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Read the lesson, work through its example, then explain the result in your own words. Interactive tools and personal progress are available in the main classroom.
Physics classroom
From your first measurements to fields, quantum physics and the Universe.
Foundations
- Measurements and unitsTurn observations into quantities that other people can compare.
- Describing motionDistinguish how far something travels from how its position changes.
- Forces and balanced motionPredict changes of motion from the combined force.
- Energy, work and powerTrack transfers rather than treating energy as a force.
- Wave languageDescribe travelling disturbances with frequency, wavelength and amplitude.
- Simple electric circuitsConnect charge flow, potential difference and resistance.
IGCSE
- Motion, forces and energyBring measurements, mechanics and energy transfers into one model.
- Thermal physicsExplain temperature changes using particles and energy transfers.
- Waves, light and soundUse one wave model to describe reflection, refraction and communication.
- Electricity and magnetismBuild circuit and field models, then connect them to useful devices.
- Nuclear physicsSeparate atomic structure from random radioactive change.
- Space physicsConnect orbital motion, starlight and the scale of the Universe.
AS level
- Physical quantities and unitsUse SI units, vectors and uncertainty to make quantitative claims.
- KinematicsUse graphs and constant-acceleration equations without assuming every journey is uniform.
- DynamicsExplain force as a rate of change of momentum.
- Forces, density and pressureAnalyse equilibrium, turning effects and fluid forces.
- Work, energy and powerUse energy conservation while accounting for direction and efficiency.
- Deformation of solidsConnect force–extension behaviour with material stiffness and stored energy.
- WavesDescribe phase, intensity and the Doppler effect.
- SuperpositionExplain interference and stationary waves from the addition of displacements.
- ElectricityModel charge transport, resistance and electrical power.
- D.C. circuitsApply charge and energy conservation to networks and sources.
- Particle physicsUse charge and particle families to describe matter and decay.
- AS practical skillsDesign reliable measurements and explain what a graph can establish.
A2 level
- Motion in a circleExplain constant-speed turning with a changing velocity.
- Gravitational fieldsConnect inverse-square force, potential and orbital energy.
- TemperatureConnect thermometry, thermal equilibrium and absolute temperature.
- Ideal gasesLink a macroscopic gas law to random particle motion.
- ThermodynamicsApply the first law with an explicit work sign convention.
- OscillationsRecognise simple harmonic motion and distinguish it from forced resonance.
- Electric fieldsDistinguish the direction of force from scalar electric potential.
- CapacitanceDescribe charge storage and the energy transferred while charging.
- Magnetic fieldsConnect magnetic forces, flux and electromagnetic induction.
- Alternating currentsUse rms values to compare varying current with steady heating.
- Quantum physicsExplain photons, threshold behaviour and discrete atomic energies.
- Nuclear physicsUse binding energy and exponential decay quantitatively.
- Medical physicsConnect imaging signals with interactions while respecting model limits.
- Astronomy and cosmologyInfer stellar properties and cosmic expansion from light.
- A2 planning, analysis and evaluationBuild an investigation and judge how strongly its data supports a model.
Mathematics
Reason with number, shape, functions and uncertainty. Pure mathematics and selectable mechanics/statistics routes.
Foundations
- Number and place valuePlace value gives a digit its size. Integers, fractions and decimals describe the same number line in different ways; a negative sign indicates a position below zero.
- Ratio, proportion and percentagesA ratio compares quantities using equal units. Scaling every part by the same factor preserves the comparison; a percentage expresses a fraction out of one hundred.
- Patterns, variables and graphsA variable stands for a quantity that may change. An expression describes a calculation; an equation asserts that two expressions have the same value.
IGCSE
- Number, sets and financial arithmeticPrime factors, indices, standard form and bounds organise calculations with very large, small or approximate numbers. Set notation distinguishes membership from inclusion.
- Algebra, equations and sequencesExpanding distributes multiplication over addition; factorising reverses the process. Linear and quadratic equations, inequalities and simultaneous equations express constraints.
