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  • kcse form 2 mathematics questions

The figure below shows the path of a ray of light passing through a rectangular glass block placed in air

23/10/2021

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​The figure below shows the path of a ray of light passing through a rectangular glass block placed in air

Picture

​Calculate the refractive index of glass (2mks)

Picture



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Two capacitors of capacitance 2 μF 1μF are connected in parallel. A p.d of 3V is applied  across them. Find the energy stored in the combination.

23/10/2021

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Two capacitors of capacitance 2 μF 1μF are connected in parallel. A p.d of 3V is applied  across them. Find the energy stored in the combination.  (2mks)

Picture



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The figure below shows an object placed in front of a concave mirror. By use of correct ray diagram, locate the position of image

23/10/2021

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​The figure below shows an object placed in front of a concave mirror. By use of correct ray diagram, locate the position of image

Picture

Solution

Picture



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The figure bellows shows a wave profile for a wave whose frequency is 2HZ

23/10/2021

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The figure bellows shows a wave profile for a wave whose frequency is 2HZ

Determine the value of t3(s) (2mks)

Picture

Solution

Picture



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The figure below shows two parallel magnets with unlike poles adjacent to each other. Sketch the magnetic field pattern around the magnets

23/10/2021

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​The figure below shows two parallel magnets with unlike poles adjacent to each other. Sketch the magnetic field pattern around the magnets (2mks)

Picture

Solution

Picture



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Define Radio-activity

21/10/2021

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​(a) Define Radio-activity (2mks)

Radioactivity is the spontaneous disintegration of a nucleus releasing 
alpha, beta and gamma radiations accompanied by the release of energy

​(b) When carrying out experiments with radioactive substances the source should never be held with bare hands but with forceps. Explain? (1mk)



​Radioactive substances are harmful to body cells when ingested 
Picture

​(i) Plot on the graph paper provided the graph of the count rate (y-axis) against time

Picture
A graph of count Rate against time(s)
A graph of count Rate against time(s)

​(ii) From the graph, determine the half-life of Radon-220 (1mk)

​Half-life of radon 220=54 sec + 2 (showing on graph a must)

​(e) The diagram in the figure below shows paths taken by three radiations A,B and C from a radioactive isotope through an electric field.

The diagram in the figure below shows paths taken by three radiations A,B and C from a radioactive isotope through an electric field.

​(i) State the charge on plate Y (1mk)

  • ​Negative

​(ii) Identify the radiations A and C (2mks)

  • A- Beta particles
  • B-Alpha particles 

​(iii) Give a reason why C deviates more than A (1mk)

C more massive than A



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A 240v mains transformer  has 800 turns in the primary and N turns in the secondary. It is used to supply energy to a 12v/21w lamp

21/10/2021

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(a) A 240v mains transformer  has 800 turns in the primary and N turns in the secondary. It is used to supply energy to a 12v/21w lamp. ​

(i) Calculate the number of turns in the secondary (2mks)

(ii) What is the efficiency of the transformer if the current drawn from the 240V mains is 100mA (2mks)



Picture
The circuit above shows a step-down transformer used to light a lamp of resistance
The circuit above shows a step-down transformer used to light a lamp of resistance.

​Calculate.

(i) the reading of voltmeter, V, with, S, open (2mks)

(ii) the reading of the ammeter A with S closed (neglect the effective resistance of the secondary winding) (2mks)

(iii) the power dissipated in the lamp (2mks)

(iv) the primary current if the transformer is 90% efficient (3mks)

Picture



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State two advantages of a C.R.O as a voltmeter

21/10/2021

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​(a) State two advantages of a C.R.O as a voltmeter

  • ​Measures both D.C and A.C (1mk)
  • ​Its accurate and does not take any current (1mk)

​(b) A television tube is a cathode ray tube modified. State two modifications



  • Presence of magnetic coils
  • Incoming signal from the aerial is fed into the grid

​(c) State the functions of the following parts of a C.R.O

(i) Grid

  • Grid controls brightness of the spot

(ii) X-plates

  • horizontal displacement
  • time base control

(iii) Fluorescent screen

  • Identify the position of the electron beam

​(d) A modern X-ray tube is shown below

Picture

​(i) Name the parts labeled A-D (2mks)

