1. Measurement and data
Measurement, graphs and uncertainty
Learn repeats, data processing, graphs and reliability before tackling other investigations.
40 minutesGuided self-study
STEM Knowledge Library
Study Physics, Chemistry, Mathematics and Biology with accurate theory, worked examples, virtual experiments and practice questions.
Open the interactive learning pathway9 lessons
Physics
Open subject page2. Forces and fluids
Buoyancy and density
Investigate upthrust and the conditions for floating, sinking and neutral buoyancy.
40 minutes3. Forces, motion and energy
Resultant force, acceleration, work and energy
Connect force diagrams to motion and test energy transfers.
40 minutes4. Waves and optics
Refraction and Snell’s law
Measure incidence and refraction angles and determine refractive index from evidence.
40 minutes5. Thermal physics and gases
Particles, temperature, heat transfer and gases
Explain thermal phenomena with particles and investigate pressure–volume behaviour.
40 minutes6. Electricity and magnetism
Charge, current, potential difference and circuits
Build circuit reasoning from charge and energy conservation rather than isolated formulas.
40 minutes7. Waves and sound
Travelling waves, sound and standing waves
Connect frequency, wavelength and speed; explain reflection, resonance and harmonics with wave models.
45 minutes8. Quantum physics and photons
Light quanta, photons and the photoelectric effect
Investigate photon energy, metal work function, stopping voltage and experimental determination of Planck’s constant h.
40 minutes9. Nuclear physics and radioactivity
Atomic nucleus, binding energy and radioactive decay
Investigate mass defect, binding energy per nucleon, exponential radioactive decay law and nuclear reactions.
40 minutes11 lessons
Chemistry
Open subject page1. Particles, atoms and the Periodic Table
Particle model, atoms and ions
Build from particles to electrons, ions and spectral evidence.
40 minutes2. Bonding and structure
Bonding, structure and material properties
Use microscopic structure to explain melting point, conductivity and solubility.
40 minutes3. Stoichiometry and mole calculations
Amount of substance, moles and solution concentrations
Master conversions between mass, gas volume (modern 24.79 dm³ standard), solution concentration and reaction stoichiometry.
40 minutes4. Acids, bases and pH scale
Acids, bases, pH scale and titrations
Explore proton donor-acceptor behavior, calculate pH, and quantify solution concentrations accurately via volumetric titration.
40 minutes5. Rates and equilibrium
Reaction rates and dynamic equilibrium
Explain rates with collisions and predict equilibrium shifts with proper limits.
40 minutes6. Redox and electrochemistry
Electrons, oxidation states and electrochemical cells
Track electron transfer from displacement reactions to current in cells.
40 minutes7. Analysis and practical skills
Identifying substances from converging evidence
Design controlled tests, avoid interfering ions and make appropriately cautious conclusions.
40 minutes8. Organic chemistry and functional groups
Structure, functional groups and organic reactions
Recognise functional groups, predict products and connect conditions with equilibrium and safety.
40 minutes9. Chemical energetics
Exothermic and endothermic reactions and enthalpy
Track energy transfer and use simple calorimetry and Hess’s law to calculate enthalpy changes.
45 minutes10. Coordination chemistry and complex ions
Coordination compounds, coordinate bonding and crystal field theory
Investigate central metal atoms, ligands, coordination numbers, geometries and biomedical applications of complexes.
40 minutes11. Spectroscopy and structure determination
Infrared (IR) and mass spectrometry (MS) in structural elucidation
Interpret characteristic wavenumbers on IR spectra and molecular ion fragments on MS to deduce molecular structures.
40 minutes11 lessons
Mathematics
Open subject page1. Number, ratio and numerical reasoning
Numerical foundations for problem solving
Build number sense, connect fractions–ratios–percentages and use factorisation instead of guesswork.
40 minutes2. Expressions, equations and inequalities
Algebra as a language of relationships
Translate situations into expressions, transform equivalently and check solutions in context.
40 minutes3. Functions and graphs
Function graphs and transformations
Predict parameter effects, then test them using graphs, tables, and monotonic characteristic functions.
40 minutes4. Geometry and measurement
From diagram to geometric proof
Use definitions, angle relations, similarity and Pythagoras to reason rather than measure a sketch.
40 minutes5. Coordinates, vectors and transformations
Describing geometry with coordinates, transformation matrices and Bézier curves
Connect visual geometry to coordinate rules, vectors, 2D transformation matrices (rotation, reflection, scaling, shear) and parametric Bézier curves in computer graphics.
40 minutes6. Probability and statistics
From randomness to models, Bayes theorem and Markov chains
Construct sample spaces, Law of Total Probability & Bayes theorem, grouped data summary statistics, and discrete-time Markov chains with stationary distributions in real-world modeling.
40 minutes7. Sequences and series
Arithmetic and geometric progressions and growth models
Recognise patterns, build nth-term rules, calculate finite sums and test convergence of infinite geometric series.
45 minutes8. Calculus & Differential Equations
Derivatives, integrals, ODEs, Taylor series and matrix decompositions
Comprehensive calculus: tangent limits, Riemann integrals, canonical first/second-order ODE methods, Taylor/Maclaurin series expansions, and modern matrix factorizations (LU, Cholesky, QR, SVD).
40 minutes9. Trigonometry and trigonometric equations
Unit circle and the six canonical trigonometric equations
Master trigonometric identities, addition, double-angle, power-reduction, and the six canonical trigonometric equation methods.
40 minutes10. Normal distribution and statistical inference
Random variables, Gaussian normal distribution and statistical inference
Investigate probability density functions, the 68-95-99.7 rule, Z-score standardisation and predictive data science.
40 minutes11. Complex numbers and De Moivre formula
Complex numbers, polar form, Euler identity and De Moivre theorem
Explore complex field C, Argand plane geometry, trigonometric polar form, Euler’s formula and De Moivre theorem.
40 minutes10 lessons
Biology
Open subject page1. Cells and microscopy
Cells as the basic unit of life
Learn cell structure through scaled observation, separating visible evidence from inferred structures.
40 minutes2. Membranes and transport
Diffusion, osmosis and active transport
Predict transport direction from gradients and test it using percentage mass change.
40 minutes3. Enzymes and metabolism
Enzymes, temperature and reaction rate
Design a fair test for the effect of temperature or substrate concentration.
40 minutes4. Photosynthesis and respiration
Energy flow in living cells
Connect photosynthesis, respiration and limiting factors through controlled investigation.
40 minutes5. Coordination and homeostasis
Negative feedback, nervous and endocrine control
Model homeostasis and explain nerve signals using ion gradients rather than wire-like electricity.
40 minutes6. Inheritance and variation
Alleles, genotypes and genetic probability
Use genetic crosses to predict ratios and distinguish probability from certainty.
40 minutes7. Ecology and populations
Ecosystems, energy flow and population change
Analyse food webs, productivity and population data without confusing correlation with causation.
40 minutes8. Cellular respiration
Cellular respiration, gas exchange and respiratory quotient
Connect respiration equations to ATP, measure O₂ uptake with a respirometer and infer substrates from RQ within valid limits.
45 minutes9. Molecular genetics and gene regulation
Central dogma: Transcription, translation and gene regulation
Explore the flow of genetic information DNA → RNA → Protein and genetic switches via the classic Lac operon model.
40 minutes10. Immune system and defence mechanisms
Immune system, antibodies and vaccine protection mechanisms
Explore the body’s defence lines: innate immunity, B cells, T cells, antibodies and immunological memory.
40 minutes