Tick off each objective as you master it. These are the exact learning objectives from the Cambridge 0625 syllabus (2026-2028).
Physics is built on measurement. Every formula you use, every calculation you do, and every experiment you run depends on measuring quantities accurately. In IGCSE, roughly 20% of your marks come from experimental skills — and those skills begin with knowing how to measure things properly and why certain instruments are better than others for particular jobs.
Think of it this way: if a doctor measures your temperature with an instrument that's off by 2°C, they might miss that you have a fever. In physics, using the wrong instrument or reading it incorrectly can make your entire experiment worthless. That's why Cambridge tests this topic so carefully.
All measurements in physics are built from a small set of base units agreed upon internationally (SI = Système International). For IGCSE, you need to know these key ones:
| Quantity | SI Base Unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric current | ampere | A |
| Temperature | kelvin | K |
Every other unit you encounter in physics is derived from these base units. For example, speed is measured in metres per second (m/s) — that's just length ÷ time. Force is measured in newtons (N), but 1 N = 1 kg·m/s² — it's built from mass, length, and time. Understanding this helps you check your answers: if you calculate a force and your units come out as "kg/m", you know something went wrong.
Physics deals with everything from the size of atoms (0.000000001 m) to the distance to stars (thousands of billions of metres). Prefixes save us from writing all those zeros:
| Prefix | Symbol | Multiplier | Example |
|---|---|---|---|
| giga | G | 10⁹ = 1,000,000,000 | 3.2 GHz (processor speed) |
| mega | M | 10⁶ = 1,000,000 | 50 MW (power station) |
| kilo | k | 10³ = 1,000 | 2.5 km (distance) |
| centi | c | 10⁻² = 0.01 | 30 cm (ruler length) |
| milli | m | 10⁻³ = 0.001 | 250 mA (current) |
| micro | μ | 10⁻⁶ = 0.000001 | 50 μs (time interval) |
| nano | n | 10⁻⁹ = 0.000000001 | 550 nm (wavelength of light) |
Understanding how units are derived is crucial for IGCSE. The examiner may ask you to "show that" a unit is correct, or you'll need to check your calculation by looking at units:
| Quantity | Formula | Unit | Built from |
|---|---|---|---|
| Speed | v = s/t | m/s | metre ÷ second |
| Acceleration | a = Δv/Δt | m/s² | (m/s) ÷ s |
| Force | F = ma | N (newton) | kg × m/s² = kg·m/s² |
| Pressure | p = F/A | Pa (pascal) | N/m² = kg/(m·s²) |
| Energy | E = Fd | J (joule) | N·m = kg·m²/s² |
| Power | P = E/t | W (watt) | J/s = kg·m²/s³ |
| Density | ρ = m/V | kg/m³ | kilogram ÷ metre³ |
Rulers are the simplest length-measuring instrument. A standard ruler measures to the nearest millimetre (1 mm = 0.1 cm), so its resolution is 1 mm. When using a ruler:
• Place the zero mark exactly at one end of the object (don't always trust the very end of the ruler — it may be worn)
• Read the scale with your eye directly above the mark to avoid parallax error — this is when you read a different value because you're looking at an angle
• For thin objects, measure multiple thicknesses and divide (e.g., stack 20 sheets of paper, measure the total, divide by 20)
Vernier Calipers are used for lengths between about 1 cm and 15 cm, with a resolution of 0.01 cm (0.1 mm). They have two scales:
Micrometer Screw Gauge measures small lengths (up to about 25 mm) with a resolution of 0.01 mm. It's used for things like wire diameter, paper thickness, or ball bearing diameter.
Measuring Cylinders measure the volume of liquids. The liquid surface curves (this curve is called the meniscus). For water and most liquids, the meniscus curves downward, and you should read from the bottom of the meniscus with your eye level with the liquid surface.
Electronic Balance measures mass (not weight!). Make sure it reads zero before placing the object (tare/zero function). Digital balances typically read to 0.1 g or 0.01 g.
Stopwatch/Digital Timer measures time intervals. Human reaction time is about 0.3–0.5 seconds, so for short intervals, this introduces significant error. To reduce this error: measure multiple cycles and divide. For a pendulum, time 20 complete swings and divide by 20 — this makes the reaction time error negligible compared to the total time measured.
Accuracy means how close a measurement is to the true value. If the true length of a rod is 25.0 cm and you measure 24.9 cm, that's accurate.
Precision means how close repeated measurements are to each other. If you measure the rod five times and get 24.1, 24.1, 24.2, 24.1, 24.1 cm — that's precise (they're very close together) but not accurate (they're all about 1 cm too low — maybe there's a zero error).
An analogy: Imagine throwing darts at a dartboard. Accurate = the darts cluster around the bullseye. Precise = the darts cluster tightly together (but maybe not at the bullseye).
