Sample WAEC-style Practice Questions (Original Content)
WAEC Style
Question 1
Which of the following represents the correct dimensions of the Universal Gravitational Constant (G)?
A. M^-1 L^3 T^-2
B. M L^2 T^-2
C. M L T^-2
D. M^2 L^3 T^-1
Answer: A. M^-1 L^3 T^-2
Explanation: From F = G m1 m2 / r^2, we get G = F r^2 / m1 m2. Substituting dimensions: (MLT^-2 * L^2) / M^2 = M^-1 L^3 T^-2.
Question 2
Which of the following is a fundamental quantity?
A. Electric Charge
B. Thermodynamic Temperature
C. Potential Difference
D. Resistance
Answer: B. Thermodynamic Temperature
Explanation: Temperature (measured in Kelvin) is one of the seven base/fundamental quantities in the S.I. system.
Question 3
A body is projected with a velocity of 40 m/s at an angle of 30 degrees to the horizontal. Calculate the time taken to reach the maximum height. (g = 10 m/s^2)
A. 2.0 s
B. 4.0 s
C. 2.5 s
D. 8.0 s
Answer: A. 2.0 s
Explanation: Time to reach max height t = (u * sin theta) / g. t = (40 * sin 30) / 10 = (40 * 0.5) / 10 = 2 seconds.
Question 4
The slope of a displacement-time graph represents:
A. Acceleration
B. Velocity
C. Momentum
D. Force
Answer: B. Velocity
Explanation: Slope = Change in displacement / Change in time = Velocity.
Question 5
A car of mass 800kg moves round a circular track of radius 40m with a speed of 20 m/s. Calculate the centripetal force acting on the car.
A. 4,000 N
B. 8,000 N
C. 16,000 N
D. 2,000 N
Answer: B. 8,000 N
Explanation: Force F = (m * v^2) / r. F = (800 * 20^2) / 40 = (800 * 400) / 40 = 8,000 N.
Question 6
The weight of a body at the center of the Earth is:
A. Infinite
B. Same as on the surface
C. Zero
D. Twice its surface weight
Answer: C. Zero
Explanation: At the center of the Earth, gravitational pull from all directions cancels out, making g = 0.
Question 7
A force of 100N is applied to a box at an angle of 60 degrees to the horizontal. Calculate the horizontal component of the force.
A. 50 N
B. 86.6 N
C. 100 N
D. 200 N
Answer: A. 50 N
Explanation: Fx = F * cos(theta) = 100 * cos(60) = 100 * 0.5 = 50 N.
Question 8
Which of the following will reduce friction between two surfaces?
A. Increasing the normal reaction
B. Roughening the surfaces
C. Using ball bearings
D. Increasing the surface area
Answer: C. Using ball bearings
Explanation: Ball bearings replace sliding friction with rolling friction, which is much smaller.
Question 9
In simple harmonic motion, the kinetic energy of the system is maximum at the:
A. Point of maximum displacement
B. Equilibrium position
C. Extreme positions
D. Middle of the amplitude
Answer: B. Equilibrium position
Explanation: At the equilibrium position, velocity is maximum, and therefore kinetic energy is maximum.
Question 10
A ball of mass 0.5kg moving at 4 m/s collides with a stationary ball of mass 0.5kg. If they stick together after collision, calculate their common velocity.
A. 4 m/s
B. 2 m/s
C. 1 m/s
D. 0 m/s
Answer: B. 2 m/s
Explanation: m1 u1 + m2 u2 = (m1 + m2)v. (0.5 * 4) + 0 = (0.5 + 0.5)v. 2 = 1 * v. v = 2 m/s.
Question 11
The Velocity Ratio (V.R.) of a pulley system with 4 pulleys is:
A. 2
B. 4
C. 8
D. 1
Answer: B. 4
Explanation: For a block and tackle system, the V.R. is equal to the number of pulleys or the number of strings supporting the movable block.
Question 12
The property of a material to return to its original shape after being stretched is:
A. Plasticity
B. Ductility
C. Elasticity
D. Brittleness
Answer: C. Elasticity
Explanation: Elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence is removed.