A

​Copper Anode  

B

​Tungsten Target 

C

​Filament

D

​Cooling fins  

​(ii) Give the functions of:- (1mk)

(i) Shielding with lead

​Lead absorbs the radiation (1mk)

(ii) Evacuating the tube

Prevents collisions, avoid secondary electrons (1mk)



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Distinguish between a p-type and n-type semi conductors

21/10/2021

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​(a) Define doping (1mk)

​Process of introducing foreign element (impurity) into a pure semi-conductor,

​(b) Distinguish between a p-type and n-type semi conductors (2mks)



Distinguish between a p-type and n-type semi conductors

​(c) Using a diagram illustrate a forward P-N junction (2mks)

​(d) The figure below shows a bridge circuit 

A capacitor has been connected across the resistor as shown
A capacitor has been connected across the resistor as shown

​(i) Sketch of the figure below the wave form when a CRO is connected across the resistor, R

Picture

​(ii) On the same axes, sketch a wave form when C.R.O is connected across R when the capacitor has been removed (1mk)

Picture



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Explain why bulbs in along corridor are not wired in series

21/10/2021

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​(a) Explain why bulbs in along corridor are not wired in series (2mks)

  • High resistance, dim light
  • When one goes off, all others go off


​(b) An electric cooker has an oven rated 2500w, a grill rated 1500w and two plates each of 1000W. This cooker operates directly from 240v supply. What is the costs of operating all the parts at once for 30 minutes if electricity costs sh.10.00 per unit? (3mks)

Picture

​(c) Study the figure below

Picture

​(i) What name is given to the fitting in the diagram (1mk)

​3 pin plug

​(ii) Identify the parts labeled (2mks)

A

​Neutral wire

B

​Earth wire 

C

​Live wire 

D

​Fuse



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Give two advantages of a circuit breaker instead of a fuse in domestic  wiring

21/10/2021

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Give two advantages of a circuit breaker instead of a fuse in domestic  wiring (2mks)

  • It disconnects current immediately unlike the fuse that takes time  to melt
  • It is not damaged 



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​State the conditions for generation of e.m.f from a magnet

21/10/2021

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​State the conditions for generation of e.m.f from a magnet (2mks)

  • Relative movement of magnet and coil/charge of flux
  • Complete circuit



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The following is a part of a radio-active series

20/10/2021

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​The following is a part of a radio-active series

Picture

​Identify the radiation r, find the values of c and d (3mks)

r

​r is βeta particle

c

​c is 206

d

​d is 82



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​State two uses of optical fibres whose working relies on total internal reflection

20/10/2021

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​State two uses of optical fibres whose working relies on total internal reflection (2mks)

  1. Communicating data
  2. Endoscope (inspection of internal organs)



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​Give a reason why gases are poor transmitters of sound

20/10/2021

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​Give a reason why gases are poor transmitters of sound (1mk)

​Molecules in gases are much further apart



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Other than penetrating powers, state two differences between soft and hard X-rays

20/10/2021

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​Other than penetrating powers, state two differences between soft and hard X-rays (2mks)

  • Hard X-ray have short wavelength and are produced at high voltages (1mk)
  • Soft X-rays have longer wavelength and are produced at lower voltages (1mk)

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Two mirrors are inclined at 60 degrees centigrade to each as shown:

20/10/2021

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Two mirrors are inclined at 60o to each as shown:

Two mirrors are inclined at 60 degrees centigrade to each as shown:


Complete the ray diagram to show how it travels after striking the two mirrors and find the angle of reflection on each surface (2mks)

Solution

Picture

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The diagram in the figure below represents a wheel and axle used as a machine, whose efficiency is 80% to raise 400N of building materials. The wheel and axles have diameters of 75cm and 15cm respectively.

19/10/2021

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​(a) The diagram in the figure below represents a wheel and axle used as a machine, whose efficiency is 80% to raise 400N of building materials. The wheel and axles have diameters of 75cm and 15cm respectively.



