IGCSE Physics (0625) — Complete Revision Notes (Core & Extended)

<h1 class="notes-h1">IGCSE Physics (0625) — Complete Revision Notes</h1>
<h2 class="notes-h2">Cambridge International IGCSE | Syllabus Code: 0625</h2>
<h3 class="notes-h3">CBCEduKenya.com — Kenya's Complete Learning Hub</h3>
<hr class="section-divider">
<p><strong>Syllabus:</strong> Cambridge IGCSE Physics (0625)</p>
<p><strong>Level:</strong> Core and Extended ([E] = Extended only)</p>
<p><strong>Sessions:</strong> May/June and October/November</p>
<p><strong>Papers:</strong> Paper 1 (MCQ), Paper 2 (Core), Paper 3 (Extended), Paper 4 (Alternative to Coursework), Paper 5 (Practical), Paper 6 (Alternative to Practical)</p>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Paper</th><th>Type</th><th>Marks</th><th>Duration</th><th>Who Takes It</th></tr>
</thead><tbody>
<tr><td>Paper 1</td><td>Multiple Choice (Core)</td><td>40</td><td>45 min</td><td>Core candidates</td></tr>
<tr><td>Paper 2</td><td>Structured (Core)</td><td>80</td><td>1 hr 30 min</td><td>Core candidates</td></tr>
<tr><td>Paper 3</td><td>Structured (Extended)</td><td>80</td><td>1 hr 15 min</td><td>Extended candidates</td></tr>
<tr><td>Paper 4</td><td>Coursework Alternative</td><td>40</td><td>1 hr</td><td>Both (instead of Paper 5)</td></tr>
<tr><td>Paper 5</td><td>Practical</td><td>40</td><td>1 hr 15 min</td><td>Both</td></tr>
<tr><td>Paper 6</td><td>Alternative to Practical</td><td>40</td><td>1 hr</td><td>Both (instead of Paper 5)</td></tr>
</tbody></table></div>
<p><strong>Grade boundaries:</strong> A* requires approximately 90%+ on Extended papers.</p>
<hr class="section-divider">
<h2 class="notes-h2">TOPIC 1: GENERAL PHYSICS — MEASUREMENTS AND UNITS</h2>
<h3 class="notes-h3">SI Units</h3>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Quantity</th><th>SI Unit</th><th>Symbol</th></tr>
</thead><tbody>
<tr><td>Length</td><td>metre</td><td>m</td></tr>
<tr><td>Mass</td><td>kilogram</td><td>kg</td></tr>
<tr><td>Time</td><td>second</td><td>s</td></tr>
<tr><td>Temperature</td><td>kelvin</td><td>K (°C also accepted)</td></tr>
<tr><td>Electric current</td><td>ampere</td><td>A</td></tr>
<tr><td>Amount of substance</td><td>mole</td><td>mol</td></tr>
</tbody></table></div>
<h3 class="notes-h3">Prefixes</h3>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Prefix</th><th>Symbol</th><th>Multiplier</th></tr>
</thead><tbody>
<tr><td>nano</td><td>n</td><td>× 10⁻⁹</td></tr>
<tr><td>micro</td><td>μ</td><td>× 10⁻⁶</td></tr>
<tr><td>milli</td><td>m</td><td>× 10⁻³</td></tr>
<tr><td>centi</td><td>c</td><td>× 10⁻²</td></tr>
<tr><td>kilo</td><td>k</td><td>× 10³</td></tr>
<tr><td>mega</td><td>M</td><td>× 10⁶</td></tr>
<tr><td>giga</td><td>G</td><td>× 10⁹</td></tr>
</tbody></table></div>
<h3 class="notes-h3">Measuring Instruments</h3>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Instrument</th><th>Quantity Measured</th><th>Typical Precision</th></tr>
</thead><tbody>
<tr><td>Ruler / metre rule</td><td>Length</td><td>1 mm</td></tr>
<tr><td>Vernier calipers [E]</td><td>Small lengths</td><td>0.1 mm</td></tr>
<tr><td>Micrometer screw gauge [E]</td><td>Very small lengths</td><td>0.01 mm</td></tr>
<tr><td>Measuring cylinder</td><td>Volume of liquid</td><td>1 cm³</td></tr>
<tr><td>Stopwatch</td><td>Time</td><td>0.01 s</td></tr>
<tr><td>Thermometer</td><td>Temperature</td><td>1°C</td></tr>
<tr><td>Ammeter</td><td>Current</td><td>varies</td></tr>
<tr><td>Voltmeter</td><td>Voltage</td><td>varies</td></tr>
</tbody></table></div>
<h3 class="notes-h3">Scalar and Vector Quantities</h3>
<p><strong>Scalar</strong> — magnitude only:</p>
<ul class="notes-list">
<li>Distance, speed, mass, time, temperature, energy, pressure</li>
</ul>
<p><strong>Vector</strong> — magnitude AND direction:</p>
<ul class="notes-list">
<li>Displacement, velocity, acceleration, force, weight, momentum</li>
</ul>
<h3 class="notes-h3">Length, Area, Volume</h3>
<ul class="notes-list">
<li>Area of circle: A = πr²</li>
<li>Volume of sphere: V = (4/3)πr³</li>
<li>Volume of cylinder: V = πr²h</li>
<li>Volume by displacement: submerge irregular object in measuring cylinder</li>
</ul>
<hr class="section-divider">
<h2 class="notes-h2">TOPIC 2: MOTION</h2>
<h3 class="notes-h3">Key Definitions</h3>
<ul class="notes-list">
<li><strong>Distance</strong> — total length of path travelled (scalar)</li>
<li><strong>Displacement</strong> — shortest straight-line distance from start to finish, with direction (vector)</li>
<li><strong>Speed</strong> — distance ÷ time (scalar)</li>
<li><strong>Velocity</strong> — displacement ÷ time (vector)</li>
<li><strong>Acceleration</strong> — change in velocity ÷ time (vector)</li>
</ul>
<h3 class="notes-h3">Key Equations</h3>
<pre class="code-block"><code>
speed = distance / time v = d / t
average speed = total distance / total time
velocity = displacement / time
acceleration = change in velocity / time a = (v - u) / t
</code></pre>
<h3 class="notes-h3">[E] Equations of Motion (SUVAT)</h3>
<p>For uniform acceleration:</p>
<pre class="code-block"><code>
v = u + at
s = ut + ½at²
v² = u² + 2as
s = (u + v)t / 2
</code></pre>
<p>where: s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time</p>
<p><strong>Worked Example:</strong> A car accelerates from rest at 3 m/s² for 5 s. Find distance travelled.</p>
<ul class="notes-list">
<li>u = 0, a = 3, t = 5</li>
<li>s = ut + ½at² = 0 + ½ × 3 × 25 = <strong>37.5 m</strong></li>
</ul>
<h3 class="notes-h3">Distance-Time Graphs</h3>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Shape of Graph</th><th>Meaning</th></tr>
</thead><tbody>
<tr><td>Horizontal line</td><td>Stationary (at rest)</td></tr>
<tr><td>Straight line sloping up</td><td>Constant speed</td></tr>
<tr><td>Straight line sloping down</td><td>Constant speed (returning)</td></tr>
<tr><td>Curved line (increasing gradient)</td><td>Accelerating</td></tr>
<tr><td>Curved line (decreasing gradient)</td><td>Decelerating</td></tr>
</tbody></table></div>
<p><strong>Gradient of distance-time graph = speed</strong></p>
<h3 class="notes-h3">Velocity-Time Graphs</h3>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Shape of Graph</th><th>Meaning</th></tr>
</thead><tbody>
<tr><td>Horizontal line</td><td>Constant velocity (zero acceleration)</td></tr>
<tr><td>Straight line sloping up</td><td>Uniform acceleration</td></tr>
<tr><td>Straight line sloping down</td><td>Uniform deceleration</td></tr>
<tr><td>Curved line</td><td>Non-uniform acceleration</td></tr>
</tbody></table></div>
<p><strong>Gradient of velocity-time graph = acceleration</strong></p>
<p><strong>Area under velocity-time graph = distance (displacement)</strong></p>
<h3 class="notes-h3">Free Fall and Gravity</h3>
<ul class="notes-list">
<li>On Earth, g = 10 m/s² (gravitational field strength / acceleration due to gravity)</li>
<li>All objects fall with the same acceleration in a vacuum</li>
<li>Air resistance reduces acceleration; terminal velocity reached when weight = air resistance</li>
</ul>
<p><strong>Terminal Velocity:</strong></p>
<ol class="notes-list">
<li>Object falls → weight > air resistance → accelerates</li>
<li>Speed increases → air resistance increases</li>
<li>Eventually air resistance = weight → zero resultant force → <strong>terminal velocity</strong> (constant speed)</li>
