# WAEC SYLLABUS FOR PHYSICS 2017

|### WAEC SYLLABUS FOR PHYSICS 2017

DETAILED SYLLABUS

It is important that candidates are involved in practical activities in covering this syllabus. Candidates will be expected to answer questions on the topics set out in the column headed ‘TOPICS’. The ‘NOTES’ are intended to indicate the scope of the questions which will be set but they are not to be considered as an exhaustive list of limitations and illustrations.

N.B. Questions will be set in S.I. units. However, multiples or sub-multiples of the units may be used.

1. Concepts of matter

2. Fundamental and derived quantities and units

(a) Fundamental quantities and units

(b) Derived quantities and unit

3. Position, distance and displacement.

(a) Concept of position as a location of point – rectangular coordinates.

(b) Measurement of distance

(c) Concept of direction as a way of locating a point – bearing

(d) Distinction between distance and displacement

Simple structure of matter should be discussed. The three states of matter, namely solid, liquid and gas. Evidence of the particle nature of matter e.g. Brownian motion experiment, Kinetic theory of matter. Use of the theory to explain: states of matter (solid, liquid and gas), pressure in a gas, evaporation and boiling; cohesion, adhesion, capillarity. Crystalline and amorphous substances to be compared (Arrangement of atoms in crystalline structure not required.)

Length, mass, and time as examples of fundamental quantities and m, kg and s as their respective units. Volume, density and speed as derived quantities and m3, kgm-3 and ms-1 as their respective units. Position of objects in space using the X,Y,Z axes can be mentioned.

Use of string, metre rule, vernier callipers and micrometer screw gauge. Degree of accuracy should be noted. Metre (m) as unit of distance. Use of compass and a protractor. Graphical location and directions by axes to be stressed.

4. Mass and weight Distinction between mass and weight

5. Time

(a) Concept of time as intervalbetween physical events

(b) Measurement of time

6. Fluids at rest

(a) Volume, density and relative density

(b) Pressure in fluids

(c) Equilibrium of bodies

(i) Archmedes’ principle

(ii) Law of flotatio

Use of lever balance and chemical/beam balance to measure mass and spring balance to measure weight. Kilogram (kg) as unit of mass and newton (N) as unit of weight.

The use of heart-beat, sand-clock, ticker-timer, pendulum and stopwatch/clock. Seconds (s) as units of time. Experimental determination for solids and liquids.

Concept and definition of pressure. Pascal’s principle, application of principle to hydraulic press and car brakes. Dependence of pressure on the depth of a point below a liquid surface. Atmospheric pressure. Simple barometer, manometer, siphon, syringes and pumps, determination of the relative density of liquids with U-tube and Hare’s apparatus.

Identification of the forces acting on a body partially or completely immersed in a fluid.

Use of the principle to determine the relative densities of solids and liquids.

Establishing the conditions for a body to float in a fluid. Applications in hydrometer, balloons, boats, ships, submarines etc.

7. Motion

(a) Types of motion: Random, rectilinear, translational, rotational, circular, orbital, spin, oscillatory

(b) Relative motion

(c) Cause of motion

(d) Types of force:

(i) Contact force

(ii) Force Field

(e) Solid friction

(f) Friction in fluids (Viscosity)

(g) Simple ideas of circular motion

Only qualitative treatment is required. Illustration should be given for the various types of motion.

Numerical problems on co-linear motion may be set. Force as cause of motion. Push and pull.

Electric and magnetic attractions and repulsion; gravitational pull.

Frictional force between two stationary bodies (static) and between two bodies in relative motion (dynamic). Coefficients of limiting friction and their determination. Advantages of friction e.g. in locomotion, friction belt, grindstone. Disadvantages of friction e.g. reduction of efficiency, wear and tear of machines. Methods of reducing friction. Use of ball bearings, rollers and lubrication.

