Section 1

IGCSE Physics: Key Concepts and Formulas

STUDY GUIDE

🎓 IGCSE Physics - Study Guide

📋 Course Structure


code
📚 IGCSE Physics
├── 📖 Chapter 1: Motion, Forces, and Energy
│   ├── 🔹 Speed, Velocity, and Acceleration
│   ├── 🔹 Mass, Weight, and Density
│   ├── 🔹 Forces and Hooke's Law
│   ├── 🔹 Moments and Equilibrium
│   ├── 🔹 Momentum and Impulse
│   ├── 🔹 Work, Energy, and Power
│   └── 🔹 Pressure
├── 📖 Chapter 2: Thermal Physics
│   ├── 🔹 Temperature and Absolute Zero
│   ├── 🔹 Boyle's Law
│   └── 🔹 Specific Heat Capacity
├── 📖 Chapter 3: Waves and Optics
│   ├── 🔹 General Wave Properties
│   ├── 🔹 Refractive Index
│   └── 🔹 Echoes and Sound Waves
├── 📖 Chapter 4: Electricity and Magnetism
│   ├── 🔹 Current, Charge, and Electromotive Force (EMF)
│   ├── 🔹 Resistance and Ohm's Law
│   ├── 🔹 Electrical Power and Energy
│   ├── 🔹 Potential Dividers
│   └── 🔹 Transformers
├── 📖 Chapter 5: Radioactivity and Nuclear Physics
│   ├── 🔹 Nuclear Notation and Radioactive Decay
│   └── 🔹 Half-Life
└── 📖 Chapter 6: Astronomy
    ├── 🔹 Orbital Speed
    ├── 🔹 Speed of Light and Light Years
    └── 🔹 Hubble's Law

Section 2

📖 Chapter 1: Motion, Forces, and Energy

What this chapter covers: This chapter lays the groundwork for understanding mechanics. It explores the concepts of motion, forces, and energy, detailing how they are related and quantified. Key topics include speed, acceleration, mass, weight, density, momentum, work, energy, power, Hooke's Law, Newton's Laws of Motion, and equilibrium. The chapter emphasizes the application of formulas to solve problems related to these concepts.

🔑 Essential Concepts & Formulas

Concept/Formula	Definition/Equation	When to Use	Quick Check
Speed	$v = \frac{d}{t}$	Calculating average speed	Ensure units are consistent (m/s)
Acceleration	$a = \frac{v_{final} - v_{initial}}{t}$	Calculating average acceleration	Check for constant acceleration
Weight	$w = m \cdot g$	Calculating force due to gravity	Use $g = 9.8 \, m/s^2$ on Earth
Density	$\rho = \frac{m}{V}$	Calculating mass per unit volume	Ensure mass is in kg and volume in $m^3$
Hooke's Law	$F = k \cdot x$	Calculating force exerted by a spring	Limit of proportionality not exceeded
Moment	$Moment = Force \cdot Distance$	Calculating turning effect of a force	Distance is perpendicular to the force
Momentum	$p = m \cdot v$	Calculating the quantity of motion	Momentum is a vector quantity
Kinetic Energy	$KE = \frac{1}{2} \cdot m \cdot v^2$	Calculating energy of motion	Velocity is squared
Potential Energy	$PE = m \cdot g \cdot h$	Calculating energy due to height	Height is relative to a reference point
Power	$P = \frac{Work \, done}{Time}$	Calculating rate of energy transfer	Work done is in Joules, time in seconds
Pressure	$P = \frac{F}{A}$	Calculating force per unit area	Force is perpendicular to the area
Pressure in Liquid	$P = h \cdot \rho \cdot g$	Calculating pressure at depth	Depth is from the surface

🛠️ Problem Types

Type A: Calculating Acceleration from a Speed-Time Graph

Setup: "When given a speed-time graph, and asked to find the acceleration at a specific time."

Method: "Draw a tangent to the curve at the specified time. Calculate the gradient of the tangent line. The gradient represents the instantaneous acceleration at that point."

Example: "A car's speed-time graph shows a curve. At t=5s, a tangent is drawn with points (4,8) and (6,12). Acceleration = $\frac{12-8}{6-4} = 2 \, m/s^2$ "

Type B: Equilibrium Problems with Moments

Setup: "If presented with a situation where an object is in equilibrium under multiple forces and you need to find an unknown force or distance."

Method: "Apply the principle of moments: Sum of clockwise moments = Sum of anticlockwise moments about a pivot point. Choose a pivot point that eliminates one or more unknown forces from the equation."