</ol>
<hr class="section-divider">
<h2 class="notes-h2">TOPIC 3: FORCES AND PRESSURE</h2>
<h3 class="notes-h3">Types of Forces</h3>
<ul class="notes-list">
<li><strong>Gravitational force (weight):</strong> W = mg</li>
<li><strong>Normal contact force:</strong> perpendicular to surface</li>
<li><strong>Friction:</strong> opposes motion, acts along surface</li>
<li><strong>Tension:</strong> in stretched materials (ropes, springs)</li>
<li><strong>Upthrust/Buoyancy:</strong> upward force from fluid on submerged object</li>
</ul>
<h3 class="notes-h3">Newton's Laws of Motion</h3>
<p><strong>Newton's First Law:</strong></p>
<p>An object remains at rest or moves with constant velocity unless acted upon by a resultant (net) force.</p>
<p><strong>Newton's Second Law:</strong></p>
<p>Resultant force = mass × acceleration</p>
<pre class="code-block"><code>
F = ma
</code></pre>
<p>Units: F in N, m in kg, a in m/s²</p>
<p><strong>Worked Example:</strong> A 5 kg object accelerates at 3 m/s². Find the resultant force.</p>
<p>F = ma = 5 × 3 = <strong>15 N</strong></p>
<p><strong>Newton's Third Law:</strong></p>
<p>When object A exerts a force on object B, object B exerts an equal and opposite force on object A.</p>
<p><em>(Forces act on DIFFERENT objects — they are NOT balanced forces)</em></p>
<h3 class="notes-h3">Weight and Mass</h3>
<pre class="code-block"><code>
Weight = mass × gravitational field strength
W = mg
</code></pre>
<ul class="notes-list">
<li>Mass is measured in kg, is constant everywhere</li>
<li>Weight is measured in N, varies with gravitational field</li>
<li>On Earth: g = 10 N/kg (or 10 m/s²)</li>
<li>On the Moon: g ≈ 1.6 N/kg</li>
</ul>
<h3 class="notes-h3">Friction</h3>
<p><strong>Useful friction:</strong> walking, brakes, writing</p>
<p><strong>Harmful friction:</strong> machinery wear, air resistance slowing vehicles</p>
<p><strong>Reducing friction:</strong> lubrication (oil/grease), smooth surfaces, ball bearings, streamlining</p>
<h3 class="notes-h3">Turning Effect of Forces (Moments)</h3>
<pre class="code-block"><code>
Moment = force × perpendicular distance from pivot
M = F × d
</code></pre>
<p>Units: N m (newton-metres)</p>
<p><strong>Principle of Moments (equilibrium):</strong></p>
<p>Sum of clockwise moments = Sum of anticlockwise moments</p>
<p><strong>Worked Example:</strong> A 20 N force acts 0.5 m from a pivot. What force at 1 m on the other side balances it?</p>
<ul class="notes-list">
<li>Clockwise: 20 × 0.5 = 10 N m</li>
<li>Anticlockwise: F × 1 = 10 → F = <strong>10 N</strong></li>
</ul>
<h3 class="notes-h3">Centre of Gravity (Centre of Mass)</h3>
<p>The single point through which the entire weight of an object appears to act.</p>
<p><strong>Finding centre of gravity of irregular shape:</strong></p>
<ol class="notes-list">
<li>Hang object from a pin</li>
<li>Hang a plumb line from the same pin</li>
<li>Mark the line on the object</li>
<li>Repeat from a different point</li>
<li>Centre of gravity = intersection of lines</li>
</ol>
<p><strong>Stability:</strong></p>
<ul class="notes-list">
<li>Lower centre of gravity → more stable</li>
<li>Wider base → more stable</li>
<li>Object topples when line of action of weight falls outside base</li>
</ul>
<h3 class="notes-h3">Pressure</h3>
<pre class="code-block"><code>
Pressure = force / area
P = F / A
</code></pre>
<p>Units: N/m² = Pa (pascal)</p>
<p><strong>Pressure in fluids:</strong></p>
<pre class="code-block"><code>
P = ρgh
</code></pre>
<p>where ρ = density (kg/m³), g = 10 N/kg, h = depth (m)</p>
<p>Pressure in a fluid:</p>
<ul class="notes-list">
<li>Increases with depth</li>
<li>Acts equally in all directions at the same depth</li>
<li>Transmits equally through incompressible fluids (hydraulics)</li>
</ul>
<h3 class="notes-h3">Hydraulic Systems</h3>
<p>Hydraulic press principle (Pascal's Law):</p>
<pre class="code-block"><code>
F₁/A₁ = F₂/A₂ (pressure is same throughout)
</code></pre>
<p>A small force on small piston → large force on large piston</p>
<p><strong>Atmospheric Pressure:</strong></p>
<ul class="notes-list">
<li>Standard: 101,325 Pa ≈ 100 kPa</li>
<li>Measured by barometer (mercury column, ~760 mm Hg)</li>
<li>Decreases with altitude</li>
</ul>
<h3 class="notes-h3">Density</h3>
<pre class="code-block"><code>
density = mass / volume
ρ = m / V
</code></pre>
<p>Units: kg/m³ or g/cm³ (1 g/cm³ = 1000 kg/m³)</p>
<ul class="notes-list">
<li>Water: ρ = 1000 kg/m³ = 1 g/cm³</li>
<li>Object denser than fluid → sinks; less dense → floats</li>
</ul>
<p><strong>Upthrust = weight of fluid displaced</strong> (Archimedes' Principle)</p>
<hr class="section-divider">
<h2 class="notes-h2">TOPIC 4: ENERGY, WORK, AND POWER</h2>
<h3 class="notes-h3">Forms of Energy</h3>
<ul class="notes-list">
<li>Kinetic energy (KE) — energy of motion</li>
<li>Gravitational potential energy (GPE) — energy due to height</li>
<li>Chemical energy — stored in bonds (fuel, food, batteries)</li>
<li>Thermal/heat energy</li>
<li>Electrical energy</li>
<li>Nuclear energy</li>
<li>Elastic/strain potential energy</li>
<li>Light (radiant) energy</li>
<li>Sound energy</li>
</ul>
<p><strong>Law of Conservation of Energy:</strong> Energy cannot be created or destroyed; it can only be converted from one form to another.</p>
<h3 class="notes-h3">Work Done</h3>
<pre class="code-block"><code>
Work done = force × distance moved in direction of force
W = F × d
</code></pre>
<p>Units: J (joules) = N m</p>
<p>1 J = 1 N m</p>
<p>Work is done only when force causes movement in its direction.</p>
<p>No movement → no work done.</p>
<h3 class="notes-h3">Kinetic Energy</h3>
<pre class="code-block"><code>
KE = ½mv²
</code></pre>
<p>where m = mass (kg), v = speed (m/s)</p>
<p><strong>Worked Example:</strong> A 2 kg ball moves at 5 m/s. Find its KE.</p>
<p>KE = ½ × 2 × 5² = ½ × 2 × 25 = <strong>25 J</strong></p>
<h3 class="notes-h3">Gravitational Potential Energy</h3>
<pre class="code-block"><code>
GPE = mgh
</code></pre>
<p>where m = mass (kg), g = 10 N/kg, h = height (m)</p>
<p><strong>Worked Example:</strong> A 3 kg book is lifted 2 m. Find change in GPE.</p>
<p>GPE = 3 × 10 × 2 = <strong>60 J</strong></p>
<h3 class="notes-h3">Conservation of Energy — Practical Example</h3>
<p>Ball dropped from height h:</p>
<ul class="notes-list">
<li>At top: GPE = mgh, KE = 0</li>
<li>At bottom: GPE = 0, KE = ½mv²</li>
<li>Therefore: mgh = ½mv² → v = √(2gh)</li>
</ul>
<h3 class="notes-h3">Power</h3>
<pre class="code-block"><code>
Power = work done / time taken
P = W / t
</code></pre>
<p>Units: W (watts) = J/s</p>
<p>Also: P = Fv (force × velocity) [E]</p>
<p><strong>Worked Example:</strong> A motor lifts 500 J in 10 s. Find power.</p>
<p>P = 500/10 = <strong>50 W</strong></p>
<h3 class="notes-h3">Efficiency</h3>
<pre class="code-block"><code>
Efficiency = (useful energy output / total energy input) × 100%
</code></pre>
<p>or</p>
<pre class="code-block"><code>
Efficiency = (useful power output / total power input) × 100%
</code></pre>
<ul class="notes-list">
<li>Efficiency is always < 100% (lost energy goes to heat/sound due to friction)</li>
<li>No unit (it's a ratio/percentage)</li>
</ul>
<p><strong>Worked Example:</strong> A machine takes in 200 J, outputs 150 J of useful work.</p>
<p>Efficiency = 150/200 × 100% = <strong>75%</strong></p>