Definition and effects. Simple explanation as extension of friction in fluids. Fluid friction and its application in lubrication should be treated qualitatively. Terminal velocity and its determination.

Experiments with a string tied to a stone at one end and whirled around should be carried out to

(i) demonstrate motion in a vertical/horizontal circle.

8. Speed and velocity

(a) Concept of speed as change of distance with time

(b) Concept of velocity as change of displacement with time

(c) Uniform/non-uniform speed/velocity

(d) Distance/displacement-time graph

9. Rectilinear acceleration

(a) Concept of acceleration as change of velocity with time.

(b) Uniform/non-uniform acceleration

(c) Velocity-time graph,

(d) Equations of motion with constant acceleration;

(i) Gravitational acceleration as a special case.

(ii) show the difference between angular speed and velocity.

(iii) show centripetal force. Banking of roads in reducing sideways friction should be qualitatively discussed.

Metre per second (ms-1) as unit of speed/velocity. Ticker-timer or similar devices should be used to determine speed/velocity. Definition of velocity as ds/dt. Determination of instantaneous speed/velocity from distance/displacement-time graph and by calculation.

Unit of acceleration as ms-2. Ticker timer or similar devices should be used to determine acceleration. Definition of acceleration as dv/dt. Determination of acceleration and displacement from velocity-time graph Use of equations to solve numerical problems.

10. Scalars and vectors

(a) concept of scalars as physical quantities with magnitude and no direction

(b) concept of vectors as physical quantities with both magnitude and direction.

(c) Vector representation

(d) Addition of vectors

(e) Resolution of vectors

(f) Resultant velocity using vector representation.

11. Equilibrium of forces

(a) Principle of moments

(b) Conditions for equilibrium of rigid bodies under the action of parallel and non-parallel forces.

(c) Centre of gravity and stability

12. Simple harmonic motion

(a) Illustration, explanation and definition of simple harmonic motion (S.H.M.) Mass, distance, speed and time as examples of scalars. Weight, displacement, velocity, and acceleration as examples of vectors. Use of force board to determine the resultant of two forces. Obtain the resultant of two velocities analytically and graphically.Moment of force/Torque. Simple treatment of a couple, e.g. turning of water tap, corkscrew, etc. Use of force board to determine resultant and equilibrant forces. Treatment should include resolution of forces into two perpendicular directions and composition of forces. Parallelogram of forces. Triangle of forces should be treated experimentally. Treatment should include stable, unstable and neutral equilibria. Use of a loaded test-tube oscillating vertically in a liquid, simple pendulum, spiral spring and bifilar suspension to demonstrate simple harmonic motion.

(b) Speed and acceleration of S.H.M.

(c) Period, frequency and amplitude of a body executing S.H.M.

(d) Energy of S.H.M.

(e) Forced vibration and resonance

13. Newton’s laws of motion:

(a) First Law: Inertia of rest and inertia of motion

(b) Second Law: Force, acceleration, momentum and impulse

(c) Third Law: Action and reaction

Relate linear and angular speeds, linear and angular accelerations. Experimental determination of ‘g’ with the simple pendulum and helical spring. The theory of the principles should be treated but

derivation of the formula for ‘g’ is not required. Simple problems may be set on simple harmonic motion. Mathematical proof of simple harmonic motion in respect of spiral spring, bililar suspension and loaded test-tube is not required.

Distinction between inertial mass and weight. Use of timing devices e.g. ticker-timer to determine the acceleration of a falling body and the relationship when the accelerating force is constant.

Linear momentum and its conservation. Collision of elastic bodies in a straight line.

Applications: recoil of a gun, jet and rocket propulsions.

ENERGY: Mechanical and Heat

14. Energy:

(a) Forms of energy

(b) World energy resources

(c) Conservation of energy

15. Work, Energy and Power

(a) Concept of work as a measure of energy transfer

(b) Concept of energy as capability to do work

(c) Work done in a gravitational field.

(d) Types of mechanical energy

(i) Potential energy (P.E.)

