JAMB UTME Physics
Past Questions

AI Explanation

**The reasoning** This is **conservation of momentum** in action. When objects stick together after collision, total momentum before equals total momentum after. **Before collision:** - Moving body: momentum = mass × velocity = 5 kg × 10 m/s = 50 kg·m/s - Stationary body: momentum = 3 kg × 0 m/s = 0 kg·m/s - **Total momentum = 50 kg·m/s** **After collision:** - Combined mass = 5 kg + 3 kg = 8 kg - They move together with common velocity *v* - Total momentum = 8v Since momentum is conserved: 50 = 8v v = 50/8 = **6.25 m/s** **Why the wrong options tempt you** **A) 5.0 m/s** — You might average the velocities (10 + 0)/2, but momentum depends on mass too, not just speed! **C) 7.5 m/s** — You used only the moving mass (50/5 + 3 = 50/8? No!). You forgot to add both masses. **D) 13.0 m/s** — You added velocities like 10 + 3. Velocity doesn't simply add; momentum does! **Quick takeaway** In sticky collisions, the heavier object "wins" more—here the 5 kg pulls the final velocity closer to its original 10 m/s than to zero. Always: **(m₁v₁ + m₂v₂)/(m₁ + m₂)**.

AI Explanation

## **The reasoning** When the ball reaches maximum height, its velocity becomes **zero**. Using the principle of **conservation of energy** (or the kinematic equation): **For maximum height:** v² = u² − 2gh At the top, v = 0, u = 30 m/s, g = 10 m/s² 0 = (30)² − 2(10)h 0 = 900 − 20h h = **45 m** **For total flight time:** What goes up must come down! Time to go up = time to come down. Using v = u − gt: 0 = 30 − 10t t = 3 s (time to reach the top) Total flight time = 3 + 3 = **6 s** --- ## **Why the wrong options tempt you** **Option B (45 m, 3 s)** — You calculated height correctly but forgot the ball must come back down! 3 s is only one-way time. **Option C (90 m, 3 s)** — You used h = ut instead of the correct formula, and made the same time mistake. **Option D (90 m, 6 s)** — Right time logic, but wrong height calculation. --- ## **Quick takeaway** For vertical projection: **total time = 2 × time to maximum height**, and always use v² = u² − 2gh for height when final velocity is zero!

AI Explanation

**The reasoning** When a body slides down a *smooth* (frictionless) inclined plane, only one component of gravity pulls it down the slope. We need to **resolve gravity** into two parts: - Component parallel to the plane = g sin θ (this accelerates the body) - Component perpendicular to plane = g cos θ (balanced by normal force) The acceleration down the plane = **g sin θ** With θ = 30° and g = 10 m/s²: a = 10 × sin 30° a = 10 × 0.5 **a = 5 m/s²** **Why the wrong options tempt you** - **A (10 m/s²)** — This is if you forgot the angle matters and used full gravity - **B (8.66 m/s²)** — You used *cos 30°* instead of sin 30° (cos 30° ≈ 0.866). Easy mix-up! - **D (2.5 m/s²)** — Maybe you divided by 4 instead of 2, or confused the setup entirely **Quick takeaway** On a smooth incline, acceleration = **g sin θ** — only the *sine* component pulls the object down the slope, and sin 30° always equals ½.

AI Explanation

## The reasoning This is the **wave equation**: **v = fλ** (speed = frequency × wavelength) Think of it like this: if a wave completes 50 cycles every second (frequency = 50 Hz), and each cycle is 4 meters long (wavelength = 4 m), then in one second the wave travels: v = 50 Hz × 4 m = **200 m/s** It's that straightforward! The wave covers 50 complete wavelengths per second, so multiply to get total distance per second. ## Why the wrong options tempt you **A) 12.5 m/s** — You divided instead of multiplying (4 ÷ 50 or 50 ÷ 4). The wave equation is multiplication, not division! **B) 54 m/s** — You added them (50 + 4). Addition doesn't work here; we're finding how far the wave travels. **C) 100 m/s** — You might have halved the correct answer by mistake, or used wrong values somewhere. ## Quick takeaway **"Wave speed = frequency × wavelength"** — always multiply these two. If 50 waves pass you every second, each being 4 m long, that's 200 m covered per second!