<hr class="section-divider">
<h2 class="notes-h2">TOPIC 5: THERMAL PHYSICS</h2>
<h3 class="notes-h3">Temperature and Heat</h3>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Term</th><th>Definition</th></tr>
</thead><tbody>
<tr><td>Temperature</td><td>Measure of average kinetic energy of particles</td></tr>
<tr><td>Heat (thermal energy)</td><td>Total internal energy — depends on temperature AND number of particles</td></tr>
<tr><td>Absolute zero</td><td>0 K = -273°C — particles have minimum energy (no KE)</td></tr>
</tbody></table></div>
<p>Converting: K = °C + 273</p>
<h3 class="notes-h3">Thermal Expansion</h3>
<p><strong>Solids:</strong> particles vibrate more → push apart → expand</p>
<p><strong>Liquids:</strong> expand more than solids</p>
<p><strong>Gases:</strong> expand most, obey gas laws</p>
<p><strong>Applications of expansion:</strong></p>
<ul class="notes-list">
<li>Bimetallic strip (thermostat) — two metals expand at different rates, strip bends</li>
<li>Gaps in railway tracks (allow expansion)</li>
<li>Expansion joints in bridges and roads</li>
</ul>
<p><strong>Anomalous expansion of water:</strong> Water expands when freezing (0°C → 4°C, water contracts; 4°C → 0°C, water expands). Ice less dense than water → floats.</p>
<h3 class="notes-h3">Specific Heat Capacity [E]</h3>
<pre class="code-block"><code>
Q = mcΔT
</code></pre>
<p>where Q = heat energy (J), m = mass (kg), c = specific heat capacity (J/kg°C), ΔT = temperature change</p>
<p><strong>Specific heat capacity:</strong> Energy required to raise temperature of 1 kg of substance by 1°C</p>
<ul class="notes-list">
<li>Water: c = 4200 J/kg°C (high — water is good at storing/releasing heat)</li>
</ul>
<p><strong>Worked Example:</strong> How much energy heats 2 kg of water from 20°C to 50°C?</p>
<p>Q = 2 × 4200 × 30 = <strong>252,000 J = 252 kJ</strong></p>
<h3 class="notes-h3">Specific Latent Heat [E]</h3>
<pre class="code-block"><code>
Q = mL
</code></pre>
<p>where L = specific latent heat (J/kg)</p>
<p><strong>Specific latent heat:</strong> Energy required to change state of 1 kg of substance at constant temperature.</p>
<ul class="notes-list">
<li>Latent heat of fusion (solid ↔ liquid)</li>
<li>Latent heat of vaporisation (liquid ↔ gas)</li>
</ul>
<p>During change of state: temperature stays constant while energy is used to break/form bonds.</p>
<h3 class="notes-h3">Gas Laws [E]</h3>
<p><strong>Boyle's Law</strong> (constant temperature):</p>
<pre class="code-block"><code>
P₁V₁ = P₂V₂ (pressure × volume = constant)
</code></pre>
<p><strong>Charles' Law</strong> (constant pressure):</p>
<pre class="code-block"><code>
V₁/T₁ = V₂/T₂ (volume / temperature = constant) [T in Kelvin]
</code></pre>
<p><strong>Pressure Law</strong> (constant volume):</p>
<pre class="code-block"><code>
P₁/T₁ = P₂/T₂ (pressure / temperature = constant) [T in Kelvin]
</code></pre>
<p><strong>Combined Gas Law:</strong></p>
<pre class="code-block"><code>
P₁V₁/T₁ = P₂V₂/T₂
</code></pre>
<p><strong>IMPORTANT:</strong> Temperature MUST be in Kelvin for gas law calculations.</p>
<h3 class="notes-h3">Methods of Heat Transfer</h3>
<h4 class="notes-h4">Conduction</h4>
<ul class="notes-list">
<li>Transfer through solids (and to a lesser extent, liquids/gases)</li>
<li>Particles vibrate → transfer energy to neighbouring particles</li>
<li>Metals are good conductors (free electrons carry energy)</li>
<li>Non-metals, air, and wood are poor conductors (insulators)</li>
</ul>
<p><strong>Applications:</strong> cooking pans (conductors), oven gloves (insulators), double glazing (trapped air)</p>
<h4 class="notes-h4">Convection</h4>
<ul class="notes-list">
<li>Transfer through liquids and gases only</li>
<li>Heated fluid becomes less dense → rises</li>
<li>Cooler fluid sinks to replace it → convection current</li>
</ul>
<p><strong>Applications:</strong> heating systems, sea breezes, hot water tank (hot water rises to top)</p>
<p><strong>Convection cannot occur in solids</strong> — particles cannot move freely.</p>
<h4 class="notes-h4">Radiation (Infra-Red Radiation)</h4>
<ul class="notes-list">
<li>Transfer through vacuum (and transparent media) — does NOT need particles</li>
<li>All objects emit and absorb infra-red (IR) radiation</li>
<li>Hotter objects emit more radiation</li>
<li>Dark, matt surfaces: good emitters AND good absorbers</li>
<li>Light, shiny surfaces: poor emitters AND poor absorbers (good reflectors)</li>
</ul>
<p><strong>Applications:</strong></p>
<ul class="notes-list">
<li>Black kettles cool faster (better emitter)</li>
<li>Solar panels are black (better absorber)</li>
<li>Teapots are shiny (poor emitter — keeps tea hot)</li>
<li>Vacuum flask (Thermos): silvered walls reduce radiation, vacuum eliminates conduction/convection</li>
</ul>
<h3 class="notes-h3">Kinetic Theory of Gases</h3>
<p>All matter is made of particles in constant random motion.</p>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>State</th><th>Arrangement</th><th>Particle Motion</th><th>Energy</th></tr>
</thead><tbody>
<tr><td>Solid</td><td>Regular lattice, close together</td><td>Vibrate about fixed positions</td><td>Lowest</td></tr>
<tr><td>Liquid</td><td>Irregular, close together</td><td>Move randomly, flow</td><td>Medium</td></tr>
<tr><td>Gas</td><td>Far apart, random</td><td>Move rapidly in all directions</td><td>Highest</td></tr>
</tbody></table></div>
<p><strong>Gas pressure:</strong> caused by gas molecules colliding with container walls.</p>
<ul class="notes-list">
<li>Higher temperature → higher KE → more frequent, harder collisions → higher pressure</li>
</ul>
<hr class="section-divider">
<h2 class="notes-h2">TOPIC 6: WAVES</h2>
<h3 class="notes-h3">Key Wave Terms</h3>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Term</th><th>Definition</th></tr>
</thead><tbody>
<tr><td>Amplitude (A)</td><td>Maximum displacement from equilibrium position (m)</td></tr>
<tr><td>Wavelength (λ)</td><td>Distance between successive identical points on wave (m)</td></tr>
<tr><td>Frequency (f)</td><td>Number of complete waves per second (Hz)</td></tr>
<tr><td>Period (T)</td><td>Time for one complete wave (s)</td></tr>
<tr><td>Wave speed (v)</td><td>Distance travelled by wave per second (m/s)</td></tr>
</tbody></table></div>
<h3 class="notes-h3">Wave Equation</h3>
<pre class="code-block"><code>
wave speed = frequency × wavelength
v = fλ
</code></pre>
<p>Also: T = 1/f (period and frequency are reciprocals)</p>
<p><strong>Worked Example:</strong> A wave has frequency 200 Hz and wavelength 1.5 m. Find wave speed.</p>
<p>v = fλ = 200 × 1.5 = <strong>300 m/s</strong></p>
<h3 class="notes-h3">Transverse vs. Longitudinal Waves</h3>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Property</th><th>Transverse</th><th>Longitudinal</th></tr>
</thead><tbody>
<tr><td>Direction of vibration</td><td>Perpendicular to wave travel</td><td>Parallel to wave travel</td></tr>
<tr><td>Features</td><td>Crests and troughs</td><td>Compressions and rarefactions</td></tr>
<tr><td>Examples</td><td>Light, water waves, EM waves</td><td>Sound, seismic P-waves</td></tr>
<tr><td>Can travel in vacuum?</td><td>Yes (EM waves)</td><td>No</td></tr>
</tbody></table></div>
<h3 class="notes-h3">Reflection</h3>
<ul class="notes-list">
