WAEC WASSCE course

Physics

WAEC WASSCE

48 topics sit in this course for WAEC WASSCE.

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course outline

Topics

  • Interaction of Matter, Space & Time

    This part covers the fundamental concepts of matter, its properties, motion, and forces, laying the groundwork for understanding the physical world.

  • Concepts of Matter

    Simple structure of matter, three physical states (solid, liquid, gas). Evidence of particle nature (Brownian motion, Kinetic theory). Use of kinetic theory to explain states, pressure in gas, evaporation, boiling, cohesion, adhesion, capillarity. Comparison of crystalline and amorphous substances, including arrangement of atoms (face centred, body centred).

  • Fundamental and Derived Quantities and Units

    Fundamental quantities and their units (length, mass, time, electric current, luminous intensity, thermodynamic temperature, amount of substance; m, kg, s, A, cd, K, mol). Derived quantities and their units (volume, density, speed; m³, kgm⁻³, ms⁻¹).

  • Position, Distance and Displacement

    Concept of position as a location point using rectangular coordinates (X,Y,Z axes). Measurement of distance using string, metre rule, vernier calipers, micrometer screw gauge, noting degree of accuracy (unit m). Concept of direction using bearing, compass, protractor. Distinction between distance and displacement, emphasizing graphical location and directions by axes.

  • Mass and Weight

    Measurement of mass using lever balance and chemical/beam balance; measurement of weight using spring balance. Mention of electronic/digital balance. Kilogram (kg) as unit of mass and newton (N) as unit of weight. Distinction between mass and weight.

  • Time

    Concept of time as interval between physical events, using heart-beat, sand-clock, ticker-timer, pendulum, and stopwatch/clock. Measurement of time with second(s) as the unit.

  • Fluid at Rest

    Experimental determination of volume, density, and relative density for solids and liquids. Concept and definition of pressure in fluids. Pascal's principle and its application to hydraulic press and car brakes. Dependence of pressure on depth below a liquid surface. Atmospheric pressure, simple barometer, manometer, siphon, syringe, and pump. Determination of relative density of liquids with U-tube and Hare's apparatus. Identification of forces acting on a body partially or completely immersed in a fluid. Archimedes' principle: Use to determine relative densities of solids and liquids. Law of flotation: Conditions for a body to float, applications in hydrometer, balloons, boats, ships, submarines etc.

  • Motion

    Qualitative treatment of types of motion: Random, rectilinear, translational, rotational, circular, orbital, spin, oscillatory, with illustrations. Numerical problems on co-linear relative motion. Force as the cause of motion, including contact forces (push and pull) and non-contact (field) forces (electric, magnetic, gravitational pull). Solid friction: static and dynamic, coefficients of limiting friction and their determinations, advantages and disadvantages, methods of reducing friction (ball bearings, rollers, streamlining, lubrication). Viscosity (friction in fluids): Definition and effects, simple explanation as extension of fluid friction, application in lubrication qualitatively treated, terminal velocity and its determination. Simple ideas of circular motion: Experiments demonstrating vertical/horizontal circular motion, difference between angular speed and velocity. Diagram to illustrate centripetal force. Qualitative discussion of banking of roads in reducing sideways friction.

  • Speed and Velocity

    Concept of speed as change of distance with time. Concept of velocity as change of displacement with time (unit ms⁻¹). Use of ticker-timer or similar devices to determine speed/velocity. Definition of velocity as Δs/Δt. Uniform/non-uniform speed/velocity. Distance/displacement-time graph: Determination of instantaneous speed/velocity from graphs and by calculation.

  • Rectilinear Acceleration

    Concept of acceleration/deceleration as increase/decrease in velocity with time (unit ms⁻²). Uniform/non-uniform acceleration. Use of ticker timer or similar devices to determine acceleration. Definition of acceleration as Δv/Δt. Velocity-time graph: Determination of acceleration and displacement from graphs. Equations of motion with constant acceleration, use in numerical problems, and motion under gravity as a special case.

  • Scalars and Vectors

    Concept of scalars as physical quantities with magnitude but no direction (e.g., mass, distance, speed, time). Concept of vectors as physical quantities with both magnitude and direction (e.g., weight, displacement, velocity, acceleration). Vector representation. Addition of vectors: Use of force board to determine the resultant of two forces. Resolution of vectors. Resultant velocity using vector representation (analytically and graphically).

