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Ndugu/Mzazi / Mlezi, Uongozi wa shule ya Sekondari Baobab unaendelea kutoa kazi kwa wanafunzi. Hii itakuwa kazi ya tano (assignment 05).Tunakuomba upakue na umpatie mwanao afanye kulingana na ratiba inavyoelekeza. Akimaliza tunasisitiza utume hizo kazi kwa e-mail ya kidato husika. KIDATO CHA SITA Mkondo wa wavulana: [email protected] Mkondo wa wasichana: [email protected] ZINGATIA:i) Kupiga picha kurasa zote za somo husika na kutuma kama “single document” na kama uta-scan tunakuomba utume masomo yote kwenye e-mail moja badala ya kuwa na e-mail nyingi kwa mwanafunzi mmoja. ii) Mwanafunzi aendelee kufanya kazi zake kwenye madaftari ya mazoezi ya somo husika. Kwa msaada zaidi wasiliana na walimu wa Taaluma: 0754 611 538 / 0768 611 538 / 0763 367 567 na 0768 628 925 Asanteni kwa Ushirikiano wenu. Mkuu wa Shule Shule ya Sekondari Baobab. BAOBAB SECONDARY SCHOOL MapingaVillage - BagamoyoDistrict. P. O. Box 35692, Dar es Salaam, Tanzania. : +255 754 611538/ 0768 611538/ 0763367 567/ 0768628 925 Website: www.baobab.ac.tz

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Page 1: BAOBAB SECONDARY SCHOOLBAOBAB SECONDARY SCHOOL MapingaVillage - BagamoyoDistrict. P. O. Box 35692, Dar es Salaam, Tanzania. : +255 754 611538/ 0768 611538/ 0763367 567/ 0768628 925

Ndugu/Mzazi / Mlezi,

Uongozi wa shule ya Sekondari Baobab unaendelea kutoa kazi kwa wanafunzi. Hii itakuwa kazi ya tano

(assignment 05).Tunakuomba upakue na umpatie mwanao afanye kulingana na ratiba inavyoelekeza.

Akimaliza tunasisitiza utume hizo kazi kwa e-mail ya kidato husika.

KIDATO CHA SITA

Mkondo wa wavulana: [email protected]

Mkondo wa wasichana: [email protected]

ZINGATIA:i) Kupiga picha kurasa zote za somo husika na kutuma kama “single document” na kama

uta-scan tunakuomba utume masomo yote kwenye e-mail moja badala ya kuwa na e-mail

nyingi kwa mwanafunzi mmoja.

ii) Mwanafunzi aendelee kufanya kazi zake kwenye madaftari ya mazoezi ya somo husika.

Kwa msaada zaidi wasiliana na walimu wa Taaluma: 0754 611 538 / 0768 611 538 / 0763 367 567 na

0768 628 925

Asanteni kwa Ushirikiano wenu.

Mkuu wa Shule

Shule ya Sekondari – Baobab.

BAOBAB SECONDARY SCHOOL MapingaVillage - BagamoyoDistrict.

P. O. Box 35692, Dar es Salaam, Tanzania.

☎: +255 754 611538/ 0768 611538/ 0763367 567/ 0768628 925

Website: www.baobab.ac.tz

Page 2: BAOBAB SECONDARY SCHOOLBAOBAB SECONDARY SCHOOL MapingaVillage - BagamoyoDistrict. P. O. Box 35692, Dar es Salaam, Tanzania. : +255 754 611538/ 0768 611538/ 0763367 567/ 0768628 925

SHULE YA SEKONDARI BAOBAB

RATIBA YA MAZOEZI MUDA WA LIKIZO

TAREHE YA

KUFANYA DARASA MASOMO

TAREHE YA

KUKUSANYA

IJUMAA

15/05/2020

F I, II, III & IV B/MATHS & ENGLISH LANG.