(ii) Kinetic energy (K.E.)

(e) Conservation of mechanical energy.

Examples of various forms of energy should be mentioned e.g. mechanical (potential and kinetic), heat, chemical, electrical, light, sound, nuclear etc. Renewable (e.g. solar, wind, tides, hydro,

ocean waves) and non-renewable (e.g. petroleum, coal, nuclear, Biomass). Sources of energy should be discussed briefly. Statement of the principle of conservation of energy and its use in explaining energy transformations.

Unit of work as the joule (J)

Unit of energy as the joule (J) while unit of electrical consumption is kWh.

Work done in lifting a body and by falling bodies.

Derivation of P.E. and K.E. are expected to be known. Identification of types of energy

possessed by a body under given conditions.

Verification of the principle

(f) Concept of power as time rate of doing work.

(g) Application of mechanical energy – machines. Levers, pulleys, inclined plane, wedge, screw, wheel and axle, gears.

16. Heat Energy

(a) Temperature and its measurement

(b) Effects of heat on matter e.g.

(i) Rise in temperature

(ii) Change of state

(iii) Expansion

(iv) Change of resistance

(c) Thermal expansion – Linear, area and volume expansiveness, Unit of power as the watt (W).

The force ratio (F.R.), mechanical advantage (M.A.), velocity ratio (V.R.) and efficiency of each machine should be treated. Identification of simple machines that make up a given complicated machine e.g. bicycle. Effects of friction on machines. Reduction of friction in machines.

Concept of temperature as degree of hotness or coldness of a body. Construction and

graduation of a simple thermometer. Properties of thermometric liquids. The following thermometers should be treated:

Constant

– volume gas thermometer, resistance thermometer, thermocouple, liquid-in-glass thermometer including maximum and minimum thermometer and clinical thermometer.

Pyrometer should be mentioned.

Celsius and Absolute scales of temperature.

Kelvin and degree Celsius as units of temperature. Use of the Kinetic theory to explain effects of heat.

Qualitative and quantitative treatment.

Consequences and applications of expansions.

Expansion in buildings and bridges, bimetallic strips, thermostat, over-head cables causing sagging and in railway lines causing buckling.

Real and apparent expansion of liquids. Anomalous expansion of water.

(d) Heat transfer –

Conduction, convection and radiation

(e) The gas laws-Boyle’s law, Charles’ law, pressure law and general gas law

(f) Measurement of heat energy:

(i) Concept of heat capacity

(ii) Specific heat capacity

(g) Latent heat

(i) Concept of latent heat

(ii) Melting point and boiling point

(iii) Specific latent heat of fusion and of vaporization Per kelvin (K-1) as the unit of expansivity.

Use of the kinetic theory to explain the modes of heat transfer. Simple experimental illustrations. Treatment should include the explanation of land and sea breezes, ventilation and applications in cooling devices. The vacuum flask. The laws should be verified using simple apparatus. Use of the kinetic theory to explain the laws. Simple problems may be set.

Use of the method of mixtures and the electrical method to determine the specific heat capacities of solids and liquids. Land and sea breezes related to the specific heat capacity of water and land, Jkg-1 K-1 as unit of specific heat capacity.

Explanation and types of latent heat.

Determination of the melting point of a solid and the boiling point of a liquid. Effects of impurities and pressure on melting and boiling points. Application in pressure cooker.

Use of the method of mixtures and the electrical method to determine the specific latent heat of fusion of ice and of vaporization of steam. Applications in refrigerators and air conditioners.

Jkg-1 as unit of specific latent heat.

(h) Evaporation and boiling

(i) Vapour and vapour pressure

(j) Humidity, relative humidity and dew point

(k) Humidity and the weather

Effect of temperature, humidity, surface area and draught on evaporation to be discussed.

Explanation of vapour and vapour pressure. Demonstration of vapour pressure using

simple experiments. Saturated vapour pressure and its relation to boiling.