AI Explanation

**The reasoning** When resistors are in **parallel**, we use the reciprocal formula: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ Let's substitute our values: 1/R_total = 1/2 + 1/3 + 1/6 Finding a common denominator (6): 1/R_total = 3/6 + 2/6 + 1/6 = 6/6 = 1 Therefore: R_total = 1/1 = **1Ω** This is the **principle of parallel resistance** — parallel resistors always give you a *smaller* total resistance than the smallest individual resistor! **Why the wrong options tempt you** - **A) 11Ω** — You added them directly (2+3+6). That's the series formula! Wrong connection type. - **B) 5.5Ω** — You found the average (11÷2). Sounds logical but parallel circuits don't work that way. - **D) 0.5Ω** — A calculation slip, maybe dividing incorrectly at the final step. **Quick takeaway** Parallel = reciprocals first, then flip back. Series = just add. And remember: parallel resistance is *always* less than the smallest resistor in the group — it opens more paths for current!

AI Explanation

**The reasoning** Momentum is defined as **mass × velocity**. Let's build the unit step by step: - Mass is measured in kilograms (kg) - Velocity is measured in meters per second (m/s) So momentum = mass × velocity = kg × (m/s) = **kg·m/s** This is a fundamental principle: **the unit of any quantity comes from multiplying the units of its components**. Just like area (length × width) gives m², momentum (mass × velocity) gives kg·m/s. **Why the wrong options tempt you** - **A) kg/s** — You might think "per second" alone works, forgetting velocity already has distance (meters) in it. - **C) kg·m/s²** — This is actually the unit of **force** (F = ma), where acceleration is m/s². Don't confuse momentum with force! - **D) kg·m²/s²** — This is the unit of **energy** (KE = ½mv²). The squared terms come from v², not from simple v. **Quick takeaway** Momentum = mass × velocity, so its unit is simply kg × m/s = **kg·m/s** — no squares, no tricks!

AI Explanation

## The reasoning In physics, **work** has a very specific meaning. Work is only done when a force causes an object to move in the direction of that force. The formula is: **W = F × d × cos θ** where F is force, d is displacement, and θ is the angle between them. Key point: **Both force AND displacement must happen**. If you push a wall with all your strength but it doesn't move, you've done zero work (in physics terms) — no matter how tired you feel! The force must actually cause the object to shift position. ## Why the wrong options tempt you **A)** Seems right because you're exerting effort, but effort ≠ work. That immovable wall scenario proves it. **C)** Obvious trap — if it's at rest, nothing's moving. No displacement = no work. **D)** Gravity *acts* on you right now as you sit, but if you're not moving vertically, gravity does no work on you at that moment. ## Quick takeaway **"No movement, no work"** — both force and displacement must happen together for work to be done in physics.

AI Explanation

**The reasoning** When two forces act at 90° (perpendicular), we can't just add them directly — we use **vector addition**. Picture a right-angled triangle: one force points right (10 N), the other points up (10 N). The resultant is the hypotenuse. Using Pythagoras' theorem: R² = F₁² + F₂² R² = 10² + 10² R² = 100 + 100 = 200 R = √200 = √(100 × 2) = 10√2 N ≈ 14.14 N **Why the wrong options tempt you** - **0 N** — You might think equal forces cancel out, but that only happens when they act in *opposite* directions (180°), not at 90°. - **10 N** — Tempting if you assume the forces "balance" somehow, but perpendicular forces don't cancel. - **20 N** — This is if you just add them arithmetically (10 + 10), forgetting that forces are vectors with direction, not simple numbers. **Quick takeaway** When forces meet at 90°, think Pythagoras! The resultant is always larger than either individual force but smaller than their sum — specifically, it's the hypotenuse of your force triangle.