F.V & VI PHY/ACCOUNTANCY/KISWAHILI

JUMAMOSI

16/05/2020

F I, II, III & IV GEOGRAPHY & CIVICS

IJU

MA

A 2

2/0

5/2

02

0

F.V & VI BIOLOGY/ ECONOMICS/ ENGLISH

JUMAPILI

17/05/2020

F I, II, III & IV KISWAHILI & HISTORY

F.V GEOGRAPHY

F.VI GS

JUMATATU

18/05/2020

F I, II, III & IV BIOLOGY & BIBLE/ ISLAMIC

KNOW.

F.V & VI ADV-MATHS/ COMMERCE

JUMANNE

19/05/2020

F.I & F.II CHEMISTRY & COMMERCE

F.III & IV CHEM/COMMERCE & CHINESE

F.V & VI CHEMISTRY

JUMATANO

20/05/2020

F.I & F.II PHYSICS & B.KEEPING

F.III & IV PHY/B.KEEPING & ARABIC

F.V & VI BAM

ALHAMISI

21/05/2020

F.I & F.II ICS & CHINESE

F.III & IV LITERATURE/ ICS

F.V & VI HISTORY

Page 3: BAOBAB SECONDARY SCHOOLBAOBAB SECONDARY SCHOOL MapingaVillage - BagamoyoDistrict. P. O. Box 35692, Dar es Salaam, Tanzania. : +255 754 611538/ 0768 611538/ 0763367 567/ 0768628 925

CHEMISTRY

1 (a) Draw the structural orientation of the following atomic orbitals:-

(i) Px, (ii) Py (iii) Pz (iv) Pxy (v) P xz (vi) pz2 (vii) Px

2-y

2

(b) Give the name of geometrical structure and one example of the molecule formed from the

following hybridized atomic orbitals

i. SP3 hybridized orbitals

ii. SP2 hybridized orbitals

iii. d2SP

3 hybridized orbitals

iv. SP3d

2 hybridized orbitals

(c) Justify the meaning of the following statements

i. Electron are lazy

ii. Electrons are unfriendly

iii. Quantum numbers are signature for electrons in the atom

(d) Give the set of quantum numbers of the followings:-

i. Last electron in copper

ii. Last electron in sodium

iii. 6th

electron in nitrogen

2 (a) A 2.0g of sample of water is vaporized completely into 10 litres container at 2000C. Calculate the

pressure of the water vapour in this container at 2000C

(b) Show how Graham’s law can be deduced from kinetic theory of gases

(c) A saturated hydrocarbon having the molecular formula CnH2n+2 diffuses through a porous

membrane twice as fast as sulphur dioxide. Determine the molecular formula and IUPAC name of

the hydrocarbon

3 (a) Deduce the following gas laws from knetic theory of gases.

(i) Grahms law of diffusion.

(ii) Daltons law of patial pressure.

(b) Liquid B and C form an ideal solution at any proportion. If 6.7 moles of B were mixed with

20.9cm3 of C with density of 1.76 g/cc and their vapour pressure were 1.25 atm and 1.0625 x 10

5

N/m2 respectively. Calculate the partial pressure of liquid B and C in a mixture, If the R.M.M of

C was 60 g/mol

4 (a) If Ksp for NaOH at 120 K is 11106.1 ,Calculate the solubility of magnesium Hydroxide in g/l

when dissolved in sodium hydroxide at the same temperature. Ksp for magnesium hydroxide is 10104.2 . Given Mg = 24,O = 16, H = 1, Cr = 52, Ag = 108.

(b) Ammonium hydrogen sulphide solid was allowed to dissociate into an evacuated 250dm3 flask to

ammonia and hydrogen sulphide gas at 400k. if Kc for the reaction was found to be 2.7x 103 mol

2

dm3 . Calculate the total pressure of gases in the flask.