Measurement of dew point and relative humidity. Estimation of humidity of the atmosphere using wet and dry-bulb hygrometer. Formation of dew, fog and rain.

17. Production and propagation of waves

(a) Production and propagation of mechanical waves

(b) Pulsating system: Energy transmitted with definite speed, frequency and wavelength

(c) Waveform

(d) Mathematical relationship connecting frequency (f), wavelength (), period (T) and velocity (v)

18. Types of waves

(a) Transverse, longitudinal and stationary waves

(b) Mathematical representation of wave motion.

19. Properties of waves:

Reflection, refraction, diffraction, interference, superposition of progressive waves producing standing/stationary waves.

20. Light waves

(a) Sources of light

Use of ropes and springs (slinky) to generate mechanical waves.

Use of ripple tank to show water waves and to demonstrate energy propagation by waves.

Hertz (Hz) as unit of frequency.

Description and graphical representation.

Amplitude, wavelength, frequency and period.

Sound and light as wave phenomena.

v = f and T = 1. Simple problems may be set.

Examples to be given.

Equation y = A sin (wt+ 2 x) to be explained

Questions on phase difference will not be set.

Ripple tank should be extensively used to demonstrate these properties with plane and circular waves. Explanation of the properties.

Natural and artificial. Luminous and non-luminous bodies.

(b) Rectilinear propagation of light

(c) Reflection of light at plane surface: plane mirror

(d) Reflection of light at curvedsurfaces: concave and convex mirrors

(e) Refraction of light at plane surfaces: rectangular glass prism (block) and triangular prism.

(f) Refraction of light at curved surfaces: Converging and diverging lenses

Formation of shadows and eclipse. Pinhole camera. Simple numerical problems may be set.

Regular and irregular reflection. Verification of laws of reflection. Formation of images.

Inclined plane mirrors. Rotation of mirrors. Applications in periscope, sextant and kaleidoscope.

Laws of reflection. Formation of images. Characteristics of images. Use of mirror formulae: 1 + 1 = 1 and magnification m = v to solve u v f u numerical problems (Derivation of formulae is not required)

Experimental determination of the focal length of concave mirror. Applications in searchlight, parabolic and driving mirrors, car headlamps, etc. Laws of refraction. Formation of images, Real

and Apparent depth. Critical angle and total internal reflection. Lateral displacement and

angle of deviation. Use of minimum deviation equation:

sin (A + D m)

= 2

sin A/2

(Derivation of the formula is not required)

Applications: periscope, prism binoculars, optical fibres. The mirage.

Formation of images. Use of lens formulae 1 + 1 = 1 and magnification v to solve u v f u numerical problems.

(g) Application of lenses in optical instruments.

(h) Dispersion of white light by a triangular glass prism.

21. Electromagnetic waves:

Types of radiation in electromagnetic spectrum

22. Sound Waves

(a) Sources of sound

(b) Transmission of sound waves

(c) Speed of sound in solid, liquid and air

(d) Echoes and reverberation

(e) Noise and music

(f) Characteristics of sound (Derivation of the formulae not required).

Experimental determination of the focal length of converging lens. Power of lens in dioptres D. Simple camera, the human eye, film projector, simple and compound microscopes, terrestrial

and astronomical telescopes. Angular magnification. Prism binoculars. The structure and function of the camera and the human eye should be compared. Defects of the human eye and their corrections.

Production of pure spectrum of a white light. Recombination of the components of the spectrum. Colour of objects. Mixing coloured lights. Elementary description and uses of various types of radiation: Radio, infrared, visible light, ultra-violet, X-rays, gamma rays. Experiment to show that a material medium is required. To be compared. Dependence of velocity of sound on temperature and pressure to be considered.