In IGCSE, your answer should have the same number of significant figures as the data given in the question (usually 2 or 3). Key rules:
• All non-zero digits are significant: 345 has 3 sig figs
• Zeros between non-zero digits are significant: 3045 has 4 sig figs
• Leading zeros are NOT significant: 0.0034 has 2 sig figs
• Trailing zeros after a decimal point ARE significant: 3.40 has 3 sig figs
One of the most important experimental techniques in IGCSE is measuring multiples to improve accuracy. If you need to find the thickness of one sheet of paper:
1. Measure the thickness of 50 sheets together (say, 4.2 mm)
2. Divide by 50: 4.2 ÷ 50 = 0.084 mm
This is far more accurate than trying to measure one sheet, which might be thinner than your instrument's resolution.
Similarly, for timing a pendulum: time 20 complete oscillations, then divide by 20 to get the period of one oscillation. This reduces the impact of reaction time error.
These definitions use the exact wording expected in IGCSE mark schemes. Click each term to reveal.
A student uses a micrometer screw gauge to measure the diameter of a wire. The zero error of the micrometer is +0.04 mm. The micrometer reading with the wire between the jaws is 1.58 mm.
Calculate the true diameter of the wire.
✓ True reading = observed reading − zero error [1 mark for method]
True diameter = 1.58 − 0.04
✓ True diameter = 1.54 mm [1 mark for correct answer]
A student times 20 complete oscillations of a pendulum and records the following times: 28.4 s, 28.2 s, 28.6 s.
(a) Calculate the average time for 20 oscillations. [1]
(b) Calculate the period of one oscillation. [1]
(c) Explain why the student times 20 oscillations rather than just one. [1]
(a)
Average = (28.4 + 28.2 + 28.6) ÷ 3 = 85.2 ÷ 3
✓ Average = 28.4 s [1 mark]
(b)
Period = 28.4 ÷ 20
✓ Period = 1.42 s [1 mark]
(c)
✓ Timing 20 oscillations reduces the effect of human reaction time error / makes the percentage error in the timing smaller, giving a more accurate value for the period. [1 mark]
Explain why a micrometer screw gauge is more suitable than a ruler for measuring the diameter of a thin wire.
✓ A micrometer has a higher resolution / smaller scale divisions (0.01 mm) than a ruler (1 mm). [1 mark]
✓ The wire diameter is very small (perhaps less than 1 mm), so a ruler cannot measure it precisely enough / the percentage uncertainty with a ruler would be too large. [1 mark]
A student wants to find the thickness of one page of a textbook. Describe a method the student could use.
✓ Measure the total thickness of a large number of pages (e.g., 100 pages) using a ruler or vernier caliper. [1 mark]
✓ Divide the total thickness by the number of pages to find the thickness of one page. [1 mark]
✓ This is more accurate because measuring one page directly would give a reading smaller than the resolution of the instrument / the percentage error is reduced when measuring a larger value. [1 mark]
Convert the following:
(a) 0.075 km to cm [1]
(b) 4500 mg to kg [1]
(a) 0.075 km × 1000 = 75 m; 75 m × 100 = 7500 cm
✓ 7500 cm [1 mark]
(b) 4500 mg ÷ 1000 = 4.5 g; 4.5 g ÷ 1000 = 0.0045 kg
✓ 0.0045 kg (or 4.5 × 10⁻³ kg) [1 mark]
Which instrument is most suitable for measuring the internal diameter of a test tube?
A student measures the time for 20 swings of a pendulum as 34.0 s. What is the period of one swing?
A micrometer has a zero error of −0.03 mm. When measuring a ball bearing, the reading is 5.62 mm. Calculate the true diameter of the ball bearing.
Explain two precautions a student should take when using a measuring cylinder to measure the volume of a liquid accurately.
Which of these is a systematic error?
Convert 0.056 km into (a) metres and (b) centimetres.
A student wants to determine the thickness of one sheet of aluminium foil. Describe a suitable method and explain why this method is better than trying to measure one sheet directly.
The vernier caliper reading shows 3.4 cm on the main scale and the 7th vernier division aligns with a main scale mark. What is the reading?
Explain the difference between accuracy and precision, giving an example of measurements that are precise but not accurate.
A student investigates how the period of a pendulum depends on its length. State the independent variable, the dependent variable, and one variable that should be controlled.
Units & Measurements questions typically appear at the start of Paper 4 (the "easy marks" section) and in Paper 6 (practical). Budget about 10–15 minutes across both papers. These are marks you cannot afford to lose — they're straightforward if you know the instruments.
Paper 2 (MCQ): 2–4 questions on instruments, units, prefixes, errors. Know your instruments and how to read them.
Paper 4 (Theory): Usually 1 structured question, often combined with density or motion (e.g., "describe how you would measure the density of an irregularly shaped solid").
Paper 6 (Practical): This is where measurements are tested most heavily — reading scales, recording data, identifying errors, plotting graphs.
"Describe" → Give the steps of a method (e.g., "Describe how to measure the period of a pendulum" — list the equipment, the steps, and any precautions).
"Explain" → Say WHY (e.g., "Explain why timing 20 oscillations is better" — because it reduces the effect of reaction time error).