(c) A quantity of 2.4g of organic compound fills 934cm3 as a vapour at 298k and 740 mmHg. The

vapour escape through the porous pore in 25min and 46 seconds. If the compound contains 37.21%

carbon, 7.8% hydrogen and chlorine only. Calculate the molecular formulae of the compound

Page 4: BAOBAB SECONDARY SCHOOLBAOBAB SECONDARY SCHOOL MapingaVillage - BagamoyoDistrict. P. O. Box 35692, Dar es Salaam, Tanzania. : +255 754 611538/ 0768 611538/ 0763367 567/ 0768628 925

5 (a) Draw the bonhabber cycle of Lithium flouride, and calculate the Enthalpy of its information if

Li (s) Li(g) = 155.1 KJmol-1

F2(g) 2F(g) =151.0 KJmol-1

Li Li+ + e = 518.3 KJmol

-1

F + e F-

= -351.1 KJmol-1

Li+ + F

- LiF = -1030.0 KJmol

-1

(c) 0.0240mol sample of N2O4 (g) is allowed to dissociated and come to equilibrium with NO2(g) in a

0.372L flask at 250C. What is the percentage dissociation of the

N2O4 2NO2 KC = 4.61 x 10-3

at 25oC

(b) Given the following reactions

Fe2 O3 + 3CO 2Fe + 3CO2 -28kJmol-1

3Fe2O3 + CO 2Fe3O4 + CO2 -59kJmol-1

Fe3O4 + CO 3FeO + CO2 38kJmol-1

Calculate the enthalpy change for the reaction

FeO + CO Fe + CO2

(c) Calculate the enthalpy change for the reaction

C2H5OH CH3 ̶ O ̶ CH3

If at 25oC, the heat of formation of C2H5OH is -276 KJmol

-1, the heat of combustion of CH3 ̶ O ̶

CH3 is -1456 KJmol-1

, the heat of formation of water is-284 KJmol-1

and heat of combustion of

carbon is -393 KJmol-1

(d) 100cm3 of 1M KOH and 100cm

3 of 1M HCl were mixed in a calorimeter. The temperature rise

was 6.25K. The heat capacity of calorimeter was 95J/k and the specific heat capacity of the

solution was 4.2J/Kg. Calculate the standard enthalpy of neutralization

6 (a) Summarize the reactions (by using chemical equations) which take place in the blast furnace

during extraction of iron at:-

i. 5000C to 800

oC

ii. 900oC to 1200

oC

(b) Explain the process of extraction of zinc under the following steps:-

i. Concentration of the ore

ii. Roasting of the ore

iii. Conversion of ZnO to Zn

iv. Purification of the obtained Zn

(c) Give reasons to account for the followings:-

i. Anhydrous magnesium chloride cannot be prepared by heating the hydrated crystals of

MgCl2.6H2O

ii. Aluminium which is abundant in the earth’s surface, its extraction started just recently

Page 5: BAOBAB SECONDARY SCHOOLBAOBAB SECONDARY SCHOOL MapingaVillage - BagamoyoDistrict. P. O. Box 35692, Dar es Salaam, Tanzania. : +255 754 611538/ 0768 611538/ 0763367 567/ 0768628 925

PHYSICS

1. (a) (i) What is meant by dimensional variables? Give two (2) examples

(ii) Give one fact on which the principle of homogeneity of dimensions is based

(b) (i) What is the basic requirement for a physical relation to be correct?

(ii) If the velocity of light, acceleration due to gravity and normal atmospheric pressure are chosen

as the fundamental units, find the values of length, mass and time

(c) (i) Suggest the dimensions consistency of the expression 𝑌 = 𝑎 𝑆𝑖𝑛 𝜔 (𝑥

𝑣− 𝑘𝜋), where all

symbols carry their usual meaning

(ii) From the given expression in 1 (c) (i), show that 𝑘 is a dimensional constant

2. (a) (i) What is meant by the term vertex as used in projectile motion?

(ii) Give two factors which determine the span of jump in long jump

(b) An aeroplane travelling horizontally at 80 m/s and at a height of 196 m drops a bomb to hit target.

(i) What horizontal distance from the target should the bomb is released?