  • Equilibrium of Forces

    Principle of moments: Torque/Moment of force, simple treatment of a couple (e.g., turning water tap, corkscrew, steering wheel). Conditions for equilibrium of rigid bodies under parallel and non-parallel forces: Use of force board for resultant and equilibrant forces, resolution into perpendicular directions, composition of forces, parallelogram of forces, triangle of forces. Centre of gravity and stability: Experimental treatment, including stable, unstable, and neutral equilibra.

  • Simple Harmonic Motion (S.H.M.)

    Illustration, explanation, and definition of S.H.M. using a loaded test-tube, simple pendulum, spiral spring, and bifilar suspension. Speed and acceleration of S.H.M., relating linear and angular speeds/accelerations. Period, frequency, and amplitude of a body executing S.H.M. Experimental determination of 'g' with simple pendulum and helical spring (theory but not formula derivation). Energy of S.H.M. with simple problems. Forced vibration and resonance. Distinction between inertia mass and weight.

  • Newton's Laws of Motion

    First Law: Inertia of rest and inertia of motion. Second Law: Force, acceleration, momentum, and impulse. Use of timing devices (e.g., ticker-timer) to determine acceleration and relationship when accelerating force is constant. Linear momentum and its conservation, including collision of elastic bodies in a straight line. Third Law: Action and reaction, with applications like recoil of a gun, jet and rocket propulsions.

  • Energy: Mechanical and Heat

    This section explores various forms of energy, work, power, and detailed aspects of heat energy, including temperature, transfer, and gas laws.

  • Energy

    Examples of various forms of energy (e.g., mechanical (potential and kinetic), heat, chemical, electrical, light, sound, nuclear). World energy resources: Brief discussion of renewable (e.g., solar, wind, tides, hydro, ocean waves) and non-renewable (e.g., petroleum, coal, nuclear, biomass) sources. Statement of the principle of conservation of energy and its use in explaining energy transformations.

  • Work, Energy and Power

    Concept of work as a measure of energy transfer (unit joule (J)). Concept of energy as capability to do work (unit joule (J), KWh for electrical consumption). Work done in a gravitational field (lifting a body and by falling bodies). Types of mechanical energy (Potential energy (P.E.) and Kinetic energy (K.E.), derivation of P.E. and K.E. expected to be known, identification of types of energy possessed by a body under given conditions). Conservation of mechanical energy and its verification. Concept of power as time rate of doing work (unit watt (W)). Application of mechanical energy-machines: Levers, pulleys, inclined plane, wedge, screw, wheel and axle, gears. Treatment of force ratio (F.R), mechanical advantage (M.A), velocity ratio (V.R) and efficiency of each machine. Identification of simple machines within complicated machines (e.g., bicycle). Effects of friction on machines and methods of reducing it.

  • Heat Energy

    Temperature and its measurement: Concept of temperature as degree of hotness or coldness. Construction and graduation of a simple thermometer. Properties of thermometric liquids. Specific thermometers to be treated: Constant-volume gas thermometer, resistance thermometer, thermocouple, liquid-in-glass thermometer (including maximum and minimum thermometer and clinical thermometer), pyrometer to be mentioned. Celsius and Absolute scales of temperature, Kelvin and degree Celsius as units. Effects of heat on matter (Kinetic theory explanation): Rise in temperature, change of phase state, expansion, change of resistance, change of colour, thermionic emission, change in chemical properties. Thermal expansion: Linear, area and volume expansivities (qualitative and quantitative treatment). Consequences and application of expansions in buildings and bridges, bimetallic strips, thermostat, over-head cables (sagging), and railway lines (buckling). Real and apparent expansion of liquids. Anomalous expansion of water. Unit of expansivity: Per Kelvin (K⁻¹). Heat transfer: Conduction, convection and radiation. Use of the kinetic theory to explain modes of heat transfer. Simple experimental illustrations. Explanation of land and sea breezes, ventilation, and applications in cooling devices. The vacuum flask. The gas laws: Boyle's law, Charles' law, pressure law and general gas law. Verification using simple apparatus. Use of the kinetic theory to explain the laws. Simple problems may be set. Mention of safety air bags in vehicles. Measurement of heat energy: Concept of heat capacity and specific heat capacity. 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. Unit of specific heat capacity: Jkg⁻¹K⁻¹. Latent heat: Concept and types of latent heat. Melting point and boiling point: Determination, effects of impurities and pressure, application in pressure cooker. Specific latent heat of fusion and of vaporization: Use of method of mixtures and electrical method to determine for ice and steam. Applications in refrigerators and air conditioners. Unit of specific latent heat: Jkg⁻¹. Evaporation and boiling: Effect of temperature, humidity, surface area and draught on evaporation. Vapour and vapour pressure: Explanation, demonstration using simple experiments. Saturated vapour pressure and its relation to boiling. Humidity, relative humidity and dew point: Measurement of dew point and relative humidity. Estimation of atmospheric humidity using wet and dry-bulb hygrometer. Humidity and the weather: Formation of dew, fog and rain.

