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What a 15-year-old learns

215 topics open up at age 15, across 13 subjects. They are listed in the order they build on each other, not by importance: each one needs the ones above it.

age 14age 16
What should a 15-year-old be learning?

At age 15, 215 topics open up across Science, Mathematics, Computing, English, Civics & Economics, History, Personal & Social Development, Languages, Life Skills, Arts & Music, Geography, Design & Technology, Learning to Learn. Each one has prerequisites that come first, so the order matters more than the list: Thermistors, Light-Dependent Resistors and Sensing Circuits is a typical starting point.

How do I know what a 15-year-old already knows?

LightMySky starts by assuming everything below the learner’s level is already known, then checks the assumption as they practise. What holds up stays lit; what does not comes back for review.

Science

  1. Thermistors, Light-Dependent Resistors and Sensing CircuitsEnergy
  2. The wave equationWaves, Light & Sound
  3. Ultrasound and Echo SoundingWaves, Light & Sound
  4. Impulse and Crash SafetyForces & Motion
  5. Calculating work done and powerEnergy
  6. Kinetic and gravitational potential storesEnergy
  7. Stopping Distances and Braking EnergyForces & Motion
  8. Specific Heat Capacity as a Material PropertyEnergy
  9. Specific Heat Capacity and Specific Latent Heat in CalculationsEnergy
  10. Red-Shift and the Expanding UniverseSpace Systems & Earth's History
  11. Refraction and lensesWaves, Light & Sound
  12. Transpiration and Transport in PlantsOrganisms & Life Processes
  13. Sediment on the Move: Rivers, Coasts and Where It SettlesEarth's Systems
  14. Density and How to Measure ItMatter & Materials
  15. Pressure in Liquids and the AtmosphereForces & Motion
  16. Giant Covalent Structures: Diamond, Graphite and GrapheneMatter & Materials
  17. Metallic Bonding and AlloysMatter & Materials
  18. Molecular Shapes from Electron Pair RepulsionMatter & Materials
  19. Electronegativity and the Polar BondMatter & Materials
  20. Reaction Profiles and Activation EnergyMatter & Materials
  21. Bond Energies and the Overall Energy ChangeMatter & Materials
  22. Alkanes and Alkenes: The First Homologous SeriesMatter & Materials
  23. Reading Structure from PropertiesMatter & Materials
  24. Forces Between MoleculesMatter & Materials
  25. Nanoparticles and Why Surface Area Changes EverythingMatter & Materials
  26. Relative Formula Mass and the MoleMatter & Materials
  27. Balancing Equations and Conservation of MassMatter & Materials
  28. Reacting Masses, Limiting Reactants and YieldMatter & Materials
  29. Concentration of Solutions in Moles per Cubic DecimetreMatter & Materials
  30. Empirical and Molecular Formulas from CompositionMatter & Materials
  31. The Gas Laws and the Ideal Gas EquationMatter & Materials
  32. Titration: Finding an Unknown ConcentrationMatter & Materials
  33. Why Some Things Dissolve and Others Do NotMatter & Materials
  34. Human Impact on Ecosystems: Land, Waste and a Warming WorldOrganisms & Life Processes
  35. Crude Oil, Fractional Distillation and CrackingMatter & Materials
  36. Testing for Ions and GasesMatter & Materials
  37. Electrolysis: Half Equations at the ElectrodesMatter & Materials
  38. Potable Water and Treating Waste WaterMatter & Materials
  39. Decomposers and the Rate of DecayOrganisms & Life Processes
  40. Fertilisers, Leaching and EutrophicationOrganisms & Life Processes
  41. Electrolysis of Solutions and Getting Reactive Metals Out of OresMatter & Materials
  42. Pollutants from Burning FuelsMatter & Materials
  43. Rates of Reaction: Collision Theory and What Changes a RateMatter & Materials
  44. Reversible Reactions, Dynamic Equilibrium and Le ChatelierMatter & Materials
  45. The Haber Process and the Industrial CompromiseMatter & Materials
  46. Inside the Atom: the Nuclear ModelMatter & Materials
  47. Radioactive Decay: Alpha, Beta and GammaMatter & Materials
  48. Half-Life and ActivityMatter & Materials
  49. Irradiation, Contamination and DoseMatter & Materials
  50. Nuclear Fission and FusionMatter & Materials
  51. The Electromagnetic Spectrum: Uses and DangersWaves, Light & Sound
  52. Infrared Emission, Absorption and the Temperature of a BodyWaves, Light & Sound
  53. Reading a Rock Sequence: Superposition, Fossils and CorrelationEarth's Systems
  54. Deep Time: Radiometric Dating and the Geological ColumnEarth's Systems
  55. Measuring the Rate of an Enzyme ReactionOrganisms & Life Processes
  56. Photosynthesis and Limiting FactorsOrganisms & Life Processes
  57. Food Security: What Limits Yield and What It Costs to Raise ItOrganisms & Life Processes
  58. Respiration: Energy Yield, Oxygen Debt and FermentationOrganisms & Life Processes
  59. Blood Components and Blood VesselsThe Human Body
  60. Heart Rate, Stroke Volume and Cardiac OutputThe Human Body
  61. How Communicable Diseases SpreadThe Human Body
  62. Non-Communicable Disease and What Counts as a Risk FactorThe Human Body
  63. The Brain: Regions and the Evidence for What They DoThe Human Body
  64. The Eye as a Receptor OrganThe Human Body
  65. Vaccination and Antibiotic ResistanceThe Human Body
  66. Testing a New Drug: Controls, Placebo and the Blind TrialScientific Inquiry
  67. DNA Structure and Base PairingGenetics & Evolution
  68. From Gene to ProteinGenetics & Evolution
  69. Mutations and Their Effect on ProteinsGenetics & Evolution
  70. Punnett Squares and Monohybrid RatiosGenetics & Evolution
  71. Sex Determination and Inherited DisordersGenetics & Evolution
  72. Selective Breeding and Genetic EngineeringGenetics & Evolution
  73. Cloning: Cuttings, Tissue Culture and Adult Cell CloningGenetics & Evolution
  74. Speciation and the Rate of EvolutionGenetics & Evolution
  75. Sampling Ecosystems with Quadrats and TransectsScientific Inquiry
  76. Estimating Population Size by Mark, Release and RecaptureScientific Inquiry