(ii) Calculate the velocity of the bomb as it reaches the ground

(c) Two projectile are launched at projection angles of 30° and 60° with the same initial speed of

5.0 × 104 𝑚/𝑠 With the horizontal

(i) Show that the two projectiles will be focused on the same point as they reach the ground

(ii) Calculate the difference in the maximum height reached by the two projectiles

3. (a) (i) List down two practical examples of uniform circular motion

(ii)How does uniform circular motion differ from projectile motion?

(b) A racing car of mass 2.5 × 103kg moves around a banked track at a constant speed of 72km/hr.

Assuming that the total reactions at the wheels is normal to the track and the horizontal radius of

the track is 100m, calculate the;

(i) Angle of inclination of the track to the horizontal

(ii) Total reaction at the wheels

(c) (i) Define angular displacement and give its S.I unit

(ii) A particle of mass 0.2kg is attached to one end of a light inextensible string of length 50cm. If

the particle moves in a horizontal circle with an angular velocity of 5rad/s, calculate the angle

of inclination that a string would make with the vertical

4. (a) (i) Give an expression for the restoring force acting on the body executing simple harmonic motion

(S.H.M)

(ii) How would the period of a simple harmonic oscillator be affected if the amplitude of oscillation

is doubled?

(b) Two particles of masses 0.8kg and 0.3kg are suspended by a weightless spring of a force constant

12.5N/m. If the first particle is gently removed at equilibrium, calculate the;

(i) Amplitude of the second particle

(ii) Angular frequency of the second particle

(c) A body in S.H.M is described by the displacement function 𝑌 = 𝑎 𝐶𝑜𝑠 (𝜔𝑡 + 𝜙) where all

Page 6: BAOBAB SECONDARY SCHOOLBAOBAB SECONDARY SCHOOL MapingaVillage - BagamoyoDistrict. P. O. Box 35692, Dar es Salaam, Tanzania. : +255 754 611538/ 0768 611538/ 0763367 567/ 0768628 925

symbols carry their usual meaning. If the phase constant 𝜙 is equal to zero, sketch the graph of:

(i) Velocity against time

(ii) Acceleration against time

5. (a) Write down the angular quantity that is analogous to each of the following linear quantities:

(i) Force, 𝐹 =𝑑

𝑑𝑡(𝑚𝑣)

(ii) 𝐾. 𝐸 =1

2𝑚𝑣2

(b) A constant force of 40N is applied tangentially to the rim of a wheel of radius 10cm mounted on a

fixed axle which is initially at rest. If the wheel has a moment of inertial of 0.2kg𝑚2,

calculate the:

(i) Torque acting on the wheel

(ii) Work done on the wheel after 5 revolutions

(c) (i) A flywheel has a kinetic energy of 200J. Calculate the number of revolution it makes before

coming to rest if a constant opposing couple of 5Nm is applied

(iii) How long does a flywheel in 5 (c) (i) it take to come to rest if the moment of inertia

about its centre is 4kg𝑚2

6. (a) (i) What is meant by escape velocity?

(ii) Why the escape velocity in does not depend on the direction of the projection?

(b) (i) How much would the gravitational potential energy of a body of mass 𝑚 increase if it was

moved from the earth’s surface to infinity?

(ii) A body of mass 5.0 × 103 kg is at a height of 6.4 × 106𝑚 above the earth’s surface.

Determine the kinetic energy required by the body in order to escape the earth’s field

(c) A man jumps a height of 1.5m on the earth’s surface. Calculate the height he might be able to jump

on the planet whose density is one quarter of that of the earth and whose radius is on third

that of the earth

7. (a) Briefly explain why the:

(i) Tile floor feels colder than the wooden floor, even though both floor materials are at the

same temperature

(ii) Good absorber of radiant energy appear black

(b) An aluminium foil of relative emittance 0.2 is placed between two concentric spheres at

temperatures of 200K and 100K respectively. Calculate the;

(i) Temperature of the foil at steady state condition

(ii) Rate of heat transfer between one of the spheres and the foil

(c) (i) How does triple point differ from critical temperature?