  • Waves

    This module examines the production, propagation, and properties of waves, focusing on light and sound waves and the electromagnetic spectrum.

  • Production and Propagation of Waves

    Production and propagation of mechanical waves using ropes and springs (slinky). Pulsating system: Energy transmitted with definite speed, frequency and wavelength. Use of ripple tank to show water waves and demonstrate energy propagation. Hertz (Hz) as unit of frequency. Waveform: Description and graphical representation, amplitude, wave length, frequency and period. Sound and light as wave phenomena. Mathematical relationship connecting frequency (f), wavelength(λ), period (T) and velocity (v): V= fλ and T = 1/f; simple problems may be set.

  • Types of Waves

    Examples of transverse and longitudinal waves. Mathematical representation of wave motion: Equation y = A sin (wt ± 2πx/λ) to be explained (questions on phase difference will not be set). Extensive use of ripple tank to demonstrate wave properties with plane and circular waves, including explanation of these properties.

  • Properties of Waves

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

  • Light Waves

    Sources of light: Natural and artificial, luminous and non-luminous bodies. Rectilinear propagation of light: Formation of shadows and eclipse, pinhole camera (simple numerical problems). Reflection of light at plane surface (plane mirror): Regular and irregular reflections, verification of laws of reflection, formation of images, inclined plane mirrors, rotation of mirrors. Applications in periscope, sextant and kaleidoscope. Reflection of light at curved surfaces (concave and convex mirrors): Laws of reflection, formation of images, characteristics of images. Use of mirror formulae: 1/u + 1/v = 1/f and magnification m = v/u to solve numerical problems (derivation not required). Experimental determination of the focal length of concave mirror. Applications in searchlight, parabolic and driving mirrors, car headlamps etc. Refraction of light at plane surfaces (rectangular glass prism/block and triangular prism): Laws of refraction, formation of images, real and apparent depths, critical angle and total internal reflection, lateral displacement and angle of deviation. Use of minimum deviation equation: μ = Sin (A + Dm)/2 / Sin A/2 (derivation not required). Applications: periscope, prism binoculars, optical fibres. The mirage. Refraction of light at curved surfaces (converging and diverging lenses): Formation of images. Use of lens formulae 1/u + 1/v = 1/f and magnification m = v/u to solve numerical problems (derivation not required). Experimental determination of the focal length of converging lens. Power of lens in dioptres (D). Application of lenses in optical instruments: Simple camera, the human eye, film projector, simple and compound microscopes, terrestrial and astronomical telescopes. Angular magnification. Prism binoculars. Comparison of structure and function of the camera and the human eye. Defects of the human eye and their corrections. Dispersion of white light by a triangular glass prism: Production of pure spectrum, recombination of components, colours of objects, mixing coloured lights.

  • Electromagnetic Waves

    Elementary description and uses of various types of radiation in the electromagnetic spectrum: Radio, infrared, visible light, ultra-violet, X-rays, gamma rays.

  • Sound Waves

    Sources of sound. Transmission of sound waves: Experiment to show material medium is required. Speed of sound in solid, liquid and air (comparison, dependence on temperature and pressure). Echoes and reverberation: Use of echoes in mineral exploration and ocean depth determination. Thunder and multiple reflections as examples of reverberation. Noise and music. Characteristics of sound: Pitch, loudness and quality. Vibration in strings: Use of sonometer to demonstrate dependence of frequency (f) on length (l), tension (T) and mass per unit length (m) of string. Use of formula: f₀ = (1/(2l))√(T/m) in solving simple numerical problems. Applications in stringed instruments (e.g., guitar, piano, harp, violin). Forced vibration: Use of resonance boxes and sonometer. Resonance. Harmonies and overtones: Use of overtones to explain quality of musical note. Applications in percussion instruments (e.g., drum, bell, cymbals, xylophone). Vibration of air in pipes (open and closed pipes): Measurement of velocity of sound in air or frequency of tuning fork using resonance tube. Use of relationship v = fλ in solving numerical problems. End correction to be mentioned. Applications in wind instruments (e.g., organ, flute, trumpet, horn, clarinet, saxophone).