<li>Angle of incidence = Angle of reflection</li>
<li>Both angles measured from the normal (perpendicular to surface)</li>
<li>Applies to all waves (light, sound, water)</li>
</ul>
<h3 class="notes-h3">Refraction</h3>
<ul class="notes-list">
<li>Change in speed (and direction) as wave passes from one medium to another</li>
<li>Speed changes → wavelength changes → frequency stays CONSTANT</li>
<li>If slowing down → bends towards normal</li>
<li>If speeding up → bends away from normal</li>
</ul>
<pre class="code-block"><code>
Snell's Law [E]:
n₁ sin θ₁ = n₂ sin θ₂
</code></pre>
<p>or:</p>
<pre class="code-block"><code>
n = sin i / sin r (refractive index)
n = c / v
</code></pre>
<p>where c = speed of light in vacuum, v = speed of light in medium</p>
<p><strong>Critical angle and total internal reflection [E]:</strong></p>
<ul class="notes-list">
<li>When light goes from denser to less dense medium</li>
<li>If angle of incidence > critical angle → total internal reflection (no refraction)</li>
</ul>
<pre class="code-block"><code>
sin C = 1/n
</code></pre>
<p><strong>Applications:</strong> optical fibres (communications, endoscopes), diamond sparkle</p>
<h3 class="notes-h3">Diffraction</h3>
<ul class="notes-list">
<li>Spreading of waves around obstacles or through gaps</li>
<li>Most noticeable when gap size ≈ wavelength</li>
<li>All waves diffract (light, sound, water, EM)</li>
</ul>
<h3 class="notes-h3">Sound Waves</h3>
<ul class="notes-list">
<li><strong>Longitudinal</strong> mechanical waves</li>
<li>Require a medium to travel (cannot travel through vacuum)</li>
<li>Speed in air: ~340 m/s</li>
<li>Speed in solids > speed in liquids > speed in gases</li>
<li>Frequency range: 20 Hz – 20,000 Hz (human hearing)</li>
<li><strong>Ultrasound:</strong> frequency > 20,000 Hz</li>
</ul>
<p><strong>Pitch:</strong> determined by frequency (higher frequency → higher pitch)</p>
<p><strong>Loudness:</strong> determined by amplitude (larger amplitude → louder)</p>
<p><strong>Timbre/Quality:</strong> determined by waveform shape (different instruments at same pitch sound different)</p>
<p><strong>Ultrasound applications:</strong> sonar (echo sounding), foetal scanning, cleaning (breaking down deposits)</p>
<p><strong>Worked Example (echo):</strong> A ship sends a sonar pulse. Echo returns after 0.6 s. Speed of sound in water = 1500 m/s.</p>
<p>Distance = speed × time / 2 = 1500 × 0.6 / 2 = <strong>450 m</strong> (÷ 2 because pulse travels there and back)</p>
<hr class="section-divider">
<h2 class="notes-h2">TOPIC 7: LIGHT</h2>
<h3 class="notes-h3">Reflection of Light</h3>
<p><strong>Laws of Reflection:</strong></p>
<ol class="notes-list">
<li>Angle of incidence = Angle of reflection</li>
<li>Incident ray, reflected ray, and normal all lie in the same plane</li>
</ol>
<p><strong>Image in a plane mirror:</strong></p>
<ul class="notes-list">
<li>Same size as object</li>
<li>Same distance behind mirror as object in front</li>
<li>Laterally inverted (left-right reversed)</li>
<li>Virtual (cannot be projected on screen)</li>
<li>Upright</li>
</ul>
<h3 class="notes-h3">Refraction of Light</h3>
<p>Light bends at a boundary between materials of different optical density.</p>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Going from...</th><th>Speed</th><th>Bends</th></tr>
</thead><tbody>
<tr><td>Less dense to more dense (e.g., air → glass)</td><td>Decreases</td><td>Towards normal</td></tr>
<tr><td>More dense to less dense (e.g., glass → air)</td><td>Increases</td><td>Away from normal</td></tr>
</tbody></table></div>
<p><strong>Refractive index:</strong></p>
<pre class="code-block"><code>
n = sin(angle of incidence) / sin(angle of refraction)
n = speed in vacuum / speed in medium
n = real depth / apparent depth
</code></pre>
<h3 class="notes-h3">Total Internal Reflection [E]</h3>
<p>Occurs when:</p>
<ol class="notes-list">
<li>Light travels from more optically dense to less optically dense medium</li>
<li>Angle of incidence exceeds the critical angle</li>
</ol>
<pre class="code-block"><code>
sin C = 1/n (C = critical angle, n = refractive index)
</code></pre>
<p><strong>Optical fibres:</strong> light travels along core by total internal reflection</p>
<ul class="notes-list">
<li>Used in: telecommunications, medical endoscopes</li>
</ul>
<h3 class="notes-h3">Lenses [E]</h3>
<p><strong>Converging (convex) lens:</strong> thicker in middle, converges parallel rays to <strong>focal point</strong></p>
<p><strong>Diverging (concave) lens:</strong> thinner in middle, diverges parallel rays (appear to come from focal point on same side)</p>
<p><strong>Key terms:</strong></p>
<ul class="notes-list">
<li>Principal axis: horizontal line through centre of lens</li>
<li>Focal length (f): distance from lens centre to focal point</li>
<li>Optical centre: centre of lens</li>
</ul>
<p><strong>Image formation by converging lens:</strong></p>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Object position</th><th>Image type</th><th>Image position</th><th>Image size</th></tr>
</thead><tbody>
<tr><td>Beyond 2F</td><td>Real, inverted</td><td>Between F and 2F</td><td>Smaller</td></tr>
<tr><td>At 2F</td><td>Real, inverted</td><td>At 2F</td><td>Same size</td></tr>
<tr><td>Between F and 2F</td><td>Real, inverted</td><td>Beyond 2F</td><td>Larger</td></tr>
<tr><td>At F</td><td>No image (parallel rays)</td><td>At infinity</td><td>—</td></tr>
<tr><td>Between F and lens</td><td>Virtual, upright</td><td>Same side as object</td><td>Larger (magnifying glass)</td></tr>
</tbody></table></div>
<p><strong>Magnification:</strong></p>
<pre class="code-block"><code>
magnification = image height / object height = image distance / object distance
</code></pre>
<h3 class="notes-h3">The Electromagnetic Spectrum</h3>
<p>All EM waves:</p>
<ul class="notes-list">
<li>Travel at speed of light: c = 3 × 10⁸ m/s (in vacuum)</li>
<li>Are transverse waves</li>
<li>Transfer energy</li>
<li>Can travel through vacuum</li>
</ul>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Type</th><th>Wavelength</th><th>Frequency</th><th>Uses</th><th>Source</th></tr>
</thead><tbody>
<tr><td>Radio waves</td><td>Longest (>0.1 m)</td><td>Lowest</td><td>Radio/TV broadcast</td><td>Oscillating charges</td></tr>
<tr><td>Microwaves</td><td>1 mm – 0.1 m</td><td></td><td>Cooking, satellite comms, radar</td><td>Magnetron</td></tr>
<tr><td>Infra-red (IR)</td><td>700 nm – 1 mm</td><td></td><td>Heat transfer, remote controls, night vision</td><td>Hot objects</td></tr>
<tr><td>Visible light</td><td>400–700 nm</td><td></td><td>Sight, photography</td><td>Hot objects, LEDs</td></tr>
<tr><td>Ultraviolet (UV)</td><td>10–400 nm</td><td></td><td>Tanning, sterilisation, security marks</td><td>Very hot objects, UV lamps</td></tr>
<tr><td>X-rays</td><td>0.01–10 nm</td><td></td><td>Medical imaging, security scanners</td><td>X-ray tubes</td></tr>
<tr><td>Gamma rays</td><td>Shortest (<0.01 nm)</td><td>Highest</td><td>Cancer treatment, sterilisation, tracers</td><td>Radioactive decay</td></tr>
</tbody></table></div>
<p><strong>Hazards of EM waves:</strong></p>
<ul class="notes-list">
<li>UV: skin cancer, eye damage, sunburn</li>
<li>X-rays and gamma: ionising radiation — cell damage, cancer, mutation</li>
</ul>
<hr class="section-divider">