(ii) In an arbitrary scale of a temperature, water freezes at 50℃ and boils at 290℃. Find the

boiling point of a liquid in this scale if it boils at 75℃

8. (a) What is meant by the following terms as used in thermodynamics:

(i) Isolated system

(ii) Closed system

(b) (i) Briefly explain the idea on which the first law of thermodynamics is based

Page 7: BAOBAB SECONDARY SCHOOLBAOBAB SECONDARY SCHOOL MapingaVillage - BagamoyoDistrict. P. O. Box 35692, Dar es Salaam, Tanzania. : +255 754 611538/ 0768 611538/ 0763367 567/ 0768628 925

(ii) 1.0 g of water becomes 1254 𝑐𝑚3of steam at a pressure of 1.013× 105 Pa. If the latent heat of

vaporization at this pressure is 1752J/g, calculate the external work and increase in internal

energy

(c) (i) Give two (2) examples of irreversible process

(ii) A motor car tyre has a pressure of four time atmospheres at a room temperature of 27℃. If the

tyre suddenly bursts, calculate the temperature of the escaping air

9. (a) (i) What is the physical significance of the term conductivity?

(ii) Give one (1) factor which causes the movement of electrons in a conductor

(b) (i) A researcher has 4.0 g of gold and wishes to form it into a wire having a resistance of 75Ω at

0℃. What will be the length of the wire?

(ii) The resistivity of constantan wire at room temperature is 49 × 10−8 Ω𝑚. If the density of

mobile electrons through the wire is 9.7 × 1028 𝑚−3, find the relaxation time for its free

electrons

(c) A coil of copper wire has a resistance of 1.51Ω at 10℃ and 2.18Ω at 40℃. Calculate the;

(i) temperature coefficient of copper

(ii) resistance of the wire at 30℃

10. (a) Sketch the graph of current against voltage for the following devices:

(i) Gas discharge tube

(ii) Thermionic diode

(b) (i) Briefly explain why the lights of a motor car becomes slightly dim when the car is started?

(ii) A potentiometer of length 50 cm and a resistance of 2.0 Ω is connected to a 4.0 V

accumulator of internal resistance 0.5 Ω. What length of this wire will be required to

balance a cell of e.m.f 1.6V?

(c) Study the circuit diagram below and respond to the questions that follow:

3Ω C 3Ω D 3Ω

A B

(i) Identify the name of the equivalent network circuit

(ii) Find the total resistance between points A and B from the circuit obtained in 10 (c) (i)

11. (a) (i) Why is a semiconductor virtually an insulator at room temperature?

(ii) How does the forbidden energy gap of an intrinsic semiconductor vary with an increase in

temperature?

(b) (i) What is meant by breakdown voltage?

(ii) In which energy band do free electrons and valence electrons exist?

(c) (i) List down two (2) applications of photodiode

(ii) Briefly explain the property of photo conductivity in semiconductors

Page 8: BAOBAB SECONDARY SCHOOLBAOBAB SECONDARY SCHOOL MapingaVillage - BagamoyoDistrict. P. O. Box 35692, Dar es Salaam, Tanzania. : +255 754 611538/ 0768 611538/ 0763367 567/ 0768628 925

12. (a) Name three electronic circuits in which multivibrators can be constructed

(b) (i) List down three (3) types of multivibrators

(ii) Briefly explain the applications of multivibrators listed in 12 (b) (i)

(c) (i) Mention two (2) characteristics of OPAMPS

(ii) Briefly explain why OPAMPS are sometimes called differential amplifiers?

13. (a) (i) Define a logic gate

(ii) Draw the circuit symbol and give the truth table for a two input AND gate and two input OR

gate

(b) (i) Write down the truth table of the logic gate circuit in the figure below

C

A o

o Q

B o

D

(ii)Draw a single gate symbol which is equivalent to the circuit in the figure above

(c) (i) Why is a NOT gate called an inverter?

(ii) Give reasons as to why a NAND gate is referred to as a universal gate

14. (a) (i) Account for aerial environment

(ii) Describe four (4) ways on how the aerial environment is threatened

(b) (i) What do you understand by the term aerogenerator?