Example: "A seesaw is balanced with a 50N child 2m from the pivot and a 40N child on the other side. What is the distance of the 40N child from the pivot? $50N * 2m = 40N * d$ , so $d = 2.5m$ "

🧮 Solved Example

Problem: A 2 kg object accelerates from rest to 10 m/s in 5 seconds. Calculate the force acting on the object.

Given: Mass (m) = 2 kg Initial velocity ( $v_i$ ) = 0 m/s Final velocity ( $v_f$ ) = 10 m/s Time (t) = 5 s

Steps:

Calculate acceleration: $a = \frac{v_f - v_i}{t} = \frac{10 \, m/s - 0 \, m/s}{5 \, s} = 2 \, m/s^2$
Apply Newton's Second Law: $F = m \cdot a = 2 \, kg \cdot 2 \, m/s^2$
Calculate the force: $F = 4 \, N$

"

✅
Answer: The force acting on the object is 4 N.

⚠️ Common Mistakes

❌ Mistake 1: Forgetting to convert units (e.g., cm to m).

✅ How to avoid: Always use SI units (meters, kilograms, seconds) in calculations.

❌ Mistake 2: Incorrectly calculating the gradient from a graph.

✅ How to avoid: Ensure you choose two points far apart on the line for accurate gradient calculation.

💡 Study Tip

Practice converting between different units and always write down the units in each step of your calculation to avoid errors.

📖 Chapter 2: Thermal Physics

What this chapter covers: This chapter delves into the concepts of thermal physics, focusing on temperature, gas laws, and specific heat capacity. It explains the relationship between Kelvin and Celsius temperature scales, explores Boyle's Law, and introduces the formula for specific heat capacity. Understanding these concepts is crucial for solving problems related to heat transfer and gas behavior.

🔑 Essential Concepts & Formulas

Concept/Formula	Definition/Equation	When to Use	Quick Check
Kelvin Conversion	$Kelvin = Celsius + 273$	Converting Celsius to Kelvin	Ensure correct addition
Boyle's Law	$P_1V_1 = P_2V_2$	Calculating pressure/volume changes	Constant temperature, fixed mass
Specific Heat Capacity	$Q = mc\Delta\theta$	Calculating heat transfer	Mass in kg, temperature change in °C or K

🛠️ Problem Types

Type A: Boyle's Law Calculations

Setup: "When given initial and final pressures and volumes of a gas at constant temperature, and asked to find an unknown pressure or volume."

Method: "Use Boyle's Law: $P_1V_1 = P_2V_2$ . Rearrange the formula to solve for the unknown variable. Ensure units are consistent."

Example: "A gas has a volume of 2 $m^3$ at a pressure of 100 kPa. What is its volume if the pressure is increased to 200 kPa? $200kPa * V_2 = 100kPa * 2m^3$ , so $V_2 = 1 m^3$ "

Type B: Specific Heat Capacity Problems

Setup: "If presented with a problem involving heat transfer, mass, specific heat capacity, and temperature change, and asked to find an unknown quantity."

Method: "Use the formula $Q = mc\Delta\theta$ . Identify each variable and ensure correct units. Rearrange the formula to solve for the unknown."

Example: "How much energy is required to raise the temperature of 0.5 kg of water by 10°C? (Specific heat capacity of water = 4200 J/kg°C). $Q = 0.5kg * 4200 J/kg°C * 10°C = 21000 J$ "

🧮 Solved Example

Problem: A container of gas has a volume of 3.0 $m^3$ at a pressure of 200 kPa. If the volume is reduced to 1.5 $m^3$ at constant temperature, what is the new pressure?

Given: Initial volume ( $V_1$ ) = 3.0 $m^3$ Initial pressure ( $P_1$ ) = 200 kPa Final volume ( $V_2$ ) = 1.5 $m^3$

Steps:

Apply Boyle's Law: $P_1V_1 = P_2V_2$
Rearrange to solve for $P_2$ : $P_2 = \frac{P_1V_1}{V_2} = \frac{200 \, kPa \cdot 3.0 \, m^3}{1.5 \, m^3}$
Calculate the final pressure: $P_2 = 400 \, kPa$

"

✅
Answer: The new pressure is 400 kPa.

⚠️ Common Mistakes

❌ Mistake 1: Using Celsius instead of Kelvin in gas law calculations.

✅ How to avoid: Always convert Celsius to Kelvin before applying gas laws.

❌ Mistake 2: Forgetting to use consistent units.

✅ How to avoid: Ensure all quantities are in SI units (Pa, $m^3$ , K) before calculations.

💡 Study Tip

Remember that Boyle's Law only applies when the temperature and mass of the gas are constant.