<h2 class="notes-h2">TOPIC 8: ELECTRICITY</h2>
<h3 class="notes-h3">Static Electricity</h3>
<ul class="notes-list">
<li>Friction causes electrons to transfer from one material to another</li>
<li>Object gaining electrons → negatively charged</li>
<li>Object losing electrons → positively charged</li>
<li><strong>Like charges repel; unlike charges attract</strong></li>
</ul>
<p><strong>Applications:</strong> photocopiers, inkjet printers, electrostatic precipitators (removing dust)</p>
<p><strong>Dangers:</strong> fuel tanker earthing, lightning</p>
<h3 class="notes-h3">Electric Current</h3>
<pre class="code-block"><code>
Current = charge / time
I = Q / t
</code></pre>
<p>Units: A (amperes), Q in coulombs (C), t in seconds</p>
<ul class="notes-list">
<li>Current is the rate of flow of charge</li>
<li><strong>Conventional current</strong> flows from + to – (opposite to electron flow)</li>
<li>Electrons flow from – to +</li>
</ul>
<h3 class="notes-h3">Potential Difference (Voltage)</h3>
<pre class="code-block"><code>
Voltage = energy / charge
V = W / Q
</code></pre>
<p>Units: V (volts)</p>
<ul class="notes-list">
<li>1 volt = 1 joule per coulomb</li>
</ul>
<h3 class="notes-h3">Resistance</h3>
<pre class="code-block"><code>
Resistance = voltage / current
R = V / I (Ohm's Law)
</code></pre>
<p>Units: Ω (ohms)</p>
<p><strong>Ohm's Law:</strong> Current is proportional to voltage for a metallic conductor at constant temperature.</p>
<p><strong>Worked Example:</strong> A resistor has 12 V across it and 3 A through it. Find resistance.</p>
<p>R = V/I = 12/3 = <strong>4 Ω</strong></p>
<p><strong>Ohmic conductor:</strong> straight line through origin on V-I graph</p>
<p><strong>Non-ohmic:</strong> filament lamp (resistance increases with temperature), diode (only conducts one way)</p>
<h3 class="notes-h3">Factors Affecting Resistance of a Wire</h3>
<ul class="notes-list">
<li>Length: longer → more resistance (R ∝ L)</li>
<li>Cross-sectional area: thicker → less resistance (R ∝ 1/A)</li>
<li>Material: different resistivities</li>
<li>Temperature: for metals, higher temperature → more resistance</li>
</ul>
<h3 class="notes-h3">Series Circuits</h3>
<ul class="notes-list">
<li>Components connected in a single loop</li>
<li>Same current throughout: I₁ = I₂ = I₃</li>
<li>Voltages add up: V_total = V₁ + V₂ + V₃</li>
<li>Resistances add: R_total = R₁ + R₂ + R₃</li>
</ul>
<h3 class="notes-h3">Parallel Circuits</h3>
<ul class="notes-list">
<li>Components connected in branches</li>
<li>Voltages are same across each branch: V₁ = V₂ = V₃</li>
<li>Currents add up: I_total = I₁ + I₂ + I₃</li>
<li>Combined resistance is less than smallest: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ [E]</li>
</ul>
<p><strong>Worked Example [E]:</strong> Two resistors, 6 Ω and 3 Ω, in parallel. Find combined resistance.</p>
<p>1/R = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2</p>
<p>R = <strong>2 Ω</strong></p>
<h3 class="notes-h3">Electrical Power and Energy</h3>
<pre class="code-block"><code>
Power = voltage × current
P = VI

Also: P = I²R and P = V²/R
</code></pre>
<pre class="code-block"><code>
Energy = power × time
E = Pt = VIt
</code></pre>
<p><strong>Worked Example:</strong> A bulb runs at 240 V, 0.5 A for 60 s. Find energy used.</p>
<p>E = VIt = 240 × 0.5 × 60 = <strong>7,200 J</strong></p>
<h3 class="notes-h3">Electrical Components</h3>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Component</th><th>Symbol description</th><th>Function</th></tr>
</thead><tbody>
<tr><td>Resistor</td><td>Box or rectangle</td><td>Restricts current</td></tr>
<tr><td>Variable resistor</td><td>Box with arrow</td><td>Adjustable resistance</td></tr>
<tr><td>Thermistor</td><td>Resistor with T or θ</td><td>Resistance decreases as temperature rises</td></tr>
<tr><td>LDR</td><td>Resistor with arrows</td><td>Resistance decreases as light increases</td></tr>
<tr><td>Diode</td><td>Triangle with bar</td><td>Allows current in one direction only</td></tr>
<tr><td>LED</td><td>Diode with arrows</td><td>Light-emitting diode</td></tr>
<tr><td>Capacitor [E]</td><td>Two parallel lines</td><td>Stores charge</td></tr>
<tr><td>Cell / Battery</td><td>Long and short lines</td><td>EMF source</td></tr>
<tr><td>Switch</td><td>Gap in line</td><td>Opens/closes circuit</td></tr>
<tr><td>Ammeter</td><td>Circle with A</td><td>Measures current (in series)</td></tr>
<tr><td>Voltmeter</td><td>Circle with V</td><td>Measures voltage (in parallel)</td></tr>
<tr><td>Fuse</td><td>Line through box</td><td>Safety device — melts if current too high</td></tr>
</tbody></table></div>
<h3 class="notes-h3">Domestic Electricity</h3>
<ul class="notes-list">
<li>UK/Kenya: 230–240 V AC (alternating current), 50 Hz</li>
<li><strong>AC:</strong> current direction reverses periodically</li>
<li><strong>DC:</strong> current flows in one direction only (batteries)</li>
</ul>
<p><strong>Three-pin plug wiring:</strong></p>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Wire</th><th>Colour</th><th>Connection</th></tr>
</thead><tbody>
<tr><td>Live</td><td>Brown (or red)</td><td>Fuse, then appliance</td></tr>
<tr><td>Neutral</td><td>Blue (or black)</td><td>Appliance return</td></tr>
<tr><td>Earth</td><td>Green/yellow stripes</td><td>Metal casing (safety)</td></tr>
</tbody></table></div>
<p><strong>Fuse:</strong> thin wire that melts if current exceeds rated value — protects appliance and wiring</p>
<p><strong>Earth wire:</strong> connects metal casing to earth — if live wire touches casing, current flows safely to earth and blows fuse</p>
<p><strong>Choosing fuse rating:</strong> just above normal operating current</p>
<ul class="notes-list">
<li>1 kW hairdryer at 240 V: I = P/V = 1000/240 ≈ 4.2 A → use 5 A fuse</li>
</ul>
<p><strong>Units of electrical energy (kWh):</strong></p>
<pre class="code-block"><code>
Energy (kWh) = Power (kW) × time (hours)
Cost = energy (kWh) × price per unit
</code></pre>
<hr class="section-divider">
<h2 class="notes-h2">TOPIC 9: MAGNETISM AND ELECTROMAGNETISM</h2>
<h3 class="notes-h3">Permanent Magnets</h3>
<ul class="notes-list">
<li><strong>Poles:</strong> north and south</li>
<li>Like poles repel; unlike poles attract</li>
<li>Magnetic field: region where a magnetic material experiences a force</li>
<li>Field lines run from north to south (outside the magnet)</li>
<li>Closer field lines → stronger field</li>
</ul>
<p><strong>Magnetic materials:</strong> iron, steel, nickel, cobalt (ferromagnetic)</p>
<p><strong>Non-magnetic:</strong> copper, aluminium, wood, plastic</p>
<p><strong>Hard magnetic materials</strong> (e.g., steel): retain magnetism → permanent magnets</p>
<p><strong>Soft magnetic materials</strong> (e.g., iron): magnetise and demagnetise easily → electromagnets, transformer cores</p>
<p><strong>Demagnetising:</strong> heating, hammering, AC current</p>
<h3 class="notes-h3">Magnetic Effect of a Current</h3>
<p>A wire carrying current produces a magnetic field around it.</p>
<p><strong>Right-hand grip rule (straight wire):</strong></p>
<ul class="notes-list">
<li>Thumb points in direction of conventional current</li>
<li>Fingers curl in direction of field lines</li>
</ul>
<p><strong>Magnetic field of a solenoid:</strong></p>
<ul class="notes-list">