(ii) An aerogenerator has a power output that is proportional to the square of its wind speed

and its efficiency varies with wind speed. On a day there is a steady wind of speed 9.0 m/s,

the power output is 40.0 kW operating at an efficiency of 20%. If the wind speed on the

next

day is found to be 13.5 m/s and the efficiency increases to 25%, what will be its new power

output?

(c) (i) State any four (4) sources of heat in the interior of the earth

(ii) A large explosion at the earth’s surface creates primary waves (P) and secondary waves (S)

moving with constant speeds of 6.0 km/s and 4.0 km/s respectively. If both waves arrive at

the seismological station at an interval of 30 seconds, calculate the distance measured

between the station and the site of explosion

Page 9: BAOBAB SECONDARY SCHOOLBAOBAB SECONDARY SCHOOL MapingaVillage - BagamoyoDistrict. P. O. Box 35692, Dar es Salaam, Tanzania. : +255 754 611538/ 0768 611538/ 0763367 567/ 0768628 925

GEOGRAPHY

1. The student of Arusha High School conducted a study tour in Sweden 2020 and the found larger part

of the country was covered by ice. Using seven (7) points show the reasons for the occurrence of that

ice.

2. The larger area of Southern Highland Tanzania was surrounded by many mountains.

Using five (4) points, explain the cons and pros of Mountains to the people of that area.

3. Write short notes on the following meteorological concepts:

i. Warm air front

ii. Cold air Front

iii. Tropical Cyclones

iv. Subsistence Inversion

Page 10: BAOBAB SECONDARY SCHOOLBAOBAB SECONDARY SCHOOL MapingaVillage - BagamoyoDistrict. P. O. Box 35692, Dar es Salaam, Tanzania. : +255 754 611538/ 0768 611538/ 0763367 567/ 0768628 925

ADVANCE MATHEMATICS 1

1. By using a non- programmable calculator:

(a) (i) √0.3854

3 (12.87)2

(0.04382)4( √63.75

) , correct to seven significant figures.

(ii) log6 (𝑒3 sin−1

2

3

0.0199) , correct to four significant figures.

(b) (i) Compute )!1120(!8

!93

7

3

7

CP.

(ii) By using the statistical functions of your calculator, find the Mean (�̅�) and the standard

deviation (𝜎𝑛−1) of the following values (correct to 6 decimal places).

Value 96 100 104 108 112 116 120 124 128

Frequency 10 41 24 2 4 6 6 11 19

2. (a) If sinh 𝑥 =3

4 , calculate the value of tanh 2𝑥

(b) Sketch the graphs of the functions xy 1cosh and xhy 1sin on the same xy plane.

(c) Prove that sinh−1 𝑥 = 𝑙𝑛(𝑥 + √𝑥2 + 1).

(d) Solve the equation 3sech2x + 4tanhx + 1 = 0 and write your answer correct to 4 d.p

(e) Evaluate ∫𝑑𝑥

√𝑥2−6𝑥+13 using a hyperbolic function substitution.

3. (a) Mention two limitations of linear programming

(b)A person required 10, 12, and 12 units of mineral elements A, B and C respectively for diet.

A liquid diet contains 5, 2 and 1 units of A, B and C respectively per can; and a dry diet

contains 1, 2 and 4 units of A, B and C respectively per carton. If the liquid diet is sold at

the price of Tshs. 3,000/= per can and dry diet is sold at the price of Tshs. 2,000/= per

carton, how many cans and cartons should a person purchase to minimize the costs and

meet the requirements?

4. (a) The table shows below shows the weights of 100 students at a certain institute as follows:

WEIGHTS (KG) FREQUENCY

60-62 5

63-65 18

66-68 42

69-71 27

72-74 8

Find the mode, median, mean and standard deviation for the weights of the students (use

the coding method to find the mean and standard deviation).

(b) Use the information in 4(a) above find:

(i) The inter-quartile and semi quartile range.

(ii) The class interval where the 40𝑡ℎ percentile and 8𝑡ℎ deciles are located and

hence find their real values.

