JAMB Physics 2018 Past Questions & Answers

The man's movement creates a right-angled triangle, with the 1km east path and the 1km north path as the two perpendicular sides. The displacement is the hypotenuse of this triangle, and its magnitude is found using Pythagoras' theorem: magnitude = $√(1² + 1²)$ = $√2$ km. The direction is the angle (θ) north of the east direction, found using tan(θ) = Opposite/Adjacent = $1/1$ = 1, which means θ = 45°. Therefore, the displacement is $√2$ km N 45°E.

Common mistake: A common mistake is to correctly calculate the magnitude but guess the angle or misapply trigonometric rules, leading to incorrect direction choices like 30° or 60°.

The key principle is that the mass of the palm oil remains constant since no oil was lost. First, calculate the mass using the initial values: Mass = Density × Volume = 0.9 g/cm³ × 400 cm³ = 360 g. Since this mass stays the same after frying, we can find the new volume using the new density: New Volume = Mass / New Density = 360 g / 0.6 g/cm³ = 600 cm³.

Common mistake: Students might mistakenly multiply the new density by the old volume (0.6 g/cm³ × 400 cm³ = 240 cm³), leading them to incorrectly choose option C.

Natural radioactivity is the process where an unstable atomic nucleus spontaneously breaks down to become more stable. In doing so, it releases energy in the form of radiation. The three main types of radiation emitted are alpha (α) particles, beta (β) particles, and gamma (γ) rays.

Common mistake: Students sometimes confuse X-rays with gamma rays because both are high-energy electromagnetic waves, but X-rays are produced by electron transitions while gamma rays are emitted from the nucleus during radioactive decay.

Option D is correct because all the statements are true definitions related to electric charge. An object becomes positively charged when it loses electrons, creating a deficit. It becomes negatively charged when it gains extra electrons, creating an excess, and electric current is defined as the flow of these charges (usually electrons) through a conductor.

Common mistake: Students may choose only one of the options like A or B because they know it is a correct statement, but they fail to verify that all the other statements are also correct.

A plane mirror forms an image with specific characteristics known by the acronym 'VUSLI': Virtual, Upright, Same size, and Laterally Inverted. The question asks for the property that does NOT describe the image. Since the image formed by a plane mirror is always the same size as the object (magnification is 1), it is never magnified (made bigger). Therefore, 'Magnified' is the incorrect description.

Common mistake: Students sometimes get confused by the term 'laterally inverted' and may incorrectly choose it, but this is a correct property describing how a mirror image swaps left and right.

To find the resultant resistance, first calculate the equivalent resistance for the parallel section. The two 2Ω resistors are in parallel, so their combined resistance is $(2 * 2)$ / $(2 + 2)$ = 4 / 4 = 1Ω. This 1Ω resistance is now in series with the 3Ω and 4Ω resistors. To get the total resistance, add the series components: 3Ω + 1Ω + 4Ω = 8Ω.

Common mistake: A common mistake is to add all the resistances together as if they are all in series $(3 + 2 + 2 + 4 = 11Ω)$, which incorrectly leads to option B.

The process starts with a steam engine, which uses heat from steam to create motion, converting heat energy into kinetic energy. This motion then drives a generator, which transforms the kinetic energy into electrical energy. Finally, the electricity powers the lamp, which converts the electrical energy into both heat and light energy, making the correct sequence Heat -> Kinetic -> Electricity -> Heat and Light.

Common mistake: Students may mistakenly choose option B, focusing on the engine's movement (kinetic energy) as the starting point, but forgetting that the heat from steam is what initially causes that movement.

Cathode rays are beams produced in a vacuum tube when a high voltage is applied across the electrodes. Experiments conducted by scientists like J.J. Thomson showed that these rays are deflected by electric and magnetic fields, proving they are made of negatively charged particles. These fundamental particles were later identified as electrons, so cathode rays are simply a stream of electrons moving at high speed.

Common mistake: Students often mistakenly choose 'High-energy electromagnetic waves' because the term 'rays' makes them think of light or X-rays, but cathode rays are streams of particles (electrons), not waves.

The splitting of white light into its different colours by a prism is a phenomenon called dispersion. This happens because when light enters the glass prism, it refracts or bends. The speed of light in glass is not the same for all colours; red light travels fastest, while violet light travels slowest. Because they have different speeds, each colour bends at a slightly different angle, causing them to separate and form a spectrum.

Common mistake: Students often confuse dispersion with total internal reflection (option D), which is a different phenomenon that can occur in a prism but does not explain the splitting of light into colours.