  • Fields

    This part introduces the concepts of gravitational, electric, and magnetic fields, their properties, and applications in electrostatics and current electricity.

  • Description and Properties of Fields

    Concept of fields: Gravitational, electric and Magnetic. Properties of a force field: Use of compass needle and iron filings to show magnetic field lines.

  • Gravitational Field

    Acceleration due to gravity, (g): G as gravitational field intensity, g = F/m. Gravitational force between two masses: Newton's law of gravitation, including protons, electrons and planets. Universal gravitational constant (G) and relationship between 'G' and 'g'. Gravitational potential and escape velocity: Calculation of escape velocity of a rocket from the earth's gravitational field.

  • Electric Field - Electrostatics

    Production of electric charges by friction, induction and contact. Types of distribution of charges: Simple electroscope to detect and compare charges on differently-shaped bodies. Storage of charges: Application in light conductors. Electric lines of force: Determination, properties and field patterns of charges. Electric force between point charges: Coulomb's law, permittivity of a medium. Concepts of electric field, electric field intensity (potential gradient) and electric potential: Calculation for simple systems. Capacitance: Definition, arrangement and application. 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 and Television (derivation of formulae not required).

  • Electric Field - Current Electricity

    Production of electric current from primary and secondary cells: Simple cell and its defects, Daniel cell, Lechanché cell (wet and dry). Lead-acid accumulator. Alkalne-cadium cell. E.m.f. of a cell, the volt (V) as unit of e.m.f. Potential difference and electric current: Ohm's law and resistance, verification of Ohm's law. The volt (V), ampere (A) and ohm (Ω) as units of p.d., current and resistance respectively. Electric circuit: Series and parallel arrangement of cells and resistors. Lost volt and internal resistance of batteries. Electric conduction through materials: Ohmic and non-ohmic conductors (examples like metals vs. semiconductors). Electric energy and power: Quantitative definition of electrical energy and power. Heating effect of an electric current 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). Shunt and multiplier: Use in conversion of a galvanometer into an ammeter and a voltmeter. Resistivity and Conductivity: Factors affecting the electrical resistance of a material; simple problems may be set. Measurement of electric current, potential difference, resistance, e.m.f. and internal resistance of a cell: Principle of operation and use of ammeter, voltmeter, potentiometer, the Wheatstone bridge and metre bridge.

  • Magnetic Field

    Properties of magnets and magnetic materials (practical examples such as soft iron, steel and alloys). Magnetization and demagnetization: Temporary and permanent magnets, comparison of iron and steel as magnetic materials. Concept of magnetic field: Magnetic flux and magnetic flux density. Magnetic field around a permanent magnet, a current-carrying conductor and a solenoid. Plotting of line of force to locate neutral points. Units of magnetic flux and magnetic flux density as weber (Wb) and tesla (T) respectively. Magnetic force on: a current-carrying conductor placed in a magnetic field (qualitative treatment, applications: electric motor and moving-coil galvanometer); between two parallel current-carrying conductors (examples in electric bell, telephone earpiece etc.). Use of electromagnets. The earth's magnetic field: Mariner's compass, angles of dip and declination. Magnetic force on a moving charged particle: Solving simple problems involving the motion of a charged particle in a magnetic field, using F=qvB sin θ.

  • Electromagnetic Field

    Concept of electromagnetic field: Identifying the directions of current, magnetic field and force in an electromagnetic field (Fleming's left-hand rule). Electromagnetic induction: Applications include Generator (d.c. and a.c.), induction coil and transformer. Principles underlying the production of direct and alternating currents should be treated. Equation E = E₀ sinwt should be explained. Faraday's law, Lenz's law and motor-generator effect. Inductance: Qualitative explanation of self and mutual inductance. The unit of inductance is henry (H). (E = ½ LI²), application in radio, T.V., transformer (derivation of formula not required). Eddy currents: A method of reducing eddy current losses should be treated. Applications in induction furnace, speedometer, etc. Power transmission and distribution: Reduction of power losses in high-tension transmission lines. Household wiring system should be discussed.