"State" → A brief, factual answer (e.g., "State the resolution of a micrometer" → 0.01 mm).
"Calculate" → Show your working: formula → substitution → answer with units.
• Always include units in your final answer
• For "calculate" questions, show: FORMULA → SUBSTITUTION → ANSWER. Even if your arithmetic is wrong, you get marks for the method
• If asked about zero error: state whether it's positive or negative, then show: True = Observed − Zero error
• For "describe a method" questions: state the instrument, the procedure, and how you'd get the final answer
Speed is defined as the distance travelled per unit time: v = s/t. It's a scalar quantity — it only has magnitude (size), not direction. If you run around a circular track and end up where you started, your speed might have been 5 m/s throughout, even though you haven't gone anywhere in a straight line.
Velocity is speed in a given direction. It's a vector quantity — it has both magnitude AND direction. This distinction matters: if you run at 5 m/s north then turn and run at 5 m/s south, your speed hasn't changed, but your velocity has (it changed direction).
Acceleration is the rate of change of velocity: a = Δv/Δt = (v − u)/t, where u is initial velocity, v is final velocity, and t is the time taken. Acceleration is also a vector. If an object slows down, it has a negative acceleration (deceleration). Units: m/s².
These graphs show how far an object has travelled from its starting point over time. The key thing to remember: the gradient (slope) of a distance-time graph = speed.
• Horizontal line → object is stationary (speed = 0)
• Straight diagonal line → constant speed (the steeper the line, the faster the object)
• Curve getting steeper → object is accelerating (speed is increasing)
• Curve getting flatter → object is decelerating (speed is decreasing)
To calculate speed from a straight section: pick two points on the line, then speed = change in distance ÷ change in time = (d₂ − d₁) ÷ (t₂ − t₁).
These are more information-rich. Two key rules:
1. Gradient = acceleration (positive gradient = acceleration, negative gradient = deceleration, zero gradient = constant speed)
2. Area under the graph = distance travelled
• Horizontal line → constant speed (acceleration = 0)
• Line sloping upward → constant acceleration
• Line sloping downward → constant deceleration
• Curve → changing acceleration
To calculate distance from a speed-time graph, find the area under the line. For a triangle: ½ × base × height. For a trapezoid: ½ × (sum of parallel sides) × height. For complex shapes, split into rectangles and triangles.
Near the Earth's surface, all objects fall with the same acceleration regardless of their mass (ignoring air resistance). This acceleration is g ≈ 9.8 m/s² (often rounded to 10 m/s² in IGCSE calculations). This means that every second, a falling object's speed increases by about 10 m/s.
Note: g is both the acceleration of free fall AND the gravitational field strength. Its value as acceleration is 9.8 m/s², and as field strength is 9.8 N/kg. These are numerically the same but conceptually different.
Mass is the quantity of matter in an object. It's measured in kilograms (kg) and does NOT change with location. Your mass is the same on Earth, on the Moon, or in space.
Weight is the gravitational force acting on an object. It's calculated using W = mg where m is mass and g is the gravitational field strength. Weight DOES change with location — on the Moon (g ≈ 1.6 N/kg), you'd weigh about 1/6 of your Earth weight.
Density is mass per unit volume: ρ = m/V. It tells you how "packed together" the matter is. Water has a density of 1000 kg/m³ (or 1 g/cm³). Objects with density less than water will float; those with higher density will sink.
First Law: An object remains at rest, or continues to move in a straight line at constant speed, unless acted on by a resultant force. This is about inertia — objects resist changes to their motion. A book on a table stays still because the forces on it (gravity down, normal contact force up) are balanced — the resultant force is zero.
Second Law: The resultant force on an object is equal to the rate of change of its momentum. For a constant mass, this gives us F = ma. The acceleration is in the same direction as the resultant force. Double the force → double the acceleration. Double the mass → half the acceleration.
Third Law: When object A exerts a force on object B, object B exerts an equal and opposite force on object A. These forces are the same type, act on different objects, and are equal in magnitude but opposite in direction. Example: when you push a wall, the wall pushes you back with equal force.
Friction is a force that opposes motion between two surfaces in contact. Air resistance (drag) is a type of friction that acts on objects moving through air. Key facts about air resistance:
• It increases as the object moves faster
• It depends on the object's shape and surface area
• It acts in the opposite direction to the motion
Terminal velocity is reached when a falling object's air resistance equals its weight. At this point, the resultant force is zero, so acceleration is zero, and the object falls at constant speed. The full sequence:
1. Object starts falling → air resistance is small (low speed) → weight > air resistance → resultant force downward → object accelerates
2. As speed increases → air resistance increases → resultant force decreases → acceleration decreases
3. Eventually → air resistance = weight → resultant force = 0 → acceleration = 0 → terminal velocity reached
Momentum (p) = mass × velocity: p = mv. It's a vector quantity, measured in kg·m/s. Momentum is important because it is conserved in collisions.
Conservation of momentum: In a collision (or explosion) where no external forces act, the total momentum before = total momentum after.