Question 13
Which of the following phenomena is used in a clinical thermometer to ensure the reading remains constant after removal from the mouth?
A. Capillarity
B. A constriction in the tube
C. Low specific heat of mercury
D. Expansion of glass
Answer: B. A constriction in the tube
Explanation: The kink (constriction) prevents mercury from flowing back into the bulb until the thermometer is shaken.
Question 14
The pressure at a point in a liquid at a depth of 5m is 50,000 Pa. What is the pressure at a depth of 15m in the same liquid?
A. 100,000 Pa
B. 150,000 Pa
C. 200,000 Pa
D. 25,000 Pa
Answer: B. 150,000 Pa
Explanation: Pressure P is directly proportional to depth h (P = h * rho * g). If depth triples (5 to 15), pressure triples. 50,000 * 3 = 150,000 Pa.
Question 15
The heat required to change 100g of ice at 0 degrees Celsius to water at 0 degrees Celsius is: (Latent heat of fusion of ice = 336,000 J/kg)
A. 33,600 J
B. 3,360 J
C. 336,000 J
D. 33.6 J
Answer: A. 33,600 J
Explanation: Q = m * L. Convert mass to kg: 100g = 0.1kg. Q = 0.1 * 336,000 = 33,600 Joules.
Question 16
Which of the following modes of heat transfer does not require a material medium?
A. Conduction
B. Convection
C. Radiation
D. Evaporation
Answer: C. Radiation
Explanation: Radiation travels via electromagnetic waves, which can pass through a vacuum.
Question 17
Real expansivity of a liquid is the sum of apparent expansivity and the expansivity of the:
A. Environment
B. Thermometer
C. Container
D. Atmosphere
Answer: C. Container
Explanation: Gamma-real = Gamma-apparent + Gamma-vessel (container).
Question 18
A gas has a volume of 100 cm^3 at a pressure of 2 atm. What is its volume when the pressure is increased to 5 atm at constant temperature?
The temperature at which the water vapor in the air is just sufficient to saturate it is the:
A. Boiling point
B. Dew point
C. Melting point
D. Critical point
Answer: B. Dew point
Explanation: When air is cooled to its dew point, condensation begins.
Question 20
The silvered surfaces of a vacuum flask (Thermos) reduce heat loss by:
A. Conduction
B. Convection
C. Radiation
D. Evaporation
Answer: C. Radiation
Explanation: Shiny/silvered surfaces are poor emitters and good reflectors of radiant heat.
Question 21
Which of the following is an example of a transverse wave?
A. Sound waves in air
B. Water waves
C. Waves in a compressed spring
D. Ultrasound waves
Answer: B. Water waves
Explanation: Water waves vibrate perpendicular to the direction of travel. Sound and compressed springs are longitudinal.
Question 22
The number of images formed by two plane mirrors inclined at an angle of 60 degrees to each other is:
A. 6
B. 5
C. 4
D. 7
Answer: B. 5
Explanation: Number of images n = (360 / theta) - 1. n = (360 / 60) - 1 = 6 - 1 = 5.
Question 23
A ray of light passes from air into a medium of refractive index 1.5. If the angle of incidence is 45 degrees, calculate the sine of the angle of refraction.
Which of the following is true about a convex mirror?
A. It always forms a virtual and diminished image
B. It forms a real and magnified image
C. It forms a virtual and magnified image
D. It is used as a dentist's mirror
Answer: A. It always forms a virtual and diminished image
Explanation: Convex mirrors diverge light rays and always produce upright, virtual, and smaller images, providing a wide field of view.
Question 25
The speed of sound in air is 340 m/s. Calculate the wavelength of a sound wave with a frequency of 1700 Hz.
A. 0.2 m
B. 2.0 m
C. 5.0 m
D. 0.5 m
Answer: A. 0.2 m
Explanation: v = f * lambda. 340 = 1700 * lambda. lambda = 340 / 1700 = 0.2 m.
Question 26
Polarization is a property that can only be exhibited by ______ waves.