  • Simple A.C. Circuits

    Graphical representation of e.m.f and current in an a.c. circuit: Graphs of equation I – I₀ sin wt and E = E₀ sinwt should be treated. Peak and r.m.s. values. Phase relationship between voltage and current in the circuit elements; resistor, inductor and capacitor. Series circuit containing resistor, inductor and capacitor: Simple calculations involving a.c. circuit (derivation of formulae not required). Reactance and impedance: X_L and X_C should be treated; simple numerical problems may be set. Vector diagrams. Resonance in an a.c. circuit: Applications in tuning of radio and T.V. should be discussed. Power in an a.c. circuit.

  • Atomic and Nuclear Physics

    This module covers the structure of the atom and nucleus, radioactivity, nuclear reactions, and the wave-particle duality of matter.

  • Structure of the Atom

    Models of the atom: Thomson, Rutherford, Bohr and electron-cloud (wave-mechanical) models should be discussed qualitatively, including their limitations. Quantization of angular momentum (Bohr). Energy quantization: Energy levels in the atom, colour and light frequency. Treatment should include: Frank-Hertz experiment, Line spectra from hot bodies, absorption spectra and spectra of discharge lamps. Photoelectric effect: Explanation, dual nature of light, work function and threshold frequency. Einstein's photoelectric equation and its explanation. Application in T.V., camera, etc. (simple problems may be set). Thermionic emission: Explanation and applications. X-rays: Production of X-rays and structure of X-ray tube. Types, characteristics, properties, uses and hazards of X-rays, including safety precautions.

  • Structure of the Nucleus

    Composition of the nucleus: 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. Radioactivity: Natural and artificial. Radioactive elements, radioactive emissions (α,β, γ) 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. Nuclear reactions: Fusion and Fission. Distinction between fusion and fission. Binding energy, mass defect and energy equation: E=Δmc². Nuclear reactors. Atomic bomb. Radiation hazards and safety precautions. Peaceful uses of nuclear reactions.

  • Wave-Particle Paradox

    Electron diffraction. Duality of matter: Simple illustration of the dual nature of light.

  • Harmonised Topics for Structured Questions

    This section outlines additional topics for short structured questions, including advanced concepts in mechanics, material properties, and electronics.

  • Derived Quantities and Dimensional Analysis

    Fundamental quantities and units (e.g., Length, mass, time, electric current, luminous intensity etc., m, kg,s, A, cd, etc. as their respective units). Derived quantities and units (e.g., volume, density, speed etc. m³, kgm⁻³, ms⁻¹ etc. as their respective units). Explanation of dimensions in terms of fundamental and derived quantities. Uses of dimensions: to verify dimensional correctness of a given equation, to derive the relationship between quantities, to obtain derived units.

  • Projectile Motion

    Concept of projectiles as an object thrown/released into space. Applications of projectiles in warfare, sports etc. Simple problems involving range, maximum height and time of flight may be set.

  • Satellites and Rockets

    Meaning of a satellite, comparison of natural and artificial satellites. Parking orbits, Geostationary satellites and period of revolution and speed of a satellite. Uses of satellites and rockets.

  • Elastic Properties of Solids

    Hooke's law, Young's modulus and work done in springs and string. Behaviour of elastic materials under stress – features of load - extension graph. Simple calculations on Hook's law and Young's modulus. Thermal conductivity: Solar energy collector and Black body Radiation. Solar energy: solar panel for heat energy supply. Explanation of a blackbody. Variation of intensity of black body radiation with wavelength at different temperatures.

  • Fibre Optics

    Explanation of concept of fibre optics. Principle of transmission of light through an optical fibre. Applications of fibre optics e.g. local area networks (LAN), medicine, sensing devices, carrying laser beams etc.

  • Introduction to LASER

    Meaning of LASER. Types of LASERS (Solid state, gas, liquid and semi-conductor LASERS). Application of LASERS (in Scientific research, communication, medicine, military technology, Holograms etc.). Dangers involved in using LASERS.

  • Electrical Conduction through Materials (Electronics)

    Distinction between conductors, semiconductors and insulators in terms of band theory. Semi conductor materials (silicon and germanium). Meaning of intrinsic semiconductors. Charge carriers. Doping: production of p-type and n-type extrinsic semiconductors. Junction diode: forward and reverse biasing, voltage characteristics. Uses of diodes: Half and full wave rectification.

  • Wave-Particle Paradox

    Electron diffraction. Duality of matter. Simple illustrations of dual nature of light.