one (1) is compulsory
1. Carefully study the map extract of MAFINGA sheet 232/4 and answer the following
questions.
(a) What is the length of the all weather road with bound surface 480778 to 567870.
(b) From the map, outline the merits of using contours as a technique of
representing relief on the topographical maps.
(c) Give an account on the population distribution of the area.
(d) Calculate the forward bearing of hospital 519819 from Race Track 532785.
(e) Use the precise evidences to explain the economic activities which are
undertaken in the area shown in the map.
2. Carefully study the following data in table and answer the questions that follow:
PRODUCTION OF MAJOR EXPORT CROPS IN 2013
COUNTRY COTTON COCOA PALM OIL COPRA COFFEE
TANZANIA 220 180 120 100 200
KENYA 100 120 75 80 100
(a) Present the data by means of proportional semi-circles.
(b) What is the usefulness of the method you have used?
3. (a) Describe the characteristics of extraterrestrial photographs?
(b) A swamp in a topographical map whose scale is 1:50,000 measures 80 cm2.
Find the area of this swamp in a photograph whose scale is 1:40,000.
4. A research process proceeds through a logical manner in order to obtain meaningful
information. Give an outline of research procedures.
SECTION B
Attempt three questions from this section
Page 11 of 28
5. Plate tectonic theory is a new version of the old statement of continental drift. Justify
the statement.
6. Discuss the role played by climate on weathering process.
7. Critically examine the processes behind the occurrences of sedimentary rocks. Why is
this type of rock beneficial to Man?
8. Using concrete examples explain how faulting has been responsible for landscape
evolution.
9. Discuss the classification of mass movements. What are the controlling factors in mass
wasting?
Page 12 of 28
ECONOMICS
INSTRUCTIONS:-
1. This paper consists of two (2) sections.
2. Attempt five (5) questions at least two (2) questions from each section.
SECTION A
1. (a) Outline five (5) roles of the Government in the mixed Economic system.
(b) Critically analyse the assumptions of the production possibility frontier. (Give five points)
2. (a) Three local comic book collectors have expressed an interest in buying Adam’s collection.
The
individual demand equation for each of these three individuals is:
QD,1 = QD,2 = QD,3 = 550 – 2.5 P.
Where P is measured in Tshs. Per comic book.
(i) What is the market demand equation for Adam’s comic books?
(ii) How many more comic books can Adam sell for each Tshs. reduction in price?
(iii) If Adam has 900 comic books in all, what price should he charge to sell his entire
collection?
(b) With examples each, explain four (4) types of supply.
3. (a) Outline five (5) negative impacts for non-existence of specialization and division of labour.
(b) Define capital intensive technique of production. Explain four (4) disadvantages of capital
intensive
technique of production.
4. (a) Outline five (5) ways of minimizing costs, in the production process.
(b) Consider the following diagram.
Find:
(i) Total cost (T)
(ii) Total Revenue (TR)
(iii) Average cost (AC)
MC
AC
P
Outputs
O Q = 125
Cost Revenue
10
8.3
5
Page 13 of 28
(iv) Profit or loss.
(v) Shade the area where the firm makes profit or loss, and given reason.
SECTION B
5. (a) Explain four (4) ways in which the term market can be defined.
(b) Outline six (6) basis or ways in which monopoly can exist.
6. (a) Describe the three (3) types of elasticity of demand.
(b) When Anna’s income increased by 40%. Find the income elasticity of demand and comment
your
answer.
(c) Briefly explain how time can affect price elastasticity of demand in the short-run.
7. (a) Show mathematically and graphically that MPL and APL are images of MC and AC (AVC),
respectively.
(b) Distinguish between the following.
(i) Specific factor of production and noon specific factor of production.
(ii) Specialization by process and specialization by craft.
(iii) Capital productivity and capital consumption.
8. In detail explain eight (08) causes of internal economies of scale; explain why the SR and LR AC
are
U-shaped.
Page 14 of 28
BIOLOGY
INSTRUCTION:
1. Answer all questions in section A and any three questions from section B.
SECTION A
1. a) Account for the following statements:-
i) Not all genetic information is found in nucleus.
ii) A dominant role for the mitochondria is the production of ATP, but in plants not all
energy are
produced by mitochondria
iii) The cell will stop its functions if all ribosome are removed from it. (3 marks)
b) Draw a typical eukaryotic cell and show the organelles which are responsible for the
following:
i) Movement of water and dissolved mineral salts from cell to cell.
ii) Increase in internal surface area without increase in volume by a change in shape.
iii) Prevent the cell from bursting when exposed to the hypertonic solution.
iv) Stores glycoprotein and protein molecules synthesized from different organelle.
v) Associated with initiation and control of cell division. (5marks)
2. a) With example explain the meaning of cell differentiation. (4marks)
b) Explain the adaptation of that cell. (4marks)
3. a) Imagine that you are coordinator of biology and you have decided to eliminate the topic of
classification from biology syllabus. Briefly explain what will happen to future biologist.