<li>Field pattern similar to a bar magnet (field lines run along the axis)</li>
<li><strong>Right-hand rule for solenoid:</strong> curl fingers in direction of current → thumb points to north pole</li>
<li>Field strength increases with: more turns, higher current, iron core</li>
</ul>
<h3 class="notes-h3">Electromagnets</h3>
<p><strong>Structure:</strong> coil of insulated wire wrapped around soft iron core</p>
<p><strong>Uses:</strong> electric bells, relays (switching large currents with small currents), circuit breakers, loudspeakers, MRI scanners</p>
<h3 class="notes-h3">Force on a Current-Carrying Conductor</h3>
<p>A wire carrying current in a magnetic field experiences a force.</p>
<pre class="code-block"><code>
F = BIL [E]
</code></pre>
<p>where B = magnetic flux density (T), I = current (A), L = length in field (m)</p>
<p><strong>Fleming's Left-Hand Rule (motor effect):</strong></p>
<ul class="notes-list">
<li><strong>F</strong>irst finger: magnetic <strong>F</strong>ield (N to S)</li>
<li>se<strong>C</strong>ond finger: <strong>C</strong>onventional <strong>C</strong>urrent direction</li>
<li>thu<strong>M</strong>b: direction of <strong>M</strong>otion (force)</li>
</ul>
<p>Force is maximum when current ⊥ field; zero when current ∥ field.</p>
<p><strong>Uses:</strong> electric motors, loudspeakers, galvanometers</p>
<h3 class="notes-h3">The DC Electric Motor</h3>
<p><strong>Components:</strong> coil, commutator (split ring), brushes, permanent magnet</p>
<p><strong>Working principle:</strong></p>
<ol class="notes-list">
<li>Current in coil → forces on opposite sides of coil in opposite directions → rotational torque</li>
<li>Commutator reverses current direction every half-turn → coil keeps rotating the same way</li>
</ol>
<p><strong>Increasing motor speed:</strong> more current, stronger magnet, more turns in coil</p>
<h3 class="notes-h3">Electromagnetic Induction</h3>
<p>A voltage (EMF) is induced in a conductor when:</p>
<ul class="notes-list">
<li>It moves through a magnetic field</li>
<li>The magnetic field through it changes</li>
</ul>
<p><strong>Faraday's Law:</strong> The magnitude of induced EMF is proportional to the rate of change of magnetic flux. [E]</p>
<p><strong>Lenz's Law [E]:</strong> The induced current opposes the change causing it (conservation of energy).</p>
<p><strong>Fleming's Right-Hand Rule (generator effect):</strong></p>
<ul class="notes-list">
<li><strong>F</strong>irst finger: magnetic <strong>F</strong>ield</li>
<li>se<strong>C</strong>ond finger: induced <strong>C</strong>urrent</li>
<li>thu<strong>M</strong>b: direction of <strong>M</strong>otion</li>
</ul>
<p><strong>Increasing induced EMF:</strong> move faster, stronger magnet, more turns on coil</p>
<h3 class="notes-h3">The AC Generator</h3>
<p><strong>Components:</strong> coil, slip rings, brushes, magnets</p>
<p>As coil rotates:</p>
<ul class="notes-list">
<li>Cutting field lines → EMF induced</li>
<li>Slip rings (not commutator) → AC output</li>
<li>Output is sinusoidal (sine wave)</li>
</ul>
<h3 class="notes-h3">Transformers</h3>
<p>Change AC voltage (cannot change DC voltage).</p>
<pre class="code-block"><code>
Vₚ/Vₛ = Nₚ/Nₛ
</code></pre>
<p>where V = voltage, N = number of turns, p = primary, s = secondary</p>
<p><strong>Step-up transformer:</strong> Nₛ > Nₚ → Vₛ > Vₚ</p>
<p><strong>Step-down transformer:</strong> Nₛ < Nₚ → Vₛ < Vₚ</p>
<p><strong>For 100% efficiency [E]:</strong></p>
<pre class="code-block"><code>
Vₚ × Iₚ = Vₛ × Iₛ (input power = output power)
</code></pre>
<p><strong>Why transmit at high voltage?</strong></p>
<ul class="notes-list">
<li>Higher voltage → lower current (P = VI, same power)</li>
<li>Lower current → less power lost as heat in cables (P = I²R)</li>
<li>Energy more efficiently transmitted over long distances</li>
</ul>
<p><strong>National Grid:</strong> power stations → step-up transformer → high voltage cables → step-down transformer → homes/factories</p>
<p><strong>Worked Example:</strong> A transformer has 100 turns on primary, 500 turns on secondary. Input voltage = 12 V. Find output voltage.</p>
<p>Vₛ = Vₚ × (Nₛ/Nₚ) = 12 × (500/100) = <strong>60 V</strong></p>
<hr class="section-divider">
<h2 class="notes-h2">TOPIC 10: ATOMIC PHYSICS</h2>
<h3 class="notes-h3">The Nuclear Atom</h3>
<ul class="notes-list">
<li><strong>Nucleus:</strong> central, contains protons (+) and neutrons (no charge)</li>
<li><strong>Electrons:</strong> orbit nucleus in shells, negatively charged</li>
<li>Atom is mostly empty space</li>
</ul>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Particle</th><th>Charge</th><th>Mass (relative)</th><th>Location</th></tr>
</thead><tbody>
<tr><td>Proton</td><td>+1</td><td>1</td><td>Nucleus</td></tr>
<tr><td>Neutron</td><td>0</td><td>1</td><td>Nucleus</td></tr>
<tr><td>Electron</td><td>-1</td><td>1/1840</td><td>Shells around nucleus</td></tr>
</tbody></table></div>
<p><strong>Atomic number (Z):</strong> number of protons</p>
<p><strong>Mass number (A):</strong> number of protons + neutrons</p>
<p><strong>Number of neutrons = A − Z</strong></p>
<p><strong>Isotopes:</strong> atoms of the same element with the same number of protons but different numbers of neutrons.</p>
<p>Example: Carbon-12 (⁶₁₂C) and Carbon-14 (⁶₁₄C) — both have 6 protons, but 6 and 8 neutrons respectively.</p>
<h3 class="notes-h3">Radioactivity</h3>
<p><strong>Radioactive decay:</strong> unstable nuclei emit radiation spontaneously and randomly.</p>
<p><strong>Three types of radiation:</strong></p>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Type</th><th>Symbol</th><th>Composition</th><th>Charge</th><th>Mass</th><th>Penetration</th><th>Stopped by</th></tr>
</thead><tbody>
<tr><td>Alpha</td><td>α</td><td>2 protons + 2 neutrons (helium nucleus)</td><td>+2</td><td>4</td><td>Least</td><td>Paper, skin, few cm air</td></tr>
<tr><td>Beta</td><td>β</td><td>Fast electron from nucleus</td><td>-1</td><td>~0</td><td>Medium</td><td>Few mm aluminium</td></tr>
<tr><td>Gamma</td><td>γ</td><td>High-energy EM wave (photon)</td><td>0</td><td>0</td><td>Most</td><td>Several cm lead, thick concrete</td></tr>
</tbody></table></div>
<p><strong>Ionising ability:</strong> α > β > γ (alpha is most ionising, gamma is least)</p>
<p><strong>Penetrating ability:</strong> γ > β > α (gamma is most penetrating)</p>
<p><strong>Background radiation:</strong> naturally occurring radiation from:</p>
<ul class="notes-list">
<li>Rocks and soil (radon gas from granite)</li>
<li>Cosmic rays from space</li>
<li>Food and drink (potassium-40)</li>
<li>Medical sources (X-rays)</li>
<li>Nuclear power stations (small contribution)</li>
</ul>
<p><strong>Detecting radiation:</strong> Geiger-Muller (GM) tube</p>
<h3 class="notes-h3">Radioactive Decay Equations</h3>
<p><strong>Alpha decay:</strong></p>
<ul class="notes-list">
<li>Mass number decreases by 4</li>
<li>Atomic number decreases by 2</li>
<li>Example: ²³⁸U → ²³⁴Th + ⁴He (alpha particle)</li>
</ul>
<p><strong>Beta decay:</strong></p>
<ul class="notes-list">
<li>Mass number stays the same</li>
<li>Atomic number increases by 1</li>
<li>A neutron turns into a proton + electron</li>
<li>Example: ¹⁴C → ¹⁴N + ⁰₋₁e (beta particle)</li>
</ul>
<p><strong>Gamma emission:</strong></p>
<ul class="notes-list">
<li>No change in mass number or atomic number</li>