A. Sound
B. Longitudinal
C. Transverse
D. Stationary
Answer: C. Transverse
Explanation: Only waves that vibrate perpendicular to the direction of travel can be restricted to a single plane (polarized).
Question 27
A converging lens of focal length 15cm forms an image at a distance of 30cm from the lens. Calculate the object distance.
A. 15 cm
B. 30 cm
C. 10 cm
D. 45 cm
Answer: B. 30 cm
Explanation: 1/f = 1/u + 1/v. 1/15 = 1/u + 1/30. 1/u = 1/15 - 1/30 = 1/30. u = 30cm.
Question 28
The colors of the visible spectrum in increasing order of frequency are:
A. VIBGYOR
B. ROYGBIV
C. BIVROYG
D. GYORBIV
Answer: B. ROYGBIV
Explanation: Red has the lowest frequency (longest wavelength) and Violet has the highest frequency (shortest wavelength).
Question 29
A note produced by a piano has the same frequency as a note produced by a guitar, yet they sound different. This is due to difference in:
A. Pitch
B. Loudness
C. Quality (Timbre)
D. Intensity
Answer: C. Quality (Timbre)
Explanation: Quality or Timbre depends on the overtones (harmonics) produced by the instrument.
Question 30
For a person with hypermetropia, the image of a near object is formed:
A. On the retina
B. In front of the retina
C. Behind the retina
D. On the blind spot
Answer: C. Behind the retina
Explanation: Hypermetropia (long-sightedness) occurs when the eyeball is too short or the lens too thin.
Question 31
Which of the following particles is the carrier of electric current in a electrolyte?
A. Electrons
B. Protons
C. Ions
D. Holes
Answer: C. Ions
Explanation: In gases and electrolytes, current is carried by ions. In metals, it is carried by electrons.
Question 32
Calculate the effective resistance of two 4-ohm resistors connected in parallel.
A. 8 ohms
B. 2 ohms
C. 4 ohms
D. 1 ohm
Answer: B. 2 ohms
Explanation: 1/R = 1/4 + 1/4 = 2/4 = 1/2. R = 2 ohms.
Question 33
A 12V battery is connected to a 3-ohm resistor. Calculate the energy dissipated in 10 seconds.
A. 40 J
B. 480 J
C. 120 J
D. 360 J
Answer: B. 480 J
Explanation: Energy E = (V^2 / R) * t = (12^2 / 3) * 10 = (144 / 3) * 10 = 48 * 10 = 480 Joules.
Question 34
The purpose of the lightning conductor on a building is to:
A. Attract lightning to the building
B. Provide a safe path for charge to the ground
C. Accumulate charge from the air
D. Dispel clouds from the sky
Answer: B. Provide a safe path for charge to the ground
Explanation: It safely conducts the electrical discharge from a lightning strike to the earth, protecting the structure.
Question 35
Which of the following devices works on the principle of electromagnetic induction?
A. Electric motor
B. Transformer
C. Electric iron
D. Filament bulb
Answer: B. Transformer
Explanation: Transformers change voltage levels via mutual induction between two coils.
Note: Questions 36-50 cover magnetism, electronics, and nuclear physics.
Question 36
The horizontal component of the Earth's magnetic field is zero at the:
A. Magnetic equator
B. Magnetic poles
C. Geographic equator
D. Greenwich meridian
Answer: B. Magnetic poles
Explanation: At the poles, the magnetic field is purely vertical (angle of dip is 90 degrees).
Question 37
A galvanometer can be converted into an ammeter by connecting a:
A. High resistance in series
B. High resistance in parallel
C. Low resistance (shunt) in parallel
D. Low resistance in series
Answer: C. Low resistance (shunt) in parallel
Explanation: This allows most of the current to bypass the delicate galvanometer coil.
Question 38
Which of the following is a pentavalent impurity used to dope a semiconductor?
A. Boron
B. Aluminum
C. Indium
D. Phosphorus
Answer: D. Phosphorus
Explanation: Phosphorus has 5 valence electrons and creates an n-type semiconductor. Boron, Aluminum, and Indium are trivalent (p-type).