(3marks)
b) Study the diagram below then answer the following questions:-
i) Outline General characteristics of the kingdom to which the specimen belong (2 marks)
ii) Draw a well labeled diagram of the specimen in the diagram above. (3 marks)
Page 15 of 28
4. a) Outline the principle sources of a wide variety of polysaccharides. (4 marks)
b) Which part of lipid is responsible for its characteristic? In briefly describe the features of
that part. (3 marks)
5. a) Give the differences between the following:-
i. Conjugated and derived protein
ii. Fibrous and conjugated protein
iii. Secondary and primary protein. (3 marks)
b) Using examples classify protein according to their functions. (5 marks)
6. a) i) Define refractory period and state it’s significant.
ii) You have noticed that one of your child have trouble seeing at night and in the dark and
the other
child is colorblindness. What could be the problem of each child? (4 marks)
b) Briefly explain the factors which affects the speed of transmition of nerve impulse. (3 marks)
7. a) Small invisible organisms are more dangerous and trouble makers than large organisms like
lion. Justify
this statement by using relevant example. (5 marks)
b) i) What do you understand by the term feedback mechanism.
ii) With example state main type of feedback mechanism. (3 marks)
SECTION B
8. a) Give an example of the most primitive plant. Why are they most primitive? (5 marks)
b) Discuss the life cycle of mango plant. (10 marks)
9. a) Is it necessary for the eye to adjustment the pupil size and to Refract light rays before the
light rays are focused on retina? Give reasons for your answer. (5 marks)
b) Draw a well labeled diagram of synapse and briefly describe its transmition. (10 marks)
10. a) i) Define nyctinasty movement.
ii) With relevant example, explain the mechanism of nyctinasty movement.
iii) State significances of nyctinasty movement. (10 marks)
b) Each receptor has the lowest threshold for the adequate stimulus. Use this concept to
classify receptors. (5 marks)
11. a) Describe the structural adaptation of the HIV virus. (7 marks)
b) Draw a well labeled diagram of positively phototactic unicellular eukaryote and outline its
adaptation. (8 marks)
Page 16 of 28
PHYSICS
INSTRUCTIONS
► This paper consists of thirteen questions (13) questions.
► Answer any eight (8) questions.
► Each weighs 12.5 marks.
► The following constants may be used
- Radius of Earth 6400km,
- g = 10m/s2
- G = 6.67x10-11Nm2
kg-2
,
- At STP P = 105
Pa,
- T = 273k
- Linear expansivity of copper
= 20x10-6K
-1
,
- Young modulus of copper E = 1.2 x 1011 Pa.
- Coefficient of viscosity of water
4
10
Pas.
- Density of water
3
10
kg/m3
1. (a) (i) Distinguish between dimensional analysis and error analysis. [2.5 Marks]
(ii) A liquid having small depth but large volume is forced by an applied
pressure P above
it to escape with velocity
v
through small hole below.
v
is given by
x y
v CP
where
is the liquid’s density and C,
x
and
y
are dimensional constants.
(i)
Determine
x
and
y
(ii) If
v
= 14 m/s when P = 1.0 x 105
Pa and = 1000
kg/m3
, deduce
C [05 Marks]
(b) The resistance R of a uniform conducting wire is calculated using
measurement of its length l and radius r. The instrument for measuring l has a
systematic error of -1% and that of r has systematic error of -1%. If there is no error
in the value of the resistivity, calculate the value of R of systematic error.
[05 Marks]
2. (a) A certain bedspring is observed to compress by 1.00 cm when a certain
person is at rest atop the spring. What would be the spring’s compression if the same person was
dropped onto the spring from a height of 0.250 m above the top of the spring? Assume the
person is dropped from rest. [05.5 Marks]
(b) A solid sphere of radius R is floating in a liquid of density
with half of its
volume submerged. If sphere is slightly pushed and released, it starts
Page 17 of 28
performing SHM. Find frequency of these oscillations.