<li>Often follows alpha or beta decay</li>
<li>Just emits energy as gamma ray</li>
</ul>
<h3 class="notes-h3">Half-Life</h3>
<p><strong>Half-life (t½):</strong> the time taken for half the nuclei in a sample to decay (or activity to halve).</p>
<ul class="notes-list">
<li>Radioactive decay is random (cannot predict which nucleus will decay next)</li>
<li>Half-life is constant for a given isotope</li>
<li>Activity = number of decays per second (Bq = becquerels)</li>
</ul>
<p><strong>Worked Example:</strong> An isotope has half-life 2 hours. Initial count rate = 400 Bq. Find count rate after 6 hours.</p>
<p>6 hours = 3 half-lives</p>
<p>After 1 half-life: 200 Bq</p>
<p>After 2 half-lives: 100 Bq</p>
<p>After 3 half-lives: <strong>50 Bq</strong></p>
<p><strong>Reading half-life from a graph:</strong> find time for activity to halve on the y-axis; read corresponding time on x-axis.</p>
<h3 class="notes-h3">Uses of Radioactivity</h3>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Use</th><th>Radiation Used</th><th>Why</th></tr>
</thead><tbody>
<tr><td>Medical tracers</td><td>Gamma (e.g., ⁹⁹mTc)</td><td>Penetrates body, detected outside</td></tr>
<tr><td>Treating cancer</td><td>Gamma</td><td>Kills tumour cells</td></tr>
<tr><td>Sterilising medical equipment</td><td>Gamma</td><td>Kills bacteria</td></tr>
<tr><td>Thickness gauging (paper/metal)</td><td>Beta</td><td>Partially absorbed; monitor thickness</td></tr>
<tr><td>Smoke detectors</td><td>Alpha (⁲⁴¹Am)</td><td>Alpha ionises air; smoke interrupts ionisation</td></tr>
<tr><td>Carbon dating</td><td>Beta (¹⁴C)</td><td>Known half-life, compares ratio in organic material</td></tr>
</tbody></table></div>
<h3 class="notes-h3">Safety with Radioactive Sources</h3>
<ul class="notes-list">
<li>Handle with long tongs (not bare hands)</li>
<li>Minimise time of exposure</li>
<li>Increase distance from source</li>
<li>Use shielding (lead, thick glass)</li>
<li>Store in lead-lined containers</li>
<li>No eating/drinking near sources</li>
<li>Monitor exposure with dosimeter badge</li>
</ul>
<h3 class="notes-h3">Nuclear Fission and Fusion [E]</h3>
<p><strong>Fission:</strong> Large nucleus splits into two smaller nuclei + neutrons + energy</p>
<ul class="notes-list">
<li>Example: uranium-235 bombarded by neutron → splits → releases 2–3 neutrons → chain reaction</li>
<li>Used in nuclear power stations and atomic bombs</li>
<li>Releases large amounts of energy</li>
</ul>
<p><strong>Fusion:</strong> Two small nuclei combine to form a larger nucleus + energy</p>
<ul class="notes-list">
<li>Example: hydrogen isotopes (deuterium + tritium) → helium + neutron + energy</li>
<li>The process powering the Sun and stars</li>
<li>More energy released than fission</li>
<li>Requires extreme temperatures (plasma) — not yet sustained for power generation</li>
</ul>
<hr class="section-divider">
<h2 class="notes-h2">TOPIC 11: SPACE PHYSICS [E]</h2>
<h3 class="notes-h3">The Solar System</h3>
<ul class="notes-list">
<li>Sun + 8 planets + moons + asteroids + comets + dwarf planets</li>
<li>Planets orbit Sun due to gravitational attraction</li>
<li>Inner planets (rocky): Mercury, Venus, Earth, Mars</li>
<li>Outer planets (gas giants): Jupiter, Saturn, Uranus, Neptune</li>
</ul>
<p><strong>Orbital period:</strong> time to complete one orbit</p>
<p><strong>Closer to Sun → shorter orbital period → faster orbital speed</strong></p>
<h3 class="notes-h3">Stars and Galaxies</h3>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Object</th><th>Scale</th></tr>
</thead><tbody>
<tr><td>Earth diameter</td><td>~13,000 km</td></tr>
<tr><td>Sun diameter</td><td>~1.4 million km</td></tr>
<tr><td>Solar System diameter</td><td>~9 × 10¹² m</td></tr>
<tr><td>Milky Way galaxy</td><td>~10²¹ m across</td></tr>
<tr><td>Observable universe</td><td>~10²⁶ m</td></tr>
</tbody></table></div>
<p><strong>Light year:</strong> distance light travels in one year ≈ 9.46 × 10¹⁵ m</p>
<h3 class="notes-h3">Life Cycle of a Star</h3>
<p><strong>Small/medium stars (like the Sun):</strong></p>
<p>Nebula → Protostar → Main sequence star → Red giant → White dwarf → Black dwarf</p>
<p><strong>Massive stars:</strong></p>
<p>Nebula → Protostar → Main sequence star → Red supergiant → Supernova → Neutron star or Black hole</p>
<p><strong>Main sequence:</strong> star is stable — inward gravitational collapse balanced by outward radiation pressure from nuclear fusion.</p>
<h3 class="notes-h3">The Big Bang Theory</h3>
<ul class="notes-list">
<li>Universe began ~13.8 billion years ago from a very hot, very dense point</li>
<li>Evidence: universe is expanding (galaxies moving apart), cosmic microwave background radiation</li>
<li><strong>Red shift:</strong> light from distant galaxies is shifted to longer (red) wavelengths, indicating they are moving away from us</li>
<li>The further the galaxy, the greater the red shift (Hubble's Law) — the universe is expanding uniformly</li>
</ul>
<hr class="section-divider">
<h2 class="notes-h2">PRACTICAL SKILLS — PAPER 5 & 6 GUIDE</h2>
<h3 class="notes-h3">Common Practical Investigations</h3>
<h4 class="notes-h4">Measuring g (acceleration of free fall)</h4>
<ul class="notes-list">
<li>Use a ticker timer or photogate with a falling mass</li>
<li>Measure time to fall known distance</li>
<li>Calculate g = 2s/t²</li>
</ul>
<h4 class="notes-h4">Determining Density</h4>
<ol class="notes-list">
<li>Mass: use balance</li>
<li>Volume: regular shape (calculate) or irregular (displacement can)</li>
<li>Density = mass/volume</li>
</ol>
<h4 class="notes-h4">Ohm's Law Investigation</h4>
<ol class="notes-list">
<li>Circuit: battery, variable resistor, ammeter (in series), voltmeter (in parallel with resistor)</li>
<li>Vary resistance → record V and I</li>
<li>Plot V vs I → gradient = resistance</li>
<li>Ohmic conductor: straight line through origin</li>
</ol>
<h4 class="notes-h4">Specific Heat Capacity [E]</h4>
<ol class="notes-list">
<li>Heat a known mass of substance using electrical heater</li>
<li>Record temperature change</li>
<li>Measure energy: E = Pt or E = VIt</li>
<li>Calculate c = Q/(mΔT)</li>
</ol>
<h4 class="notes-h4">Speed of Sound (echo method)</h4>
<ul class="notes-list">
<li>Stand measured distance from a wall</li>
<li>Clap boards → listen for echo → time the echoes</li>
<li>Speed = 2d/t</li>
</ul>
<h3 class="notes-h3">Graph Skills</h3>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Task</th><th>Method</th></tr>
</thead><tbody>
<tr><td>Drawing best-fit line</td><td>Straight line with equal scatter on both sides (not dot-to-dot)</td></tr>
<tr><td>Finding gradient</td><td>Choose two distant points on line; rise/run</td></tr>
<tr><td>Finding y-intercept</td><td>Read off where line crosses y-axis</td></tr>
<tr><td>Identifying anomalous point</td><td>Point clearly off the trend line — circle it, do not include in best-fit</td></tr>
</tbody></table></div>
<p><strong>Error bars [E]:</strong> show uncertainty in measurements; best-fit line should pass through all error bars.</p>
<h3 class="notes-h3">Common Practical Errors</h3>
<ul class="notes-list">
<li><strong>Zero error:</strong> instrument reads non-zero when measuring nothing → subtract from all readings</li>
<li><strong>Parallax error:</strong> reading scale at an angle → view straight on</li>