AI Explanation

## The reasoning At **standard atmospheric pressure** (which is 1 atm or 101.3 kPa at sea level), water boils at **100°C**. This is when water changes from liquid to gas (steam). The boiling point is the temperature where the vapor pressure of the liquid equals the surrounding atmospheric pressure, allowing bubbles to form throughout the liquid. This is a fundamental property you must memorize: *standard pressure = 100°C boiling point*. ## Why the wrong options tempt you **0°C** is water's *freezing/melting point*, not boiling point — students confuse these two important temperatures. **50°C** might seem "medium" but it's just warm water, not boiling. No scientific basis here, just a distractor. **200°C** is way too high — water would have evaporated long before this at standard pressure. (Though water *can* boil at higher temperatures under increased pressure, like in a pressure cooker!) ## Quick takeaway **Remember the two magic numbers for water: 0°C freezes it, 100°C boils it — both at standard pressure.**

AI Explanation

**The reasoning** The Kelvin scale and Celsius scale measure the same thing (temperature), but they start at different points. The key formula is: **K = °C + 273** (Some textbooks use 273.15, but for JAMB/WAEC, 273 is standard) So: K = 27 + 273 = **300 K** Think of it this way: 0°C (water freezes) = 273 K. You're just shifting the scale up by 273 units. The *size* of one degree is the same on both scales—only the starting point differs. **Why the wrong options tempt you** - **A (27 K):** You forgot to add 273—you just wrote the same number with K instead of °C - **B (100 K):** Maybe you confused this with the boiling point of water (100°C = 373 K), or did random math - **C (246 K):** You *subtracted* 273 instead of adding it—sign error! **Quick takeaway** To go from Celsius to Kelvin, always **add 273**—you're counting up from absolute zero, not from the freezing point of water.

AI Explanation

**The reasoning** In solids, particles are **tightly packed and vibrating in fixed positions**. When you heat one end of a metal spoon, the particles there vibrate faster. These energetic particles collide with neighboring particles, passing kinetic energy along the solid — this chain reaction is **conduction**. Think of it like a relay race where runners (particles) pass the baton (heat energy) while staying in their lanes. The particles don't move from place to place; only the energy travels through. **Why the wrong options tempt you** - **Convection** needs particles that can *flow* (liquids/gases). Solid particles can't move around, so no convection here. - **Radiation** transfers heat through electromagnetic waves (like the sun warming your skin), but it's not the *main* method in solids — conduction dominates when particles touch. - **Evaporation** is a cooling process involving liquid changing to gas. Not a heat transfer mechanism in solids at all. **Quick takeaway** Solids transfer heat by **conduction** because their particles stay put but pass energy through collisions — like whispering a secret down a crowded row without anyone changing seats.

AI Explanation

**The reasoning** Electrical resistance measures how much a material *opposes* the flow of electric current. Think of it like friction for electricity. The SI unit for resistance is the **Ohm (Ω)**, named after German physicist Georg Ohm. Here's how it connects: Ohm's Law states that **V = IR** (Voltage = Current × Resistance). When we rearrange this to R = V/I, we see that resistance equals voltage divided by current. So 1 Ohm = 1 Volt / 1 Ampere. **Why the wrong options tempt you** - **Volt (A)** measures electrical *potential difference* or "push" — it's what drives current, not what resists it. - **Ampere (B)** measures the *flow* of current itself — the thing being resisted, not the resistance. - **Watt (D)** measures *power* (energy per second) — how fast energy is used. It's calculated as P = VI. All four are electrical units, so they cluster together in your mind during exams. That's the trap. **Quick takeaway** **Resistance = Ohm.** Remember: "Ohm resists" — when current tries to flow, Ohms fight back. Lock that in and you'll never confuse it with Volts, Amps, or Watts again!