The efficiency of a machine is given by the formula: Efficiency = (Mechanical Advantage / Velocity Ratio) × 100%. From the diagram, the number of ropes supporting the load is 6, so the Velocity Ratio (VR) is 6. The Mechanical Advantage (MA) is Load ÷ Effort, which is 120N ÷ W. Substituting these into the formula, we get 40 = ((120/W) / 6) × 100. Solving for W gives W = $(120 × 100)$ / $(40 × 6)$ = 12000 / 240 = 50.0N.

Common mistake: Students might mistakenly calculate the effort by simply multiplying the load by the efficiency as a decimal $(120N × 0.40 = 48.0N)$, which incorrectly leads to option B.

The reaction shows two light nuclei, X and Y, combining to form a single, heavier nucleus, Z, along with the release of a neutron and energy. This process of joining or 'fusing' smaller atomic nuclei to create a larger one is the definition of a nuclear fusion reaction. This is the same type of reaction that powers the sun.

Common mistake: Students often confuse fusion with fission, but fission is the opposite process where one large, heavy nucleus splits into smaller ones.

Heat capacity is the amount of heat energy required to raise the temperature of a specific body or object by 1 Kelvin (1K). The question asks for the heat needed for a 10kg mass of copper, which is a specific body. This is the definition of heat capacity, which is the product of mass and specific heat capacity (C = mc).

Common mistake: Students often mistakenly choose 'specific heat capacity' because they confuse it with 'heat capacity', but specific heat capacity is for a unit mass (1kg), not a given mass like 10kg.

This question is based on Faraday's first law of electrolysis, which uses the formula m = ZIt, where 'm' is the mass deposited, 'Z' is the electrochemical equivalent, 'I' is the current, and 't' is the time. First, convert the time from minutes to seconds: t = 5 minutes × 60 = 300 seconds. To find the current (I), rearrange the formula to I = m / (Zt). Substituting the given values, we get I = 36.0 / $(0.0012 × 300)$, which calculates to I = 36.0 / 0.36 = 100A.

Common mistake: A common mistake is forgetting to convert the time from minutes to seconds, which leads to an incorrect calculation (36 / (0.0012 x 5) = 6000A) and choosing option A.

Shadows and eclipses are formed because light travels in a straight line, which is called rectilinear propagation. When an opaque object blocks the path of light, the light cannot bend around it, creating a dark area (a shadow) behind the object. An eclipse is simply a very large-scale shadow, like when the Moon blocks the Sun's light from reaching the Earth.

Common mistake: Students may mistakenly choose reflection or refraction because they are well-known properties of light, but these describe light bouncing off or bending through a surface, not being blocked to form a shadow.

Ohm's law states that the voltage across a conductor is directly proportional to the current flowing through it, as long as physical conditions like temperature are constant. Materials that follow this rule are called ohmic conductors. Metals are the best examples of ohmic conductors, which is why option A is correct. Other materials like diodes, electrolytes, and glass are non-ohmic because their resistance changes with the applied voltage.

Common mistake: Students may mistakenly choose 'all electrolytes' because they know electrolytes conduct electricity, but they fail to remember that their resistance is not constant, making them non-ohmic conductors.

Isotopes are atoms of the same element, so by definition, they must have the same number of protons (making statement III true). Because they have the same number of protons, a neutral atom will also have the same number of electrons, which determines their identical chemical properties (making statement I true). However, isotopes have different numbers of neutrons, which gives them different mass numbers; this physical difference in mass is the basis for separating them (making statement II true).

Common mistake: Students often choose option B, correctly identifying that isotopes share proton numbers and chemical properties, but they mistakenly believe that statement II is false, not realizing that the mass difference is a physical property used for separation.

When mass m1 is on the verge of sliding, the pulling force is equal to the limiting static friction. The pulling force is the tension in the string, which is equal to the weight of the hanging mass, T = m₂g. The limiting static friction (f) is given by f = μR, where μ is the coefficient of static friction and R is the normal reaction, which equals the weight of m1 (R = m₁g). Equating the pulling force and friction (T = f), we get m₂g = μ * m₁g, and solving for μ gives μ = m₂/m₁.

Common mistake: Students often confuse the roles of the two masses, leading them to incorrectly calculate the ratio as m₁/m₂.

A mirage is an optical illusion caused by the bending (refraction) of light. On a hot day, the air near the road is hotter and less dense than the air above, creating layers with varying refractive indices (Statement I). Light from the sky travelling towards the ground is bent upwards as it enters the less dense, hotter air, a process called total internal refraction (Statement III). An observer sees this bent light and interprets it as a reflection from a pool of water.