[07 Marks]
3. (a) Two soap bubbles combine to form a single bubble. In this process, the
change in volume and surface area are respectively V’ and A’. If P is the atmospheric pressure,
and
is surface tension of the soap solution, then derive the relation
3PV 4A 0
[06 Marks]
(b) A drop of water is placed between two glass plates which are then pushed
together until water is squashed out into a thin circular film of radius 5 cm and thickness
0.2 mm. Calculate the force applied normal to the plates, which is required to separate them.
Give underlying theory of your calculation. [06.5 Marks]
4. (a) A man stands on the surface of the earth at the latitude of 600 North.
Calculate
(i) its linear velocity
(ii) its acceleration due to rotation of the earth. [04.5 Marks]
(b) (i) An Aeroplane in level flight makes a complete circular turn in 2 minutes
at constant speed of 100 m/s. What is the centripetal force as fraction of its weight? [04 Marks]
(ii) A satellite is said to be in geosynchronous orbit if it rotates around the
earth once every day. For the earth, all satellite in geosynchronous orbit must rotate at distance of
4.23 x 107m from earth centre. What is the magnitude of acceleration felt by geosynchronous?
[04 Marks]
5. (a) Use kinetic theory of gases to deduce each of the following laws;
(i) Avogadro’s law
(ii) Dalton law of partial pressure
(iii) graham law of diffusion [06 Marks]
(b) State two conditions and assumptions of real gases and use them to derive Van
der Waals equation given by;
3 V
a
P b V Rt where P is pressure and V is volume.
[06.5 Marks]
6. (a) (i) A block initially sliding on the floor of a room is eventually brought to rest by
friction. Is the momentum of the box conserved? Explain. [02.5 Marks]
(ii) A block of mass is placed in a frictionless spring gun at the bottom of the
incline so that it compresses the spring by an amount xc The spring has spring constant k. The
incline makes an angle θ with the horizontal and the coefficient of kinetic friction between the
block and the incline is
k
. The block is released, exits the muzzle of the gun, and slides up an
incline a total distance L. Find an expression for L in terms of the other quantities described plus
the acceleration due to gravity.
Page 18 of 28
(b) A neutron of mass m collide elastically with nucleus of mass M. Show that, if the
neutrons kinetic energy is Eo, the maximum kinetic energy it can lose during collision is
given by
2
4
M m
mMEo
[05 Marks]
7. (a) The mean free path of molecule of gas of air at 0 0C and 1 atmosphere is 2 x 10-7 m.
What will be the mean free path at 1 atmosphere and temperature 227 0C.[03.5
Marks]
(b) A uniform rod of length land mass M rests on a smooth horizontal table. A point
mass
m M
2
1
moving at right angles to the rod with speed
v
collides with one end of the
rod and sticks to it.
(i) Describe the subsequent motion of the rod
(ii) Derive the velocity (speed and direction) of the centre of mass (of the combined
rod and mass) after the collision.
(iii) Derive the angular speed of the combined rod and mass after the collision.
(iv) Find the point on the rod that is stationary immediately after the collision.
[09 Marks]
8. (a) (i) Using principle of conservation of angular momentum, explain how does a person
perform summersault. [02.5 Marks]
(ii) Pendulum consists of small mass m at the end of string of length L. the pendulum
is pulled aside to an angle
with vertical. At an instant of release, using the suspension
point as axis, find the torque of pendulum and its angular acceleration. [05 Marks]
(c) What is speed of efflux? With assumptions derive the relation for speed of efflux
given by
v 2gh
where h is the original height of liquid in large, open container.
[05 Marks]
9. (a) Calculate the critical velocity of water flowing in a pipe of cylindrical shape of radius
30 cm.[05 Marks]
[05 Marks]
Page 19 of 28
(b) Two particles of mass m are constrained to move along two horizontal frictionless rails
that make an angle 2
with respect to each other. They are connected by a spring with spring
constant k. What is the frequency of oscillations for the motion where the two masses always
stay parallel to each other (ie: the distance between the meeting point of the rails and each
particle is equal)?
[07.5 Marks]
10. (a) A solid copper rod is of cross sectional area 15 mm2
and length 2.0 m. Calculate (i)
its change in length when its temperature rises by 300 C, (ii) the force needed to prevent it
from expanding by amount in (iii). Assume that the proportional limit is not exceeded.
[06.5 Marks]
(b) Four identical hallow cylindrical column of steel, support a bit structure of mass
50,000/= kg. The inner and outer radii of each column are 30 cm and 40 cm respectively.