Use of echoes in mineral exploration, and determination of ocean depth. Thunder and multiple reflections in a large room as examples of reverberation. Pitch, loudness and quality

(g) Vibration in strings

(h) Forced vibration

(i) Resonance

(ii) Harmonics and overtones

(i) Vibration of air in pipe – open and closed pipes

The use of sonometer to demonstrate the dependence of frequency (f) on length (l), tension (T) and linear density (m) of string should be treated. Use of the formula: fo = 1 T: 2lM in solving simple numerical problems. Applications in stringed instruments e.g. guitar, piano, harp, violin etc.

Use of resonance boxes and sonometer to illustrate forced vibration. Use of overtones to explain the quality of a musical note. Applications in percussion instruments e.g. drum, bell, cymbals, xylophone, etc.

Measurement of velocity of sound in air or frequency of tuning fork using the resonance tube. Use of the relationship v = f in solving numerical problems. End correction is expected. Applications in wind instruments e.g. organ, flute, trumpet, horn, clarinet, saxophone, etc.

PART IV (FIELDS)

23. Description and property of fields.

(a) Concept of fields: Gravitational, electric and magnetic

(b) Properties of a force field

24. Gravitational field

(a) Acceleration due to gravity, (g)

(b) Gravitational force between two masses: Newton’s law of gravitation

(c) Gravitational potential and escape velocity.

25. Electric Field

(1) Electrostatics

(a) Production of electric charges

(b) Types of distribution of charges

(c) Storage of charges

(d) Electric lines of force

Use of compass needle and iron filings to show magnetic field lines. g as gravitational field intensity should be mentioned, g = F/m. Masses include protons, electrons and planets. Universal gravitational constant (G).

Relationship between ‘G’ and ‘g’. Calculation of the escape velocity of a rocket from the earth’s gravitational field. Production by friction, induction and contact. A simple electroscope should be used to detect and compare charges on differently-shaped bodies. Application in light conductors. Determination, properties and field patterns of charges.

(e) Electric force between point charges: Coulomb’s law

(f) Concepts of electric field, electric field intensity

(potential gradient) and electric potential.

(g) Capacitance – Definition, arrangement and application

(2) Current electricity

(a) Production of electric current from primary and secondary cells

(b) Potential difference and electric current

(c) Electric circuit

(d) Electric conduction through materials

(e) Electric energy and power

Permitivity of a medium. Calculation of electric field intensity and electric potential of simple systems. Factors affecting the capacitance of a parallel – plate capacitor. The farad (F) as unit of

capacitance. Capacitors in series and in parallel. Energy stored in a charged capacitor. Uses of

capacitors e.g. in radio, T.V. etc. (Derivation of formulae for capacitance is not required). Simple cell and its defects. Daniell cell, Leclanché cell (wet and dry). Lead-acid accumulator, Alkaline-cadium cell. E.m.f. of a cell, the volt (V) as unit of e.m.f.

Ohm’s law and resistance. Verification of Ohm’s law. The volt (V), ampere (A) and ohm () as units of p.d., current and resistance respectively.

Series and parallel arrangements of cells and resistors. Lost volt and internal resistance of batteries.

Ohmic and non ohmic conductors. Examples should be given.

Quantitative definition of electrical energy and power. Heating effect of electrical energy and its application. Conversion of electrical energy to mechanical energy e.g. electric motors. Conversion of solar energy to electrical and heat energies e.g. solar cells, solar heaters, etc.

(f) Shunt and multiplier

(g) Resistivity and Conductivity

(h) Measurement of electric current, potential difference, resistance, e.m.f. and internal resistance of

a cell.

26. Magnetic field

(a) Properties of magnets; Magnetic materials.

(b) Magnetization and de-magnetization

(c) Concept of magnetic field

(d) Force on a current-carrying conductor placed in a magnetic field and between two parallel current-carrying conductors

(e) Use of electromagnets

(f) Earth’s magnetic field

(g) Magnetic force on a moving charged particle

27. Electromagnetic field

(a) Concept of electromagnetic field. Use in conversion of a galvanometer into an ammeter or a voltmeter. Factors affecting the electrical resistance of a material should be treated. Simple problems may be set. Principle of operation and use of ammeter, voltmeter, potentiomete1, metre bridge, and

wheatstone bridge. Practical examples such as soft iron, steel and alloys.