Page 11: BAOBAB SECONDARY SCHOOLBAOBAB SECONDARY SCHOOL MapingaVillage - BagamoyoDistrict. P. O. Box 35692, Dar es Salaam, Tanzania. : +255 754 611538/ 0768 611538/ 0763367 567/ 0768628 925

5. (a) Using the Venn diagram show that:

(i) 𝐴 ⋂(𝐵 ⋃ 𝐶) = (𝐴 ⋂ 𝐵) ⋃(𝐴 ⋂ 𝐶)

(ii) 𝐴 ⋃(𝐴 ⋂ 𝐵) = 𝐴

(iii) (𝐵 − 𝐴) ⋂(𝐴 − 𝐵) = ∅ , where ∅ is empty set.

(b) Using set properties, simplify the following:

(i) [(𝐴 − 𝐵) ⋃(𝐴 − 𝐶)] ⋂ 𝐴𝑐

(ii) (𝐴 ⋂ 𝐵 ′) ⋂(𝐴′⋃ 𝐵′)

(iii) (𝑋 ⋂ 𝑌′) ⋃( 𝑋 ⋂ 𝑌 ) ⋃(𝑌 ⋂ 𝑋′)

(c) A group of 40 people are asked whether they like tennis ( T) and Football ( F). The number of

people who like both tennis and Football was 3 times the number liking only tennis. Adding 3 to

the number of liking only tennis and doubling the answer equals to the number of people liking

only Football. Four said they didn’t like sport at all.

(i) Draw Venn-diagram to represent these in formations.

(ii)Calculate 𝑛(𝑇 ⋂ 𝐹), 𝑛(𝑇 ⋂ 𝐹′)and 𝑛(𝑇′⋂ 𝐹).

6. (a) Sketch a graph of 4

)3)(1(2

x

xxy and give the value of its domain and range

(b) Given the function 127)( 2 xxxf

(i) Find the stationary point of f(x) and identify its nature.

(ii) Sketch the graph of f(x)

(iii)Find maxima or minimum value of f(x)

(c) If (𝑥) = 3𝑥 − 2 , 𝑔(𝑥) = 𝑥 + 7 and ℎ(𝑥) =1

1+𝑥 ,find the value of 𝑓𝑜𝑔𝑜ℎ(2).

7. (a) Show that the area under the curve x

y1

, From 1 nx to 1 nx is

1

1ln

n

n, by using

Simpson’s rule with 3 ordinates, deduce that the approximate value of

1

1ln

n

n=

nnn

4

1

1

1

1

3

1

(b) Show that Newton Raphson Method for approximating the reciprocal of number ‘N’ is

given by )2(1 nnn NXXX . Hence use the iterative formula to find the reciprocal of number

6. Such that 1.00 X perform three iterations

8. (a) Sketch the diagram for the locus of points which move such it covers a distance 𝑎 units from

the curve 𝑥2 + 𝑦2 + 2𝑥 − 4𝑦 = 20 where |𝑎| = 5 .

(b) (i) Show that 𝑦 = 𝑚𝑥 is a tangent to the circle 𝑥2 + 𝑦2 + 2𝑓𝑥 + 2𝑔𝑦 + 𝑐 = 0 if: (𝑔 +𝑚𝑓)2 = 𝑐(1 + 𝑚2).

(ii) A straight line AB of length 10 units is free to move with its ends on the axes. Find the

locus of a point P on the line at a distance of 3 units from the end on the 𝑥-axis.

(c) If 𝑝 and 𝑞 are the lengths of perpendiculars from the origin to the lines 𝑥 cos 𝜃 −𝑦 sin 𝜃 = 𝑘 cos 2𝜃 and 𝑥 sec 𝜃 + 𝑦 csc 𝜃 = 𝑘 respectively, prove that 𝑝2 + 4𝑞2 = 𝑘2 .

9. (a) Differentiate from the first principle 𝑦 = 2𝑠𝑖𝑛2𝑥.