Assuming the load distribution to be uniform. Calculate the compression strain of each
column. [06 Marks]
11. (a) (i) List down two (2) ways of describing
g
as applied to gravitation. Give its
appropriate units in each case. [02 Marks]
(ii) Calculate the work done in taking a 5.0 kg mass from the surface to a point where
gravitational field strength is negligible. [05 Marks]
(b) A solid spherical ball of radius R is sliding along a surface and rotating the “wrong”
way. There is friction between the ball and the surface. What is the minimum initial value of
w
in terms of initial speed of the ball’s center of mass (
cm v
) in order to ensure that the ball ends up
moving to the left in the picture below?
[07 Marks]
Page 20 of 28
12. A 2.0 g particle moves at constant speed of 3.0 mm/s around in circle of radius 4.0mm.
(a) Find magnitude of angular momentum of particle.
(b) If
L where
is integer, find the value of
and approximate
value of
.
(c) By how much does the
change if the particles speed increases by one-millionth of
a percent, and nothing else changing? Use your result to explain why the quantization of
angular momentum is not noticed in microscopic physics. [12.5 Marks]
13. (a) A block of mass m is moving on a smooth table when it collides elastically with a
second block of mass 2m, which then elastically strikes a mass less spring which compresses an
amount d before the block comes to rest
Find the original velocity at which the first block was moving, in terms of the other variables in
the problem. [06.5 Marks]
(b) A projectile is launched from a cliff a height h above the ground at an angle θ above
the horizontal. After a time t1 has elapsed since the launch, the projectile passes the level of the
cliff top moving downward. It eventually lands on the ground a horizontal distance d from its
launch site. Find θ in terms of the other given quantities and the acceleration of gravity (g).
(Ignore air resistance)
[06.5 Marks]
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CHEMISTRY
INSTRUCTIONS:
- Answer any five (5) questions.
- In your calculation you may use the following constants
C = 12, H = 1, O = 16, Cl = 35.5, P = 31, N= 14, Zn =65, Cu =64, S =32
h = 6.626 10-34J.S, RH = 1.0967 107
/m
c = 3.0 108m/s R = 0.0821L atm/mol. k, R = 8.314 J/mol.k
Kf of water = 1.86 o
c/m. Kb of water = 0.510C/m, 1 mmHg = 1 torr, 1 atm = 760 mmHg.
SECTION A
1. (a) Explain the meaning of the following terms:
(i) Ionization energy
(ii) Standard heat of formation
(iii) Electronic affinity
(iv) Atomization energy. [08 marks]
(b) State Hess’s law of constant heat of summation. [02 marks]
(c) The enthalpy of formation of ammonia is -46 kJmol-1
and the bond dissociation enthalpies
of nitrogen gas and hydrogen gas are +945 kJmol-1
and +436 kJmol-1
respectively.
Calculate the average bond enthalpy of an N-H bond. [05 marks]
(d) Magnesium will also displace copper from copper (II) sulphate solution. If an excess of
magnesium is added to 100 cm3
of 1.0 moldm-3
copper(II) sulphate, the temperature
increases by 46.3 oC.
(i) Calculate the molar enthalpy change for the reaction
(ii) Calculate the minimum quantity of magnesium required to ensure it is in
excess.
(iii) Calculate the temperature change if only 0.8 g of magnesium is added. [05
marks]
2. (a) (i) State Raoult’s law. [02 marks]
(ii) Under what conditions does a solution formed up on mixing two liquids A and B
behaves as an ideal solution. [04 marks]
(b) A solution contains 50.0 g of heptane (C7H16) and 50.0 g of octane (C8H18) at 25 oC. The
vapor pressures of pure heptanes and pure octane at 25 oC are 45.8 torr and 10.9 torr,
respectively. Assuming ideal behavior, answer the following:
(i) What is the vapor pressure of each of the solution components in the mixture?
(ii) What is the total pressure above the solution?
(iii) What is the composition of the vapor in mass percent?
(iv) Why is the composition of the vapor different from the composition of the
solution? [08 marks]
(c) Answer the following questions, using the accompanying figure.
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(i) A liquid mixture consists of 33 g of component A and 99 g of component B. At
what temperature would the mixture begin to boil?
(ii) Under the conditions in (a), what is the composition of the vapor when boiling
first occurs?
(iii) If the distillation is continued until the boiling point is raised by 5.0 °C, what
would be the composition of the liquid left in the still?