Mathematics

  1. Constructions and LociGeometry
  2. Fractional Indices and RootsNumber Representation & Place Value
  3. Standard FormNumber Representation & Place Value
  4. Surds: Simplifying and RationalisingNumber Representation & Place Value
  5. Counting Outcomes with the Product RuleProbability
  6. The Addition Rule and Mutually Exclusive EventsProbability
  7. Independent Events and the Multiplication RuleProbability
  8. Vectors: Notation, Addition and Scalar MultiplesGeometry
  9. Exact Values of Sine, Cosine and TangentGeometry
  10. The Sine RuleGeometry
  11. The Cosine RuleGeometry
  12. Triangle Area with Half ab sin CGeometry
  13. Lines of Best Fit: Prediction and Its LimitsData & Statistics
  14. Quartiles and the Interquartile RangeData & Statistics
  15. Box Plots and Comparing DistributionsData & Statistics
  16. Cumulative Frequency CurvesData & Statistics
  17. Histograms and Frequency DensityData & Statistics
  18. Percentage Change with MultipliersRatio & Proportion
  19. Compound Growth and DecayRatio & Proportion
  20. Upper and Lower BoundsNumber Representation & Place Value
  21. Pythagoras and Trigonometry in Three DimensionsGeometry
  22. Choosing a Triangle MethodGeometry
  23. Arc Length, Sector Area and SegmentsGeometry
  24. Bearing Problems with the Sine and Cosine RulesGeometry
  25. Circle Theorems: Angles at the Centre and in a SemicircleGeometry
  26. Circle Theorems: Cyclic Quadrilaterals and the Same SegmentGeometry
  27. Tangents, Radii and the Alternate Segment TheoremGeometry
  28. Volume and Surface Area of Cones, Spheres and PyramidsGeometry
  29. Calculating with Bounds in Compound MeasuresNumber Representation & Place Value
  30. Algebraic Proof with Odd, Even and Consecutive NumbersMathematical Thinking
  31. Completing the SquareAlgebra
  32. Function notation and evaluating functionsAlgebra
  33. Composite functionsAlgebra
  34. Geometric Sequences and Common RatiosAlgebra
  35. Inverse functionsAlgebra
  36. Quadratic Sequences and Second DifferencesAlgebra
  37. Rearranging Formulae When the Subject Appears TwiceAlgebra
  38. Solving Linear Inequalities and Solution SetsAlgebra
  39. Graphical Inequalities and Regions in the PlaneAlgebra
  40. Solving Quadratic InequalitiesAlgebra
  41. The Quadratic FormulaAlgebra
  42. The Discriminant and the Number of RootsAlgebra
  43. Sketching Quadratic Graphs from Roots and the Turning PointAlgebra
  44. Simultaneous Equations with One QuadraticAlgebra
  45. Transformations of GraphsAlgebra
  46. Recognising cubic, reciprocal and exponential graphsAlgebra
  47. Relative Frequency and Expected OutcomesProbability
  48. Tree Diagrams Without ReplacementProbability
  49. Conditional Probability from Tables and Venn DiagramsProbability
  50. Proving Geometry Facts with VectorsGeometry