AI Explanation

**The reasoning** Ohm's Law states that **voltage is directly proportional to current and resistance**. Think of it like water flowing through a pipe: the pressure (voltage) needed depends on how much water flows (current) and how narrow the pipe is (resistance). The formula is: **V = IR** Where: - V = Voltage (in Volts) - I = Current (in Amperes) - R = Resistance (in Ohms) So if current is 2A and resistance is 5Ω, then V = 2 × 5 = 10V. **Why the wrong options tempt you** - **A) I/R** — This is what you'd get if you incorrectly rearranged V = IR. It would give you current squared per resistance, which has no physical meaning. - **C) I²R** — This is the formula for **electrical power loss** (heat dissipated), not voltage! It's easy to mix up because it also uses I and R. - **D) R/I** — Just resistance divided by current. Makes no sense physically and gives wrong units. **Quick takeaway** Remember: "**V**ery **I**mportant **R**ule" — V = IR. Voltage equals current times resistance, always!

AI Explanation

## The reasoning Power dissipation in a resistor follows the formula **P = I²R** (Power equals current squared times resistance). Here's the working: - Current I = 2A - Resistance R = 10Ω - P = I²R = (2)² × 10 = 4 × 10 = **40 W** You could also use P = V²/R or P = VI, but you'd first need to find voltage using Ohm's law (V = IR = 2 × 10 = 20V). Then P = 2A × 20V = 40W. Same answer! ## Why the wrong options tempt you **A) 10W** — You just multiplied I × R (2 × 10), forgetting to *square* the current first. **B) 20W** — You calculated V = IR = 20V correctly, but then mistook voltage for power. Voltage and power are different quantities! **D) 200W** — You might have done (I × R)² = (20)² = 400, then divided randomly, or mixed up your formulas entirely. ## Quick takeaway For power in resistors, always remember: **"I-squared-R"** — square the current first, then multiply by resistance. It's the most direct route when current is given!

AI Explanation

**The reasoning** Sound is a **mechanical wave** — it travels by vibrating particles (molecules or atoms) that bump into each other, passing energy along. In air, water, or steel, there are plenty of particles to vibrate. But in a **vacuum**, there are *no particles at all* — it's completely empty space. No particles means nothing to vibrate, so sound waves literally have nothing to travel through. That's why in space (which is mostly vacuum), even massive explosions happen in total silence! **Why the wrong options tempt you** - **A) Air** — You hear sounds daily through air, so this seems obviously wrong - **B) Water** — This tricks students who forget whales communicate underwater, or that you can hear splashes beneath the surface - **D) Steel** — Many think solid materials block sound, but metals actually carry sound *faster* than air (particles are closer together!) **Quick takeaway** Remember: **Sound needs matter to travel** — if there's no particles (vacuum), there's no sound, which is why astronauts use radios even when standing next to each other in space.

AI Explanation

**The reasoning** Light is an electromagnetic wave that travels at different speeds through different materials. The key principle here is **optical density and refractive index**. In a vacuum (empty space with no particles), light travels at its maximum possible speed: approximately 3 × 10⁸ m/s (300,000 km/s). This is the universal speed limit — nothing goes faster! When light enters any material medium (water, glass, diamond), it interacts with the atoms and molecules there. These interactions slow it down. The denser the material's atomic structure, the more light gets slowed. - Vacuum: 3.0 × 10⁸ m/s (fastest) - Water: about 2.25 × 10⁸ m/s - Glass: about 2.0 × 10⁸ m/s - Diamond: about 1.24 × 10⁸ m/s (slowest here) **Why the wrong options tempt you** Students sometimes think "solid = stronger = faster" or confuse hardness with speed. Diamond is the hardest substance, but that actually means its atoms are tightly packed — which slows light down more! Water and glass feel "transparent," so you might assume light zips through easily, but particles still create resistance. **Quick takeaway** Light sprints fastest where there's nothing to slow it down — in the emptiness of a vacuum.

AI Explanation

**The reasoning** A **non-renewable** energy source is one that cannot be replaced within a human lifetime — once you use it up, it's gone. Coal is formed from ancient plants that were buried and compressed over **millions of years**. When we burn coal for energy, we're depleting reserves that took geological ages to form. We can't make more coal in any practical timeframe. In contrast, solar, wind, and geothermal are **renewable** because they regenerate naturally and continuously. The sun shines every day, wind keeps blowing, and Earth's internal heat persists for billions of years. **Why the wrong options tempt you** - **A & B (Solar/Wind):** You might forget that these are *naturally replenished* daily. They never "run out." - **D (Geothermal):** This one tricks students! Though it uses heat from deep underground, that heat is continuously produced by Earth's core and will last billions of years — making it renewable on human timescales. **Quick takeaway** If it took **millions of years to form** (like fossil fuels: coal, oil, gas), it's non-renewable; if nature **replaces it continuously**, it's renewable.