- Functions, coordinates and graphsA function gives one output for each input in its domain. Coordinate geometry connects equations with intercepts, gradients, distance and midpoint.
- Geometry, constructions and mensurationAngle rules, similarity and congruence justify geometric relationships. Circle theorems connect angles at centres, circumferences, tangents and cyclic quadrilaterals.
- Trigonometry and bearingsSine, cosine and tangent connect right-triangle side ratios with angles. The sine and cosine rules extend calculations to general triangles.
- Transformations and vectorsTranslations, reflections, rotations and enlargements map shapes while changing specified features. A vector describes displacement with magnitude and direction.
- Statistics and probabilityTables, histograms, cumulative frequency and scatter diagrams summarise data. Means use all values; medians describe the middle and may resist extreme values.
AS level
- Quadratics, functions and coordinate geometryCompleting the square exposes a quadratic’s turning point. The discriminant counts real roots and links algebra with intersections of a line and curve.
- Series and binomial expansionArithmetic progressions add a fixed difference; geometric progressions multiply by a fixed ratio. Summation expresses the total rather than a single term.
- Radians and trigonometric identitiesRadians measure angle through arc length divided by radius. Trigonometric graphs are periodic; transformations change amplitude, period or phase.
- Differentiation and applicationsA derivative measures instantaneous rate of change and tangent gradient. A stationary point has zero first derivative, but classification needs a sign change or further reasoning.
- Integration and areaIntegration reverses differentiation and accumulates signed change. An indefinite integral represents a family of functions differing by a constant.
- Mechanics option: forces and motionMathematical mechanics models particles using kinematics, Newton’s laws, momentum, work and energy. A model may neglect size, air resistance or string mass.
- Statistics option: distributionsPermutations count ordered arrangements; combinations count selections. Discrete distributions assign probabilities to numerical outcomes and allow expectations to be calculated.
A2 level
- Advanced algebra and numerical methodsPolynomial division and the factor theorem reduce higher-degree equations. Partial fractions rewrite rational expressions into forms useful for integration.
- Exponential and logarithmic functionsLogarithms reverse exponentiation and convert products into sums. Natural logarithms use base e and require positive real arguments.
- Advanced calculus and differential equationsProduct, quotient and chain rules differentiate combined functions. Integration by substitution and by parts reverse different patterns of differentiation.
- Advanced trigonometry and parametric curvesAddition and double-angle formulae transform expressions and solve equations. Radian measure is essential for calculus involving trigonometric functions.
- Vectors and complex numbersThree-dimensional vectors express lines, distances and angles. The scalar product connects components with the angle between nonzero vectors.
- Statistics option: inference and continuous modelsPoisson distributions model counts under constant-rate, independent-event assumptions. A probability density integrates to probability; its height alone is not a point probability.
- Proof, modelling and component choicesA proof establishes a statement from assumptions using valid deductions; examples can suggest a conjecture but cannot prove a universal claim. A counterexample disproves one.
Chemistry
Connect particles, bonding, reactions and evidence, from everyday materials to quantitative and organic chemistry.
Foundations
- Particles, states and changesMatter is described using particles: solids retain closely arranged particles, liquids flow and gases spread through the available space. Particle diagrams are models, not pictures at true scale.
- Atoms, elements and compoundsAn element contains atoms with the same proton number. A compound contains two or more elements chemically combined in a fixed ratio.
- Chemical evidence and safe investigationA fair investigation changes a planned variable and measures a response while controlling relevant conditions. Repeats help estimate random variation; a control experiment tests an alternative explanation.
IGCSE
- Atomic structure, bonding and periodicityAtoms contain protons, neutrons and electrons. Isotopes differ in neutron number; ions form when electrons are gained or lost. Electron arrangements help explain periodic patterns.
- Formulae, equations and chemical amountsBalanced equations conserve atoms and charge. Relative atomic and formula masses connect microscopic composition to measurable masses; a mole counts a fixed number of entities.