Common mistake: Students often mistakenly choose option D, including statement II, because it describes an observation of a mirage, but it is an effect, not a scientific explanation of how it is formed.

The diagram shows a manometer where the pressure in chamber G is greater than the atmospheric pressure, as it pushes the liquid up on the open side. The pressure of the gas is the sum of the atmospheric pressure and the pressure due to the height difference of the liquid. The height difference is 10 cm - 3 cm = 7 cm, which is 70 mm. Therefore, the pressure in chamber G is 760 mm + 70 mm = 830 mm.

Common mistake: A common mistake is to subtract the height difference from the atmospheric pressure $(760 - 70 = 690 mm)$, which would be the case if the atmospheric pressure was greater than the gas pressure.

An accumulator, also known as a secondary or rechargeable cell, is designed to deliver a very large current quickly, like when starting a car engine. To achieve this, it is constructed with large plates and a strong electrolyte, which results in a very low internal resistance. Primary cells like the Leclanche, Daniell, and torch batteries have higher internal resistance and are not designed to supply such large currents.

Common mistake: Students might choose 'Torch battery' because it is a common household item, but they often don't realize that these disposable cells have a significantly higher internal resistance than a rechargeable accumulator.

Pitch is the quality of a sound that describes how high or low it is. In physics, the pitch of a sound is determined by its frequency, which is the number of vibrations per second. A high frequency produces a high pitch (a sharp sound), while a low frequency produces a low pitch (a deep sound).

Common mistake: Students often confuse pitch with loudness, mistakenly thinking that increasing the intensity or loudness of a sound will make its pitch higher, but loudness is actually related to the amplitude of the wave, not its frequency.

Nuclear fission is the process where a heavy atomic nucleus splits into smaller nuclei, releasing a large amount of energy. A key feature of this process is the release of several neutrons. These released neutrons can then strike other heavy nuclei, causing them to also split and release more neutrons, creating a self-sustaining process called a chain reaction.

Common mistake: Students might mistakenly choose option D, applying the law of conservation of mass from chemistry, but in nuclear reactions like fission, a small amount of mass (mass defect) is converted into a large amount of energy.

To solve this, we first find the cubical (volume) expansivity, which is three times the linear expansivity: γ = 3α = 3 × $(2 × 10⁻⁵)$ = 6 × 10⁻⁵ °C⁻¹. Next, we use the formula for the change in volume, ΔV = γV₁Δθ, where V₁ is the initial volume (15.00cm³) and Δθ is the temperature change (100°C - 0°C = 100°C). This gives a volume increase of ΔV = $(6 × 10⁻⁵)$ × 15 × 100 = 0.09cm³. Finally, add this increase to the original volume to get the new volume: 15.00cm³ + 0.09cm³ = 15.09cm³.

Common mistake: Students often make the mistake of using the given linear expansivity instead of the cubical expansivity (which is 3 times the linear value), leading to the incorrect answer 15.03cm³.

First, we use the principle of conservation of momentum to find the final velocity of the combined bullet and block, as this is an inelastic collision. The initial momentum (mass of bullet × its velocity) equals the final momentum (combined mass × final velocity), so (0.05kg × 200m/s) = (0.05kg + 0.95kg) × v, which gives a final velocity v = 10 m/s. Then, we calculate the final kinetic energy using the formula KE = ½mv², where 'm' is the total mass (1.0kg) and 'v' is the final velocity (10 m/s). This results in ½ × 1.0 × 10² = 50J.

Common mistake: A common mistake is to calculate the initial kinetic energy of the bullet (1000J) and assume energy is conserved, or to incorrectly calculate the final kinetic energy by mixing up values, for example by squaring the final momentum (10² = 100J).

In a series R-L-C circuit, the special condition called 'resonance' occurs when the inductive reactance $(X_L)$ equals the capacitive reactance $(X_C)$. Since the voltage across the inductor is $V_L$ = I × $X_L$ and the voltage across the capacitor is $V_C$ = I × $X_C$, and the current (I) is the same for all components in series, it means that at resonance, $V_L$ must equal $V_C$. Therefore, if the voltage across the inductor is 40V, the voltage across the capacitor must also be 40V.

Common mistake: Students often mistakenly add the given voltages (30V + 40V = 70V), forgetting that voltages in a series AC circuit do not add up arithmetically because they are out of phase.