Question 39
The process by which an alternating current is converted to a direct current is:
A. Amplification
B. Rectification
C. Modulation
D. Induction
Answer: B. Rectification
Explanation: Diodes are commonly used as rectifiers to allow current to flow in only one direction.
Question 40
In a nuclear reactor, the purpose of the control rods (boron or cadmium) is to:
A. Speed up the neutrons
B. Absorb excess neutrons
C. Cool the reactor core
D. Reflect neutrons back into the core
Answer: B. Absorb excess neutrons
Explanation: This controls the rate of the chain reaction to prevent it from becoming explosive.
Question 41
Which of the following radiations has the shortest wavelength?
A. Gamma rays
B. X-rays
C. Ultraviolet rays
D. Infrared rays
Answer: A. Gamma rays
Explanation: Gamma rays have the highest frequency and therefore the shortest wavelength in the electromagnetic spectrum.
Question 42
The work function of a metal is 3.0 eV. Calculate the threshold frequency. (h = 6.6 x 10^-34 Js, 1 eV = 1.6 x 10^-19 J)
A. 7.27 x 10^14 Hz
B. 4.80 x 10^14 Hz
C. 2.20 x 10^15 Hz
D. 1.33 x 10^14 Hz
Answer: A. 7.27 x 10^14 Hz
Explanation: W = h * f0. (3.0 * 1.6 x 10^-19) = (6.6 x 10^-34) * f0. f0 = 4.8 x 10^-19 / 6.6 x 10^-34 = 7.27 x 10^14 Hz.
Question 43
A radioactive sample has an initial activity of 800 counts/min. If its half-life is 4 hours, what is its activity after 12 hours?
A. 200 counts/min
B. 100 counts/min
C. 400 counts/min
D. 50 counts/min
Answer: B. 100 counts/min
Explanation: 12 hours is 3 half-lives. 800 -> 400 -> 200 -> 100 counts/min.
Question 44
Which of the following particles is identical to the nucleus of a Helium atom?
A. Alpha particle
B. Beta particle
C. Gamma ray
D. Neutron
Answer: A. Alpha particle
Explanation: An alpha particle consists of 2 protons and 2 neutrons, which is a Helium-4 nucleus.
Question 45
The energy level of an atom is given by E = -13.6 / n^2 eV. Calculate the energy of the first excited state (n=2).
A. -13.6 eV
B. -3.4 eV
C. -6.8 eV
D. -27.2 eV
Answer: B. -3.4 eV
Explanation: E = -13.6 / 2^2 = -13.6 / 4 = -3.4 eV.
Question 46
The binding energy of a nucleus is the energy required to:
A. Move an electron to a higher orbit
B. Separate the nucleus into its individual nucleons
C. Start a chemical reaction
D. Ionize the atom
Answer: B. Separate the nucleus into its individual nucleons
Explanation: It is the energy equivalent to the mass defect of the nucleus.
Question 47
Which of the following describes the nature of light based on the De Broglie hypothesis?
A. Wave nature only
B. Particle nature only
C. Dual nature (wave and particle)
D. Neither wave nor particle
Answer: C. Dual nature (wave and particle)
Explanation: De Broglie proposed that all matter and radiation exhibit both wave-like and particle-like properties.
Question 48
Which of the following planets is closest to the Sun?
A. Venus
B. Mars
C. Mercury
D. Earth
Answer: C. Mercury
Explanation: The order from the sun is Mercury, Venus, Earth, Mars, etc.
Question 49
The time taken for a radioactive element to decay to half of its initial mass is the:
A. Decay constant
B. Mean life
C. Half-life
D. Period
Answer: C. Half-life
Explanation: This is a constant value for any specific radioactive isotope.
Question 50
A solar cell converts ______ energy directly into ______ energy.
A. Chemical, Electrical
B. Light, Electrical
C. Heat, Mechanical
D. Nuclear, Light
Answer: B. Light, Electrical
Explanation: Photovoltaic cells use the photoelectric effect to generate electricity from sunlight.