Computing

  1. Condition-Controlled LoopsProgramming
  2. Strings: Indexing, Slicing and LengthProgramming
  3. Lists: Many Values Under One NameProgramming
  4. Tracing a Program by HandProgramming
  5. Traversing a List to Build a ResultProgramming
  6. Defining a Function with ParametersProgramming
  7. Linear SearchProgramming
  8. Binary Search on Sorted DataProgramming
  9. Return Values and Variable ScopeProgramming
  10. Decomposing a Problem into SubprogramsProgramming
  11. Checking a Model's Claim Against a SourceArtificial Intelligence
  12. Compression: Lossy and LosslessComputer Systems
  13. Logic Gates and Truth TablesComputer Systems
  14. Inside the CPU: Fetch, Decode, ExecuteComputer Systems
  15. Memory and Storage: RAM, ROM and the Backing StoreComputer Systems
  16. Packets and Protocols on a NetworkComputer Systems
  17. How a Web Page Reaches Your ScreenComputer Systems
  18. Cyber Threats and How Systems DefendComputer Systems
  19. The Impacts of Computing: Law, Ethics and the EnvironmentComputer Systems
  20. What You Owe a Reader When a Model HelpedArtificial Intelligence
  21. Agents That Take Actions, Not Just AnswerArtificial Intelligence

English

  1. Editing for EffectWriting Composition
  2. Images and Charts as ArgumentReading Comprehension
  3. Poetry: Imagery and the Speaker's VoiceReading Comprehension
  4. Poetry: Form, Sound, and Line as MeaningReading Comprehension
  5. Comparing Two PoemsReading Comprehension
  6. Shaping a Short NarrativeWriting Composition
  7. Structuring an ArgumentWriting Composition
  8. Rhetoric in Persuasion, Used SparinglyWriting Composition
  9. Sustaining a Narrative VoiceWriting Composition
  10. Using Researched Evidence in ArgumentWriting Composition
  11. Drama: Stagecraft as MethodReading Comprehension
  12. Reading Nineteenth-Century Prose UnseenReading Comprehension
  13. Context That Serves the ReadingReading Comprehension
  14. Comparing Writers' Viewpoints Across Non-FictionReading Comprehension
  15. Critical Evaluation of a Writer's SuccessReading Comprehension
  16. Holding an InterpretationEnglish Thinking
  17. Speaking to a Brief and Taking QuestionsSpeaking & Listening

Civics & Economics

  1. Inflation, Price Indexes and Real ValuesEconomics
  2. GDP: Measuring an Economy and What It MissesEconomics
  3. Money and How Banks Create ItEconomics
  4. Interest, Compound Growth and the Cost of BorrowingEconomics
  5. Price Elasticity of DemandEconomics
  6. Price Ceilings and Price FloorsEconomics
  7. Competition, Market Power and Barriers to EntryEconomics
  8. Market Failure: Externalities and Public GoodsEconomics
  9. Risk, Insurance and PoolingEconomics
  10. Taxes, Public Spending and the Government BudgetEconomics
  11. Comparative Advantage and the Gains from TradeEconomics
  12. Wages and the Labour MarketEconomics
  13. Civil Servants, Councils and Everyday GovernmentGovernment
  14. Where the Money GoesGovernment
  15. When Democracies FailGovernment

History

  1. Telling a Cause From a CoincidenceHistorical Thinking
  2. Why Historians DisagreeHistorical Thinking
  3. The Second World WarThe Modern World
  4. The HolocaustThe Modern World
  5. The Cold WarThe Modern World
  6. Decolonisation and New NationsThe Modern World
  7. Civil Rights and Equal CitizenshipThe Modern World
  8. The Digital AgeThe Modern World

Personal & Social Development

  1. Repair, Distance, or Let GoFriendship & Cooperation
  2. How Short Nights Change Your JudgementSelf-Regulation & Resilience
  3. Asking for Help Beyond Your FriendsSelf-Regulation & Resilience
  4. Consent, Pressure, and the Right to Change Your MindResponsible Decision-Making
  5. What a feed is optimised forResponsible Decision-Making
  6. The version of you a stranger can findResponsible Decision-Making

Languages

  1. Saying What Might Be: Mood and ModalityGrammar Across Languages
  2. Following Media Without SubtitlesTexts, Media & Translation
  3. Formal and Informal: Choosing RegisterTexts, Media & Translation
  4. Reading an Argument in Another LanguageTexts, Media & Translation
  5. Working Through the PlateauLanguage Learning

Life Skills

  1. The Four Moves Behind a ScamMoney & Finance
  2. What Comes Out of a First PayslipMoney & Finance
  3. Reading What You Agree ToMoney & Finance
  4. Subscriptions and the Default to RenewMoney & Finance
  5. The Real Cost of Buying Now and Paying LaterMoney & Finance

Arts & Music

  1. How Recording Changed MusicMusic
  2. Digital Images as an Art MediumVisual Art
  3. What Galleries Keep and Who DecidedVisual Art
  4. Watching a Live Performance and Saying Why It WorkedPerforming Arts

Geography

  1. Measuring Development GapsPlaces & Regions
  2. Water, Food and Energy FuturesPeople & Environments
  3. Living With Climate RiskPeople & Environments
  4. Why Biomes Sit Where They DoPeople & Environments

Design & Technology

  1. The Whole Life of a ProductDesigning & Making
  2. Processing, Packaging and Food MilesFood & Cooking

Learning to Learn

  1. Protecting One Block of AttentionLearning to Learn
  2. Working Backwards From a DeadlineLearning to Learn
What a 15-year-old learns · LightMySky