AI Explanation

**The reasoning** The **atomic number** is literally *defined* as the number of protons in an atom's nucleus. It's the atom's unique identity card. For example, hydrogen always has 1 proton (atomic number = 1), carbon always has 6 protons (atomic number = 6), and oxygen always has 8 protons (atomic number = 8). If you change the number of protons, you change the element entirely! **Why the wrong options tempt you** **A) Mass number** — This is the *total* of protons + neutrons. Students confuse it because both involve counting particles, but mass number includes neutrons too. **C) Atomic mass** — This is the average mass of all isotopes of an element (measured in atomic mass units). It sounds similar to "mass number" but includes decimals and considers isotope abundance. **D) Valency** — This tells you how many bonds an atom can form (based on electrons in the outer shell), not the protons in the nucleus. **Quick takeaway** Remember: **Atomic number = Protons = Element's ID**. It never changes for a given element, unlike mass number (which varies with isotopes) or valency (which depends on electron arrangement).

AI Explanation

**The reasoning** When parallel rays from a distant object (like the sun or a faraway tree) hit a convex lens, they converge and meet at the **focal point** on the opposite side of the lens. This creates an image you can catch on a screen — that's what makes it **real**. Because light rays cross over as they pass through the lens, the image flips upside down — making it **inverted**. Think of how a magnifying glass can project an upside-down image of a window onto paper. That's the principle: *real images form where light actually converges, and convex lenses flip the image*. **Why the wrong options tempt you** - **B & D (Virtual)**: Virtual images can't be caught on a screen — they only happen when rays *appear* to come from somewhere (like in a mirror). Convex lenses make real images for distant objects. - **C (Real and erect)**: This sounds nice, but physics doesn't allow it here. When rays cross through a lens, they must invert. **Quick takeaway** For distant objects, convex lenses always produce **real, inverted** images at the focal point — the kind you can project onto a screen.

AI Explanation

**The reasoning** In visible light, wavelength determines colour. The electromagnetic spectrum follows a pattern: **wavelength increases as you move from violet to red**. Think of it like this — violet light has wavelengths around 380-450 nm (nanometers), while red sits at 620-750 nm. Red has nearly double the wavelength of violet! Here's the order from shortest to longest wavelength: **Violet → Blue → Green → Yellow → Orange → Red** Remember the acronym **ROYGBIV** (rainbow colours), but flip it backwards for wavelength: **Red has the longest, Violet has the shortest**. **Why the wrong options tempt you** - **Violet** is the most energetic visible light, so students confuse "high energy" with "long wavelength" — but they're actually *inversely* related. - **Green and Yellow** sit in the middle of the spectrum, so they feel like safe, middle-ground answers when you're unsure. **Quick takeaway** In visible light, **red light travels in the longest waves, violet in the shortest** — remember: energy and wavelength move in opposite directions.

AI Explanation

**The reasoning** Force is defined as **mass × acceleration** (F = ma). In the SI system: - Mass is measured in kilograms (kg) - Acceleration is measured in meters per second squared (m/s²) So force = kg × m/s² = **Newton (N)** The unit is named after Sir Isaac Newton, who gave us the laws of motion. When you push a 1 kg object with an acceleration of 1 m/s², you're applying exactly 1 Newton of force. Simple as that! **Why the wrong options tempt you** All these options are SI units, which is the trap: - **Joule** measures *energy* or *work done* (force × distance) - **Watt** measures *power* (energy per time) - **Pascal** measures *pressure* (force per area) They're related to force but aren't force itself. JAMB loves testing if you can distinguish between related quantities. **Quick takeaway** Think "**N** for **N**ewton = Force" — if you're pushing, pulling, or weighing something, you're dealing with Newtons! 💪