(b) If 𝑦 = 𝑠𝑖𝑛𝑛+1𝑥𝑐𝑜𝑠𝑚−1𝑥 , find 𝑑𝑦

𝑑𝑥 .

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(c) A piece of wire is of length L, is cut into two parts of length X and L-X. The former is bent

into the shape of square and the latter into a rectangle of which the base double the height . Find an

expression for the sum of the areas of this two figures. Prove that the only value of x for which this

sum is a maximum or minimum is 17

8Lx .

10. (a) Find (i) ∫ 𝑒√𝑥𝑑𝑥

(ii) ∫ (cos 𝜃

1+𝑠𝑖𝑛2𝜃) 𝑑𝜃

𝜋

20

(b) Find the area enclosed by the ellipse 𝑥 = cos 𝜃, 𝑦 = sin 𝜃, 0x and 2

x

(c) Find the length of the arc of the curve 6𝑥𝑦 = 3 + 𝑥4 between the points whose abscissa are 1 and 3

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GENERAL STUDIES

1. “Today’s generation is covered by the deterioration of, moral values”: As an expert of General studies

uses the knowledge you learnt in moral values to educate the society members on how to rescue the

situation. Give six points.

2. “It is the matter of facts that technological transfer is inevitable so as to promote social and economic

development of our nation”. By using six points comment on the factors or qualities to be considered

by Tanzania in acceptability of Transferred Technology.

3. “The fight against corruption in Tanzania has become a cross cutting issue for some decades since it

combines efforts of various stakeholders”. With reference to this statement illustrates six measures

taken by Tanzanian government in preventing and combating corruption.

4. “The process towards the creation of East African Political federation is too faster”. In regard to this

contention discuss six steps or stages to be followed so as to reach a political federation.

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BASIC APPLIED MATHEMATICS

1. (a) Differentiate from first principle

i) y=√2𝑥 + 1 ii)y=x2+2x-1

(b) Find dy/dx if

i) y = xx

ii) x2

y + 4xy2

+ 4y = 5

(c) A farmer has 120 metres of fencing with which to enclose a rectangular sheep pen, using a

wall for one side. Find the maximum area that he can enclose.

2. (a)Find i)∫ 𝑥(3𝑥2+6)dx

ii)∫ 𝑥(x+1) 1/2

dx

(b) Evaluate ∫ √𝑥2

0(x

2+2) dx

(c)Find the area lying between the curve y=x2-3x+2 and the x-axis

3. The terminals marks in the basic applied mathematics examination obtained by 40 students of

form six are as follows;

66 87 79 74 84 72 81 78 68 74

80 71 91 62 77 86 87 72 80 77

76 83 75 71 83 67 94 64 82 78

77 67 76 82 78 88 66 79 74 64

From the above data;

(i) Prepare a frequency distribution table with class mark 62, 67, 72….

(ii) Calculate lower quartiles, middle quartile and upper quartiles

(iii) Find P80 and p55.Hence calculate the percentile range

4. (a) solve the following equations 4loga√𝑥-loga27x=loga(1

𝑥)

(b) Differentiate with respect to x;

i) y=𝑒4𝑥(1+x2)

ii) y=log(1+x)

(c) Sketch the graph of y=logex

Page 15: BAOBAB SECONDARY SCHOOLBAOBAB SECONDARY SCHOOL MapingaVillage - BagamoyoDistrict. P. O. Box 35692, Dar es Salaam, Tanzania. : +255 754 611538/ 0768 611538/ 0763367 567/ 0768628 925

BIOLOGY

1. Describe the economic importance of bacteria.

2. Compare and contrast between oxidative phosphorylation and photosynthetic phosphorylation.

3. Justify how analogous, homologous and vestigial organs supports evolution

4. a) What are the contributions of Swedish naturalist Carl Linnaeus in classification of living

organisms?

b) Describe the rules used in constructing dichotomous key

5. a) Describe the functions of

i. Cellulose

ii. Starch

iii. Glycogen

b) Explain five significance of membrane bound organelles.