For two objects colliding: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Impulse = force × time = change in momentum: FΔt = Δ(mv). This explains why catching a ball hurts less if you move your hands back — you increase the time over which the momentum changes, reducing the force.
The moment of a force is its turning effect about a pivot: moment = force × perpendicular distance from the pivot. Measured in N·m.
Principle of moments: For an object in equilibrium, the sum of clockwise moments about any point = sum of anticlockwise moments about that point.
The centre of gravity is the point where all the weight of an object can be considered to act. For a uniform object, it's at the geometric centre. A low centre of gravity and wide base = more stable object (harder to topple).
Kinetic energy: Ek = ½mv² (energy of a moving object)
Gravitational potential energy: ΔEp = mgΔh (energy stored due to height)
Work done: W = Fd (energy transferred when a force moves through a distance)
Power: P = W/t = E/t (rate of energy transfer or work done)
Efficiency = (useful energy output / total energy input) × 100%
The principle of conservation of energy states that energy cannot be created or destroyed, only transferred from one store to another. In practice, energy is often transferred to thermal energy (heat) by friction, which is the "wasted" energy.
A car accelerates from rest to 25 m/s in 10 s. Calculate:
(a) the acceleration of the car [2]
(b) the distance travelled during this acceleration [1]
(a)
a = (v − u) / t
✓ a = (25 − 0) / 10 [1 mark for correct substitution]
✓ a = 2.5 m/s² [1 mark for correct answer with unit]
(b)
Distance = area under speed-time graph = ½ × base × height = ½ × 10 × 25
✓ Distance = 125 m [1 mark]
A stone of mass 0.2 kg is dropped from a height of 45 m. Assuming no air resistance and g = 10 m/s²:
(a) Calculate the gravitational potential energy of the stone before it is dropped. [2]
(b) State the kinetic energy of the stone just before it hits the ground. [1]
(c) Calculate the speed of the stone just before it hits the ground. [1]
(a)
✓ Ep = mgΔh = 0.2 × 10 × 45 [1 mark for formula and substitution]
✓ Ep = 90 J [1 mark]
(b)
✓ Ek = 90 J (by conservation of energy, all GPE converts to KE since no air resistance) [1 mark]
(c)
Ek = ½mv² → 90 = ½ × 0.2 × v² → v² = 900 → v = √900
✓ v = 30 m/s [1 mark]
A 1200 kg car is travelling at 15 m/s. The brakes are applied and the car stops in 5.0 s.
(a) Calculate the momentum of the car before braking. [1]
(b) Calculate the braking force. [2]
(a)
✓ p = mv = 1200 × 15 = 18 000 kg·m/s [1 mark]
(b)
F = Δp / Δt = (mv − mu) / t
✓ F = (0 − 18000) / 5.0 [1 mark for method]
✓ F = −3600 N (or 3600 N in the opposite direction to motion) [1 mark]
A uniform beam of length 4.0 m and weight 200 N is balanced on a pivot at its centre. A 50 N weight is placed 1.5 m from the pivot on the left side. Where must a 30 N weight be placed on the right side to balance the beam?
The beam's weight acts at the centre (the pivot), so it creates no moment.
✓ For equilibrium: clockwise moments = anticlockwise moments [1 mark for principle]
Anticlockwise moment = 50 × 1.5 = 75 N·m
✓ Clockwise moment must also = 75 N·m [1 mark]
30 × d = 75
✓ d = 75 / 30 [1 mark]
✓ d = 2.5 m from the pivot [1 mark]
Describe the motion of a skydiver from the moment they jump out of the aircraft until they reach terminal velocity. Your answer should refer to the forces acting.
✓ Initially, the only significant force is weight (gravity) acting downward, so the skydiver accelerates at approximately g (9.8 m/s²). [1 mark]
✓ As the skydiver's speed increases, air resistance (drag) increases and acts upward, opposing the motion. [1 mark]
✓ The resultant downward force decreases (weight − drag gets smaller), so the acceleration decreases, even though the skydiver is still speeding up. [1 mark]
✓ Eventually, air resistance equals the weight. The resultant force is zero, so acceleration is zero, and the skydiver falls at a constant speed — this is terminal velocity. [1 mark]
A car travels 150 km in 2.5 hours. What is its average speed in m/s?
A cyclist decelerates uniformly from 12 m/s to rest in 8.0 s. Calculate the deceleration.
A box of mass 8.0 kg rests on a horizontal surface. A horizontal force of 20 N is applied. A friction force of 5.0 N opposes the motion. Calculate the acceleration of the box.
Which of these is a vector quantity?
A 0.5 kg ball moving at 6.0 m/s collides head-on with a stationary 1.5 kg ball. After the collision, the 0.5 kg ball bounces back at 2.0 m/s. Calculate the velocity of the 1.5 kg ball after the collision.
A metal cube has sides of length 2.0 cm and a mass of 24 g. Calculate its density in kg/m³.
Explain, using Newton's laws, why wearing a seatbelt reduces the risk of injury in a car crash.