The diagram in the figure below represents a wheel and axle used as a machine, whose efficiency is 80% to raise 400N of building materials. The wheel and axles have diameters of 75cm and 15cm respectively.
The diagram in the figure below represents a wheel and axle used as a machine, whose efficiency is 80% to raise 400N of building materials. The wheel and axles have diameters of 75cm and 15cm respectively.

​(i) Mark on the diagram the correct position and direction of the load to be lifted (1mk)

Picture

​(ii) Name the principle on which this machine works (1mk)

​The principle of moments

​(iii) Calculate the effort needed to raise the load (3mks)

Picture

​(iv) The machine is operated manually and raises the load to a height of 5m in 20 seconds. Calculate the power developed by the operator (2mks)

Picture

(b)
​(i) State two factors that determines the efficiency of an inclined plane as a machine (2mks)



  1. ​Smoothness of plane
  2. angle of inclination

​(ii) Explain how these factors affect efficiency (2mks)

  • Smoothness: Efficiency increases with smoothness since loses due to friction and minimized
  • Angle –efficiency increases with the angle of inclination since normal reaction decreases and so does friction.

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Explain what you understand by each of the following terms

19/10/2021

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​Explain what you understand by each of the following terms: 

(​i) Angular velocity (1mk)

​The angle covered in radians per second by an object in circular motion

​(ii) Centripetal force (1mk)

​The force that keeps an object in circular motion


​b) A bicycle wheel with radius 28cm moves with a linear velocity of 8m/s, determine 

​(i) the angular velocity of the wheel (2mks)

Picture

​(ii) the centripetal acceleration of a point on the rim of the wheel (2mks)

Picture

​(c) To determine the relationship between angular velocity w and tension T, a student used a smooth disc with a hole at the centre,  a string and cylindrical object of mass m, as shown below

To determine the relationship between angular velocity w and tension T, a student used a smooth disc with a hole at the centre, a string and cylindrical object of mass m, as shown below
To determine the relationship between angular velocity w and tension T, a student used a smooth disc with a hole at the centre, a string and cylindrical object of mass m, as shown above

​Describe how the student went about determining the relationship, specifying any other necessary material or instrument not shown in the diagram (3mks)



​The cylindrical mass was attached to a known weight, T, hanging freely below the hole. The disc was rotated with an increasing angular velocity w, till the hanging weight was steady. The experiment was repeated to obtain other values of w and their corresponding hanging weights

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A student set-up the apparatus as shown below to determine the power of an electric heater.

19/10/2021

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A student set-up the apparatus as shown below to determine the power of an electric heater
A student set-up the apparatus as shown above to determine the power of an electric heater

(a)
​(i) Other than time, state the measurements that would be used to determine the quantity of heat P absorbed by ice in a unit time (2mks)

​Current, voltage (p.d) mass of water collected temperature of the melt

​(ii) Complete the circuit to show the connection of the essential circuit components (2mks)

Complete the circuit to show the connection of the essential circuit components

​(iii) Describe how the student would proceed to determine P (3mks)

  • Switch on the current and start the clock simultaneously
  • Record the steady venus current I and P.d.v 
  • Note the temperature of the melt( should be 0oC)
  • Weighs the melt to obtain its mass m, collected over a known length of time , t
Apply Ivt=mlf

​(iv) Give a reason why P may not be equal to the value indicated by the manufacturer (1mk)

​It may not be operating at its optimum conditions of p.d and temperature, T. the heater also absorbs heat


(b) In another experiment, 100g of hot water at 90oC was mixed with 20g of ice at 0oC in a lagged plastics colorimeter. After stirring, all the ice melted and the temperature of the mixture was found to be 61.5oC. Determine the latent heat of fusion of ice (3mks)

(Specific heat capacity of water  = 4200Jkg-1k-1)
Picture

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The readings tabulated below shows how the length of a helical spring varied with the load hanging on it

18/10/2021

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The readings tabulated below shows how the length of a helical spring varied with the load hanging on it
The readings tabulated below shows how the length of a helical spring varied with the load hanging on it

(a)
​(i) Complete the table to show the values of extension (2mks)