(iv) Under the conditions in (iii), what are the composition and mass of the two
components collected over the initial 5.0 °C interval? [06 marks]
3. (a) State
(i) Dalton’s law of partial pressure.
(ii) Charles law [04 marks]
(b) (i) Write down the main postulates of the kinetic theory of gases.
(ii) Which postulates of the kinetic theory are not strictly true, and why?
(iii) What does a small value for the van der Waals constant a suggest about the
molecules of the
gas?
(iv) Compare the values obtained for the pressure of 3.00 mol CO
2
at 298.15 K held in a
8.25-dm
3
bulb using the ideal gas, and van der Waals equations. For CO
2
the equation
constants are
a = 0.462 Pa m
6
mol
–2
, b = 4.63 × 10
–5
m
3
mol
–1
[10 marks]
(c) Two chambers are connected by a valve. One chamber has a volume of 15 L and contains
N2 gas at a pressure of 2.0 atm. The other has a volume of 1.5 L and contains O2 gas at
3.0 atm. The valve is opened, and the two gases are allowed to mix thoroughly. The
temperature is constant at 300 K throughout this process.
(i) How many moles each of N2 and O2 are present?
(ii) What are the final pressures of N2 and O2, and what is the total pressure?
(iii) What fraction of the O2 is in the smaller chamber after mixing? [06 marks]
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4. (a) Define the following terms:
(i) Colligative properties
(ii) Distillation.
(iii) Immiscible liquid [06 marks]
(b) (i) State the law defining the equilibrium distribution of a solute between two
immiscible liquids. [02 marks]
(ii) Obtain an expression for the ratio of masses of the materials distilled in a steam
distillation in terms of the molar masses and the partial pressures of the two
components. [02 marks]
(iii) The distribution coefficient of isobutric acid between ether and water is 3 at 250C.
What will be the amount of isobutric acid removed if 4 g of isobutric in 100 ml of
water is extracted with 100 ml of ethoxyethane (ether) at 25oC? What would be the
effect have been if two successive 50 ml portions of ether had been used to extract
the aqueous layer? [05 marks]
(c) An aqueous solution of MCl3 is prepared by dissolving 31.15 g of the electrolyte in 725
mL of H2O (d = 1.00 g/mL). The solution freezes at 22.118C. What is the atom
represented by M3+? (Assume complete dissociation of MCl3 to M3+
and Cl-
.)[05 marks]
5 (a) Define the term electronegativity and explain why the electronegativity values of
the
Group II elements Be–Ba decrease down the group. [03 marks]
(b) (i) Sketch the shapes of each of the following molecules, showing any lone pairs
of electrons. In each case, state the bond angle(s) present in the molecule and
name the shape.
[06 marks]
Molecule Sketch of shape Bond angle(s) Name of shape
BF3
NH3
PCl5
(ii) State the types of intermolecular force which exist, in the liquid state,
between pairs of BF3 molecules and between pairs of NH3 molecules.
[02 marks]
(iii) Name the type of bond which you would expect to be formed between a
molecule of BF3 and a molecule of NH3. Explain how this bond is able to
form [02 marks]
(c) Name the type of bond which you would expect to be formed between a molecule
of BF3 and a molecule of NH3. Explain how this bond is able to form. [03 marks]
(d) The time taken for effusion of equal volumes of CO2 and a mixture of CO2 and CO were
32 sec and 27sec respectively. Calculate the molar mass of the mixture and the
proportions of each gas in the mixture.
[04 marks]
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6. (a) What are the four quantum numbers? Explain the physical significance of each of the
four quantum numbers. [06 marks]
(b) Write the electronic configuration of each of the following
(i) 32
16S
2-
(ii) 137
56Ba (iii) 52
24Cr3+ [4.5 marks]
(c) Use the Rydberg equation to calculate the wavelength in nanometers of the spectral line
of hydrogen for which n2 = 6 and n1 = 3. (Report your answer using three significant
figures.) Would we be expected to see the light corresponding to this spectral line?
Explain your answer.
(d) With the idea of diagram, outline how the mass spectrometer is used to determine the
masses and relative abundance of isotopes. [5.5 marks]
(e) When a sample of natural copper is vaporised and injected in a mass spectrometer, the
result are as shown.