A beam is 3.0 m long and pivoted at one end. A 40 N weight hangs from the other end. Calculate the moment about the pivot, and state a force that could be applied 1.0 m from the pivot to balance the beam.
A crane lifts a 500 kg load to a height of 20 m in 40 s. Calculate (a) the work done, (b) the power output of the crane. (Use g = 10 N/kg)
An object is moving at constant speed in a circle. Which statement is correct?
Forces and Motion typically accounts for 25-30% of Paper 4 marks. Expect at least 2-3 major questions. Practise graph interpretation and calculation questions thoroughly.
For calculation questions: (1) Write the formula, (2) Show substitution, (3) Give the answer with units. Even if your final number is wrong, you get method marks for steps 1 and 2.
This comes up almost every year. The full sequence must include: forces involved → how they change → why acceleration changes → when terminal velocity is reached. Use the words: weight, air resistance/drag, resultant force, acceleration, constant speed.
IGCSE 0625 Section 1.8 — exactly as examined.
Pressure (P) is defined as the perpendicular force (F) acting on a surface divided by the area (A) of that surface: P = F/A. Units: Pascals (Pa) or N/m². Key insight: the same force on a smaller area creates higher pressure.
Everyday examples: Sharp knives cut well (force concentrated on tiny area → high pressure). Snowshoes prevent sinking (weight distributed over large area → low pressure). Tank treads distribute weight → low ground pressure.
• Increase force (same area) → pressure increases proportionally
• Decrease area (same force) → pressure increases proportionally
• Increase area (same force) → pressure decreases proportionally
In a static liquid, pressure at any point depends on:
1. Depth (Δh): More liquid above → higher pressure. Pressure increases linearly with depth.
2. Density (ρ): Denser liquids create higher pressure at same depth (mercury > seawater > fresh water).
Crucial fact: Pressure does NOT depend on container shape — only on depth. A tall narrow tube and a wide shallow container with the same depth have the same pressure at the bottom.
Δp = ρgΔh where Δp = pressure increase (Pa), ρ = density (kg/m³), g = 10 N/kg, Δh = depth increase (m)
Total pressure at depth: P_total = P_atmospheric + ρgΔh
A heel exerts 600 N on ground. Contact area = 0.8 cm². Calculate pressure.
✓ Convert: 0.8 cm² = 0.8 × 10⁻⁴ m² [1 mark]
✓ p = 600 / (0.8 × 10⁻⁴) = 7.5 × 10⁶ Pa [1 mark]
Diver at 30 m in seawater (ρ=1025 kg/m³). Calculate pressure increase. (g=10 N/kg)
✓ Δp = ρgΔh = 1025 × 10 × 30 [1 mark]
✓ Δp = 307,500 Pa [1 mark]
Block exerts 5000 N on 0.5 m² area. Calculate pressure.
At 10 m depth in fresh water (ρ=1000 kg/m³), pressure increase equals: (g=10 N/kg)
A sharp knife with blade area 0.5 mm² exerts the same force as a blunt knife with area 5 mm². Explain why the sharp knife cuts better.
Convert 50,000 Pa to kPa and to atm (1 atm = 101,325 Pa).
Describe how pressure changes as you go deeper into the ocean.
At sea level, Δp = 0 Pa. At 20 m depth in sea water (ρ=1025 kg/m³), calculate the pressure increase. (g=10 N/kg)
Which statement explains pressure at different depths?
A stiletto heel (area 1 cm²) exerts 600 N of force. A sneaker sole (area 200 cm²) exerts the same 600 N. Calculate the pressure from each and explain which is more damaging to a wooden floor.
IGCSE 0625 Sections 2.1 (Kinetic Model), 2.2 (Thermal Properties), 2.3 (Heat Transfer)
All matter is made of tiny particles (atoms/molecules) in constant random motion. The state (solid, liquid, gas) depends on:
• Particle arrangement (ordered/random)
• Strength of intermolecular forces (strong/weak)
• Kinetic energy of particles (low/high)
| Property | Solid | Liquid | Gas |
|---|---|---|---|
| Arrangement | Fixed lattice | Random/close | Random/far apart |
| Shape | Fixed | Container shape | Container shape |
| Volume | Fixed | Fixed | Expands to fill |
| Density | High | High | Low |
| Compressibility | Incompressible | Incompressible | Compressible |
Temperature is a measure of the average kinetic energy of particles. Higher T → faster moving particles → higher average KE.
Absolute zero: −273°C (0 K) is where particle motion theoretically stops. This is the lowest possible temperature.
Kelvin scale: Starts at absolute zero. T(K) = θ(°C) + 273. One kelvin = one degree Celsius (same size).
Gas pressure results from countless particle collisions with container walls. Each collision transfers momentum → force on wall → pressure = force/area.
Factors affecting pressure:
• Temperature: Higher T → faster particles → more energetic collisions → higher P (at constant V)
• Volume: Smaller V → particles hit walls more often → higher P (at constant T)
• Amount: More particles → more collisions → higher P
Boyle's Law: For fixed mass at constant temperature: pV = constant or p₁V₁ = p₂V₂
Under microscope, visible dust/pollen particles suspended in fluid move randomly. This is because invisible fluid molecules collide with them from all directions. When more collisions happen on one side, the visible particle gets "kicked" that way.