- Electrolysis, metals and redoxOxidation is electron loss and reduction is electron gain. Electrolysis uses electrical energy to drive decomposition; cations migrate to the negative cathode and anions to the positive anode.
- Energy changes, rates and reversible reactionsExothermic reactions transfer energy to surroundings; endothermic reactions take it in. Breaking bonds requires energy and making bonds releases it.
- Acids, bases, salts and chemical analysisAcids produce hydrogen ions in aqueous solution; alkalis provide hydroxide ions. Neutralisation forms water and a salt, while carbonate reactions also release carbon dioxide.
- Periodic chemistry, resources and environmentGroup trends connect electron arrangement with reactivity. Halogens can displace less reactive halide ions; noble gases are relatively unreactive. Transition metals often act as catalysts and form coloured compounds.
- Organic families, fuels and polymersOrganic compounds are classified by functional groups and homologous series. Alkanes undergo combustion and substitution; alkenes contain a carbon–carbon double bond and undergo addition.
AS level
- Atomic structure and chemical bondingElectron orbitals describe quantum states rather than planetary paths. Successive ionisation energies provide evidence for shells, while electron configurations explain periodic patterns.
- Amounts, gases and solutionsStoichiometry converts measured masses, volumes and concentrations into amounts. Empirical formulae use the simplest whole-number ratio, while molecular formulae also need molar mass.
- Enthalpy and Hess cyclesEnthalpy changes compare states under specified conditions. Formation, combustion, atomisation and bond enthalpies use different definitions; their signs cannot be assigned from names alone.
- Equilibria, acids and redoxEquilibrium constants express a composition relationship at fixed temperature. Le Chatelier’s principle predicts shifts qualitatively, while oxidation numbers track redox changes.
- Rates and inorganic periodic trendsCollision energy distributions explain why temperature affects rate. Catalysts lower activation energy but do not make every collision productive.
- Organic reactions and mechanismsFunctional groups organise reactions of hydrocarbons, halogenoalkanes, alcohols, carbonyl compounds, acids, esters and nitriles. Structural and stereoisomerism describe different relationships.
- Practical chemistry and analysisVolumetric analysis requires clean apparatus, controlled endpoints and uncertainty estimates. Concordant titres support consistency but do not by themselves prove accuracy.
A2 level
- Entropy, Gibbs energy and ionic energeticsEntropy describes the distribution of energy among accessible arrangements. Gibbs energy combines enthalpy and entropy to assess thermodynamic feasibility at a given temperature.
- Electrode potentials and electrolysisStandard electrode potentials compare reduction tendencies with a reference electrode under standard conditions. A positive calculated cell potential indicates the thermodynamically favoured direction under those conditions.
- Quantitative equilibria and buffersAcid dissociation, ionic product of water and solubility products quantify equilibria. Approximations require checking against the starting concentration and competing effects.
- Rate equations and mechanismsA rate equation is determined experimentally rather than read automatically from the overall balanced equation. Reaction order describes how rate depends on a concentration.
- Transition elements and inorganic trendsTransition-element chemistry includes variable oxidation states, coloured complexes and catalytic behaviour. Ligands donate electron pairs to metal centres; coordination number counts donor atoms attached.
- Advanced organic chemistry and synthesisArenes, phenols, acyl compounds, amines and amides expand functional-group chemistry. Delocalisation changes reactivity, so aromatic substitution differs from ordinary alkene addition.
- Spectroscopy, chromatography and planningNMR chemical shifts, integration and splitting constrain hydrogen environments; infrared and mass spectra add complementary evidence. Chromatography separates species by their interactions with two phases.
Computer Science
Explore information, connected systems and reliable algorithms, from Boolean logic to practical programming.
Foundations
- Inputs, processes, outputs and storageA computer system transforms input using instructions and produces output. Storage retains information; processing manipulates it. The same device can perform several roles.
- Bits, bytes and representationA bit has two possible values. Binary place values are powers of two, allowing bit patterns to represent numbers; character and image encodings assign other meanings to those patterns.