📖 Chapter 3: Waves and Optics

What this chapter covers: This chapter explores the properties of waves, including frequency, wavelength, and speed. It also covers the behavior of light waves, including reflection, refraction, and critical angle. Understanding refractive index and its applications is a key focus.

🔑 Essential Concepts & Formulas

Concept/Formula	Definition/Equation	When to Use	Quick Check
Frequency	$f = \frac{1}{T}$	Calculating wave frequency	T is the period in seconds
Wave Speed	$v = f \cdot \lambda$	Calculating wave speed	Frequency in Hz, wavelength in meters
Refractive Index	$n = \frac{speed \, in \, air}{speed \, in \, medium}$	Calculating refractive index	Speed in air ≈ $3 \times 10^8 \, m/s$
Refractive Index (angles)	$n = \frac{sin \, \theta_{air}}{sin \, \theta_{medium}}$	Calculating refractive index using angles	$\theta$ are angles of incidence/refraction
Critical Angle	$n = \frac{1}{sin \, c}$	Calculating refractive index using critical angle	c is the critical angle

🛠️ Problem Types

Type A: Calculating Wave Speed

Setup: "When given the frequency and wavelength of a wave, and asked to find its speed."

Method: "Use the formula $v = f \cdot \lambda$ . Ensure frequency is in Hertz and wavelength is in meters."

Example: "A wave has a frequency of 5 Hz and a wavelength of 2 meters. What is its speed? $v = 5 Hz * 2 m = 10 m/s$ "

Type B: Refractive Index Calculations

Setup: "If presented with a problem involving the speed of light in different media or angles of incidence and refraction, and asked to find the refractive index."

Method: "Use the appropriate formula: $n = \frac{speed \, in \, air}{speed \, in \, medium}$ or $n = \frac{sin \, \theta_{air}}{sin \, \theta_{medium}}$ . Ensure angles are measured correctly."

Example: "The speed of light in a medium is $2 \times 10^8 \, m/s$ . What is the refractive index of the medium? $n = \frac{3 \times 10^8 \, m/s}{2 \times 10^8 \, m/s} = 1.5$ "

Type C: Echo Problems

Setup: "When given the time taken for an echo to return and the speed of sound, and asked to find the distance to the reflecting object."

Method: "Use the formula $v = \frac{d}{t}$ , but remember that the sound travels to the object and back, so the distance calculated must be halved."

Example: "An echo returns 4 seconds after a sound is made. The speed of sound is 340 m/s. How far away is the reflecting object? $d = 340 m/s * 4s = 1360m$ . Actual distance = $\frac{1360m}{2} = 680m$ "

🧮 Solved Example

Problem: Light travels from air into glass with an angle of incidence of 45 degrees. The angle of refraction in the glass is 30 degrees. Calculate the refractive index of the glass.

Given: Angle of incidence ( $\theta_{air}$ ) = 45 degrees Angle of refraction ( $\theta_{medium}$ ) = 30 degrees

Steps:

Apply the formula: $n = \frac{sin \, \theta_{air}}{sin \, \theta_{medium}}$
Calculate the sine values: $sin \, 45^\circ \approx 0.707$ , $sin \, 30^\circ = 0.5$
Calculate the refractive index: $n = \frac{0.707}{0.5} = 1.414$

"

✅
Answer: The refractive index of the glass is approximately 1.414.

⚠️ Common Mistakes

❌ Mistake 1: Forgetting to halve the distance in echo problems.

✅ How to avoid: Always remember that the sound travels to the object and back.

❌ Mistake 2: Using incorrect angles in refractive index calculations.

✅ How to avoid: Ensure you are using the angles of incidence and refraction, not other angles.

💡 Study Tip

Practice drawing ray diagrams for refraction to visualize the angles and understand the relationship between refractive index and the bending of light.

5 more sections

Create a free account to import and read the full study notes — all 7 sections.

No credit card · 2 free imports included

IGCSE Physics: Key Concepts and Formulas

Study Notes Preview

IGCSE Physics: Key Concepts and Formulas

🎓 IGCSE Physics - Study Guide

📋 Course Structure

📖 Chapter 1: Motion, Forces, and Energy

🔑 Essential Concepts & Formulas

🛠️ Problem Types

🧮 Solved Example

⚠️ Common Mistakes

💡 Study Tip

📖 Chapter 2: Thermal Physics

🔑 Essential Concepts & Formulas

🛠️ Problem Types

🧮 Solved Example

⚠️ Common Mistakes

💡 Study Tip

📖 Chapter 3: Waves and Optics

🔑 Essential Concepts & Formulas

🛠️ Problem Types

🧮 Solved Example

⚠️ Common Mistakes

💡 Study Tip

5 more sections