Significance: Direct evidence that molecules are real, constantly moving, and in random motion.
When heated, particles vibrate more vigorously and need more space. All states expand, but by different amounts:
• Solids: Least expansion (particles in fixed lattice)
• Liquids: More expansion (particles more mobile)
• Gases: Most expansion (particles very mobile)
Practical consequences:
• Concrete roads have expansion gaps (prevent cracking in summer)
• Power lines sag more in summer (hot wires longer)
• Railway tracks buckle if not designed with expansion sections
• Thermometers work because liquid expands proportionally with temperature
Definition: Specific heat capacity (c) is energy needed to raise temperature of 1 kg by 1°C (or 1 K).
Formula: ΔE = m × c × Δθ where:
• ΔE = energy (J)
• m = mass (kg)
• c = SHC (J/(kg·K))
• Δθ = temperature change (°C or K)
Examples: Water (4200), alcohol (2400), copper (385), aluminum (900). Water's high c means it takes lots of energy to heat—used in car cooling systems and ocean temperature stabilization.
Experiment to measure SHC of solid:
1. Measure mass on balance
2. Heat with known power P (W) for time t (s)
3. Record temperature change Δθ
4. Energy supplied: E = Pt
5. Calculate: c = Pt / (m × Δθ)
Experiment for liquid: Use calorimeter (insulated container), immersion heater, stir thoroughly to ensure uniform temperature.
Melting/Freezing: Temperature stays constant at melting point while particles break free from lattice. Energy goes into breaking bonds, not speeding up particles.
Boiling/Condensation: Temperature stays at boiling point. Energy breaks all intermolecular bonds (liquid → gas). This takes huge energy—that's why boiling takes so long.
Evaporation (different!): Occurs at liquid surface at any temperature. Only highest-energy particles escape. When they leave, average KE of remaining liquid decreases → cooling effect. Evaporation rate depends on temperature, surface area, and air flow.
Heat transfer through a solid without the material moving. In metals, free electrons carry energy efficiently. In non-metals, energy transfers via vibrating particles (slow).
Good conductors: Silver, copper, aluminum (metals)
Poor conductors: Wood, cork, plastics (insulators)
Experiment: Heat one end of different rods. Rods with matches attached—first rod where matches melt is best conductor.
In fluids (liquids and gases), heat transfer via fluid movement. Heating at bottom → particles spread apart → lower density → fluid rises. Cooler, denser fluid above sinks. Creates convection currents.
Examples: Radiator warming a room, boiling water in pot, ocean currents.
All objects emit thermal radiation (infrared) at all times. Hotter objects emit more. Radiation doesn't need a medium—travels through vacuum.
Absorption/Emission depend on surface:
• Black/dull surfaces: Absorb infrared well, emit well (efficient)
• White/shiny surfaces: Absorb poorly, emit poorly (inefficient)
• Shiny also reflects
Examples:
• Black car gets hotter in sun (absorbs radiation)
• White roof keeps house cool (reflects radiation)
• Thermos bottle has shiny sides (reduces radiation loss)
Convert 50°C to kelvin and 350 K to Celsius.
✓ 50°C → T = 50 + 273 = 323 K [1 mark]
✓ 350 K → θ = 350 − 273 = 77°C [1 mark]
Gas occupies 2 m³ at 100 kPa. If volume reduces to 0.5 m³ at constant temperature, find new pressure.
✓ Boyle's Law: p₁V₁ = p₂V₂ → 100 × 2 = p₂ × 0.5 [1 mark]
✓ p₂ = 200 / 0.5 = 400 kPa [1 mark]
Heat 2 kg of water from 20°C to 80°C. (c = 4200 J/(kg·K)) Calculate energy needed.
✓ ΔE = m × c × Δθ = 2 × 4200 × (80 − 20) [1 mark]
✓ ΔE = 2 × 4200 × 60 = 504,000 J (or 504 kJ) [1 mark]
Which has the lowest specific heat capacity?
Why does evaporation cause cooling?
Explain the difference between evaporation and boiling.
Convert 25°C to kelvin and 300 K to Celsius.
A 2 kg block of aluminium (c=900 J/kg·°C) is heated by 50°C. Calculate the energy required. (ΔE = mcΔθ)
Why are metals good thermal conductors?
Describe what Brownian motion is.
Explain convection in air using the concept of density changes.
How does a vacuum flask minimize heat loss?
Describe how particles are arranged in a solid.
IGCSE 0625 Sections 3.1 (General Wave Properties) and 3.4 (Sound)
Waves transfer energy without transferring matter. When you watch waves on water, the water rises and falls but doesn't move forward with the wave. The wave carries energy across the surface.