- Algorithms, sequence and decisionsAn algorithm is a finite, precise method for solving a defined problem. Sequence orders instructions, selection chooses branches and iteration repeats actions.
IGCSE
- Data representation and compressionBinary and hexadecimal encode numbers; characters, bitmap images and sampled sound use agreed formats. Resolution, colour depth, sample rate and sample resolution affect storage and quality.
- Data transmission and error detectionSerial and parallel transmission move bits using different channel arrangements. Simplex, half-duplex and full-duplex describe permitted directions, not the number of wires.
- Hardware, architecture and embedded systemsA processor fetches, decodes and executes instructions using registers and buses. Clock rate, cache and core count affect performance, but no single specification determines every task’s speed.
- Software, translators and the internetOperating systems manage resources and provide services; applications perform user tasks. Compilers and interpreters translate or execute source according to language rules.
- Security, automated systems and ethicsThreats include malware, social engineering, unauthorised access and data loss. Authentication establishes an identity; authorisation determines allowed actions. Backups and updates address different risks.
- Programming, testing and problem solvingVariables have data types, and programs use arithmetic, Boolean conditions, loops, arrays and procedures. Pseudocode communicates an algorithm without requiring one executable language.
- Databases, Boolean logic and queriesA relational table contains records and fields. A primary key identifies records; queries select and organise data using conditions rather than changing its meaning.
AS level
- Advanced data representationSigned binary formats and floating-point representations encode negative and fractional values within finite storage. Range and precision trade off against each other.
- Networks, communication and protocolsNetwork hardware, addressing and protocols cooperate to carry messages. Circuit switching reserves a path; packet switching shares links and permits packets to travel separately.
- Processor architecture and logic circuitsRegisters, buses and instruction formats support stored-program execution. Addressing modes specify how operand locations or values are obtained.
- System software and securityOperating systems schedule work, manage memory and files, and coordinate devices. Interrupts allow a processor to respond to events without continually checking every device.
- Relational databases and normalisationRelations connect records using primary and foreign keys. Entity relationships and normalisation reduce anomalies by assigning facts to appropriate tables.
- Algorithms and data structuresArrays, records, stacks and queues organise values for different operations. Linear search examines candidates in sequence; binary search repeatedly halves a sorted interval.
- Programming and software developmentProcedures, functions, parameters and structured control flow allow programs to be decomposed. Scope defines where names are visible; pass-by-value and reference-like behaviour affect which changes reach the caller.
A2 level
- Floating point and data structuresFloating-point normalisation gives a conventional mantissa form and efficient use of precision. Finite representation creates rounding error, overflow and underflow; cancellation can amplify relative error.
- Internet structure and network reliabilityProtocols manage routing, addressing and end-to-end communication. TCP supports ordered reliable byte streams; IP routes packets without independently guaranteeing their delivery.
- Advanced architecture and operating systemsPipelining overlaps instruction stages; parallel processing divides work across processing resources. Hazards, communication and serial sections limit achievable speed-up.
- Security, cryptography and ethicsSymmetric encryption uses shared secret keys; asymmetric methods use related public/private keys. Hashes support integrity checks, and digital signatures bind verification to a private signing key.
- Artificial intelligence and learningAI includes search, knowledge representation and learning methods. Heuristic search uses a guide to explore possibilities; a heuristic’s properties affect optimality and efficiency.
- Recursion, complexity and computational thinkingRecursion solves a problem through smaller instances, requiring base cases and progress toward them. A call stack records suspended work, so elegant recursive code may use substantial memory.
- Programming paradigms, files and practical skillsObject-oriented programming groups state and behaviour; inheritance and polymorphism express relationships but need careful interfaces. Declarative styles describe desired results rather than every execution step.
Biology
Explore living systems from cells to ecosystems. Original broad-topic briefs introduce Cambridge Biology; they do not cover every syllabus objective.
Foundations
- Living systems and biological questionsBiology investigates living systems through evidence.