Use the data to compete the average mass of natural copper. The relative mass of
copper of 63Cu and copper 65Cu are 62.09 and 64.93 respectively. [04 marks]
30.91
100
69.09
Mass number
Page 25 of 28
GENERAL STUDY
INSTRUCTIONS:-
6. This paper consists of sections A and B.
7. Answer a total of FIVE questions from any of the two sections.
8. Each section carries (20) marks.
SECTION A: PHILOSOPHY AND RELIGION
1. What is the role of religion in a cecular state like Tanzania. (Give any six points)
2. Discuss six (06) guiding principles of Tanzania development philosophy by
Nyerere.
3. Why is religious tolerance important to a country like Tanzania? (Give any six
(06) points)
4. “Philosophy is a multi - sectoral discipline”. Discuss in six (06) points.
SECTION B: CONTEMPORARY/CROSS CUTTING ISSUES
5. Elucidate the six (06) impacts of environmental predicaments on the social and
economic development of Tanzania.
6. Drought is said to be man oriented problem. Discuss in six points.
7. Explain the causes and effects of Radiation pollution. (Any eight (08) points four
each).
8. Account for the constraints hampering the movement against subordination of
women in Tanzania. (Give any six (06) points).
9. Why it difficult to discuss about HIV/AIDS with your parents? (Give any six (06)
reasons).
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ENGLISH LANGUAGE
INSTRUCTIONS:-
9. This paper consists of four (4) sections.
10. Attempt five (5) questions, one from each section. Question number one is compulsory.
11. Provide valid examples where necessary to elaborate your answer.
12. Each question carries 20 marks.
SECTION A: INTRODUCTION TO LANGUAGE (40 Marks)
Answer question one and any other from this section.
9. a) Give a brief explanation on each of the following language concepts.
i. Language is the reflection of culture,
ii. Language is a system,
iii. Language variations
iv. A community language
v. Pidgin
b) Mention the two main dialects of English language and show their five differences.
2. What is an international language?
Analyze the status of English language in the world and asses its position in the Tanzanian
context.
3. a) With examples compare and contrast the following linguistic terms.
i. Linguist/polyglot
ii. Performance/competence
iii. Geographical dialect/sociolect.
iv. Code switching/code mixing.
v. Second language /foreign language
b) Explain with examples what is language learning and language acquisition.
SECTION B: WORD FORMATION (20 marks)
Answer one (1) question from this section
4. a) Read the following passage and answer the questions that follow.
Two Norwegian scientists have won the Nobel Prize for physiology and medicine for work
published in the English language. Today, though, if a scientist is going to coin a new
term, it is most likely in English. And if they are going to publish a new term, it is most
likely in English.
Look no further than the Nobel Prize awarded for physiology and medicine to Norwegian
couple. Their research was written and published in English.
The first major shock to the system of basically having a third of science published in English,
a third in French and a third in German you may think of Latin as the most dominant
language of science. And in many years it was the universal means of communication in
Page 27 of 28
western Europe from the late Medieval period to the mid 17th century. Then it began to
fracture. Latin became one of many languages in which science was done.
Questions
a) From the short passage identify the morphemes mentioned in i – iii then write the word
in which the morphemes appear.
i. Four (4) lexical morphemes
ii. Four (4) derivational morphemes.
iii. Two (two) inflectional morphemes.
b) Write new sentences by changing each of the words in capital into a noun.
i. What you DECIDE today will automatically affect your future.
ii. The names of evil doers were BLACKLISTED.
iii. It is POSSIBLE to get an A in English examination
iv. We expect to PRODUCE enough crops this year because there is enough rain.
v. They are waiting for the concert ENTHUSIASTICALLY.
c) Name the word formation process involved in the formation of the underlined words
i. Our government bought a sophisticated radar.
ii. Traffic police use breathalyzers to identify drunk drivers.
iii. You have to edit your article before sending it for printing
iv. The rice farmer erected a scare crow in the farm.
v. The manager has decided to resign due to embezzlement allegations.
5. a) (i) What is borrowing in a language?
(ii) Why do you think borrowing is inevitable in any language? Briefly discuss this in
relation to Kiswahili and English.
b) With relevant examples, differentiate the following terms
i. blending and clipping
ii. affixation and affixes
iii. transparent compounds and opaque compounds
iv. major word classes and minor word classes
v. conversion and coining
(c) Use in a sentence each of the following words as nouns.
i. Legitimate
ii. Expose
iii. Die
iv. Strategic
v. Hypothetic
SECTION C: PLAYS (20 Marks)
Answer one (1) question from this section
6. Wherever there is injustice, there is always a conflict caused by the forces attempting to
maintain the unjust system and those struggling to destroy it. By using one play you have read
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