Wave features:
• Wavelength (λ): Distance between successive crests (or troughs, or any two points in phase). Units: m
• Frequency (f): Number of complete oscillations per second. Units: Hz (Hertz = oscillations/second)
• Amplitude (A): Maximum displacement from equilibrium. Units: m
• Period (T): Time for one complete oscillation. T = 1/f
• Wave speed (v): Distance traveled by the wave per unit time. v = fλ
Transverse waves: Particles vibrate perpendicular to wave direction. Examples: light waves, water waves, S-waves in earthquakes. The wave has crests and troughs.
Longitudinal waves: Particles vibrate parallel to wave direction. Examples: sound waves, P-waves in earthquakes, springs being compressed and extended. The wave has compressions (high pressure) and rarefactions (low pressure).
Production: Sound is produced when an object vibrates. The vibrating surface pushes on nearby air molecules, creating a pressure wave that spreads outward in all directions.
Nature: Sound is a longitudinal wave. The air molecules vibrate back and forth in the same direction the sound travels. When they compress together, pressure is high (compression). When they spread apart, pressure is low (rarefaction).
Audible range: Humans hear frequencies from 20 Hz (deep bass) to 20,000 Hz (20 kHz, high-pitched squeal). Below 20 Hz is infrasound (felt but not heard). Above 20 kHz is ultrasound (inaudible to humans but used in technology).
Medium required: Sound needs a material to propagate (solid, liquid, or gas). It cannot travel through a vacuum because there are no particles to oscillate. In space, astronauts cannot hear each other without radios.
Speed in different media: Sound travels at ~330–350 m/s in air (varies with temperature). It travels faster in solids (~5000 m/s in steel) and liquids (~1500 m/s in water) than in gases because particles are closer together and transfer vibration more efficiently.
Method to measure speed of sound: Two approaches:
1. Echo method: Make a sound at a known distance from a wall. Measure time for echo to return. Speed = 2 × distance / time (factor of 2 because sound travels to wall and back)
2. Two-observer method: Observer 1 makes a sound. Observer 2 measures time delay to hear it. Distance known. Speed = distance / time
Loudness and Pitch:
• Loudness depends on amplitude. Larger amplitude → more energy → louder sound. Measured in decibels (dB)
• Pitch depends on frequency. Higher frequency → higher pitch (shriller). Lower frequency → lower pitch (deeper)
Echo: A sound that bounces off a hard surface (wall, cliff) and returns to the listener. The sound has been reflected. Echoes help animals like bats navigate (echolocation) and are used by humans to measure depth (sonar).
Ultrasound: Sound with frequency > 20 kHz (above human hearing). Uses:
• Medical: Ultrasound scanning of organs and fetuses (safe because non-ionizing)
• Non-destructive testing: Checking for cracks inside metal structures without damaging them
• Sonar: Underwater detection of objects. A ship sends ultrasound down, listens for echo. Time to echo + speed of sound in water = depth calculation
A sound wave has frequency 1000 Hz and wavelength 0.34 m. Calculate wave speed.
✓ Use v = fλ = 1000 × 0.34 [1 mark]
✓ v = 340 m/s [1 mark] (typical speed of sound in air)
A student stands 100 m from a cliff. She claps and hears the echo 0.6 s later. Calculate speed of sound in air.
✓ Echo method: v = 2d/t = 2 × 100 / 0.6 [1 mark]
✓ v = 333 m/s [1 mark]
Sound can travel through which of the following?
A tuning fork vibrates at 256 Hz. Speed of sound = 340 m/s. Calculate wavelength.
A sound wave has frequency 440 Hz and travels at 340 m/s in air. Calculate its wavelength. (v = fλ)
Explain the difference between transverse and longitudinal waves, and give one example of each.
Why cannot sound travel through a vacuum?
A sonar pulse travels 4000 m to the sea bed and back in 5.3 s. Calculate the speed of sound in sea water.
A sonar system emits a 40 kHz ultrasound pulse. In sea water (v=1500 m/s), calculate the wavelength of this ultrasound.
Explain how frequency affects the pitch of a sound wave.
IGCSE 0625 Sections 3.2 (Reflection/Refraction/Lenses), 3.3 (EM Spectrum)
Law of Reflection: Angle of incidence = angle of reflection (i = r). Both measured from the normal (perpendicular to surface), not from the surface itself.
The normal is an imaginary line perpendicular to the surface at the point where light hits.
A plane (flat) mirror forms an image that is:
• Same size as object
• Same distance behind mirror as object is in front
• Virtual (cannot be projected on screen — light rays don't actually meet)
Refraction is the bending of light as it passes from one medium to another with different density. Light bends toward the normal when entering a denser medium (air→glass), and away from the normal when entering a less dense medium (glass→air).
Refractive index (n): n = c/v where c = speed of light in vacuum (3 × 10⁸ m/s), v = speed in the medium. High n = denser medium = light bends more.
Snell's Law: n = sin i / sin r where i = angle of incidence, r = angle of refraction (both from normal).
Critical angle (c): For light traveling from dense→less dense, there's an angle beyond which all light is reflected, none refracted. This angle is the critical angle. For angles > c, total internal reflection occurs.