<li><strong>Systematic error:</strong> same in every reading — shown by graph not passing through origin</li>
<li><strong>Random error:</strong> different each time — reduced by repeating and averaging</li>
</ul>
<hr class="section-divider">
<h2 class="notes-h2">EXAM TECHNIQUE GUIDE</h2>
<h3 class="notes-h3">Cambridge Command Words</h3>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Command word</th><th>What to do</th></tr>
</thead><tbody>
<tr><td><strong>State</strong></td><td>Give a brief answer — one word or sentence, no explanation needed</td></tr>
<tr><td><strong>Define</strong></td><td>Give the precise scientific meaning</td></tr>
<tr><td><strong>Describe</strong></td><td>Say what happens — no need to explain why</td></tr>
<tr><td><strong>Explain</strong></td><td>Give reasons, use scientific vocabulary, say why</td></tr>
<tr><td><strong>Calculate</strong></td><td>Show working, give answer with unit</td></tr>
<tr><td><strong>Show that</strong></td><td>All working must be shown; verify given answer</td></tr>
<tr><td><strong>Sketch</strong></td><td>Rough diagram — labelled, not to scale</td></tr>
<tr><td><strong>Draw</strong></td><td>Accurate diagram, usually with ruler</td></tr>
<tr><td><strong>Determine</strong></td><td>Find a value from data or graph</td></tr>
<tr><td><strong>Suggest</strong></td><td>Apply knowledge to new situation — may be more than one correct answer</td></tr>
<tr><td><strong>Compare</strong></td><td>State similarities AND differences</td></tr>
</tbody></table></div>
<h3 class="notes-h3">Mark Types in Physics</h3>
<ul class="notes-list">
<li><strong>M marks:</strong> Method marks — correct approach even if arithmetic wrong</li>
<li><strong>A marks:</strong> Accuracy marks — correct answer (usually require M mark first)</li>
<li><strong>B marks:</strong> Independent marks — awarded regardless of other working</li>
<li><strong>ECF:</strong> Error carried forward — if wrong answer used correctly in next step, may still earn marks</li>
</ul>
<p><strong>ALWAYS:</strong> show substitution, working, and unit in calculations.</p>
<h3 class="notes-h3">Common Mistakes</h3>
<ol class="notes-list">
<li><strong>Forces:</strong> confusing mass (kg) and weight (N) — always use W = mg</li>
<li><strong>Circuits:</strong> connecting voltmeter in series (should be parallel) or ammeter in parallel</li>
<li><strong>Waves:</strong> saying wavelength changes during refraction (frequency is constant, not wavelength!)</li>
<li><strong>Radioactivity:</strong> confusing penetrating power with ionising power (they are inversely related)</li>
<li><strong>Graphs:</strong> drawing best-fit line through every point instead of line of best fit</li>
<li><strong>Units:</strong> forgetting units on calculated answers — always include</li>
<li><strong>Temperature:</strong> using °C instead of Kelvin in gas law calculations</li>
<li><strong>Transformers:</strong> applying transformer equations to DC (transformers only work with AC)</li>
<li><strong>Momentum:</strong> forgetting direction is important (momentum is a vector)</li>
<li><strong>Heat/Temperature:</strong> confusing the two concepts</li>
</ol>
<h3 class="notes-h3">Exam Checklist</h3>
<p>Before handing in Paper:</p>
<ul class="notes-list">
<li>[ ] Every calculation shows working and has a unit</li>
<li>[ ] Arrows on circuit diagrams (conventional current direction)</li>
<li>[ ] Graphs: axes labelled with quantity AND unit, sensible scales, best-fit line drawn</li>
<li>[ ] Diagrams: labelled, drawn in pencil (for changes)</li>
<li>[ ] "Describe" questions say what happens; "Explain" questions say WHY</li>
<li>[ ] Significant figures match precision of given data (usually 2–3 s.f.)</li>
<li>[ ] Check: have you answered every part of every question?</li>
</ul>
<hr class="section-divider">
<h2 class="notes-h2">KEY FORMULAE SUMMARY SHEET</h2>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Quantity</th><th>Formula</th><th>Units</th></tr>
</thead><tbody>
<tr><td>Speed</td><td>v = d/t</td><td>m/s</td></tr>
<tr><td>Acceleration</td><td>a = (v-u)/t</td><td>m/s²</td></tr>
<tr><td>Newton's 2nd Law</td><td>F = ma</td><td>N</td></tr>
<tr><td>Weight</td><td>W = mg</td><td>N</td></tr>
<tr><td>Momentum [E]</td><td>p = mv</td><td>kg m/s</td></tr>
<tr><td>Moment</td><td>M = Fd</td><td>Nm</td></tr>
<tr><td>Pressure</td><td>P = F/A</td><td>Pa</td></tr>
<tr><td>Fluid pressure</td><td>P = ρgh</td><td>Pa</td></tr>
<tr><td>Density</td><td>ρ = m/V</td><td>kg/m³</td></tr>
<tr><td>Work done</td><td>W = Fd</td><td>J</td></tr>
<tr><td>KE</td><td>KE = ½mv²</td><td>J</td></tr>
<tr><td>GPE</td><td>GPE = mgh</td><td>J</td></tr>
<tr><td>Power</td><td>P = W/t = VI</td><td>W</td></tr>
<tr><td>Efficiency</td><td>% = useful/total × 100</td><td>%</td></tr>
<tr><td>Specific heat [E]</td><td>Q = mcΔT</td><td>J</td></tr>
<tr><td>Latent heat [E]</td><td>Q = mL</td><td>J</td></tr>
<tr><td>Wave speed</td><td>v = fλ</td><td>m/s</td></tr>
<tr><td>Period</td><td>T = 1/f</td><td>s</td></tr>
<tr><td>Refractive index [E]</td><td>n = sin i/sin r</td><td>—</td></tr>
<tr><td>Current</td><td>I = Q/t</td><td>A</td></tr>
<tr><td>Voltage</td><td>V = W/Q</td><td>J/C</td></tr>
<tr><td>Resistance</td><td>R = V/I</td><td>Ω</td></tr>
<tr><td>Power</td><td>P = VI = I²R</td><td>W</td></tr>
<tr><td>Transformer [E]</td><td>Vp/Vs = Np/Ns</td><td>—</td></tr>
<tr><td>Force on wire [E]</td><td>F = BIL</td><td>N</td></tr>
<tr><td>Half-life</td><td>N = N₀ × (½)ⁿ</td><td>—</td></tr>
</tbody></table></div>
<p><strong>Constants:</strong></p>
<ul class="notes-list">
<li>g = 10 N/kg = 10 m/s² (on Earth)</li>
<li>Speed of light: c = 3 × 10⁸ m/s</li>
<li>Speed of sound in air: ~340 m/s</li>
</ul>
<hr class="section-divider">
<h2 class="notes-h2">FREQUENTLY TESTED TOPICS (PAST PAPER ANALYSIS)</h2>
<div class="table-wrap"><table class="notes-table">
<thead>
<tr><th>Topic</th><th>High-Probability Questions</th><th>Notes</th></tr>
</thead><tbody>
<tr><td>Velocity-time graphs</td><td>Calculating acceleration and distance</td><td>Area under graph = distance</td></tr>
<tr><td>Circuit calculations</td><td>Series/parallel, V=IR, power</td><td>Draw circuit diagram first</td></tr>
<tr><td>Transformer equations</td><td>Turns ratio, efficiency</td><td>Extended only: current ratios</td></tr>
<tr><td>Half-life</td><td>Calculating activity after n half-lives</td><td>Use graph or halving method</td></tr>
<tr><td>EM spectrum</td><td>Naming types, applications, hazards</td><td>Learn in wavelength order</td></tr>
<tr><td>Forces in equilibrium</td><td>Moments, free body diagrams</td><td>Both sides of pivot must balance</td></tr>
<tr><td>Reflection/refraction</td><td>Drawing ray diagrams, Snell's Law</td><td>Angles from normal, not surface</td></tr>
<tr><td>Pressure in fluids</td><td>P = ρgh, hydraulics</td><td>Remember depth, not height of container</td></tr>
<tr><td>Fleming's rules</td><td>Motor vs generator effect</td><td>Left hand = motor; Right hand = generator</td></tr>
<tr><td>Radioactive decay equations</td><td>Alpha/beta equations</td><td>Check proton numbers balance</td></tr>
</tbody></table></div>
<hr class="section-divider">
<h2 class="notes-h2">DOWNLOAD FULL IGCSE PHYSICS RESOURCES</h2>
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