- Cells, structures and scaleCells are small systems with a membrane controlling exchange and cytoplasm where many reactions occur.
- Organisms, resources and ecosystemsAn ecosystem includes organisms and their physical environment.
IGCSE
- Characteristics and classificationClassification groups organisms by shared features and evolutionary relationships.
- Cells and movement across membranesTissues, organs and organ systems coordinate specialised cells.
- Biological molecules and enzymesCarbohydrates and lipids provide energy stores and structural materials; proteins have varied roles including transport and catalysis.
- Plant nutrition and photosynthesisPhotosynthesis transfers light energy into chemical stores by making carbohydrates from carbon dioxide and water.
- Human nutrition and digestionA balanced diet supplies energy, building materials, fibre, water and micronutrients.
- Transport in plantsXylem carries water and mineral ions from roots and also supports the plant.
- Transport in animalsThe mammalian heart pumps blood through pulmonary and systemic circuits.
- Disease and immune defencePathogens can spread through several routes, including contaminated food, droplets and vectors.
- Gas exchange and respirationVentilation moves air into and out of lungs, gas exchange transfers gases across surfaces and respiration comprises reactions transferring energy within cells.
- Coordination, excretion and drugsReceptors detect changes and effectors produce responses.
- Reproduction and developmentAsexual reproduction produces offspring without gamete fusion and commonly preserves the parent’s genotype apart from mutation.
- Inheritance, variation and selectionGenes are DNA regions with biological functions; alleles are alternative versions.
- Ecology and human influencesFood webs connect producers, consumers and decomposers.
- Biotechnology and genetic modificationBiotechnology uses organisms or biological processes to make useful products.
AS level
- Cell structure and microscopyEukaryotic cells compartmentalise reactions in membrane-bound organelles.
- Biological molecules and waterMonosaccharides form polysaccharides, amino acids form polypeptides and nucleotides form nucleic acids.
- Enzymes and reaction kineticsEnzymes stabilise a reaction pathway with lower activation energy.
- Cell membranes and transportA phospholipid bilayer forms a hydrophobic barrier containing proteins with transport, receptor and catalytic roles.
- The mitotic cell cycleThe cell cycle includes growth, DNA replication and division.
- Nucleic acids and protein synthesisDNA stores sequence information in nucleotide bases.
- Transport in plants: water and assimilatesWater evaporating from mesophyll surfaces lowers leaf water potential.
- Transport in mammals and the heartThe cardiac cycle coordinates atrial and ventricular contraction with pressure-sensitive valves.
- Gas exchange and the respiratory systemCartilage supports larger airways, mucus traps particles and cilia move material toward the throat.
- Infectious diseases and transmissionInfectious diseases involve pathogens with different biological properties.
- Immunity, antibodies and vaccinationPhagocytes and other innate defences respond broadly, while adaptive responses involve antigen-specific lymphocytes.
- Practical skills: measurements and evidenceGood practical work links a question to a measurable variable, a suitable comparison and controlled conditions.
A2 level
- Energy and respirationATP hydrolysis can be coupled to cellular work, while respiration regenerates ATP using energy transferred from substrates.
- Photosynthesis: light reactions and carbon fixationPhotosynthetic pigments absorb light in thylakoid membranes.
- Homeostasis and internal controlHomeostasis regulates internal conditions within functional ranges rather than keeping every variable perfectly constant.
- Control and coordinationMembrane ion gradients and selective channels support resting potentials and action potentials.
- Inheritance and gene expressionCrossing over and the orientation of homologous chromosome pairs generate different allele combinations during meiosis.
- Selection and evolutionEvolution changes inherited characteristics of populations over generations.
- Classification, biodiversity and conservationClassification uses shared ancestry as well as observable traits; molecular sequence comparisons provide evidence alongside morphology.
- Genetic technology and applicationsPCR amplifies a selected DNA region through repeated cycles using primers, nucleotides and a suitable polymerase.
- Practical planning, analysis and evaluationPlanning begins with a testable question, operational definitions and a method that can produce valid comparisons.