Temporary and permanent magnets. Comparison of iron and steel as magnetic materials. Magnetic flux and magnetic flux density. Magnetic field around a permanent magnet, a current-carrying conductor and a solenoid. Plotting of lines of force to locate neutral points. Units of magnetic flux and magnetic flux density as weber (Wb) and tesla (T) respectively Qualitative treatment only. Applications: electric motor and moving-coil galvanometer. Examples in electric, bell telephone earpiece etc. Mariner’s compass. Angles of dip and declination. Solving simple problems involving the motion of a charged particle in a magnetic field. Identifying the directions of current, magnetic field and force in an electromagnetic field (Fleming’s left-hand rule).

(b) Electromagnetic induction Faraday’s law, Lenz’s law and motor-generator effect

(c) Inductance

(d) Eddy current

(e) Power transmission and distribution

28. Simple a.c. circuits

(a) Graphical representation of e.m.f. and current in an a.c. circuit.

(b) Peak and r.m.s. values Applications: Generator (d.c. and a.c.), induction coil and transformer. The principles underlying the production of direct and alternating currents should be treated. Equation E = Eo sinwt should be explained.

Explanation of inductance. Henry as unit of inductance. Energy stored in an inductor

(E = 21 LI2)

Application in radio, T.V., transformer. (Derivation of formula is not required).

A method of reducing eddy current losses should be treated. Applications in induction furnace,

speedometer, etc. Reduction of power losses in high-tension transmission lines. Household wiring system should be discussed.

Graphs of equation I =Io sin wt and E = Eo sinwt should be treated.

Phase relationship between voltage and current in the circuit elements; resistor, inductor and

capacitor.

(c) Series circuit containing resistance, inductance and capacitance

(d) Reactance and impedance

(e) Vector diagrams

(f) Resonance in an a.c. circuit

(g) Power in an a.c. circuit

Simple calculations involving a.c. circuit. (Derivation of formulae is not required.) XL and Xc should be treated. Simple numerical problems may be set. Applications in tuning of radio and T.V. should

be discussed.

ATOMIC AND NUCELAR PHYSICS

29. Structure of the atom

(a) Models of the atom

(b) Energy quantization

(c) Photoelectric effect

(d) Thermionic emission

(e) X-rays

30. Structure of the nucleus

(a) Composition of the nucleus Thomson, Rutherford, Bohr and electron-cloud (wave-mechanical) models should be discussed qualitatively. Limitations of each model. Quantization of angular momentum (Bohr) Energy levels in the atom. Colour and light frequency. Treatment should include the following: Frank-Hertz experiment, Line spectra from hot bodies, absorption spectra and spectra of discharge lamps. Explanation of photoelectric effect. Dual nature of light. Work function and threshold frequency. Einstein’s photoelectric equation and its explanation. Applications in T.V., camera, etc. Simple problems may be set. Explanation and applications. Production of X-rays and structure of X-ray tube. Types, characteristics, properties, uses and hazards of X-rays. Safety precautions. Protons and neutrons. Nucleon number (A), proton number (Z), neutron number (N) and the equation: A=Z + N to be treated. Nuclides and their notation. Isotopes.

(b) Radioactivity – Natural and artificial

(c) Nuclear reactions – Fusion and Fission

31. Wave-particle paradox

(a) Electron diffraction

(b) Duality of matter

Radioactive elements, radioactive emissions and their properties and uses. Detection of radiations by G – M counter, photographic plates, etc. should be mentioned. Radioactive decay, half-life and decay constant. Transformation of elements. Applications of radioactivity in agriculture, medicine, industry,

archaeology, etc.