Formula: n = 1 / sin c where c is in degrees.
Application: Optical fibres use total internal reflection to trap light inside thin glass/plastic strands. Light bounces along the fibre with no loss. Used for high-speed telecommunications and endoscopes (medical cameras).
Converging lens (convex): Brings parallel rays to a focus at the focal point. Forms real, inverted images (can be projected). Used in cameras, projectors, magnifying glasses.
Diverging lens (concave): Spreads out parallel rays as if coming from a virtual focus. Forms virtual, upright, smaller images. Used to correct short-sightedness.
Ray diagrams for converging lens:
1. Ray parallel to axis → passes through focal point
2. Ray through center → passes straight through
3. Ray through focal point → emerges parallel to axis
Lens corrections:
• Long-sightedness (hyperopia): Eye too weak to focus on near objects. Fix: converging lens (convex) adds focusing power.
• Short-sightedness (myopia): Eye focuses too strongly, blurs distant objects. Fix: diverging lens (concave) reduces focusing power.
Dispersion: White light is a mixture of all visible colours. When light passes through a prism (denser medium), each colour bends by a slightly different amount because they have different speeds in glass. Violet bends most, red bends least.
Visible spectrum order (by frequency & colour):
Red < Orange < Yellow < Green < Blue < Indigo < Violet
(Remember: ROY G. BIV)
Red light: Longest wavelength, lowest frequency
Violet light: Shortest wavelength, highest frequency
All EM waves:
• Travel at c = 3.0 × 10⁸ m/s in vacuum
• Are transverse waves
• Use v = fλ
Regions (by frequency, longest to shortest wavelength):
1. Radio waves: f < 10⁹ Hz. Uses: radio/TV broadcasts, astronomy, RFID tags.
2. Microwaves: 10⁹–10¹² Hz. Uses: mobile phones, satellite communication (GPS, weather), microwave ovens, Bluetooth.
3. Infrared: Heat radiation. Uses: grills, heat cameras, remote controls, optical fibres for telecommunications.
4. Visible light: 4 × 10¹⁴–8 × 10¹⁴ Hz (ROY G. BIV). Uses: vision, photography.
5. Ultraviolet: 8 × 10¹⁴–10¹⁷ Hz. Uses: sterilising water, fake note detection, security marking. Dangers: skin cancer, eye damage.
6. X-rays: 10¹⁷–10¹⁹ Hz. Uses: medical imaging (bones), airport security screening. Dangers: cell mutation, cancer.
7. Gamma rays: f > 10¹⁹ Hz. Uses: sterilising food/medical equipment, cancer treatment. Dangers: severe cell damage.
Dangers of EM radiation:
• Microwave: Heats tissue (high power sources only)
• Infrared: Skin burns (like oven heat)
• Ultraviolet: Damages skin cells → skin cancer; damages eye lens
• X-ray: Ionizes cells → mutations → cancer
• Gamma: Severely damages cells → cancer, cell death
Communications:
• Mobile phones: Microwaves (penetrate walls, short aerial needed)
• Bluetooth: Radio waves (pass through walls but weakened)
• Optical fibres: Visible/infrared (very high data rate, immune to EM interference)
Digital vs Analogue:
• Analogue: Signal varies continuously (like a sound wave). Noise degrades signal quality.
• Digital: Signal is discrete 1s and 0s. Can be regenerated perfectly at each repeater. Higher data rate, longer range.
Light travels into glass (refractive index 1.5) from air. Angle of incidence = 40°. Calculate angle of refraction.
✓ Use n = sin i / sin r: 1.5 = sin 40° / sin r [1 mark]
✓ sin r = sin 40° / 1.5 = 0.643 / 1.5 = 0.429
r = sin⁻¹(0.429) = 25.4° [1 mark]
Red light has frequency 4.3 × 10¹⁴ Hz. Calculate its wavelength in vacuum. (c = 3.0 × 10⁸ m/s)
✓ Use v = fλ: λ = v/f = (3.0 × 10⁸) / (4.3 × 10¹⁴) [1 mark]
✓ λ = 7.0 × 10⁻⁷ m (or 700 nm) [1 mark] (visible red light)
Which correctly orders EM regions by increasing frequency?
Glass has refractive index 1.5. Calculate critical angle for light going from glass to air.
State the two laws of reflection of light.
Describe the characteristics of an image formed by a plane mirror.
Light travels from glass (n=1.5) to air (n=1). If the angle of incidence is 30°, calculate the angle of refraction. (n₁sin i = n₂sin r)
Calculate the critical angle for light traveling from diamond (n=2.4) to air (n=1). (sin c = 1/n)
Explain under what conditions total internal reflection occurs.
Describe two uses of optical fibres and explain why total internal reflection is important for them.
Draw and label a ray diagram showing how a converging lens forms a real image of an object placed beyond the focal length.
List the electromagnetic spectrum in order of increasing frequency: X-rays, microwaves, radio waves, visible light, UV, infrared, gamma rays.