AI Explanation

## The reasoning This is **uniform acceleration** — when velocity increases steadily. The key formula is: **v = u + at** Where: - v = final velocity (what we're finding) - u = initial velocity = 0 m/s (starts from rest) - a = acceleration = 2 m/s² - t = time = 5 s Substituting: v = 0 + (2)(5) = **10 m/s** Think of it this way: every second, the car gains 2 m/s. After 5 seconds, it's gained 2 × 5 = 10 m/s. ## Why the wrong options tempt you **A) 5 m/s** — You might subtract instead of multiply, or confuse time with velocity. **B) 7 m/s** — This comes from adding a and t (2 + 5), which makes no physical sense — you can't add seconds to m/s²! **D) 25 m/s** — You probably used v = ½at² (which gives *distance*, not velocity) or squared something incorrectly. ## Quick takeaway **Velocity gained = acceleration × time.** If something accelerates at 2 m/s² for 5 seconds, it picks up 2 m/s every second, totaling 10 m/s. Master this, and JAMB can't trick you!

AI Explanation

**The reasoning** Work is done when a force **moves** an object through a distance. The formula is: **Work = Force × Distance** (W = F × d) Think of pushing a heavy box across the floor. You apply force, and the box moves a certain distance. The work you do depends on both how hard you push (force) and how far the box travels (distance). If the box doesn't move at all, no work is done — even if you're sweating! The unit is Joules (J), which equals Newton × meter (N·m). **Why the wrong options tempt you** - **A (Force × velocity)** confuses work with **momentum** or **power**. Velocity is speed, not distance covered. - **C (Mass × velocity)** is actually the formula for **momentum** (p = mv), not work. Easy mix-up! - **D (Power × time)** is sneaky because it *can* give you work (since Power = Work/Time), but it's not the **direct definition** of work itself. **Quick takeaway** Work needs two things: a force that **acts** and a distance the object **actually moves** — no movement, no work, no matter how hard you try!

AI Explanation

**The reasoning** Momentum is simply **mass × velocity**. Think of it as "how much motion an object carries." The formula is: **p = mv** Where: - p = momentum - m = mass = 2 kg - v = velocity = 5 m/s So: p = 2 kg × 5 m/s = **10 kg·m/s** That's it! Straight multiplication. This is the **principle of linear momentum** — the product of how heavy something is and how fast it's moving. **Why the wrong options tempt you** - **A) 2.5** — You divided (2 ÷ 5) instead of multiplying. Classic panic mistake! - **B) 7** — You added (2 + 5). Momentum isn't a sum; it's a product. - **D) 25** — You squared the velocity (5²) then forgot about the 2 kg properly, or mixed up kinetic energy formula (½mv²). **Quick takeaway** Momentum = mass × velocity. No tricks, no shortcuts — just multiply the two numbers and attach the unit kg·m/s. If you see mass and velocity, think **multiply immediately**!

AI Explanation

**The reasoning** The speed of light in a vacuum is a **fundamental constant of nature**, symbolized as *c*. It's approximately **300,000,000 meters per second** or **3 × 10⁸ m/s**. This value is fixed and appears everywhere in physics—from Einstein's E = mc² to calculations about electromagnetic waves, satellites, and even how quickly you see lightning before hearing thunder. To remember: Light travels about **300,000 kilometers per second** (since 1 km = 1000 m, that's 3 × 10⁵ km/s = 3 × 10⁸ m/s). It's the fastest speed possible in our universe. **Why the wrong options tempt you** The powers of 10 confuse students! - **Option A (10⁵)** is actually the speed of light in *km/s*, not m/s—a unit mix-up trap. - **Option B (10⁶)** and **Option D (10¹⁰)** are random large numbers that "feel" fast but aren't grounded in reality. Examiners know you might panic and pick anything that looks big. **Quick takeaway** Lock this in: **c = 3 × 10⁸ m/s**—eight zeros, universal speed limit, never changes. When you see "speed of light," see "10⁸" instantly! 🚀