​0,4.5,9.2,13.8,18.5,23.2 cm


​(ii) Draw a graph of extension (y-axis) against load for the spring (5mks)

Graph
  • Labeling of axes 
  • Straight line 
  • Location of points 
  • Scale used 
Picture

​(ii) Determining form the graph the proportionality constant of the spring (2mks)

Picture

​(b) Two springs Q and R have proportionality constants 20N/M and 25N/M respectively. Q weighs 0.2 N while the weight of R is negligible. The two springs are arranged to support a load of 3.0N as shown in the diagram below

Picture

Determine the extension in 
(i)  Q……………………………………………..(1mk)

Picture


ii)  R ……………………………………………(1mk)

Picture

​(c) State two factors that determine the proportionality constant of a helical spring (2mks)

  • Diameter of spring, length of the spring/thickness of the wire coiled to make the spring
  • Diameter of wire used

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The diagram below shows two trolleys, A and B connected to each other by an elastic strip of negligible mass. The trolleys are pulled apart on a smooth plane till tension in the elastic strip is 4.0N and are then released suddenly

18/10/2021

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The diagram below shows two trolleys, A and B connected to each other by an elastic strip of negligible mass. The trolleys are pulled apart on a smooth plane till tension in the elastic strip is 4.0N and are then released suddenly
The diagram below shows two trolleys, A and B connected to each other by an elastic strip of negligible mass. The trolleys are pulled apart on a smooth plane till tension in the elastic strip is 4.0N and are then released suddenly

​(a) State with reason the total momentum of the trolleys when they are just released (2mks)

​Zero (0) –It is because their velocities are still zero/ They are still stationary


​(b) Calculate the initial acceleration of trolley A when released (3mks)

Picture

(c) The velocity of the trolley B is 0.9ms-1 just before it collides with A. Determine the velocity of A just before the collision

Picture

​(d) Which trolley covers a longer distance before collision? Explain (2mks)

​trolley A, because of it moves with high velocity 

​(e) Explain why the elastic strip may not stretch to the same original length after impact (2mks)

​Friction force



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A student holds a sheet of paper at an end so that it hangs in the position A as shown below

17/10/2021

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A student holds a sheet of paper at an end so that it hangs in the position A as shown below
A student holds a sheet of paper at an end so that it hangs in the position A as shown above

​Explain why the paper rises to the position B when the student blows  air in the direction shown by the arrow (2mks)

There is pressure difference created as a result of air blown above  the paper i.e. high velocity , low pressure

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Two objects made of the same material and having the same mass are heated to a temperature of 35oC above that of the atmosphere and then allowed to cool in still air for 30 minutes. State one factor that will determine their final temperature

17/10/2021

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Two objects made of the same material and having the same mass are heated to a temperature of 35 degrees Centigrade above that of the atmosphere and then allowed to cool in still air for 30 minutes. State one factor that will determine their final temperature (1mk)

​Surface area to volume ratio

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​The figure below shows a sheet of material with the shape of an isosceles triangle. Mark its centre of gravity accurately showing how you arrive at the answer

17/10/2021

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​The figure below shows a sheet of material with the shape of an isosceles triangle. Mark its centre of gravity accurately showing how you arrive at the answer (1mk)

The figure below shows a sheet of material with the shape of an isosceles triangle. Mark its centre of gravity accurately showing how you arrive at the answer
Problem
Force of gravity
Solution

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    10. Gas Laws (15 Lessons)

    FORM IV - PHYSICS SYLLABUS

    1. Thin Lenses (20 Lessons)
    2. Uniform Circular Motion (10 Lessons)
    3. Floating and Sinking (15 Lessons)
    4. Electromagnetic Spectrum (15 Lessons)
    5. Electromagnetic Induction (20 Lessons)
    6. Mains Electricity (10 Lessons)
    7. Cathode Rays and Cathode Ray Tube (10 Lessons)
    8. X-rays (8 Lessons)
    9. Photoelectric Effect (15 Lessons)
    10. Radioactivity  (15 Lessons)
    11. Electronics (10 Lessons)
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